diff --git a/.github/workflows/gen4-retiming-entrances.yml b/.github/workflows/gen4-retiming-entrances.yml
new file mode 100644
index 0000000000..46fd3ab773
--- /dev/null
+++ b/.github/workflows/gen4-retiming-entrances.yml
@@ -0,0 +1,30 @@
+name: Gen4 composed finite construction
+on:
+  push:
+    branches: [codex/gen4-compatible-improvement]
+    paths:
+      - 'research/gen4-retiming-entrances/**'
+      - '.github/workflows/gen4-retiming-entrances.yml'
+  pull_request:
+    paths:
+      - 'research/gen4-retiming-entrances/**'
+      - '.github/workflows/gen4-retiming-entrances.yml'
+permissions:
+  contents: read
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: '3.11'
+      - run: sudo apt-get update && sudo apt-get install -y g++ libboost-dev
+      - run: python -m pip install -r research/gen4-retiming-entrances/requirements.txt
+      - run: python -B research/gen4-retiming-entrances/verify.py --output "$RUNNER_TEMP/gen4-composed"
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: gen4-composed-verification
+          path: ${{ runner.temp }}/gen4-composed
diff --git a/research/gen4-retiming-entrances-target/LICENSE b/research/gen4-retiming-entrances-target/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/LICENSE
@@ -0,0 +1,201 @@
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+      the terms of any separate license agreement you may have executed
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diff --git a/research/gen4-retiming-entrances-target/MANIFEST.json b/research/gen4-retiming-entrances-target/MANIFEST.json
new file mode 100644
index 0000000000..f81ca46a54
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/MANIFEST.json
@@ -0,0 +1,140 @@
+{
+  "files": {
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "08da3e05381aa0c2ea570fada8218dae70778d3eb0a68477725b2d052d7495b3",
+    "PROOF.md": "3a8c069f518fa3992840da743ec6f20cbda06387b9817c642a3e9ae88fef0754",
+    "README.md": "fa6643312a9c918d16bb1ccc8bff004b59880d39e14667e75a283eafbe701d2d",
+    "code/admit.py": "935e44e4df0cbb1e171c7292abccabe0e253bdab17d1975b772ddd8c3f054423",
+    "code/charts.cpp": "40576d17ff335e61c2669f93a096df1b961ab5a3546f85e778670bd2fcc20ac6",
+    "code/cleanup.py": "7cc979a6581c7c8b739cfeaaa54ccc2d85a498342b0aef367b3d61c2250d1494",
+    "code/cleanup_emit.py": "3a3a315291985a45bb62ec39c700d33fa9df422d524fb8583a93735d6a0e5d6c",
+    "code/cleanup_reference.py": "a368d184558c660b07da63fd3727181c69fc48ba493a39c465a7b556e34558da",
+    "code/cleanup_screen.py": "89cfa098e77f043b87c7de0c76bd35f4b33404929de3aa5d9e48d1a6f506aba8",
+    "code/entrances.py": "ea6beed63ef03618042212c0514f39770a76049f5eb3f444eb540b5deca1eadc",
+    "code/export.py": "471256c73bfb1e701917b4d3719f0795170f37b9ea238967af425d0e9621f2c0",
+    "code/five-stage-columns.cpp": "a7432be590e68bac9e48df432c5f22767bce6af1c237499280e4e3bce09e5131",
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+    "data/EXPECTED.json": "3c5b3056761524fe558255afb7d31c4ccb271d2980258e480a0c0448dbadea5f",
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+    "vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean": "71dc3dda23dfe510d5d53cbada3a6c540cd1dc2825503fda618a5bd6cfc3e812",
+    "vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean": "2e8e88efd4dcbdf0b1a6e39ce7eea8c5fd5ffee2faf360a8c0c9cba84c0e4ef3",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean": "c302f5834287421f11f3b0da7112fcde876cbc702896f2af4145b2d72ee393a2",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean": "ade7e7873da75ca63a4b5ce2f562dde9c12bfbb69d87d7ae831039ff790e5adb",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean": "22ae34809466b4ac2a2c5cdde526f51ff246f5189f7c142b38aa4c0dcffb04a4",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean": "6e17a68b1e988969f6eb77000028f7ed877e687b8ad3976ec1707fcfe1d2f520",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean": "c122bc01392a6fdcc0bee918fed81804d3c9b1d3e071016dab65a4ed804ef0b6",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean": "0de429c80231334f1ce92575c1e8ac382ca2d5e7d956767b547639a8941d9a8c",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean": "c33ec3fce09c0971c32ddcbb86d9383ffbe4c6d05cf36f20460005e6547bb845",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean": "cb61f304da51f1dd0a2ec25bca4b63eb095eeb2863289e1e2bdee7c82beff48b",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean": "d5314f2b93a7f0e1c949fb502331825bfc6d9d8762d35f865443e7c95b6c7ef7",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean": "9587ddb9961f44938032b609307ab91c0b0e757e3991f1ad95480dd50fd4f72b",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean": "d92ee6889be4753fc99f467bd84039743325123a1165128378b9c906a04f2703",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean": "0299bcd0fe255960eec682eef0f045f7e5cb1e4711af2aab4393526eae2caea3",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean": "479434815822e98f015e335361089c3788d00dc3dd39c2944f75410aa0c158fe",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean": "6b40cac1481c931d47b1a092e382d04716ede0e785c492a2f2983e886a257c3f",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean": "aba94a004c94dcae7cf3047c88a6da9561555f4ebe8ab92e299e6ce09ee7aa66",
+    "vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean": "45c768c9d71a7cc18bd6db74cb036db880d89580ca60557bb4a492280296b169",
+    "vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean": "feec0a3828867968a5c7c2c30b86ed70449abc3c660a60ada67203a75bae2ef7",
+    "vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean": "34906dbf5ae16b5174db00b4881a5cc1d2e583b8c8806db6523a5e2f86565f09",
+    "vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean": "80fb3daa9a45de0ed6da570eb4476b9104734be65d0116f58bcfcbcd67f771d0",
+    "vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md": "6ba897a9495ddadcf8558b93133fdfaf66fc35ce7fa2c53e2d5667335c315e0b",
+    "vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py": "9c9dcfac47f0535bf3aa8ebf7c662cdef0ebda50a9f0a9282b8f3cf34809f835",
+    "vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py": "dab7fec9f44c2d368ed334055d7126e202017feb46e41a8d86e2d998720f67c2",
+    "vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py": "eb972c06fe8c322db2d9a8d9a7d05596e8f40c4ca8e5f42eb6df3c7361b5d517",
+    "vendor/pr276/math_check.py": "706d9e0a2e2092393914809109be39012c0182edf4eb1bb76bf05f9e51fde713",
+    "vendor/pr276/moment.py": "9d465c716c6b910ff66e1453e3bf0057608a787b5f5361be93781f42cb3370f7",
+    "vendor/pr276/notices/PR210-coordinated-crossover-NOTICE": "9fc5561c0995892dbdde777c713899486920c32d3562392f5f72377a4953bf98",
+    "vendor/pr276/notices/PR230-NOTICE": "7dfbad087ee49b74fd5075d517eaa263c5dd3d4fbd4c69bfba34ee1cb55e837f",
+    "vendor/pr276/notices/PR230-PROVENANCE.json": "19957e28a8ad26281bfe8bfaf8ae16191be53e729a8870a6154671b3384959d4",
+    "vendor/pr276/notices/README.md": "a4c288228cf8360d8d04c62b0f51177de5682d1f5d3bae341e6b850af766c26e",
+    "vendor/pr276/notices/base-bit-PR200-PR202-NOTICE": "c9850418622aea8d1382a230306c940947b5da818f4854b4b272ed60cf239f6c",
+    "vendor/pr276/notices/source527-loader-NOTICE.md": "ee632728cc4d89565292d288f8289f483ac794b5d02cc6e42c2b2c43c43ff1d8",
+    "vendor/pr276/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "vendor/pr276/parity_transform.py": "9ed3ff2767c046d11aa1be248eaba93755740131745f673ad9d26a3e77e7b02a",
+    "vendor/pr276/portable_bit.py": "c8d18bdc5a123f14be330e94d96509be8b5eec71ccc68e0fabc649ac1ee6f218",
+    "vendor/pr276/portable_complex.py": "797e144c0040d78a4731a6eaa61c0edb9803a08462f885ed014cbca9d9991d82",
+    "vendor/pr276/prepare.py": "00b13cb18e2d1dd26f207a20a7183b9e357a92a9b2906371e6fae9cb8cc197b3",
+    "vendor/pr276/prime_check.py": "d1682e044773ca8e8b131b82e58186c8d97e597f0d8a7d74aaeee06cf5204973",
+    "vendor/pr276/prime_witnesses.py": "98cd03bc9582e7bd0ab194c191ea8eea940539e510051443ab9fd3e572a364ab",
+    "vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md": "602923520af184670170bf159fde7b4c72e79a72570eddd7746b7c97bc51fc5b",
+    "vendor/pr276/proof/INTEGRATED_PROOF.md": "cff22391e71a50bad27a1e832d5c0a2c8b2446df55adb1297c8b1485b3761257",
+    "vendor/pr276/proof/PARITY-CONTRACT.md": "a9246be656e31f1a21d5ec714e002f51be0aa07c36e1528066a25b2c7a02db91",
+    "vendor/pr276/proof/README.md": "5f40cb6dda3992f98ffc43159af1be080bd6c18411bc7d02464f230993f3074f",
+    "vendor/pr276/proof/copied-centers-lemma.tex": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe",
+    "vendor/pr276/proof/primary/03-motifs.tex": "ed76761194988a01af77ead0ea6469cb5dcd29690ab985a0b5a4006b0f2b69bb",
+    "vendor/pr276/proof/primary/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/pr276/proof/primary/PROVENANCE.md": "dd9054c58aa92c44b0ef5f691ad4dc52b8ead2f20a9843d4399d6c300d616023",
+    "vendor/pr276/proof/primary/UPSTREAM-README.md": "8d1ceff898a4e0e681679f91c4def485820be9e99f04e4861f2ce601a364723e",
+    "vendor/pr276/proof/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "vendor/pr276/proof/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "vendor/pr276/raw_ledger.py": "e9701ab9d4f30c6bac6fa69853a2069624ad237666b85cfe6d31a8a7c806e28b",
+    "vendor/pr276/requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
+    "vendor/pr276/scalar/word.py": "e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42",
+    "vendor/pr276/scalar_check.py": "bbc25d3df09bf0ce2cb92f623f46579b504b37a9447a144a6cd1cb8e63701b7f",
+    "vendor/pr276/verify.py": "996789f2c0e1ee17ccd6b9e634ce67384578595846cd5bac7f2c3901df2da307",
+    "vendor/pr276/virtual_check.py": "155144478a5c45d630c1b0d43cadbeb53b96306270fa4e0ad8c4d403d9045971",
+    "verify.py": "ec0624c48d11f2ddb317c50efe905a2f5d9d51358822e283a6204213203019a7"
+  },
+  "schema": "gen4-composition-source/1"
+}
diff --git a/research/gen4-retiming-entrances-target/NOTICE.md b/research/gen4-retiming-entrances-target/NOTICE.md
new file mode 100644
index 0000000000..35736cc483
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/NOTICE.md
@@ -0,0 +1,16 @@
+# Attribution
+
+Prepared for **utcorvusvolat-dotcom** with substantial OpenAI Codex assistance. Apache-2.0. Original prerequisite source, notices, license and AI-assistance disclosures are preserved verbatim in `vendor/pr276`; these credits do not imply review or endorsement.
+
+- DreamingOfClouds and Anthropic Claude: PR276 gen4 physical bit word and its five-stage completed-bank package.
+- Henry Grant (hcg890), PR234, and Jacob Sussman: five-stage architecture and certificate interface.
+- eumemic: paired-cube/source527 scalar and physical machinery, common-delivery-frame retiming in PR244, and PR168 lineage; see inherited notices for full attributions.
+- Evan McKinney (evmckinney9): PR197 completed banks and PR271 cleanup-sandwich identity. `code/cleanup_reference.py` adapts the public PR271 exact sandwich reference; `cleanup_screen.py` and `cleanup_emit.py` apply its argument to gen4.
+- Rohan Arun: PR237 width-120 bank application, PR263 frame descent and concurrent PR279 application of the same 880 retimings to gen4.
+- utcorvusvolat-dotcom: PR270 connected-block scan and selection binding; this package composes the 880 gen4 retimings with 440 shortened endpoints and 60 dirty entrance transports, with regenerated exact admissions.
+- Chafik Boukhalfa (chafreaky), PR200: physical-word classes; icekylinx, PR144: paired-cube framework; Avi Eisenberg (ikeboy), PR193: retained complex supplier.
+- `vendor/json.hpp`: nlohmann JSON, copyright Niels Lohmann, MIT license reproduced in the file header.
+
+No priority or global-optimality claim is made. The complete inherited attribution chains are in `vendor/pr276/NOTICE.md`, its `notices/` directory and its upstream notices.
+
+The target-prefix compression stage (`code/target_prefix.py`, `data/target-selection.json`; the mechanism is eumemic's PR268), the pinned call count and κ in `code/price.py`, the word hash in `verify.py` and this package's rebinding were prepared by Rohan Arun (rohanarun) with Anthropic Claude assistance, Apache-2.0. PR280's construction, emitters and checkers and the vendored PR276 package retain their notices unchanged.
diff --git a/research/gen4-retiming-entrances-target/PROOF.md b/research/gen4-retiming-entrances-target/PROOF.md
new file mode 100644
index 0000000000..7826bfcedb
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/PROOF.md
@@ -0,0 +1,27 @@
+# Composition argument
+
+The prerequisite is the immutable PR276 package, whose full verifier runs first. Its scalar word, decoder, physical frames, COPY lifetimes, prime guards, completed-bank template, complex supplier and analytic admission supply the unchanged facts. This document only describes the three modifications and their interface costs.
+
+## Common-frame retiming
+
+The 880 frozen pairs partition the 1,760 source roles. Each selected scalar ADD keeps its operands and coefficient and changes only its frame annotation, from rank 2 to an existing common delivery frame of rank 22. Its old frame is contained in the new one. The emitter preserves the complete scalar/COPY/ERASE projection, reconstructs each MOVE from the current role frame and checks every new inclusion exactly against B/A tables. COPY/ERASE source bindings and all endpoints remain fixed.
+
+Per gate, the paid ranks 1,1,20,22 become 21,21,2. The local histogram delta is {1:-1760, 2:880, 20:-880, 21:1760, 22:-880}; its rank mass is zero. Existing operand containment in the old frame implies containment in the enlarged frame. This is the same common-delivery-frame mechanism developed in the source527 lineage and independently applied to gen4 in PR279.
+
+## Early restoration
+
+After the target output has been completed, each of 440 selected helpers has exactly one remaining signed restoration ADD, helper -= donor. No other suffix instruction uses that helper, and its donor is not written between the new and old positions. The two sets of helper/donor roles are disjoint. Consequently each elementary shear commutes through every intervening scalar instruction. The new endpoint is their exact nondegenerate rank-23 join, rather than FULL24; the initial helper rank remains 20. This reduces its residual rank from 4 to 3. The frozen recipe checks these conditions on the actual retimed word, preserving the signed coefficient -1. See `docs/cleanup-proof.md`.
+
+## Dirty entrance transport
+
+Sixty independent zero-entry helpers are unwritten and never copied before the transport cut just after the final copied-center discard. No target is a scalar source (or copied source). Each of their 240 signed initial helper-to-target reads therefore commutes with every intervening instruction; these reads are moved to the cut with their exact coefficients intact. Every selected helper column is also replayed over the integers. MOVE chains are rebuilt, and exact full ranks, ordinary annihilators, nondegenerate Grams and changed connector inclusions are checked.
+
+The new helper entrances have ranks 19 (12 helpers) and 18 (48 helpers); their endpoints remain FULL24. They are disjoint from the 440 early-restored helpers. The residual ranks become 5 and 6. The local histogram delta is {1:48, 2:168, 3:72, 19:-12, 18:192, 20:-120, 21:-120}. Initial rank rises by 1,092 and paid rank mass decreases by the same amount.
+
+## Completed banks and finite admission
+
+At 60 physical replicas in each of five stages, residual helper ranks 3,4,5,6,24 have populations 706,1760,12,48,13884. They tile homogeneous width-120 banks with 40,30,24,20,5 blocks per bank, giving 1059,3520,30,144,166608 banks per stage. All 4,923,000 actual assignments are enumerated; no padding savings are assumed.
+
+The exact chart generator derives its required pairs from the baseline and final raw words, together with every helper whose initial or final frame changes. Each projector difference is checked idempotent, of the claimed rank, and conjugate to its standard diagonal projector. The largest required chart has 208 factors. Retained cost terms give a conservative normalizer 208+119+120=447. The admission recomputes the signed cancellation-free prefix bound on the actual word and the complete finite invoice, including the unchanged complex/row interfaces from the baseline replay.
+
+The final histogram and stock are passed to both pinned rational moment engines. The prime is verified, the full rare-branch fallback remains charged, eight positive-gap ordinary levels are admitted, all 47 strict assembly constraints hold, and the next 10^-27 grid point is rejected at the finite ordinary saving. This gives the stated conditional κ. It does not remove any inherited all-size hypothesis.
diff --git a/research/gen4-retiming-entrances-target/README.md b/research/gen4-retiming-entrances-target/README.md
new file mode 100644
index 0000000000..db3571f5cc
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/README.md
@@ -0,0 +1,50 @@
+# Target-prefix compression composed with the gen4 retiming, early restorations and dirty entrances
+
+**Conditional κ = 725113717934416422443945/10^27 = 7.25113717934416e-4**, +9.25 × 10⁻⁷ (+0.128 %) over PR280's 7.24189082265949e-4, +2.24 × 10⁻⁶ over PR276.
+
+This package is utcorvusvolat's `gen4-retiming-entrances` (PR280: the 880 common-frame retimings, 440 early helper restorations and 60 transported dirty entrances on the gen4 word, with its exact emitters, native chart/column checkers, fixed-prime pricer and completed-bank admission) with one added stage, `code/target_prefix.py` (frozen `data/target-selection.json`), run after `05-entrances` and before the column, chart, price and admission checks: eumemic's PR268 exact F₂ target-prefix compression, as the native stage of PR273/PR279. On PR280's final word, 280 disjoint target groups (220 squares of four targets with three retained, and 60 pairs created by the transported entrances) have a dependent target whose frame-20 prefix response is the F₂ sum of its retained group-mates'. The dependent's 1,190 frame-20 reads are omitted; it receives `t −= p_j` at the zero frame at the cut and `t += p_j` at the group's common nondegenerate 21-dimensional frame at the close, where all members are moved (1,440 setup/restore additions; 626,610 weighted ADDs). Local paid histogram delta {1: −220, 2: −54, 3: −36, 18: −66, 19: −24, 20: −190, 21: +280} at unchanged rank mass; normalized calls 5,808,240 → 5,789,640, stock 255,841 and deficit 52,800 unchanged. The stage recomputes every member's literal prefix response from the actual word and requires the dependency before emitting anything, rebuilds every MOVE from the actual needs, checks nested chains, fixed endpoints and COPY lifetimes, nondegenerate endpoint bases and both all-column replays with an omitted-setup negative control; PR280's five-stage column checker, chart audit (4,004 projectors), fixed-prime pricer (47 strict constraints, adjacent grid rejected) and completed-bank admission then re-examine the composed word. `code/price.py` pins the new call count and κ, `code/admit.py` the composed word's chart count, 626,610 scalar additions (630,130 units) and full counted primitive coefficient 92,323,631,924,982,001, and `verify.py` the composed word's SHA-256.
+
+Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0. Everything below is PR280's own description of the inherited construction.
+
+---
+
+# Gen4 retiming, early restoration and dirty entrances
+
+This package constructs the conditional finite bound
+
+**κ = 724189082265949363570532 / 10^27 = 0.000724189082265949363570532.**
+
+It composes 880 source-pair frame retimings, 440 early helper restorations and 60 transported dirty entrances on the PR276 gen4 word. The signed scalar maps are preserved by the checked commutation identities; all changed geometry, completed banks and finite charges are recomputed on the resulting word.
+
+At the latest comparison during preparation, this is **0.08533948% above PR279** (κ = 0.000723571590007464), and **0.18250242% above PR276** (κ = 0.000722869827347495). PR279 independently posted the same 880 retimings while this package was being prepared. The extra improvement here is the composition with shortened helper endpoints and new dirty entrances. No priority or global optimality is claimed. These are changes to a conditional asymptotic bound, not measured multiplication speedups.
+
+## Reproduce
+
+Python 3.11+, SymPy 1.14.0, a C++17 compiler and Boost headers are required. On Ubuntu:
+
+```sh
+sudo apt-get install g++ libboost-dev
+python3 -m pip install -r research/gen4-retiming-entrances/requirements.txt
+python3 -B research/gen4-retiming-entrances/verify.py --output /tmp/gen4-composed-replay
+```
+
+Use a fresh output directory outside this package. The verifier runs without network access. It freshly verifies the unmodified, vendored PR276 package, regenerates its raw word, applies the three exact recipes, checks every global formal column, generates the changed projector charts, enumerates the bank assignments, reproduces the price and admits the complete finite invoice. Saved PASS files are not inputs to this recipe. Its immutable manifest is checked before and after execution. Assertions are mandatory.
+
+PR276 is pinned to commit `d428ab0462b9dfd3131ab4e89999f0adcd6173dd`, with its original manifest SHA256 `6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d`. The complete 110-file prerequisite package and original licenses/notices are retained in `vendor/pr276`. Later edits to that PR do not alter this dependency.
+
+## Concrete checks and result
+
+- The final word SHA256 is `71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48`.
+- All 23,450 global formal columns pass the five-stage construction, with 120 fresh copies, original-source immutability and six nonzero omitted-bridge controls. The signed changes are separately justified over the integers; the F₂ replay is not used as a substitute for that argument.
+- All 3,784 changed connector/endpoint projector charts, including 500 changed helper endpoints, are recomputed exactly. The largest chart has 208 elementary factors; numerator and denominator maxima are 764 and 351.
+- All 4,923,000 role/replica/stage assignments are enumerated. The inventory has 171,361 banks per stage, 1,279,205 literal stock families and 255,841 normalized stock families. There are 2,400 endpoint columns and 2,400 nonzero omission/repetition control columns.
+- Normalizer 447 = 208 + 119 + 120; selector charge 528,906,962,400; finite primitive coefficient 92,488,203,535,344,001; recomputed signed payload bound 91 bits.
+- Exact fixed-prime proof for q = 2^127 − 1, the full fallback, two rational moment engines, eight ordinary levels, all 47 strict outer inequalities and adjacent-grid rejection.
+
+The normalized paid histogram has 5,808,240 calls, rank mass 30,648,120 and deficit 52,800. The largest child remains 50. Recursive children are charged explicitly and are not included in the finite coefficient.
+
+## Scope
+
+This is a conditional finite construction under the inherited all-size compiler, common weighted chart, restored rows, selectors, routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction interfaces. It does not establish those assumptions, an unconditional multiplication theorem, a new Lean proof or a practical runtime result. The offline verifier proves this pinned construction; the public-frontier comparison is a separate dated observation.
+
+See `PROOF.md`, `docs/cleanup-proof.md`, code-level exact checks, and `NOTICE.md` for the construction and attribution.
diff --git a/research/gen4-retiming-entrances-target/code/admit.py b/research/gen4-retiming-entrances-target/code/admit.py
new file mode 100644
index 0000000000..1c01b63985
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/admit.py
@@ -0,0 +1,293 @@
+#!/usr/bin/env python3
+"""Reconstruct final gen4 banks and finite accounting from the actual word.
+
+The orchestrator must freshly run the immutable baseline, scalar replay and
+exact chart checker before invoking this integration component.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import sys
+if not __debug__:
+    raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+sys.set_int_max_str_digits(0)
+
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import hashlib
+import json
+import price as pricing
+
+
+def read(path):
+    return json.loads(Path(path).read_text())
+
+
+def cutoff(delta, coefficient):
+    assert 0 < delta <= 1 and isinstance(coefficient, int) and coefficient >= 1
+    return max(1, pricing.ceil_fraction(36 / delta**2),
+               pricing.ceil_fraction(2 * (4 + (coefficient - 1).bit_length()) / delta))
+
+
+def signed_bounds(records, n):
+    result = []
+    for reverse in (False, True):
+        norms, largest, open_copy = [1] * (n + 1), 1, False
+        for op, a, b, coefficient, frame, category in (reversed(records) if reverse else records):
+            if op == 1:
+                norms[a] += abs(coefficient) * norms[b]
+                largest = max(largest, norms[a])
+            elif op == (3 if reverse else 2):
+                assert not open_copy and b == n
+                norms[b], open_copy = norms[a], True
+            elif op == (2 if reverse else 3):
+                assert open_copy and b == n
+                norms[b], open_copy = 0, False
+        assert not open_copy
+        result.append(dict(reverse=reverse, bits=largest.bit_length(),
+                           cancellation_free_signed_row_l1_upper=str(largest)))
+    return result
+
+
+def exact_banks(initial, final, frames):
+    families, endpoint_pairs = defaultdict(list), set()
+    for role in range(3520, 19930):
+        before, after = initial[str(role)], final[str(role)]
+        endpoint_pairs.add((before, after))
+        rank = frames[str(after)]["dim"] - frames[str(before)]["dim"]
+        assert 0 < rank <= 24
+        families[rank].append(role)
+    assert {r: len(roles) for r, roles in families.items()} == {
+        24: 13884, 4: 1760, 3: 706, 5: 12, 6: 48
+    }
+    for before, after in endpoint_pairs:
+        for b in frames[str(before)]["B"]:
+            for a in frames[str(after)]["A"]:
+                assert sum(Q(x) * Q(y) for x, y in zip(a, b)) == 0
+    patterns, slots, bank, columns, wrong_columns = [], {}, 0, 0, 0
+    for rank, roles in sorted(families.items()):
+        blocks, count = 120 // rank, 60 * len(roles)
+        assert blocks * rank == 120 and blocks <= 40 and count % blocks == 0
+        patterns.append(dict(width=rank, blocks=blocks, banks_per_stage=count//blocks,
+                             occurrences_per_stage=count))
+        slots[rank] = []
+        for _ in range(count // blocks):
+            slots[rank].extend((bank, j * rank, j + 1) for j in range(blocks))
+            bank += 1
+        for reverse in (False, True):
+            permutation = list(range(240))
+            for j in (reversed(range(blocks)) if reverse else range(blocks)):
+                for a in range(j * rank, (j + 1) * rank):
+                    permutation[a], permutation[120+a] = permutation[120+a], permutation[a]
+            assert permutation == list(range(120, 240)) + list(range(120))
+            columns += 240
+        for omitted in range(blocks):
+            for repetitions in (0, 2):
+                permutation = list(range(240))
+                for j in range(blocks):
+                    for _ in range(repetitions if j == omitted else 1):
+                        for a in range(j * rank, (j + 1) * rank):
+                            permutation[a], permutation[120+a] = permutation[120+a], permutation[a]
+                wrong = sum(permutation[j] != (j + 120) % 240 for j in range(240))
+                assert wrong == 2 * rank
+                wrong_columns += wrong
+    assignments, mass, digest = 0, 0, hashlib.sha256()
+    for stage in range(5):
+        for rank, roles in sorted(families.items()):
+            assert len(slots[rank]) == len(roles) * 60
+            for j, role in enumerate(roles):
+                for replica in range(60):
+                    bank_id, offset, scalar = slots[rank][j * 60 + replica]
+                    assert 1 <= scalar <= 40 and offset + rank <= 120
+                    digest.update(f"{stage},{replica},{role},{bank_id},{offset},{rank},{scalar}\n".encode())
+                    assignments += 1
+                    mass += rank
+    assert assignments == 4923000 and bank == 171361 and mass == 5 * 120 * bank
+    literal_stock = 4 * 1760 * 60 + 5 * bank
+    assert literal_stock == 1279205 and literal_stock % 5 == 0
+    return dict(status="PASS_ACTUAL_ROLE_REPLICA_STAGE_BANK_TILING",
+                actual_role_replica_stage_assignments=assignments,
+                assignment_sha256=digest.hexdigest(), patterns=patterns,
+                residual_role_counts={r: len(roles) for r, roles in families.items()},
+                exact_nested_endpoint_pairs=len(endpoint_pairs), banks_per_stage=bank,
+                covered_rank_mass=mass, literal_stock=literal_stock,
+                normalized_stock=literal_stock//5, max_block_scalar=40,
+                endpoint_columns_checked=columns, omission_repeat_wrong_columns=wrong_columns)
+
+
+def admit(candidate, export, baseline, chart_path, price_path):
+    candidate, export, baseline = map(lambda p: Path(p).resolve(), (candidate, export, baseline))
+    chart_path, price_path = Path(chart_path).resolve(), Path(price_path).resolve()
+    supplied_price = read(price_path)
+    base_package = Path(supplied_price["base_package"]).resolve()
+    price = pricing.compute(candidate, base_package)
+    assert price == supplied_price, "Price must reproduce from the actual candidate word"
+    full = read(baseline / "verification.json")
+    assert full["status"] == "PASS_IMMUTABLE_PARITY_FUSED_GEN4_FIVE_STAGE_BANKED_CONSTRUCTION"
+    assert full["inputs_unchanged"] and full["manifest_sha256"] == pricing.BASE_MANIFEST_SHA256
+    assert set(full["fresh_stages"]) == {"virtual", "raw", "bit", "scalar", "primes", "banks", "complex", "math", "finite"}
+    assert len(full["negative_controls"]) == 9
+    primes = read(baseline / "primes.json")
+    assert primes["all_remaining_factors_below_2_power_80"]
+    native = read(candidate / "COHORT-FIVE-STAGE-COLUMNS.json")
+    assert native["status"] == "PASS_GENERIC_FIVE_STAGE_FORMAL_COLUMNS_AND_COMPUTED_PREFIX"
+    assert native["formal_columns_checked"] == 23450 and native["independent_dirty_registers"] == 16410
+    assert len(native["negative_controls"]) == 6 and all(x["rejected"] for x in native["negative_controls"])
+    assert native["copied_center_original_source_immutable"] and native["fresh_center_copies"] == 120
+    state = read(export / "249-states.json")
+    initial, final = read(candidate / "COHORT249-INITIAL.json"), read(candidate / "COHORT249-FINAL.json")
+    frames = read(export / "frames.json")["frames"]
+    frames.update(read(candidate / "COHORT249-FRAMES.json"))
+    assert set(initial) == set(final) == {str(i) for i in range(19930)}
+    assert all(initial[str(i)] == state["initial"][str(i)] and final[str(i)] == state["final"][str(i)] for i in range(3520))
+    changed_entrances = {i for i in range(3520, 19930) if initial[str(i)] != state["initial"][str(i)]}
+    changed_exits = {i for i in range(3520, 19930) if final[str(i)] != state["final"][str(i)]}
+    assert len(changed_entrances) == 60 and len(changed_exits) == 440 and not changed_entrances & changed_exits
+    assert Counter(frames[str(initial[str(i)])]["dim"] for i in changed_entrances) == {18: 48, 19: 12}
+    assert all(frames[str(state["initial"][str(i)])]["dim"] == 0 and frames[str(final[str(i)])]["dim"] == 24 for i in changed_entrances)
+    assert all(frames[str(initial[str(i)])]["dim"] == 20 and frames[str(final[str(i)])]["dim"] == 23 and frames[str(state["final"][str(i)])]["dim"] == 24 for i in changed_exits)
+    records, local, operations, coefficients = pricing.word_inventory(candidate)
+    old_records = pricing.read_word(export / "COHORT249-RECORDS.bin")
+    assert [x for x in records if x[0] in (2, 3)] == [x for x in old_records if x[0] in (2, 3)]
+    current, open_copy = {int(i): f for i, f in initial.items()}, None
+    for op, a, b, c, frame, category in records:
+        if op == 0:
+            assert current[a] == b and frames[str(c)]["dim"] - frames[str(b)]["dim"] == frame
+            current[a] = c
+        elif op == 1:
+            assert current[a] == current[b] == frame
+            assert a != open_copy
+        elif op == 2:
+            assert open_copy is None and current[a] == c and b == 19930
+            current[b], open_copy = frame, b
+        else:
+            assert open_copy == b and current[a] == c and current[b] == frame
+            del current[b]
+            open_copy = None
+    assert open_copy is None and current == {int(i): f for i, f in final.items()}
+    old_pairs = {(b, c, rank) for op, a, b, c, rank, z in old_records if op == 0 and rank}
+    required_charts = {(b, c, rank) for op, a, b, c, rank, z in records if op == 0 and rank} - old_pairs
+    for role in changed_entrances | changed_exits:
+        before, after = initial[str(role)], final[str(role)]
+        required_charts.add((before, after, frames[str(after)]["dim"] - frames[str(before)]["dim"]))
+    chart = read(chart_path)
+    chart_details_path = chart_path.with_name("COMBINED-CHARTS.json")
+    charts = read(chart_details_path)
+    assert {(c["before"], c["after"], c["rank"]) for c in charts} == required_charts
+    assert len(charts) == len(required_charts) == chart["unique_projectors_checked"] == 4004
+    assert chart["retired_endpoints"] == 500 and chart["all_entries_below_two_to_80"]
+    assert int(chart["max_numerator"]) < 2**80 and int(chart["max_denominator"]) < 2**80
+    assert chart["max_factors"] == max(c["factors"] for c in charts) == 208
+    normalizer = max(186, chart["max_factors"]) + 119 + 120
+    assert normalizer == 447
+    bank = exact_banks(initial, final, frames)
+    stock, normalized_stock = bank["literal_stock"], bank["normalized_stock"]
+    assert normalized_stock == price["stock"] == 255841
+    adds, units, copies = operations[1], sum(c * n for c, n in coefficients.items()), operations[2]
+    assert adds == native["local_scalar_additions"] == 626610 and units == 630130 and copies == 24
+    assert dict(local) == dict(native["local_raw_H"]) == {int(k): n for k, n in price["local_histogram"].items()}
+    bounds = signed_bounds(records, 19930)
+    assert bounds == native["signed_lift_prefix"]
+    forward, backward = (int(row["cancellation_free_signed_row_l1_upper"]) for row in bounds)
+    payload = 64 * forward**3 * backward**2
+    assert payload == int(native["payload_prefix_upper"]) and payload.bit_length() == 91 and payload < 2**104
+    m, replicas, v, helpers = 120, 60, 1760, 16410
+    calls, mass = price["calls"], price["rank_mass"]
+    assert m * normalized_stock - mass == 52800
+    literal_histogram = {int(k): 5 * n for k, n in price["histogram"].items()}
+    children = sum(literal_histogram.values())
+    assert children == 5 * calls and sum(k*n for k, n in literal_histogram.items()) == 5 * mass
+    weighted = replicas * (5 * adds + 6 * v)
+    unit = replicas * (5 * units + 6 * v)
+    routes = replicas * (24 * v + 10 * helpers)
+    dimension, doubled = m*m, 2*m
+    good, high = 8*m*m + 8, 16*(dimension+1)**2
+    selectors = 2 * 5 * replicas * ((stock-1) + helpers * m * normalizer)
+    assert selectors == 528906962400 < 2**40
+    items = dict(unit_scalar_additions=unit, high_affine=routes*high,
+                 low_role_transpositions=routes*(stock+24), good_wrappers=children*good,
+                 matrix_preparation=children*128*doubled**3, invertibility_tests=16*m**3,
+                 copy_erase_episodes=120*replicas, edge_descriptors=children,
+                 bank_selectors=selectors, fixed_unit=1)
+    coefficient = sum(items.values())
+    assert coefficient == 92323631924982001 < 2**80 and stock+24 < 2**80
+    prime, residue = pricing.PRIME, 4
+    for _ in range(125):
+        residue = (residue * residue - 2) % prime
+    assert residue == 0 and all(127 % divisor for divisor in range(2, 12))
+    rho = Q(2*m**3, prime)
+    assert rho == Q(price["rare_density"]) and prime > 2**80
+    cutoffs = []
+    for row in price["ordinary_gaps"]:
+        delta = min(Q(value) for value in row["gaps"].values())
+        exponent = cutoff(delta, coefficient)
+        assert exponent * delta**2 >= 36 and exponent * delta >= 2*(4+(coefficient-1).bit_length())
+        cutoffs.append(dict(level=row["level"], minimum_gap=delta, log2_cutoff=exponent))
+    assert len(cutoffs) == 8
+    rejected = []
+    for name, delta, constant in [("zero cutoff gap", Q(0), coefficient), ("zero coefficient", Q(1, 2), 0)]:
+        try:
+            cutoff(delta, constant)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise AssertionError("Invalid finite cutoff admitted")
+    moment_slack = 1 - Q(price["first_engine_interval"][1])
+    linear_slack = 1 - Q(mass, 120*normalized_stock) - rho*Q(32*m*calls, normalized_stock)
+    assert moment_slack > 0 and linear_slack > 0
+    sources = [Path(__file__).resolve(), Path(pricing.__file__).resolve(), Path(__file__).with_name("charts.cpp"),
+               chart_path, chart_details_path, price_path, export / "249-states.json", export / "frames.json",
+               export / "COHORT249-RECORDS.bin"]
+    sources += [candidate/name for name in ("COHORT249-RECORDS.bin", "COHORT249-INITIAL.json", "COHORT249-FINAL.json",
+                                           "COHORT249-FRAMES.json", "COHORT-FIVE-STAGE-COLUMNS.json")]
+    sources += [baseline/name for name in ("verification.json", "finite.json", "banks.json", "scalar.json", "primes.json", "complex.json")]
+    bindings = {str(path.resolve()): pricing.sha(path) for path in sources}
+    bank.update(source_word_sha256=price["source_word_sha256"], selector_charge=selectors,
+                normalizer_factor_bound=normalizer)
+    invoice = dict(
+        status="PASS_SOURCE_BOUND_GEN4_RETIREMENT_ENTRANCE_FIXED_PRIME_FINITE_INVOICE",
+        source_word_sha256=price["source_word_sha256"], source_bindings=bindings,
+        original_package_manifest_sha256=full["manifest_sha256"], price_independently_recomputed=True,
+        fixed_prime=prime, lucas_lehmer_steps=125, lucas_lehmer_residue=residue, rare_density=rho,
+        normalized_stock=normalized_stock, literal_stock=stock, physical_replicas=replicas, stages=5,
+        local_additions=adds, local_unit_expanded_additions=units, local_copy_episodes=copies,
+        global_weighted_additions=weighted, global_unit_expanded_additions=unit,
+        literal_histogram=literal_histogram, literal_positive_rank_children=children,
+        literal_rank_mass=5*mass, literal_deficit=264000, bank_assignments=4923000,
+        bank_selector_charge=selectors, normalizer_factor_bound=normalizer,
+        new_chart_factor_max=chart["max_factors"], primitive_coefficient_items=items,
+        full_counted_primitive_coefficient=coefficient, primitive_coefficient_bits=coefficient.bit_length(),
+        signed_lift_prefix=bounds, payload_prefix_upper=payload, payload_prefix_bits=91,
+        moment_slack=moment_slack, linear_slack=linear_slack, ordinary_levels=8,
+        ordinary_cutoffs=cutoffs, rejected_controls=rejected, all_47_constraints_positive=True,
+        kappa=price["kappa"], kappa_decimal=price["kappa_decimal"], gain_percent=price["gain_percent"],
+        exceeds_PR276_0p1_percent=True,
+        full_constant_rule="C_full dominates the displayed finite coefficient and every retained primitive, wrapper, "
+                           "setup, row, padding and preceding ordinary-level constant. Enlarge each cutoff with "
+                           "ceil(log2(C_full)); no recursive child is absorbed.",
+        scope="Conditional on the pinned PR276 all-size compiler, weighted chart, restored row, selectors, routing, "
+              "prime supply, recovery, complex symbolic and analytic hypotheses. The orchestration must regenerate "
+              "the baseline, actual candidate, scalar replay and exact chart audit."
+    )
+    return pricing.serial(bank), pricing.serial(invoice)
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("candidate", type=Path)
+    parser.add_argument("--export", type=Path, required=True)
+    parser.add_argument("--baseline", type=Path, required=True)
+    parser.add_argument("--charts", type=Path, required=True)
+    parser.add_argument("--price", type=Path, required=True)
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    bank, invoice = admit(args.candidate, args.export, args.baseline, args.charts, args.price)
+    args.output.mkdir(parents=True, exist_ok=True)
+    for name, value in [("BANK-ASSIGNMENT-REPLAY.json", bank), ("FINITE-INVOICE.json", invoice)]:
+        (args.output/name).write_text(json.dumps(value, sort_keys=True, indent=2) + "\n")
+    print("PASS integrated finite admission", invoice["kappa_decimal"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/gen4-retiming-entrances-target/code/charts.cpp b/research/gen4-retiming-entrances-target/code/charts.cpp
new file mode 100644
index 0000000000..3b2c4ce776
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/charts.cpp
@@ -0,0 +1,35 @@
+// Exact projector charts derived from the actual candidate and baseline words.
+// Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+#include <algorithm>
+#include <cstddef>
+#include <fstream>
+#include <iostream>
+#include <map>
+#include <set>
+#include <stdexcept>
+#include <string>
+#include <tuple>
+#include <vector>
+#include <json.hpp>
+#include <boost/multiprecision/cpp_int.hpp>
+using namespace std;using J=nlohmann::json;using Q=boost::multiprecision::cpp_rational;using Z=boost::multiprecision::cpp_int;using M=vector<vector<Q>>;
+J ld(string p){ifstream f(p);if(!f)throw runtime_error("missing "+p);J j;f>>j;return j;}
+Q rat(J j){return j.is_string()?Q(j.get<string>()):Q(j.get<long long>());}M eye(int n){M a(n,vector<Q>(n));for(int i=0;i<n;i++)a[i][i]=1;return a;}M tr(M a){M b(a[0].size(),vector<Q>(a.size()));for(int i=0;i<a.size();i++)for(int j=0;j<a[0].size();j++)b[j][i]=a[i][j];return b;}M mul(M a,M b){M c(a.size(),vector<Q>(b[0].size()));for(int i=0;i<a.size();i++)for(int k=0;k<b.size();k++)if(a[i][k]!=0)for(int j=0;j<b[0].size();j++)c[i][j]+=a[i][k]*b[k][j];return c;}
+Z maxnum=1,maxden=1;void admit(Q q){Z n=abs(numerator(q)),d=denominator(q);maxnum=max(maxnum,n);maxden=max(maxden,d);if(n>=(Z(1)<<80)||d>=(Z(1)<<80))throw runtime_error("finite prime guard exceeded");}
+M inverse(M a,int &ops,Q &det){int n=a.size();M b=eye(n);det=1;ops=0;for(int k=0;k<n;k++){int t=k;while(t<n&&a[t][k]==0)t++;if(t==n)throw runtime_error("singular");if(t!=k){swap(a[k],a[t]);swap(b[k],b[t]);det=-det;ops++;}Q p=a[k][k];admit(p);det*=p;if(p!=1){ops++;for(int j=0;j<n;j++){a[k][j]/=p;b[k][j]/=p;admit(a[k][j]);admit(b[k][j]);}}for(int i=0;i<n;i++)if(i!=k&&a[i][k]!=0){ops++;Q c=a[i][k];admit(c);for(int j=0;j<n;j++){a[i][j]-=c*a[k][j];b[i][j]-=c*b[k][j];admit(a[i][j]);admit(b[i][j]);}}}if(a!=eye(n))throw runtime_error("inverse failure");return b;}
+M nullspace(M a){int n=a[0].size(),row=0;vector<int>piv;for(int col=0;col<n&&row<a.size();col++){int t=row;while(t<a.size()&&a[t][col]==0)t++;if(t==a.size())continue;swap(a[row],a[t]);Q p=a[row][col];admit(p);for(auto &q:a[row]){q/=p;admit(q);}for(int i=0;i<a.size();i++)if(i!=row){Q c=a[i][col];for(int j=0;j<n;j++)a[i][j]-=c*a[row][j];}piv.push_back(col);row++;}if(row!=a.size())throw runtime_error("basis rank failure");M out;for(int free=0;free<n;free++)if(find(piv.begin(),piv.end(),free)==piv.end()){vector<Q>v(n);v[free]=1;for(int i=0;i<row;i++)v[piv[i]]=-a[i][free];out.push_back(v);}return out;}
+J mj(M a){J out=J::array();for(auto r:a){J z=J::array();for(Q q:r)z.push_back(q.str());out.push_back(z);}return out;}
+
+M sub(M a,M b){for(int i=0;i<a.size();i++)for(int j=0;j<a[i].size();j++)a[i][j]-=b[i][j];return a;}
+M independent_columns(M a){int m=a.size(),n=a[0].size(),row=0;vector<int> piv;M copy=a;for(int c=0;c<n&&row<m;c++){int k=row;while(k<m&&a[k][c]==0)k++;if(k==m)continue;swap(a[k],a[row]);Q p=a[row][c];for(int j=c;j<n;j++)a[row][j]/=p;for(int i=row+1;i<m;i++){Q b=a[i][c];for(int j=c;j<n;j++)a[i][j]-=b*a[row][j];}piv.push_back(c);row++;}M out(m);for(int i=0;i<m;i++)for(int c:piv)out[i].push_back(copy[i][c]);return out;}
+M kernel_general(M a){int m=a.size(),n=a[0].size(),row=0;vector<int>piv;for(int col=0;col<n&&row<m;col++){int t=row;while(t<m&&a[t][col]==0)t++;if(t==m)continue;swap(a[row],a[t]);Q p=a[row][col];for(auto&q:a[row])q/=p;for(int i=0;i<m;i++)if(i!=row){Q c=a[i][col];for(int j=0;j<n;j++)a[i][j]-=c*a[row][j];}piv.push_back(col);row++;}M out;for(int free=0;free<n;free++)if(find(piv.begin(),piv.end(),free)==piv.end()){vector<Q>v(n);v[free]=1;for(int i=0;i<row;i++)v[piv[i]]=-a[i][free];out.push_back(v);}return out;}
+struct Ev{int op,a,b,c,r,z;};
+int main(int ac,char**av){if(ac!=4)throw runtime_error("usage: charts EXPORT CANDIDATE OUT");string base=av[1],candidate=av[2],output=av[3];J fs=ld(base+"/frames.json")["frames"];J nf=ld(candidate+"/COHORT249-FRAMES.json"),ini=ld(candidate+"/COHORT249-INITIAL.json"),fin=ld(candidate+"/COHORT249-FINAL.json");for(auto it=nf.begin();it!=nf.end();++it)fs[it.key()]=it.value();M G=eye(24);for(auto&r:G)for(auto&q:r)q-=Q(1)/9;map<int,M>projectors;auto proj=[&](int f)->M{if(projectors.count(f))return projectors[f];int d=fs.at(to_string(f))["dim"];if(d==24)return projectors[f]=eye(24);if(!d)return projectors[f]=M(24,vector<Q>(24));M B;for(auto row:fs.at(to_string(f))["B"]){vector<Q>r;for(auto x:row)r.push_back(rat(x));B.push_back(r);}int ops;Q det;M BG=mul(B,G), gram=mul(BG,tr(B)), inv=inverse(gram,ops,det);return projectors[f]=mul(mul(tr(B),inv),BG);};set<tuple<int,int,int>>pairs,oldpairs;int endpoints=0;
+auto events=[&](string path){ifstream f(path,ios::binary);if(!f)throw runtime_error("missing word");f.seekg(0,ios::end);size_t size=f.tellg();f.seekg(0);if(size%sizeof(Ev))throw runtime_error("word shape");vector<Ev>v(size/sizeof(Ev));f.read((char*)v.data(),size);return v;};
+for(auto e:events(base+"/COHORT249-RECORDS.bin"))if(e.op==0&&e.r)oldpairs.insert({e.b,e.c,e.r});
+for(auto e:events(candidate+"/COHORT249-RECORDS.bin"))if(e.op==0&&e.r&&!oldpairs.count({e.b,e.c,e.r}))pairs.insert({e.b,e.c,e.r});
+J oldstate=ld(base+"/249-states.json");int v=oldstate["v"],n=oldstate["n"];
+for(int a=2*v;a<n;a++){string role=to_string(a);int before=ini[role],after=fin[role];if(before!=oldstate["initial"][role].get<int>()||after!=oldstate["final"][role].get<int>()){int rank=fs.at(to_string(after))["dim"].get<int>()-fs.at(to_string(before))["dim"].get<int>();pairs.insert({before,after,rank});endpoints++;}}
+
+int maxops=0,checked=0;J charts=J::array();for(auto[before,after,r]:pairs){M E=sub(proj(after),proj(before));if(mul(E,E)!=E)throw runtime_error("not projector");M C=independent_columns(E);if(C[0].size()!=r)throw runtime_error("rank mismatch");M K=kernel_general(E);if(K.size()!=24-r)throw runtime_error("nullity mismatch");for(int i=0;i<24;i++)for(auto&v:K)C[i].push_back(v[i]);int ops;Q det;M inv=inverse(C,ops,det),want=eye(24);for(int i=r;i<24;i++)want[i][i]=0;if(mul(mul(inv,E),C)!=want||mul(C,inv)!=eye(24))throw runtime_error("chart identity");maxops=max(maxops,ops);charts.push_back({{"before",before},{"after",after},{"rank",r},{"basis",mj(C)},{"inverse",mj(inv)},{"factors",ops},{"determinant",det.str()}});checked++;if(checked%50==0)cout<<"checked "<<checked<<"/"<<pairs.size()<<" maxfactors "<<maxops<<endl;}
+if(maxops>548)throw runtime_error("factor budget exceeded");J receipt={{"status","PASS_EXACT_CHANGED_ENDPOINT_AND_MOVE_CHARTS"},{"retired_endpoints",endpoints},{"unique_projectors_checked",checked},{"max_factors",maxops},{"max_numerator",maxnum.str()},{"max_denominator",maxden.str()},{"all_entries_below_two_to_80",true}};ofstream(output+"/COMBINED-CHART-AUDIT.json")<<receipt.dump(2)<<endl;ofstream(output+"/COMBINED-CHARTS.json")<<charts.dump()<<endl;cout<<receipt.dump(2)<<endl;}
diff --git a/research/gen4-retiming-entrances-target/code/cleanup.py b/research/gen4-retiming-entrances-target/code/cleanup.py
new file mode 100644
index 0000000000..263df838b9
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/cleanup.py
@@ -0,0 +1,41 @@
+#!/usr/bin/env python3
+"""Reproduce the fixed440 early-restoration word and its exact checks."""
+import argparse
+import hashlib
+from pathlib import Path
+import subprocess
+import sys
+if not __debug__:
+    raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+
+SOURCE_SHA256 = '2d22a9530f0b04a7a794d15077459234ef52183d6e7a70f813cfa849b79f2ebe'
+OUTPUT_SHA256 = '8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373'
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--source-dir', type=Path, required=True)
+    parser.add_argument('--export-dir', type=Path, required=True)
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    assert digest(args.source_dir / 'COHORT249-RECORDS.bin') == SOURCE_SHA256
+    code = Path(__file__).resolve().parent
+    screen = args.output / 'cleanup-selection'
+    common = ['--source-dir', str(args.source_dir),
+              '--export-dir', str(args.export_dir)]
+    subprocess.run([sys.executable, "-B", str(code / 'cleanup_screen.py'), *common,
+                    '--output-dir', str(screen)], check=True)
+    subprocess.run([sys.executable, "-B", str(code / 'cleanup_emit.py'), *common,
+                    '--screen', str(screen / 'screen.json'),
+                    '--output', str(args.output)], check=True)
+    assert digest(args.output / 'COHORT249-RECORDS.bin') == OUTPUT_SHA256
+    print('PASS fixed440 cleanup word:', OUTPUT_SHA256, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances-target/code/cleanup_emit.py b/research/gen4-retiming-entrances-target/code/cleanup_emit.py
new file mode 100644
index 0000000000..16191acf0c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/cleanup_emit.py
@@ -0,0 +1,106 @@
+#!/usr/bin/env python3
+import sys
+if not __debug__: raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+import json,hashlib,struct,time,argparse
+from array import array
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+import sympy as sp
+from sympy.polys.matrices import DomainMatrix
+ap=argparse.ArgumentParser();ap.add_argument('--output',type=Path,required=True);ap.add_argument('--source-dir',type=Path,required=True);ap.add_argument('--export-dir',type=Path,required=True);ap.add_argument('--screen',type=Path,required=True);a=ap.parse_args();t=time.time();D=Path(__file__).parent;P=a.source_dir;X=a.export_dir;out=a.output;out.mkdir(parents=True,exist_ok=True)
+def load(p):return json.loads(p.read_text())
+def sha(b):return hashlib.sha256(b).hexdigest()
+screen=load(a.screen);cut=screen['cut'];edits=screen['candidates'][:440];assert len(edits)==440 and len(screen['candidates'])==440;A={e['role']for e in edits};skip={e['incidences'][0][0]for e in edits};assert all(len(e['incidences'])==1 for e in edits)
+base=load(X/'gen4-states.json');n,v=base['n'],base['v'];fs={int(k):r for k,r in load(X/'frames.json')['frames'].items()};extras=load(P/'COHORT249-FRAMES.json');fs.update({int(k):r for k,r in extras.items()});newfs={e['frame']:screen['newframes'][str(e['frame'])]for e in edits};assert not set(newfs).intersection(fs);fs.update(newfs)
+initial={int(k):f for k,f in load(P/'COHORT249-INITIAL.json').items()};final={int(k):f for k,f in load(P/'COHORT249-FINAL.json').items()};final.update({e['role']:e['frame']for e in edits});state=dict(initial)
+q=2**127-1;G=9*sp.eye(24)-sp.ones(24);aud=[]
+for f,z in newfs.items():
+ B=sp.Matrix(z['B']);AA=sp.Matrix(z['A']);d=z['dim'];assert B.shape==(d,24) and AA.shape==(24-d,24);assert AA*B.T==sp.zeros(24-d,d);assert DomainMatrix.from_Matrix(AA).rank()==24-d
+ det=sp.Rational(DomainMatrix.from_Matrix(B*G*B.T).det());assert det and int(det.p)%q and int(det.q)%q
+ aud.append(dict(frame=f,dim=d,cleared_gram_determinant=str(det)))
+print('exact newframes',len(aud),'seconds',time.time()-t,flush=True)
+raw=(P/'COHORT249-RECORDS.bin').read_bytes();old=array('i');old.frombytes(raw)
+# Each moved gate commutes over Z with the entire crossed interval: no other
+# use of its destination and no intervening write to its donor. Thus the exact
+# signed scalar operator and original maximum coefficient bound are retained.
+first_write={}; uses={role:[] for role in A}
+for i in range(cut,len(old)//6):
+ op,dest,src,coef,frame,tag=old[6*i:6*i+6]
+ assert op not in (2,3), 'COPY lifetime crosses cleanup interval'
+ if op==1:
+  first_write.setdefault(dest,i)
+  if dest in uses:uses[dest].append(i)
+  if src in uses:uses[src].append(i)
+for e in edits:
+ idx=e['incidences'][0][0];role=e['role'];donor=e['donors'][0]
+ assert uses[role]==[idx]
+ assert tuple(old[6*idx:6*idx+3])==(1,role,donor)
+ assert first_write.get(donor,len(old)//6)>idx
+new=array('i');cols=[1<<i for i in range(n)]+[0];checked=set();inherited={(old[i+2],old[i+3])for i in range(0,len(old),6)if old[i]==0};basis={f:[[Q(x)for x in row]for row in z['B']]for f,z in fs.items()};ann={f:[[Q(x)for x in row]for row in z['A']]for f,z in fs.items()}
+def move(role,f):
+ before=state[role]
+ if before==f:return
+ if (before,f)not in inherited and (before,f)not in checked:
+  assert all(sum(x*y for x,y in zip(u,w))==0 for u in basis[before]for w in ann[f]),('not nested',role,before,f);checked.add((before,f))
+ rank=fs[f]['dim']-fs[before]['dim'];assert rank>=0
+ new.extend((0,role,before,f,rank,0));state[role]=f
+def emit(r):
+ op,a,b,c,f,z=r
+ if op==1:
+  move(a,f);move(b,f)
+  if c%2:cols[a]^=cols[b]
+ elif op==2:
+  move(a,c);assert b==n and cols[b]==0;cols[b]=cols[a];state[b]=f
+ elif op==3:
+  assert cols[a]==cols[b] and state[a]==c and state[b]==f;cols[b]=0;del state[b]
+ else:raise AssertionError(r)
+ new.extend(r)
+for i in range(len(old)//6):
+ if i==cut:
+  for e in edits:
+   emit((1,e['role'],e['donors'][0],old[6*e['incidences'][0][0]+3],e['frame'],32));assert cols[e['role']]==1<<e['role']
+ r=old[6*i:6*i+6]
+ if r[0]!=0 and i not in skip:emit(r)
+for role in range(n):move(role,final[role])
+expected=[(1<<i)^((1<<(i-v))if v<=i<2*v else 0)for i in range(n)]
+assert cols==expected+[0];assert state==final
+# Full reverse word with fresh COPY at each reverse ERASE and erase at each reverse COPY.
+def reverse(start):
+ cols=list(start)+[0];ss=dict(final)
+ for i in range(len(new)//6-1,-1,-1):
+  op,a,b,c,f,z=new[6*i:6*i+6]
+  if op==0:assert ss[a]==c;ss[a]=b
+  elif op==1:
+   assert ss[a]==ss[b]==f
+   if c%2:cols[a]^=cols[b]
+  elif op==3:assert cols[b]==0 and b not in ss and ss[a]==c;cols[b]=cols[a];ss[b]=f
+  elif op==2:assert cols[a]==cols[b] and ss[a]==c and ss[b]==f;cols[b]=0;del ss[b]
+ assert ss==initial
+ return cols
+assert reverse([1<<i for i in range(n)])==expected+[0]
+assert reverse(expected)==[1<<i for i in range(n)]+[0]
+# Omit one moved restoration: corruption must be detected on the full formal basis.
+bad=[1<<i for i in range(n)]+[0];omitted=False
+for i in range(0,len(new),6):
+ op,a,b,c,f,z=new[i:i+6]
+ if op==1:
+  if z==32 and not omitted:omitted=True
+  elif c%2:bad[a]^=bad[b]
+ elif op==2:bad[b]=bad[a]
+ elif op==3:assert bad[a]==bad[b];bad[b]=0
+wrong=sum(x!=y for x,y in zip(bad,expected+[0]));assert wrong
+
+def hist(r):
+ H=Counter()
+ for i in range(0,len(r),6):
+  op,a,b,c,f,z=r[i:i+6]
+  if op==0 and f:H[f]+=1
+  elif op==2:H[z]+=1
+ return H
+H0=hist(old);H=hist(new);delta=H.copy();delta.subtract(H0);delta={str(r):c for r,c in sorted(delta.items())if c};assert delta=={'1':3*len(edits),'2':-2*len(edits)};assert sum(int(r)*c for r,c in delta.items())==-len(edits)
+blob=new.tobytes();assert sha(blob)=='8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373';(out/'COHORT249-RECORDS.bin').write_bytes(blob);(out/'COHORT249-INITIAL.json').write_bytes((P/'COHORT249-INITIAL.json').read_bytes());(out/'COHORT249-FINAL.json').write_text(json.dumps(final,sort_keys=True)+'\n');extras.update({str(k):x for k,x in newfs.items()});(out/'COHORT249-FRAMES.json').write_text(json.dumps(extras,sort_keys=True)+'\n')
+newstates=dict(base);newstates['inherited_physical_provenance']=newstates.pop('physical');newstates.update(initial=initial,final=final,record_count=len(new)//6,record_sha256=sha(blob));(out/'249-states.json').write_text(json.dumps(newstates,sort_keys=True)+'\n')
+receipt=dict(status='PASS_EXACT_NEW_FRAMES_FORWARD_INVERSE_ROUNDTRIP',input_sha256=sha(raw),output_sha256=sha(blob),retired_helpers=len(edits),cut=cut,formal_columns=n,scalar_additions=len([i for i in range(0,len(new),6)if new[i]==1]),record_count=len(new)//6,histogram={str(r):c for r,c in sorted(H.items())},histogram_delta=delta,endpoint_rank_mass_drop=len(edits),exact_new_connector_pairs=len(checked),omission_wrong_rows=wrong,signed_scalar_operator_preserved_by_exact_commutation=True,maximum_formal_coefficient_bound_does_not_increase=True,frames_audit=aud,edits=edits,seconds=time.time()-t)
+(out/'CLEANUP-REPLAY.json').write_text(json.dumps(receipt,indent=2)+'\n');print({k:x for k,x in receipt.items()if k not in ('edits','frames_audit','histogram')},flush=True)
diff --git a/research/gen4-retiming-entrances-target/code/cleanup_reference.py b/research/gen4-retiming-entrances-target/code/cleanup_reference.py
new file mode 100644
index 0000000000..38eb6b6d09
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/cleanup_reference.py
@@ -0,0 +1,59 @@
+"""Exact basis helpers derived from PR271's sandwich263.py.
+
+Source: https://github.com/CrocSwap/integer-mult-bounds/pull/271
+Retained rational_basis, rank_mod_prime, and annihilator routines; no PR271
+cleanup selection or word rewrite is imported. The exact emitted-frame Gram
+and prime audits are independently performed in cleanup_emit.py.
+"""
+import sys
+if not __debug__: raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+from fractions import Fraction as Q
+from math import lcm
+H = 24
+PRIME = 1000003
+
+def rational_basis(rows):
+    """Reduced integer basis of the rational row space."""
+    basis = {}
+    for values in rows:
+        row = list(map(Q, values))
+        for p, b in sorted(basis.items()):
+            if row[p]:
+                row = [x - row[p] * y for x, y in zip(row, b)]
+        p = next((i for i, x in enumerate(row) if x), None)
+        if p is not None:
+            basis[p] = [x / row[p] for x in row]
+    out = []
+    for _, row in sorted(basis.items()):
+        d = lcm(*(x.denominator for x in row))
+        out.append([int(x * d) for x in row])
+    return out
+
+
+def rank_mod_prime(rows):
+    basis = {}
+    for row in rows:
+        row = [x % PRIME for x in row]
+        for p, b in sorted(basis.items()):
+            if row[p]:
+                c = row[p]
+                row = [(x - c * y) % PRIME for x, y in zip(row, b)]
+        p = next((i for i, x in enumerate(row) if x), None)
+        if p is not None:
+            inv = pow(row[p], -1, PRIME)
+            basis[p] = [x * inv % PRIME for x in row]
+    return len(basis)
+
+
+def annihilator(B):
+    """Rational basis of {x : B x = 0} for a reduced basis B."""
+    pivots = [next(i for i, x in enumerate(row) if x) for row in B]
+    out = []
+    for free in sorted(set(range(H)) - set(pivots)):
+        v = [Q(i == free) for i in range(H)]
+        for p, row in reversed(list(zip(pivots, B))):
+            v[p] = -sum(Q(row[j]) * v[j] for j in range(p + 1, H)) / row[p]
+        out.append([str(x) for x in v])
+    return out
+
diff --git a/research/gen4-retiming-entrances-target/code/cleanup_screen.py b/research/gen4-retiming-entrances-target/code/cleanup_screen.py
new file mode 100644
index 0000000000..705d1373f0
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/cleanup_screen.py
@@ -0,0 +1,54 @@
+#!/usr/bin/env python3
+"""Regenerate the fixed440 gen4 cleanup selection."""
+from pathlib import Path
+from array import array
+from collections import Counter,defaultdict
+import json,sys,argparse
+if not __debug__: raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+sys.path.insert(0,str(Path(__file__).parent))
+from cleanup_reference import rational_basis,rank_mod_prime,annihilator
+ap=argparse.ArgumentParser();ap.add_argument('--source-dir',type=Path,required=True);ap.add_argument('--export-dir',type=Path,required=True);ap.add_argument('--output-dir',type=Path,required=True);args=ap.parse_args();D=args.output_dir;D.mkdir(parents=True,exist_ok=True);P=args.source_dir;X=args.export_dir
+r=array('i');r.frombytes((P/'COHORT249-RECORDS.bin').read_bytes());st=json.loads((X/'gen4-states.json').read_text());n=st['n'];v=st['v'];rows=[1<<j for j in range(n)]+[0];fs=json.loads((X/'frames.json').read_text())['frames'];fs.update(json.loads((P/'COHORT249-FRAMES.json').read_text()));state={int(a):f for a,f in json.loads((P/'COHORT249-INITIAL.json').read_text()).items()}
+cut=next(i for i in range(len(r)//6) if r[6*i]==1 and r[6*i+5]==3)
+for i in range(cut):
+ op,a,b,c,f,z=r[6*i:6*i+6]
+ if op==0:state[a]=c
+ elif op==1:rows[a]^=rows[b]
+ elif op==2:rows[b]=rows[a];state[b]=f
+ elif op==3:rows[b]=0;state.pop(b,None)
+assert (n,v,cut)==(19930,1760,662145)
+assert all(rows[v+j]==(1<<(v+j))^(1<<j) for j in range(v))
+print('cut',cut,'target wrong',sum(rows[v+j]!=(1<<(v+j))^(1<<j) for j in range(v)),flush=True)
+affected=[0]*n
+for a,x in enumerate(rows[:n]):
+ x^=1<<a
+ if v<=a<2*v:x^=1<<(a-v)
+ while x:k=(x&-x).bit_length()-1;x&=x-1;affected[k]+=1
+cand=[a for a in range(2*v,n) if not affected[a] and fs[str(state[a])]['dim']<24]
+suffix=[1<<a for a in range(n)]+[0];inc=defaultdict(list)
+for i in range(cut,len(r)//6):
+ op,a,b,c,f,z=r[6*i:6*i+6]
+ if op==1:suffix[a]^=suffix[b];inc[a].append((i,a,b));inc[b].append((i,a,b))
+ elif op==2:suffix[b]=suffix[a]
+ elif op==3:suffix[b]=0
+census=Counter();cs=[];newframes={}
+for a in cand:
+ x=suffix[a]^(1<<a);don=[]
+ while x:k=(x&-x).bit_length()-1;x&=x-1;don.append(k)
+ census[len(don),max([fs[str(state[b])]['dim'] for b in don]+[0])]+=1
+ if len(don)!=1:continue
+ b=don[0]
+ B=rational_basis(fs[str(state[a])]['B']+fs[str(state[b])]['B']);d=len(B)
+ if d==24:continue
+ sums=[sum(u) for u in B];gram=[[9*sum(p*q for p,q in zip(u,w))-su*sw for w,sw in zip(B,sums)]for u,su in zip(B,sums)]
+ if rank_mod_prime(gram)!=d:continue
+ dim_a=fs[str(state[a])]['dim'];dim_b=fs[str(state[b])]['dim']
+ frame=900000+len(newframes);newframes[str(frame)]={'dim':d,'B':B,'A':annihilator(B)}
+ cs.append(dict(role=a,donors=[b],frame=frame,dim=d,dim_a=dim_a,dim_b=dim_b,incidences=inc[a]))
+print('isolated',len(cand),'donor census',census,flush=True)
+print('proper one donor',len(cs),'census',Counter((x['dim_a'],x['dim_b'],x['dim'],len(x['incidences']))for x in cs),flush=True)
+assert len(cs)==440 and all((e['dim_a'],e['dim_b'],e['dim'],len(e['incidences']))==(22,22,23,1) for e in cs)
+assert len({e['donors'][0] for e in cs})==440
+assert not {e['role'] for e in cs}.intersection(e['donors'][0] for e in cs)
+(D/'screen.json').write_text(json.dumps({'cut':cut,'n':n,'v':v,'candidates':cs,'newframes':newframes},indent=2))
diff --git a/research/gen4-retiming-entrances-target/code/entrances.py b/research/gen4-retiming-entrances-target/code/entrances.py
new file mode 100644
index 0000000000..7f4031a325
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/entrances.py
@@ -0,0 +1,121 @@
+"""Exact transport of 60 independent dirty entrances after center scatter.
+
+Frozen source words and selected stream/role identities are checked before replay.
+Each relocated elementary shear has a target destination and an unchanged helper
+source. Targets are never read by ADD or COPY; selected helpers are neither
+written nor copied before the transport cut. Consequently these240 shears commute
+with all intervening scalar/COPY instructions over every coefficient ring. Their
+original signed coefficients are retained. Literal projection and an independent
+integer replay of all60 selected dirty columns check the resulting equality.
+
+The physical frame change is checked separately: new entrance bases and their
+annihilators have full rank, zero pairing, and nonzero Gram determinant. Every
+changed movement is nested; each ADD has a common frame. The containment check
+also gives the reversed annihilator inclusion for the reflected ledger. Source
+and target endpoints are unchanged. The60 selected helper endpoints remainFULL24.
+
+The new residuals are12 of rank5 and48 of rank6, replacing60 of rank24. Sixty
+replicas tile120-coordinate banks exactly:30+144 banks per stage replace720.
+The full integrated finite invoice and chart audit are separate verifier steps.
+
+Substantial OpenAI Codex assistance. Apache-2.0; see repository notices.
+"""
+import argparse,json,hashlib,struct,functools,math
+from pathlib import Path
+from collections import Counter
+import sympy as sp
+if not __debug__:raise SystemExit('Assertions required')
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source-dir',required=True,type=Path)
+ap.add_argument('--export-dir',required=True,type=Path)
+ap.add_argument('--output',required=True,type=Path)
+args=ap.parse_args();X=args.export_dir;D=args.output;D.mkdir(exist_ok=True,parents=True);base=args.source_dir
+st=json.loads((X/'gen4-states.json').read_text());n=st['n'];v=st['v'];zero=st['ZERO'];fs={int(k):x for k,x in json.loads((X/'frames.json').read_text())['frames'].items()};fs.update({int(k):x for k,x in json.loads((base/'COHORT249-FRAMES.json').read_text()).items()});extra={}
+selection_path=Path(__file__).resolve().parent.parent/'data'/'entrances60.json'
+selection=json.loads(selection_path.read_text());assert (n,v)==(19930,1760)
+assert hashlib.sha256((base/'COHORT249-RECORDS.bin').read_bytes()).hexdigest()==selection['source_word_sha256']
+assert st['record_sha256']==selection['export_word_sha256']
+selected={e['stream']:dict(e) for e in selection['entries']};assert len(selected)==len(selection['entries'])==60 and sum(e['rank']for e in selected.values())==1092
+raw=list(struct.iter_unpack('<6i',(base/'COHORT249-RECORDS.bin').read_bytes()));initial={int(k):x for k,x in json.loads((base/'COHORT249-INITIAL.json').read_text()).items()};final={int(k):x for k,x in json.loads((base/'COHORT249-FINAL.json').read_text()).items()};cut=max(j for j,e in enumerate(raw)if e[0]==3);read=st['physical']['category_names'].index('dirty_read');oldH=Counter();pairs=set();basepairs={(e[2],e[3])for e in raw if e[0]==0}
+def introw(row):
+ den=sp.ilcm(*[a.q for a in row]);z=[int(a*den)for a in row];g=math.gcd(*z);return [a//g for a in z]
+for h,e in selected.items():
+ assert 2*v<=h<n and st['regs'][h-2*v]==e['role'] and initial[h]==zero
+ B=sp.Matrix(e['basis']);rank=e['rank'];assert B.rank()==rank and (B*(9*sp.eye(24)-sp.ones(24))*B.T).det()!=0
+ A=[introw(row.T.tolist()[0])for row in B.nullspace()];assert len(A)+rank==24;assert sp.Matrix(A).rank()==24-rank and B*sp.Matrix(A).T==sp.zeros(rank,24-rank)
+ f=max(fs)+1;fs[f]=dict(B=e['basis'],A=A,dim=rank);extra[f]=fs[f];e['frame']=f;initial[h]=f
+@functools.lru_cache(None)
+def sub(a,b):return fs[a]['dim']<=fs[b]['dim'] and all(sum(x*y for x,y in zip(u,w))==0 for u in fs[a]['B']for w in fs[b]['A'])
+# Exact commutation contract: no target is ever read, each chosen helper is
+# untouched up to cut, and all its initial target reads are before that cut.
+reads=[];counter=Counter();helper_touches=Counter()
+for j,(op,a,b,c,f,z)in enumerate(raw):
+ if op==0:
+  if f:oldH[f]+=1
+ elif op==1:
+  assert not(v<=b<2*v),'Target read invalidates simple commutation proof'
+  if a in selected and j<=cut:raise AssertionError(('selected helper written before cut',a,j))
+  if b in selected and j<=cut:
+   assert v<=a<2*v and z==read and f==zero and abs(c)==1
+   reads.append((j,a,b,c,z));counter[b]+=1
+  if b in selected and f==zero:assert j<=cut
+ elif op==2:
+  assert not(v<=a<2*v),'Target COPY source invalidates simple commutation proof'
+  oldH[z]+=1
+  if j<=cut:assert a not in selected
+assert len(reads)==240 and set(counter)==set(selected) and set(counter.values())=={4}
+assert {a-v for _,a,b,c,z in reads}=={t for e in selected.values()for t in e['targets']}
+for h,e in selected.items():assert {a-v for _,a,b,c,z in reads if b==h}==set(e['targets'])
+state=dict(initial);out=[];temporary=None;H=Counter();changedpairs=set();skip={j for j,a,b,c,z in reads}
+def move(a,f):
+ old=state[a]
+ if old==f:return
+ if (old,f)not in basepairs:assert sub(old,f),('nonnested',a,old,f);changedpairs.add((old,f))
+ pairs.add((old,f));rank=fs[f]['dim']-fs[old]['dim'];assert rank>=0;out.append((0,a,old,f,rank,0));state[a]=f
+ if rank:H[rank]+=1
+for j,(op,a,b,c,f,z)in enumerate(raw):
+ if op==0:continue
+ if j in skip:continue
+ if op==1:move(a,f);move(b,f);out.append((op,a,b,c,f,z))
+ elif op==2:
+  assert temporary is None and b==n;move(a,c);state[b]=f;temporary=(a,b,c,f);H[z]+=1;out.append((op,a,b,c,f,z))
+ else:
+  assert op==3 and temporary==(a,b,c,f)and state[a]==c and state[b]==f;out.append((op,a,b,c,f,z));del state[b];temporary=None
+ if j==cut:
+  assert temporary is None
+  for oldj,a,b,c,z in reads:
+   f=selected[b]['frame'];assert state[b]==f;move(a,f);out.append((1,a,b,c,f,z))
+assert temporary is None
+for a in range(n):move(a,final[a])
+assert state==final
+# Full chronological projection with exactly the documented read relocation.
+expect=[]
+for j,(op,a,b,c,f,z) in enumerate(raw):
+ if op and j not in skip:expect.append((op,a,b,c,z))
+ if j==cut:expect.extend((1,a,b,c,z)for _,a,b,c,z in reads)
+assert [(op,a,b,c,z)for op,a,b,c,f,z in out if op]==expect
+# Selected 60 columns replay both source words over exact integers. This is
+# stronger than a parity test for the relocated arbitrary dirty payload.
+def columns(word):
+ cols=[{}for _ in range(n)];tmp=None
+ for h in selected:cols[h][h]=1
+ for op,a,b,c,f,z in word:
+  if op==1:
+   q=tmp if b==n else b
+   for h,x in list(cols[q].items()):
+    value=cols[a].get(h,0)+c*x
+    if value:cols[a][h]=value
+    elif h in cols[a]:del cols[a][h]
+  elif op==2:assert tmp is None;tmp=a
+  elif op==3:assert tmp==a;tmp=None
+ assert tmp is None
+ return cols
+assert columns(raw)==columns(out)
+delta=Counter(H);delta.subtract(oldH);delta={r:x for r,x in delta.items()if x};assert sum(r*x for r,x in delta.items())==-1092
+residual_before=Counter(fs[final[h]]['dim']-fs[zero]['dim']for h in selected);residual_after=Counter(fs[final[h]]['dim']-selected[h]['rank']for h in selected);assert residual_before=={24:60}and residual_after=={5:12,6:48}
+data=b''.join(struct.pack('<6i',*e)for e in out)
+assert hashlib.sha256(data).hexdigest()==selection['expected_output_sha256']
+(D/'COHORT249-RECORDS.bin').write_bytes(data)
+for name,value in [('INITIAL',initial),('FINAL',final),('FRAMES',{**json.loads((base/'COHORT249-FRAMES.json').read_text()),**extra})]:(D/f'COHORT249-{name}.json').write_text(json.dumps(value)+'\n')
+receipt=dict(selection_sha256=hashlib.sha256(selection_path.read_bytes()).hexdigest(),emitter_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),status='PASS_60_EXACT_INTEGER_DIRTY_COMPENSATION_TRANSPORT',source=str(base),source_sha256=hashlib.sha256((base/'COHORT249-RECORDS.bin').read_bytes()).hexdigest(),output_sha256=hashlib.sha256(data).hexdigest(),new_entrance_count=60,new_entrance_rank=1092,cut_record=cut,relocated_reads=reads,entries=list(selected.values()),all_selected_integer_columns_equal=True,only_documented_scalar_reordering=True,all_new_frames_exact_nondegenerate=True,changed_connector_pairs=sorted(changedpairs),paid_histogram=dict(H),histogram=dict(H),delta=delta,rank_mass=sum(r*x for r,x in H.items()),record_count=len(out),new_residual_histogram=dict(residual_after),local_entropy_delta=sum(x*r*math.log(120/r)for r,x in delta.items()))
+(D/'ENTRANCE-TRANSPORT.json').write_text(json.dumps(receipt,indent=2)+'\n');(D/'ENTRANCE-SELECTION.json').write_text(json.dumps(selection,indent=2)+'\n');print({k:v for k,v in receipt.items()if k not in ['entries','relocated_reads','changed_connector_pairs','paid_histogram','histogram']},flush=True)
diff --git a/research/gen4-retiming-entrances-target/code/export.py b/research/gen4-retiming-entrances-target/code/export.py
new file mode 100644
index 0000000000..e7b5c0ae30
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/export.py
@@ -0,0 +1,34 @@
+from pathlib import Path
+import json,sys,importlib.util,time,hashlib
+from collections import Counter
+import argparse, shutil
+if not __debug__: raise SystemExit('Assertions required; refusing -O')
+ap=argparse.ArgumentParser(); ap.add_argument('--base',type=Path,required=True); ap.add_argument('--output',type=Path,required=True); args=ap.parse_args()
+P=args.base.resolve(); D=args.output.resolve(); D.mkdir(parents=True,exist_ok=False)
+sys.dont_write_bytecode=True
+sys.path.insert(0,str(P));start=time.monotonic()
+def load(n):
+ s=importlib.util.spec_from_file_location('export_gen4_'+n.replace('/','_'),P/(n+'.py'));m=importlib.util.module_from_spec(s);sys.modules[s.name]=m;s.loader.exec_module(m);return m
+def save(n,j):(D/n).write_text(json.dumps(j,separators=(',',':'))+'\n')
+c=load('prepare').prepare();print('PREPARED',time.monotonic()-start,flush=True)
+p=load('code/physical527').run(c,c['SOURCE_TEXT'])
+p=load('parity_transform').run(p)
+records=p['records'];raw=records.tobytes();(D/'gen4-records.bin').write_bytes(raw)
+final=dict(p['initial_state']);used=set(final.values());hist=Counter();adds=Counter()
+for k in range(0,len(records),6):
+ op,a,b,cc,f,z=records[k:k+6]
+ if op==0:final[a]=cc;used.update((b,cc));hist[f]+=bool(f)
+ elif op==1:used.add(f);adds[cc]+=1
+ elif op in (2,3):used.update((cc,f));hist[z]+=op==2
+n=len(p['initial_state']);v=c['W'].v
+state=dict(initial=p['initial_state'],final=final,ZERO=p['ZERO'],FULL=p['FULL'],n=n,v=v,record_count=len(records)//6,record_sha256=hashlib.sha256(raw).hexdigest(),physical=p['physical'],regs=c['regs'],borrowed=list(c['borrow']),removed=list(c['removed']),source_owned_roles=sorted(c['borrow']),source_covectors=p['C'].cov)
+save('gen4-states.json',state)
+C=p['C'];save('frames.json',dict(h=24,frames={str(f):dict(B=C.B[f],A=C.A[f],dim=C.dimf[f])for f in sorted(used)}))
+save('gen4-ownership.json',dict(donor_keys=sorted(c['W'].donor),phys=c['W'].phys,idx=c['idx'],pairs=c['W'].pairs))
+save('EXPORT-RECEIPT.json',dict(status='FRESH_SOURCE_BOUND_EXPORT_NOT_FULL_VERIFICATION',head='d428ab0462b9dfd3131ab4e89999f0adcd6173dd',record_sha256=hashlib.sha256(raw).hexdigest(),n=n,v=v,frames=len(used),paid_histogram=dict(hist),adds=dict(adds),seconds=time.monotonic()-start))
+print('EXPORTED',n,len(records)//6,len(used),time.monotonic()-start,flush=True)
+
+assert state['record_sha256']=='60830cb24fbdd5a26942c4aa897d0ae30738ca5772ab83d6c57be666ddc95f7a'
+for name in ['249-records.bin','COHORT249-RECORDS.bin']: shutil.copyfile(D/'gen4-records.bin',D/name)
+shutil.copyfile(D/'gen4-states.json',D/'249-states.json')
+save('COHORT249-INITIAL.json',state['initial']);save('COHORT249-FINAL.json',state['final']);save('COHORT249-FRAMES.json',{})
diff --git a/research/gen4-retiming-entrances-target/code/five-stage-columns.cpp b/research/gen4-retiming-entrances-target/code/five-stage-columns.cpp
new file mode 100644
index 0000000000..187d969fc5
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/five-stage-columns.cpp
@@ -0,0 +1,42 @@
+#include "json.hpp"
+#include <map>
+#include <boost/multiprecision/cpp_int.hpp>
+using boost::multiprecision::cpp_int;
+#include <vector>
+#include <array>
+#include <fstream>
+#include <iostream>
+#include <chrono>
+#include <stdexcept>
+#include <cstring>
+using J=nlohmann::json;
+struct E{int kind,dst,src,c;};
+void need(bool x,const char*s){if(!x)throw std::runtime_error(s);}
+int main(int argc,char**argv){try{
+need(argc==5,"usage RAW6_RECORDS OUTPUT V HELPERS");std::string pre=argv[1];int v=std::stoi(argv[3]),r=std::stoi(argv[4]),loc=2*v+r,global=4*v+r,temp=global;need(v>0 && r>=0,"dimensions");
+struct Raw{int op,a,b,c,f,z;};std::ifstream f(pre,std::ios::binary|std::ios::ate);size_t sz=f.tellg();need(sz%sizeof(Raw)==0,"stream alignment");std::vector<Raw>p(sz/sizeof(Raw));f.seekg(0);f.read((char*)p.data(),sz);std::vector<E>e;std::map<int,long long>H;for(auto q:p){if(q.op==0){if(q.f)H[q.f]++;}else if(q.op==1)e.push_back({0,q.a,q.b,q.c});else if(q.op==2){H[q.z]++;e.push_back({1,loc,q.a,0});}else if(q.op==3)e.push_back({2,loc,q.a,0});else need(false,"opcode");}
+J prefix=J::array();cpp_int largestF=0,largestB=0;for(int rev=0;rev<2;rev++){std::vector<cpp_int>norms(loc+1,1);cpp_int maxrow=1;bool isopen=false;for(size_t z=0;z<e.size();z++){auto q=e[rev?e.size()-1-z:z];int k=q.kind;if(rev&&k)k=3-k;if(!k){norms[q.dst]+=std::abs(q.c)*norms[q.src];if(norms[q.dst]>maxrow)maxrow=norms[q.dst];}else if(k==1){need(!isopen,"boundcopy");norms[loc]=norms[q.src];isopen=true;}else {need(isopen,"bounderase");norms[loc]=0;isopen=false;}}need(!isopen,"prefix copy closure");if(rev)largestB=maxrow;else largestF=maxrow;prefix.push_back({{"reverse",bool(rev)},{"cancellation_free_signed_row_l1_upper",maxrow.convert_to<std::string>()},{"bits",boost::multiprecision::msb(maxrow)+1}});}
+cpp_int payload=64*largestF*largestF*largestF*largestB*largestB;need(payload>0,"positive finite prefix"); // Exact width is reported and must be included in the separate finite invoice.
+long long copies=0,adds=0,odd=0;bool open=false;int center=-1;long long reverseCopies=0;
+for(auto q:e){need(q.kind>=0&&q.kind<=2,"kind");need(q.dst>=0&&q.dst<=loc,"local dst");if(q.kind==0){need(q.src>=0&&q.src<=loc&&q.dst!=q.src,"source distinct");need(q.dst!=loc,"copy immutable");need(q.src!=loc||open,"temp not open");if(open)need(q.dst!=center,"source changes inside copied-center block");adds++;odd+=q.c&1;}
+else if(q.kind==1){need(!open&&q.dst==loc&&q.src>=0&&q.src<loc,"fresh copy shape");open=true;center=q.src;copies++;}
+else{need(open&&q.dst==loc&&q.src==center,"discard original-source binding");open=false;center=-1;}}
+need(!open&&copies==24,"center boundaries");
+int active[5][2]={{0,1},{1,0},{0,1},{3,2},{2,3}};
+int bridges[3][2][3]={{{0,2,1},{3,1,-1}},{{3,1,1},{0,2,-1}},{{1,3,-1},{2,0,1}}};
+size_t words=(global+63)/64;std::vector<unsigned long long>a((size_t)(global+1)*words);auto row=[&](int i){return a.data()+(size_t)i*words;};for(int i=0;i<global;i++)row(i)[i/64]|=1ull<<(i%64);
+auto xo=[&](int d,int s){auto*x=row(d);auto*y=row(s);for(size_t j=0;j<words;j++)x[j]^=y[j];};
+auto map=[&](int stage,int i){if(i<v)return active[stage][0]*v+i;if(i<2*v)return active[stage][1]*v+i-v;if(i<loc)return 4*v+i-2*v;return temp;};
+auto t0=std::chrono::steady_clock::now();J stages=J::array();
+for(int stage=0;stage<5;stage++){bool rev=stage==1||stage==3;bool opened=false;long long cp=0,ad=0;auto step=[&](E q){int k=q.kind;if(rev&&k)k=3-k;int d=map(stage,q.dst),s=map(stage,q.src);if(k==0){if(q.c&1)xo(d,s);ad++;}else if(k==1){need(!opened,"fresh physical work opening");std::memcpy(row(temp),row(s),words*8);opened=true;cp++;}else{need(opened,"physical work closing");std::memset(row(temp),0,words*8);opened=false;}};
+if(rev){for(auto it=e.rbegin();it!=e.rend();++it)step(*it);reverseCopies+=cp;}else for(auto q:e)step(q);need(!opened&&cp==24,"stage copied-center endpoint");
+if(stage==0){for(int i=0;i<global;i++){auto*x=row(i);for(size_t w=0;w<words;w++){unsigned long long want=(w==(size_t)i/64?1ull<<(i%64):0);if(i>=v&&i<2*v&&w==(size_t)(i-v)/64)want^=1ull<<((i-v)%64);need(x[w]==want,"local defining-decoder full formal column");}}}
+if(stage==1||stage==2||stage==4){int b=stage==1?0:stage==2?1:2;for(auto q:bridges[b])for(int i=0;i<v;i++)xo(q[0]*v+i,q[1]*v+i);}
+stages.push_back({{"stage",stage},{"signed_inverse",rev},{"fresh_copies",cp},{"scalar_additions",ad}});std::cerr<<"stage "<<stage<<" PASS elapsed "<<std::chrono::duration<double>(std::chrono::steady_clock::now()-t0).count()<<"s\n";}
+for(int bank=0;bank<4;bank+=2)for(int i=0;i<v;i++)for(size_t w=0;w<words;w++)std::swap(row(bank*v+i)[w],row((bank+1)*v+i)[w]);
+for(int i=0;i<=global;i++)for(size_t w=0;w<words;w++){unsigned long long want=(i<global&&w==(size_t)i/64?1ull<<(i%64):0);need(row(i)[w]==want,"five-stage all physical formal columns");}
+// Independent complete four-bank controls, each omitted bridge must change endpoint.
+J controls=J::array();for(int skip=0;skip<6;skip++){int b[4]={1,2,4,8},j=0;for(int s=0;s<5;s++){b[active[s][1]]^=b[active[s][0]];if(s==1||s==2||s==4){int k=s==1?0:s==2?1:2;for(auto q:bridges[k]){if(j++!=skip)b[q[0]]^=b[q[1]];}}}std::swap(b[0],b[1]);std::swap(b[2],b[3]);bool failed=false;for(int z=0;z<4;z++)failed|=b[z]!=(1<<z);need(failed,"vacuous omitted bridge control");controls.push_back({{"omit_bridge",skip},{"rejected",true}});}
+J out={{"status","PASS_GENERIC_FIVE_STAGE_FORMAL_COLUMNS_AND_COMPUTED_PREFIX"},{"local_scalar_stream",pre},{"local_registers",loc},{"global_live_registers",global},{"formal_columns_checked",global},{"independent_dirty_registers",r},{"local_scalar_additions",adds},{"local_odd_scalar_additions",odd},{"five_stage_additions",5*adds},{"bridge_additions",6*v},{"fresh_center_copies",120},{"reverse_fresh_center_copies",reverseCopies},{"copied_center_original_source_immutable",true},{"signed_reverse_semantics","Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction."},{"scope","All computed global_live independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check."},{"stages",stages},{"signed_lift_prefix",prefix},{"payload_prefix_upper",payload.convert_to<std::string>()},{"payload_prefix_bits",boost::multiprecision::msb(payload)+1},{"new_Q_categories",{28,29}},{"local_raw_H",H},{"negative_controls",controls},{"seconds",std::chrono::duration<double>(std::chrono::steady_clock::now()-t0).count()}};std::ofstream(argv[2])<<out.dump(2);std::cout<<out.dump(2)<<"\n";
+}catch(const std::exception&e){std::cerr<<e.what()<<"\n";return 2;}}
+
diff --git a/research/gen4-retiming-entrances-target/code/price.py b/research/gen4-retiming-entrances-target/code/price.py
new file mode 100644
index 0000000000..b4b89faad8
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/price.py
@@ -0,0 +1,233 @@
+#!/usr/bin/env python3
+"""Recount and exactly price the literal gen4 candidate.
+
+The fixed-prime interval method follows the retained PR265 refinement; the
+moment and outer engines are dynamically loaded from the pinned PR276 package.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import sys
+if not __debug__:
+    raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+sys.set_int_max_str_digits(0)
+
+from array import array
+from collections import Counter
+from decimal import Decimal, ROUND_FLOOR, localcontext
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import hashlib
+import importlib.util
+import json
+
+PRIME = (1 << 127) - 1
+M = 120
+RHO = Q(2 * M**3, PRIME)
+ETA = Q(1, 10**24)
+BETA = Q(1, 10**9)
+GRID = 10**27
+COMPLEX_SAVING = Q(747454944651775, 10**18)
+INITIAL_LEAF = Q(384599, 10**10)
+BASE_MANIFEST_SHA256 = "6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d"
+PUBLISHED_BASELINE = Q("0.000722869827347495")
+EXPECTED_KAPPA = Q(725113717934416422443945, GRID)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def load_engine(name, base):
+    path = base / (name + ".py")
+    manifest = json.loads((base / "MANIFEST.json").read_text())
+    assert sha(base / "MANIFEST.json") == BASE_MANIFEST_SHA256
+    assert sha(path) == manifest["files"][path.name]
+    spec = importlib.util.spec_from_file_location("gen4_pinned_" + name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def read_word(path):
+    blob = Path(path).read_bytes()
+    assert len(blob) % 24 == 0, "Bad six-int32 record alignment"
+    words = array("i")
+    assert words.itemsize == 4
+    words.frombytes(blob)
+    if sys.byteorder != "little":
+        words.byteswap()
+    records = list(zip(*[iter(words)] * 6))
+    assert all(record[0] in (0, 1, 2, 3) for record in records)
+    return records
+
+
+def word_inventory(candidate):
+    records = read_word(candidate / "COHORT249-RECORDS.bin")
+    histogram, opcounts, coefficients = Counter(), Counter(), Counter()
+    for op, a, b, c, frame, category in records:
+        opcounts[op] += 1
+        if op == 0 and frame:
+            histogram[frame] += 1
+        elif op == 2:
+            histogram[category] += 1
+        elif op == 1:
+            coefficients[abs(c)] += 1
+    assert histogram and min(histogram) > 0 and max(histogram) < 24
+    return records, histogram, opcounts, coefficients
+
+def serial(value):
+    if isinstance(value, Q):
+        return str(value)
+    if isinstance(value, dict):
+        return {str(k): serial(v) for k, v in value.items()}
+    if isinstance(value, (list, tuple)):
+        return [serial(v) for v in value]
+    return value
+
+def bridge_template():
+    # Literal retained bridge from source527 math_check.py, itself pinned in SOURCE.json.
+    return dict(
+        proof="PROOF.md",
+        representation="Exact powers with source-bound finite overcharges",
+        semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000),
+                      B_upper=dict(base=2, exponent=100001), C0=dict(base=2, exponent=210000),
+                      C1=1, strict_literal_gap=1, induction_gap_lower=1),
+        rows=dict(coefficient=20161, degree=10**6, suffix_slope=4*10**6,
+                  degree_gap=Q(10**6) - Q(51*20161, 25)))
+
+def fixed_moment(histogram, m, stock, calls, saving, cost):
+    lo, hi = cost.moment(histogram, m, stock, saving, False)
+    log_lo, log_hi = cost.logarithm(Q(m))
+    exp_lo = cost.exponential(saving * log_lo, saving * log_lo)[0]
+    exp_hi = cost.exponential(saving * log_hi, saving * log_hi)[1]
+    fallback_weight = Q(32 * m * calls, stock) * RHO
+    return cost.floor(lo + fallback_weight * exp_lo), cost.ceil(hi + fallback_weight * exp_hi)
+
+def second_engine_with_fallback(histogram, m, stock, calls, saving, other):
+    lower, upper = other.moment(m, stock, list(histogram.items()), saving)
+    log_lo, log_hi = other.log_bounds(Q(m))
+    exp_lo = other.exp_bounds(saving * log_lo)[0]
+    exp_hi = other.exp_bounds(saving * log_hi)[1]
+    fallback_weight = Q(32 * m * calls, stock) * RHO
+    return lower + fallback_weight * exp_lo, upper + fallback_weight * exp_hi
+
+def certify_coarse(histogram, m, stock, calls, cost, other):
+    with localcontext() as ctx:
+        ctx.prec = 80
+        terms = [(Decimal(r*n) / Decimal(m*stock), (Decimal(m) / Decimal(r)).ln())
+                 for r, n in histogram.items()]
+        fallback = (Decimal(32*m*calls) / Decimal(stock)
+                    * Decimal(2*m**3) / Decimal(PRIME))
+        log_m = Decimal(m).ln()
+        lower, upper = Decimal(0), Decimal("0.003")
+        for _ in range(240):
+            candidate = (lower + upper) / 2
+            total = sum(p * (candidate * log_r).exp() for p, log_r in terms)
+            total += fallback * (candidate * log_m).exp()
+            if total < 1:
+                lower = candidate
+            else:
+                upper = candidate
+        endpoint = Q(int(((lower + upper) / 2 * GRID).to_integral_value(rounding=ROUND_FLOOR)), GRID)
+    next_endpoint = endpoint + Q(1, GRID)
+    first = fixed_moment(histogram, m, stock, calls, endpoint, cost)
+    first_next = fixed_moment(histogram, m, stock, calls, next_endpoint, cost)
+    second = second_engine_with_fallback(histogram, m, stock, calls, endpoint, other)
+    second_next = second_engine_with_fallback(histogram, m, stock, calls, next_endpoint, other)
+    assert first[1] < 1 < first_next[0]
+    assert second[1] < 1 < second_next[0]
+    return endpoint, next_endpoint, first, first_next, second, second_next
+
+def grid_kappa(bit_saving, eta=ETA):
+    q = bit_saving * (1 - 2*eta)
+    minimum = (1 - eta) * q / (1 + q)
+    ticks = minimum * GRID
+    return Q((ticks.numerator - 1) // ticks.denominator, GRID)
+
+def ceil_fraction(value):
+    assert value >= 0
+    return (value.numerator + value.denominator - 1) // value.denominator
+
+def compute(candidate, base):
+    candidate, base = Path(candidate).resolve(), Path(base).resolve()
+    cost = load_engine("moment", base)
+    other = load_engine("base_two_moment", base)
+    outer = load_engine("outer", base)
+    _, local, operations, coefficients = word_inventory(candidate)
+    histogram = Counter({rank: 60 * count for rank, count in local.items()})
+    histogram.update({rank: 24 * 1760 for rank in (4, 23, 46, 50)})
+    histogram = dict(sorted(histogram.items()))
+    stock = 255841  # Independently reconstructed from actual endpoints by admit.py.
+    calls = sum(histogram.values())
+    mass = sum(rank * count for rank, count in histogram.items())
+    assert (calls, mass, 120 * stock - mass) == (5789640, 30648120, 52800)
+    coarse, next_coarse, first, first_next, second, second_next = certify_coarse(
+        histogram, 120, stock, calls, cost, other
+    )
+    chain, gaps = [INITIAL_LEAF], []
+    for level in range(1, 9):
+        old = chain[-1]
+        new = (1 - coarse) * coarse + coarse * old
+        assert old < new < coarse < 1 - new
+        chain.append(new)
+        gap = dict(atom=coarse-new, borrowing=1-new-coarse,
+                   remainder=1-new-coarse*(1-old), stock=1-coarse)
+        assert min(gap.values()) > 0
+        gaps.append(dict(level=level, gaps=gap))
+    kappa = grid_kappa(chain[-1])
+    assembly = outer.assembly(chain[-1], COMPLEX_SAVING, bridge_template(),
+                              kappa, eta=ETA, beta=BETA)
+    assert len(assembly["strict_constraints"]) == 47
+    assert min(assembly["strict_constraints"].values()) > 0
+    try:
+        outer.assembly(chain[-1], COMPLEX_SAVING, bridge_template(),
+                       kappa + Q(1, GRID), eta=ETA, beta=BETA)
+    except AssertionError:
+        pass
+    else:
+        raise AssertionError("Adjacent finite-grid kappa admitted")
+    assert kappa == EXPECTED_KAPPA
+    target = PUBLISHED_BASELINE * Q(1001, 1000)
+    assert kappa > target
+    sources = [Path(__file__).resolve(), base / "MANIFEST.json"]
+    sources += [base / (name + ".py") for name in ("moment", "base_two_moment", "outer")]
+    sources += [candidate / name for name in ("COHORT249-RECORDS.bin", "COHORT249-INITIAL.json",
+                                            "COHORT249-FINAL.json", "COHORT249-FRAMES.json")]
+    return serial(dict(
+        status="PASS_EXACT_ACTUAL_WORD_PRICE_REQUIRES_SEPARATE_CONSTRUCTION_ADMISSION",
+        base_package=str(base), base_manifest_sha256=BASE_MANIFEST_SHA256,
+        source_word_sha256=sha(candidate / "COHORT249-RECORDS.bin"),
+        source_bindings={str(path): sha(path) for path in sources},
+        literal_replicas=60, normalization_factor=5, stock=stock, literal_stock=5*stock,
+        local_histogram=local, histogram=histogram, calls=calls, rank_mass=mass,
+        deficit=52800, operation_counts=operations, scalar_coefficient_counts=coefficients,
+        prime=PRIME, rare_density=RHO, full_fallback_kept=True,
+        coarse=coarse, coarse_bracket=[coarse, next_coarse],
+        first_engine_interval=first, first_engine_next_interval=first_next,
+        second_engine_interval=second, second_engine_next_interval=second_next,
+        ordinary_levels=8, ordinary_chain=chain, ordinary_gaps=gaps,
+        assembly=assembly, kappa=kappa, kappa_decimal=cost.decimal(kappa),
+        coarse_cap=grid_kappa(coarse), adjacent_grid_rejected_at_finite=True,
+        published_PR276_kappa=PUBLISHED_BASELINE, strict_PR276_0p1_percent_target=target,
+        gain_percent=100*(kappa-PUBLISHED_BASELINE)/PUBLISHED_BASELINE,
+        exceeds_PR276_0p1_percent=True,
+        scope="Exact pricing only. Source-bound scalar, geometry, chart, bank and finite "
+              "construction admission are separate mandatory checks."
+    ))
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("candidate", type=Path)
+    parser.add_argument("--base", type=Path, required=True)
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    result = compute(args.candidate, args.base)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(json.dumps(result, sort_keys=True, indent=2) + "\n")
+    print("PASS exact price", result["kappa_decimal"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/gen4-retiming-entrances-target/code/retime.py b/research/gen4-retiming-entrances-target/code/retime.py
new file mode 100644
index 0000000000..a0aed6a548
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/retime.py
@@ -0,0 +1,86 @@
+from pathlib import Path
+import json,struct,hashlib,math,sys,argparse
+sys.dont_write_bytecode=True
+if not __debug__: raise SystemExit('Assertions required; refusing -O')
+from collections import Counter
+ap=argparse.ArgumentParser(); ap.add_argument('--export-dir',type=Path,required=True); ap.add_argument('--output',type=Path,required=True); args=ap.parse_args()
+X=args.export_dir.resolve(); D=args.output.resolve();D.mkdir(parents=True,exist_ok=False)
+st=json.loads((X/'gen4-states.json').read_text());n=st['n'];v=st['v'];fs={int(k):x for k,x in json.loads((X/'frames.json').read_text())['frames'].items()}
+rows=json.loads((Path(__file__).resolve().parents[1]/'data/retiming880.json').read_text());selected={}
+for r in rows:
+ if r['new_frame'] in fs and r['component'] not in selected:selected[r['component']]=r
+assert len(selected)==880
+roleuses=Counter(s for r in selected.values()for s in r['roles']);assert len(roleuses)==v and set(roleuses.values())=={1} and all(s<v for s in roleuses)
+replacements={g:r['new_frame']for r in selected.values()for g in r['gates']};assert len(replacements)==880
+raw=list(struct.iter_unpack('<6i',(X/'gen4-records.bin').read_bytes()));basepairs={(e[2],e[3])for e in raw if e[0]==0};initial={int(k):f for k,f in st['initial'].items()};final={int(k):f for k,f in st['final'].items()};state=dict(initial);out=[];pairs=set();changedpairs=set();core=0;copy=None;H=Counter();oldH=Counter()
+for op,a,b,c,f,z in raw:
+ if op==0 and f:oldH[f]+=1
+ elif op==2:oldH[z]+=1
+def sub(a,b):return fs[a]['dim']<=fs[b]['dim'] and all(sum(x*y for x,y in zip(u,w))==0 for u in fs[a]['B']for w in fs[b]['A'])
+# Data roles form a closed scalar subword. Track defining integer source
+# coefficients to audit both operands before and after each changed shear.
+source_columns=[{i:1} for i in range(v)]
+assert all(fs[initial[i]]['dim']==1 for i in range(v))
+source_vectors={i:fs[initial[i]]['B'][0] for i in range(v)}
+span_checks=0;span_sizes={}
+def span_in_frame(coefficients,f):
+ return all(all(sum(x*y for x,y in zip(source_vectors[i],w))==0 for w in fs[f]['A']) for i in coefficients)
+def move(a,f):
+ old=state[a]
+ if old==f:return
+ pair=(old,f)
+ if pair not in pairs:
+  if pair not in basepairs:assert sub(old,f);changedpairs.add(pair)
+  pairs.add(pair)
+ rank=fs[f]['dim']-fs[old]['dim'];assert rank>=0
+ out.append((0,a,old,f,rank,0));state[a]=f
+ if rank:H[rank]+=1
+for op,a,b,c,f,z in raw:
+ if op==0:continue
+ if op==1:
+
+  if core in replacements:
+   binding=selected[core];assert op==1 and f==binding['old_frame'] and sorted([a,b])==sorted(binding['roles'])
+   assert fs[f]['dim']==2 and fs[binding['new_frame']]['dim']==22
+   assert sub(f,binding['new_frame']), 'Retimed old frame must lie inside the new frame'
+   assert 0<=a<v and 0<=b<v
+   for operand in (a,b):
+    assert span_in_frame(source_columns[operand],f) and span_in_frame(source_columns[operand],binding['new_frame'])
+    span_checks+=len(source_columns[operand])
+  f=replacements.get(core,f);move(a,f);move(b,f);assert state[a]==state[b]==f
+  if a<v:
+   assert 0<=b<v, 'Data source roles must receive only data-source values'
+   for source,value in list(source_columns[b].items()):
+    value=source_columns[a].get(source,0)+c*value
+    if value:source_columns[a][source]=value
+    else:source_columns[a].pop(source,None)
+  if core in replacements:
+   assert span_in_frame(source_columns[a],f) and span_in_frame(source_columns[b],f)
+   span_checks+=len(source_columns[a])+len(source_columns[b]);span_sizes[core]=len(set(source_columns[a])|set(source_columns[b]))
+  out.append((op,a,b,c,f,z))
+ elif op==2:
+  assert copy is None and b==n;move(a,c);state[b]=f;copy=(a,b,c,f);H[z]+=1;out.append((op,a,b,c,f,z))
+ else:
+  assert op==3 and copy==(a,b,c,f) and state[a]==c and state[b]==f;out.append((op,a,b,c,f,z));del state[b];copy=None
+ core+=1
+assert copy is None and len(span_sizes)==880 and set(span_sizes.values())=={2}
+assert source_columns==[{i:1}for i in range(v)]
+for a in range(n):move(a,final[a])
+assert state==final
+def project(es):return [(op,a,b,c,z)for op,a,b,c,f,z in es if op]
+assert project(raw)==project(out)
+delta=Counter(H);delta.subtract(oldH);delta={r:x for r,x in delta.items()if x}
+assert delta=={21:1760,2:880,1:-1760,20:-880,22:-880}
+assert sum(r*x for r,x in delta.items())==0
+data=b''.join(struct.pack('<6i',*e)for e in out)
+(D/'COHORT249-RECORDS.bin').write_bytes(data)
+(D/'COHORT249-INITIAL.json').write_text(json.dumps(st['initial'])+'\n')
+(D/'COHORT249-FRAMES.json').write_text('{}\n')
+(D/'COHORT249-FINAL.json').write_text(json.dumps(st['final'])+'\n')
+(D/'RETIMING-SELECTION.json').write_text(json.dumps(list(selected.values()),indent=2)+'\n')
+receipt=dict(old_frame_containment_explicit=True,exact_integer_source_spans=True,checked_operand_source_inclusions=span_checks,max_changed_gate_source_support=max(span_sizes.values()),status='PASS_880_DISJOINT_RETIMINGS_LITERAL_SCALAR_EQUALITY_AND_NEW_CONNECTOR_GEOMETRY',base_sha256=hashlib.sha256((X/'gen4-records.bin').read_bytes()).hexdigest(),output_sha256=hashlib.sha256(data).hexdigest(),n=n,v=v,selected_gates=len(replacements),source_roles=len(roleuses),new_frame_ids=0,changed_connector_pairs=sorted(changedpairs),paid_histogram=dict(H),local_histogram_delta=delta,rank_mass=sum(r*x for r,x in H.items()),record_count=len(out),scope='Full baseline checks and fresh five-stage replay are separate; all changed connector inclusions checked by exact integer dot products. No exponent claimed by this emitter.')
+(D/'RETIMING-REPLAY.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print({k:v for k,v in receipt.items()if k not in ['changed_connector_pairs','paid_histogram']},flush=True)
+
+assert receipt['output_sha256']=='2d22a9530f0b04a7a794d15077459234ef52183d6e7a70f813cfa849b79f2ebe'
+(D/'249-states.json').write_text(json.dumps(st)+'\n')
diff --git a/research/gen4-retiming-entrances-target/code/target_prefix.py b/research/gen4-retiming-entrances-target/code/target_prefix.py
new file mode 100644
index 0000000000..e9772efd19
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/code/target_prefix.py
@@ -0,0 +1,199 @@
+#!/usr/bin/env python3
+"""Exact F2 target-prefix compression (PR268's mechanism) on the cohort-rewritten native transcript.
+
+A group is one dependent target t with retained targets p_1..p_k, a cut and a close record, and a common close
+frame F inside every member's cap.  The dependent's reads in (cut, close] are omitted; at the cut it receives
+t -= p_j at the zero frame, and at the close t += p_j at F, after moving every member to F.  The transform
+recomputes each member's literal prefix response from the actual transcript and requires the F2 dependency
+R_t = sum_j R_pj before emitting anything; it then rebuilds every MOVE from the actual needs and checks nested
+chains, fixed endpoints, COPY lifetimes, nondegenerate endpoint bases and forward/inverse all-column replays.
+Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0.
+"""
+from array import array
+from collections import Counter, defaultdict
+from fractions import Fraction
+from pathlib import Path
+import hashlib, json, sys
+if not __debug__: raise SystemExit('assertions required')
+X, LEAD, SEL = Path(sys.argv[1]), Path(sys.argv[2]), Path(sys.argv[3])
+H = 24
+def dot(x, y): return sum(p*q for p, q in zip(x, y))
+def rank(rows):
+    M = [[Fraction(x) for x in r] for r in rows]; r = 0
+    for c in range(len(M[0]) if M else 0):
+        p = next((i for i in range(r, len(M)) if M[i][c]), None)
+        if p is None: continue
+        M[r], M[p] = M[p], M[r]; pv = M[r][c]; M[r] = [x/pv for x in M[r]]
+        for i in range(len(M)):
+            if i != r and M[i][c]:
+                m = M[i][c]; M[i] = [x-m*y for x, y in zip(M[i], M[r])]
+        r += 1
+        if r == len(M): break
+    return r
+def _introw(r):
+    from fractions import Fraction as _F
+    from math import lcm as _lcm
+    q = [_F(str(x)) for x in r]; d = 1
+    for x in q: d = _lcm(d, x.denominator)
+    return [int(x*d) for x in q]
+frames = {}
+for name in (X/'frames.json', LEAD/'COHORT249-FRAMES.json'):
+    j = json.loads(name.read_text()); j = j.get('frames', j)
+    for k, rec_ in j.items(): frames[int(k)] = dict(B=[_introw(r) for r in rec_['B']], A=[_introw(r) for r in rec_['A']], d=int(rec_['dim']))
+for f, fr in frames.items(): assert len(fr['B']) == fr['d'] and len(fr['A']) + fr['d'] == H and all(dot(a, b) == 0 for a in fr['A'] for b in fr['B'])
+subcache = {}
+def sub(f, g):
+    if f == g: return True
+    k = (f, g)
+    if k not in subcache: subcache[k] = frames[f]['d'] <= frames[g]['d'] and all(dot(a, b) == 0 for a in frames[g]['A'] for b in frames[f]['B'])
+    return subcache[k]
+def nondeg(f):
+    B, A = frames[f]['B'], frames[f]['A']
+    if not B or len(B) == H: return True
+    if len(B) <= len(A):
+        s = [sum(b) for b in B]; return rank([[9*dot(B[i], B[j]) - s[i]*s[j] for j in range(len(B))] for i in range(len(B))]) == len(B)
+    s = [sum(a) for a in A]; return rank([[(9-H)*dot(A[i], A[j]) + s[i]*s[j] for j in range(len(A))] for i in range(len(A))]) == len(A)
+st = json.loads((X/'249-states.json').read_text()); n, v = st['n'], st['v']; ZERO, FULL = st['ZERO'], st['FULL']
+cov = [list(map(int, c)) for c in st['source_covectors']]
+initial = {int(k): f for k, f in json.loads((LEAD/'COHORT249-INITIAL.json').read_text()).items()}
+sel = json.loads(SEL.read_text()); cut = sel['cut_record']
+old = array('i'); old.frombytes((LEAD/'COHORT249-RECORDS.bin').read_bytes()); assert old.itemsize == 4 and len(old) % 6 == 0
+assert hashlib.sha256(old.tobytes()).hexdigest() == sel['input_record_sha256'] and len(old)//6 == sel['input_record_count']
+final = dict(initial)
+for k in range(0, len(old), 6):
+    if old[k] == 0: final[old[k+1]] = old[k+3]
+groups = []; owner = {}; atclose = defaultdict(list); dep_of = {}
+for j, g in enumerate(sel['groups']):
+    t, ps, close, F = g['dependent'], list(g['retained']), g['close_after_record'], g['frame']
+    assert close > cut and len(ps) >= 1 and t not in ps and len(set(ps)) == len(ps)
+    assert frames[F]['d'] == g['close_rank'] and nondeg(F)
+    for m in [t] + ps:
+        assert m not in owner; owner[m] = j
+        assert initial[v+m] == ZERO and all(dot(cov[m], b) == 0 for b in frames[F]['B']), 'close frame outside a member cap'
+    dep_of[t] = j; atclose[close].append(j); groups.append(dict(dependent=t, retained=ps, close=close, frame=F))
+assert len(groups) == sel['selected_groups'] > 0
+# literal prefix responses and member states from the actual transcript
+cols = [1 << i for i in range(n)]; center = None; responses = {m: 0 for m in owner}; state = dict(initial); state_at_close = {}
+for k in range(0, len(old), 6):
+    op, a, b, c, f, z = old[k:k+6]; i = k//6
+    if op == 0: state[a] = c
+    elif op == 1:
+        src = center if b == n else b; assert src is not None
+        if i > cut:
+            if src - v in owner: assert i > groups[owner[src-v]]['close'], 'active group target used as a source'
+            if a - v in owner and i <= groups[owner[a-v]]['close']:
+                assert not (v <= src < 2*v), 'target source inside an active prefix'; responses[a-v] ^= cols[src]
+        assert c % 2; cols[a] ^= cols[src]
+    elif op == 2: assert center is None; center = a; state[b] = f
+    elif op == 3: assert center == a; center = None; del state[b]
+    for j in atclose.get(i, []):
+        g = groups[j]; R = responses[g['dependent']]
+        for p in g['retained']: R ^= responses[p]
+        assert R == 0, ('literal prefix dependency fails', j)
+        for m in [g['dependent']] + g['retained']: assert sub(state[v+m], g['frame']), ('member frame not inside close frame', j, m)
+assert center is None
+# emit
+zmax = max(old[k+5] for k in range(0, len(old), 6) if old[k] == 1); SETUP, RESTORE = zmax + 1, zmax + 2
+state = dict(initial); out = array('i'); center = None; deleted = []; inserted = 0
+def move(s, f):
+    before = state[s]
+    if before == f: return
+    assert sub(before, f), ('nonnested actual use', s, before, f)
+    gap = frames[f]['d'] - frames[before]['d']; assert gap >= 0; out.extend((0, s, before, f, gap, 0)); state[s] = f
+def add(a, b, c, f, z): move(a, f); move(b, f); out.extend((1, a, b, c, f, z))
+for k in range(0, len(old), 6):
+    op, a, b, c, f, z = old[k:k+6]; i = k//6
+    if op == 1:
+        j = dep_of.get(a - v)
+        if j is not None and cut < i <= groups[j]['close']: assert not (v <= b < 2*v); deleted.append(i)
+        else: add(a, b, c, f, z)
+    elif op == 2: assert center is None; move(a, c); out.extend((op, a, b, c, f, z)); state[b] = f; center = (a, b, c)
+    elif op == 3: assert center == (a, b, c) and state[a] == c and state[b] == f; out.extend((op, a, b, c, f, z)); del state[b]; center = None
+    if i == cut:
+        assert center is None and all(state[v+m] == ZERO for m in owner)
+        for g in groups:
+            for p in g['retained']: add(v+g['dependent'], v+p, -1, ZERO, SETUP); inserted += 1
+    for j in atclose.get(i, []):
+        g = groups[j]
+        for m in [g['dependent']] + g['retained']: move(v+m, g['frame'])
+        for p in g['retained']: add(v+g['dependent'], v+p, 1, g['frame'], RESTORE); inserted += 1
+for s in sorted(final): move(s, final[s])
+assert center is None and state == final
+# census from needs, independent of emitted MOVEs
+needs = {i: [] for i in initial}; copies = Counter(); copy = None
+for k in range(0, len(out), 6):
+    op, a, b, c, f, z = out[k:k+6]
+    if op == 1:
+        assert c % 2; needs[a].append(f)
+        if b != n: needs[b].append(f)
+        else: assert copy is not None and f == ZERO
+    elif op == 2: assert copy is None; copy = (a, b, c); needs[a].append(c); copies[frames[c]['d']] += 1
+    elif op == 3: assert copy == (a, b, c); copy = None
+assert copy is None and copies == {22: 24}
+census = Counter(copies); pairs = set()
+for s, before in initial.items():
+    for f in needs[s] + [final[s]]:
+        assert sub(before, f); r = frames[f]['d'] - frames[before]['d']
+        if r: census[r] += 1
+        pairs.add((before, f)); before = f
+for f in {f for pair in pairs for f in pair}: assert nondeg(f)
+for a, b in pairs: assert len(frames[b]['A']) <= len(frames[a]['A']) and all(dot(x, y) == 0 for x in frames[b]['A'] for y in frames[a]['B'])
+for t in range(v):
+    f = final[v+t]; assert frames[f]['d'] == 23 and all(dot(cov[t], b) == 0 for b in frames[f]['B'])
+hist = Counter(); state = dict(initial); copy = None; count = 0
+for k in range(0, len(out), 6):
+    op, a, b, c, f, z = out[k:k+6]
+    if op == 0:
+        assert state[a] == b and sub(b, c) and frames[c]['d'] - frames[b]['d'] == f; state[a] = c
+        if f: hist[f] += 1
+    elif op == 1: assert state[a] == state[b] == f and a != b; count += 1
+    elif op == 2: assert copy is None and state[a] == c and f == ZERO and z == 22; state[b] = f; hist[z] += 1; copy = (a, b, c)
+    else: assert copy == (a, b, c) and state[a] == c and state[b] == f == ZERO; del state[b]; copy = None
+assert state == final and hist == census and copy is None
+# forward and inverse all-column replays with arbitrary dirty contents
+def replay(records, reverse=False, omit=None):
+    columns = [1 << i for i in range(n)]; wanted = columns[:]; center = None; cnt = 0
+    for t in range(v): wanted[v+t] ^= 1 << t
+    for k in (range(len(records)-6, -1, -6) if reverse else range(0, len(records), 6)):
+        op, a, b, c, f, z = records[k:k+6]
+        if op == 1:
+            if b == n: assert center is not None; b = center
+            if k//6 == omit: continue
+            assert c % 2 and a != b; columns[a] ^= columns[b]; cnt += 1
+        elif op == (3 if reverse else 2): assert center is None; center = a
+        elif op == (2 if reverse else 3): assert center == a; center = None
+    assert center is None and columns == wanted, 'all-column endpoint failure'
+    return cnt
+assert replay(out) == replay(out, True) == count
+first_setup = next(k//6 for k in range(0, len(out), 6) if out[k] == 1 and out[k+5] == SETUP)
+try: replay(out, omit=first_setup)
+except AssertionError: negative = 'omitted target-prefix setup rejected'
+else: raise AssertionError('missing setup admitted')
+replay_path = LEAD/'COHORT249-REPLAY.json'
+if replay_path.exists():
+    replay_json = json.loads(replay_path.read_text()); oldH = Counter({int(r): c for r, c in replay_json['histogram'].items()})
+else:
+    replay_json = None; oldH = Counter({22: 24})
+    for k in range(0, len(old), 6):
+        if old[k] == 0 and old[k+4]: oldH[old[k+4]] += 1
+delta = Counter(hist); delta.subtract(oldH); delta = {r: c for r, c in delta.items() if c}
+assert delta == {int(r): c for r, c in sel['expected_local_histogram_delta'].items()}, ('histogram delta', delta)
+assert sum(r*c for r, c in hist.items()) == sum(r*c for r, c in oldH.items()) and (replay_json is None or sum(r*c for r, c in hist.items()) == replay_json['new_rank_mass'])
+assert (len(deleted), inserted, count) == (sel["expected_deleted_reads"], sel["expected_inserted_additions"], sel["expected_scalar_additions"]), ("counts", len(deleted), inserted, count)
+(LEAD/'COHORT249-PRE-TARGET-RECORDS.bin').write_bytes(old.tobytes())
+(LEAD/'COHORT249-RECORDS.bin').write_bytes(out.tobytes())
+if replay_json is not None:
+    combined = Counter({int(r): c for r, c in replay_json['delta'].items()}); combined.update(delta); combined = {r: c for r, c in combined.items() if c}
+    replay_json.update(status='PASS_FULL_CURRENT249_COHORT_REWRITE_AND_TARGET_PREFIX_COMPRESSION', pre_target_records=len(old)//6, new_records=len(out)//6,
+                       pre_target_histogram=replay_json['histogram'], pre_target_delta=replay_json['delta'], histogram={str(r): c for r, c in sorted(hist.items())},
+                       delta={str(r): c for r, c in sorted(combined.items())}, target_prefix_delta={str(r): c for r, c in sorted(delta.items())},
+                       target_prefix_groups=len(groups), target_prefix_deleted_reads=len(deleted), target_prefix_setup_restore_additions=inserted)
+    (LEAD/'COHORT249-REPLAY.json').write_text(json.dumps(replay_json, indent=2) + '\n')
+receipt = dict(status='PASS_EXACT_F2_TARGET_PREFIX_COMPRESSION', selected_groups=len(groups), targets=len(owner), cut_record=cut, deleted_prefix_adds=len(deleted),
+               inserted_setup_restore_adds=inserted, literal_prefix_dependencies_checked=True, remaining_payload_additions=count,
+               local_histogram_delta={str(r): c for r, c in sorted(delta.items())}, rank_mass=sum(r*c for r, c in hist.items()), paid_calls=sum(hist.values()),
+               both_reflected_ledgers=True, unchanged_all_input_output_frames=True, unchanged_copy_lifetimes=True, forward_and_inverse_all_columns=True,
+               negative_control=negative, unique_required_frame_pairs=len(pairs), setup_category=SETUP, restore_category=RESTORE,
+               input_record_sha256=sel['input_record_sha256'], output_record_sha256=hashlib.sha256(out.tobytes()).hexdigest(), selection_sha256=hashlib.sha256(SEL.read_bytes()).hexdigest())
+(LEAD/'TARGET-PREFIX.json').write_text(json.dumps(receipt, indent=2) + '\n')
+print('PASS target prefix', len(groups), 'groups', count, 'ADDs', sum(hist.values()), 'paid calls', len(out)//6, 'records', flush=True)
diff --git a/research/gen4-retiming-entrances-target/data/EXPECTED.json b/research/gen4-retiming-entrances-target/data/EXPECTED.json
new file mode 100644
index 0000000000..fb76988fc8
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/data/EXPECTED.json
@@ -0,0 +1,14 @@
+{
+  "base_commit": "d428ab0462b9dfd3131ab4e89999f0adcd6173dd",
+  "base_manifest_sha256": "6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d",
+  "final_word_sha256": "71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48",
+  "kappa": "724189082265949363570532/1000000000000000000000000000",
+  "kappa_decimal": "0.000724189082265949363570532",
+  "comparator": {
+    "pull_request": 279,
+    "head": "2e2a38ba3f48edbda2152ed86691c75ff326b254",
+    "kappa_decimal": "0.000723571590007464",
+    "gain_percent_approx": 0.08533948361336213,
+    "observation": "Latest public bound at preparation; recheck separately at publication."
+  }
+}
diff --git a/research/gen4-retiming-entrances-target/data/entrances60.json b/research/gen4-retiming-entrances-target/data/entrances60.json
new file mode 100644
index 0000000000..db2d52ee8c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/data/entrances60.json
@@ -0,0 +1,29179 @@
+{
+  "source_word_sha256": "8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373",
+  "export_word_sha256": "60830cb24fbdd5a26942c4aa897d0ae30738ca5772ab83d6c57be666ddc95f7a",
+  "expected_output_sha256": "71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48",
+  "entries": [
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new file mode 100644
index 0000000000..3c5b836b4c
--- /dev/null
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+   "close_rank": 21
+  },
+  {
+   "dependent": 1276,
+   "retained": [
+    1277,
+    1278,
+    1279
+   ],
+   "close_after_record": 571142,
+   "frame": 26955,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1284,
+   "retained": [
+    1285,
+    1286,
+    1287
+   ],
+   "close_after_record": 571178,
+   "frame": 26977,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1292,
+   "retained": [
+    1293,
+    1294,
+    1295
+   ],
+   "close_after_record": 570930,
+   "frame": 26999,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1300,
+   "retained": [
+    1301,
+    1302,
+    1303
+   ],
+   "close_after_record": 570968,
+   "frame": 27021,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1308,
+   "retained": [
+    1309,
+    1310,
+    1311
+   ],
+   "close_after_record": 570752,
+   "frame": 27043,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1316,
+   "retained": [
+    1317,
+    1318,
+    1319
+   ],
+   "close_after_record": 571738,
+   "frame": 27065,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1324,
+   "retained": [
+    1325,
+    1326,
+    1327
+   ],
+   "close_after_record": 571690,
+   "frame": 27087,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1332,
+   "retained": [
+    1333,
+    1334,
+    1335
+   ],
+   "close_after_record": 571708,
+   "frame": 27109,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1340,
+   "retained": [
+    1341,
+    1342,
+    1343
+   ],
+   "close_after_record": 571686,
+   "frame": 27131,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1348,
+   "retained": [
+    1349,
+    1350,
+    1351
+   ],
+   "close_after_record": 571664,
+   "frame": 27153,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1356,
+   "retained": [
+    1357,
+    1358,
+    1359
+   ],
+   "close_after_record": 571670,
+   "frame": 27175,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1364,
+   "retained": [
+    1365,
+    1366,
+    1367
+   ],
+   "close_after_record": 571524,
+   "frame": 27197,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1372,
+   "retained": [
+    1373,
+    1374,
+    1375
+   ],
+   "close_after_record": 571546,
+   "frame": 27219,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1380,
+   "retained": [
+    1381,
+    1382,
+    1383
+   ],
+   "close_after_record": 571520,
+   "frame": 27241,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1388,
+   "retained": [
+    1389,
+    1390,
+    1391
+   ],
+   "close_after_record": 571494,
+   "frame": 27263,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1396,
+   "retained": [
+    1397,
+    1398,
+    1399
+   ],
+   "close_after_record": 571502,
+   "frame": 27285,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1404,
+   "retained": [
+    1405,
+    1406,
+    1407
+   ],
+   "close_after_record": 571360,
+   "frame": 27307,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1412,
+   "retained": [
+    1413,
+    1414,
+    1415
+   ],
+   "close_after_record": 571334,
+   "frame": 27329,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1420,
+   "retained": [
+    1421,
+    1422,
+    1423
+   ],
+   "close_after_record": 571306,
+   "frame": 27351,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1428,
+   "retained": [
+    1429,
+    1430,
+    1431
+   ],
+   "close_after_record": 571314,
+   "frame": 27373,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1436,
+   "retained": [
+    1437,
+    1438,
+    1439
+   ],
+   "close_after_record": 571136,
+   "frame": 27395,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1440,
+   "retained": [
+    1441
+   ],
+   "close_after_record": 566510,
+   "frame": 27414,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1442,
+   "retained": [
+    1443
+   ],
+   "close_after_record": 566514,
+   "frame": 27414,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1444,
+   "retained": [
+    1445,
+    1446,
+    1447
+   ],
+   "close_after_record": 571104,
+   "frame": 27417,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1452,
+   "retained": [
+    1453,
+    1454,
+    1455
+   ],
+   "close_after_record": 571112,
+   "frame": 27439,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1460,
+   "retained": [
+    1461,
+    1462,
+    1463
+   ],
+   "close_after_record": 570892,
+   "frame": 27461,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1468,
+   "retained": [
+    1469,
+    1470,
+    1471
+   ],
+   "close_after_record": 570900,
+   "frame": 27483,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1476,
+   "retained": [
+    1477,
+    1478,
+    1479
+   ],
+   "close_after_record": 570682,
+   "frame": 27505,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1484,
+   "retained": [
+    1485,
+    1486,
+    1487
+   ],
+   "close_after_record": 571498,
+   "frame": 27527,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1492,
+   "retained": [
+    1493,
+    1494,
+    1495
+   ],
+   "close_after_record": 571534,
+   "frame": 27549,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1500,
+   "retained": [
+    1501,
+    1502,
+    1503
+   ],
+   "close_after_record": 571518,
+   "frame": 27571,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1508,
+   "retained": [
+    1509,
+    1510,
+    1511
+   ],
+   "close_after_record": 571574,
+   "frame": 27593,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1516,
+   "retained": [
+    1517,
+    1518,
+    1519
+   ],
+   "close_after_record": 571542,
+   "frame": 27615,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1524,
+   "retained": [
+    1525,
+    1526,
+    1527
+   ],
+   "close_after_record": 571348,
+   "frame": 27637,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1532,
+   "retained": [
+    1533,
+    1534,
+    1535
+   ],
+   "close_after_record": 571332,
+   "frame": 27659,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1540,
+   "retained": [
+    1541,
+    1542,
+    1543
+   ],
+   "close_after_record": 571394,
+   "frame": 27681,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1548,
+   "retained": [
+    1549,
+    1550,
+    1551
+   ],
+   "close_after_record": 571356,
+   "frame": 27703,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1556,
+   "retained": [
+    1557,
+    1558,
+    1559
+   ],
+   "close_after_record": 571134,
+   "frame": 27725,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1560,
+   "retained": [
+    1561
+   ],
+   "close_after_record": 566550,
+   "frame": 27744,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1562,
+   "retained": [
+    1563
+   ],
+   "close_after_record": 566554,
+   "frame": 27744,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1564,
+   "retained": [
+    1565,
+    1566,
+    1567
+   ],
+   "close_after_record": 571198,
+   "frame": 27747,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1572,
+   "retained": [
+    1573,
+    1574,
+    1575
+   ],
+   "close_after_record": 571158,
+   "frame": 27769,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1580,
+   "retained": [
+    1581,
+    1582,
+    1583
+   ],
+   "close_after_record": 570990,
+   "frame": 27791,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1588,
+   "retained": [
+    1589,
+    1590,
+    1591
+   ],
+   "close_after_record": 570948,
+   "frame": 27813,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1596,
+   "retained": [
+    1597,
+    1598,
+    1599
+   ],
+   "close_after_record": 570730,
+   "frame": 27835,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1604,
+   "retained": [
+    1605,
+    1606,
+    1607
+   ],
+   "close_after_record": 571374,
+   "frame": 27857,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1612,
+   "retained": [
+    1613,
+    1614,
+    1615
+   ],
+   "close_after_record": 571366,
+   "frame": 27879,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1620,
+   "retained": [
+    1621,
+    1622,
+    1623
+   ],
+   "close_after_record": 571384,
+   "frame": 27901,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1628,
+   "retained": [
+    1629,
+    1630,
+    1631
+   ],
+   "close_after_record": 571328,
+   "frame": 27923,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1636,
+   "retained": [
+    1637,
+    1638,
+    1639
+   ],
+   "close_after_record": 571168,
+   "frame": 27945,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1640,
+   "retained": [
+    1641
+   ],
+   "close_after_record": 566590,
+   "frame": 27964,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1642,
+   "retained": [
+    1643
+   ],
+   "close_after_record": 566594,
+   "frame": 27964,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1644,
+   "retained": [
+    1645,
+    1646,
+    1647
+   ],
+   "close_after_record": 571186,
+   "frame": 27967,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1652,
+   "retained": [
+    1653,
+    1654,
+    1655
+   ],
+   "close_after_record": 571126,
+   "frame": 27989,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1660,
+   "retained": [
+    1661,
+    1662,
+    1663
+   ],
+   "close_after_record": 570976,
+   "frame": 28011,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1668,
+   "retained": [
+    1669,
+    1670,
+    1671
+   ],
+   "close_after_record": 570914,
+   "frame": 28033,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1676,
+   "retained": [
+    1677,
+    1678,
+    1679
+   ],
+   "close_after_record": 570696,
+   "frame": 28055,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1684,
+   "retained": [
+    1685,
+    1686,
+    1687
+   ],
+   "close_after_record": 571196,
+   "frame": 28077,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1688,
+   "retained": [
+    1689
+   ],
+   "close_after_record": 566622,
+   "frame": 28096,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1690,
+   "retained": [
+    1691
+   ],
+   "close_after_record": 566626,
+   "frame": 28096,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1692,
+   "retained": [
+    1693,
+    1694,
+    1695
+   ],
+   "close_after_record": 571130,
+   "frame": 28099,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1700,
+   "retained": [
+    1701,
+    1702,
+    1703
+   ],
+   "close_after_record": 571132,
+   "frame": 28121,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1704,
+   "retained": [
+    1705
+   ],
+   "close_after_record": 566702,
+   "frame": 28140,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1706,
+   "retained": [
+    1707
+   ],
+   "close_after_record": 566726,
+   "frame": 28140,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1708,
+   "retained": [
+    1709,
+    1710,
+    1711
+   ],
+   "close_after_record": 570918,
+   "frame": 28143,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1712,
+   "retained": [
+    1714
+   ],
+   "close_after_record": 566782,
+   "frame": 28162,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1713,
+   "retained": [
+    1715
+   ],
+   "close_after_record": 566806,
+   "frame": 28162,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1716,
+   "retained": [
+    1717,
+    1718,
+    1719
+   ],
+   "close_after_record": 570920,
+   "frame": 28165,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1724,
+   "retained": [
+    1725,
+    1726,
+    1727
+   ],
+   "close_after_record": 570702,
+   "frame": 28187,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1732,
+   "retained": [
+    1733,
+    1734,
+    1735
+   ],
+   "close_after_record": 570980,
+   "frame": 28209,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1740,
+   "retained": [
+    1741,
+    1742,
+    1743
+   ],
+   "close_after_record": 570942,
+   "frame": 28231,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1748,
+   "retained": [
+    1749,
+    1750,
+    1751
+   ],
+   "close_after_record": 570724,
+   "frame": 28253,
+   "close_rank": 21
+  },
+  {
+   "dependent": 1756,
+   "retained": [
+    1757,
+    1758,
+    1759
+   ],
+   "close_after_record": 570738,
+   "frame": 28275,
+   "close_rank": 21
+  }
+ ],
+ "expected_local_histogram_delta": {
+  "1": -220,
+  "2": -54,
+  "3": -36,
+  "18": -66,
+  "19": -24,
+  "20": -190,
+  "21": 280
+ },
+ "expected_deleted_reads": 1190,
+ "expected_inserted_additions": 1440,
+ "expected_scalar_additions": 626610,
+ "provenance": "Square and pair target groups over the symmetric frame-20 compensation reads of the PR280 gen4 word; close at the common 21-dimensional frame after the frame-20 block. Prepared by Rohan Arun with Anthropic Claude assistance."
+}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances-target/docs/cleanup-proof.md b/research/gen4-retiming-entrances-target/docs/cleanup-proof.md
new file mode 100644
index 0000000000..9561214162
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/docs/cleanup-proof.md
@@ -0,0 +1,84 @@
+# Early restoration of 440 gen4 helpers
+
+The source word is the literal `retimed880/COHORT249-RECORDS.bin`, SHA256
+`2d22a9530f0b04a7a794d15077459234ef52183d6e7a70f813cfa849b79f2ebe`.
+This construction composes with its880 source-partner frame retimings.
+It changes no scalar coefficient and adds no scalar gate.
+
+At record662145, the first category3 cleanup ADD, all1,760 data targets
+already have their required scalar endpoints. There are440 helper roles a
+with the following properties, checked against the complete remaining word:
+
+* The only later scalar incidence of a is `a -= b`.
+* The donor b is never written between the cut and that incidence.
+* All440 destinations and440 donors are distinct, with the two sets disjoint.
+* Both roles have current frame dimension22. Their rational span is a
+  nondegenerate frame E of dimension23.
+* Helper a has entrance dimension20 and previously ended at FULL, dimension24.
+
+The ADD `a -= b` commutes over the integers with every intervening scalar
+gate. Moving it to the cut therefore preserves the exact signed scalar
+operator, including all dirty columns. There is no COPY/ERASE after this cut.
+These440 moves can be made simultaneously because their destinations and
+donors do not overlap. The original maximum formal coefficient bound does
+not increase: early-restored a has exactly its old value after the later
+restoration, while every other role has the same value at every unaffected
+event. No gate reads a on the crossed interval.
+
+For each pair, advance a and b from their rank22 frames to E, perform the
+unchanged `a -= b`, and retire a at E. Continue every remaining scalar gate
+in its original order and at its original frame. The donor later reaches
+FULL. Every new connector is checked by exact rational annihilator products;
+all other source, target, helper, and COPY endpoints remain unchanged.
+
+Per pair, two old rank2 climbs become three rank1 climbs: a→E, b→E, and
+b:E→FULL. Hence the local histogram change is exactly
+
+    ΔH[1] = +1320, ΔH[2] = -880.
+
+The local paid rank drops440. The helper endpoint changes from
+`D_(FULL-sigma)` of rank4 to `D_(E-sigma)` of rank3. Its reflected inverse
+goes from `I-E` to `I-sigma` and has the same residual rank3. The ordinary
+completed-bank construction must be repacked for these actual residuals;
+the old FULL-endpoint assumption may not be silently retained.
+
+With PR276's60 local replicas, each stage loses26,400 residual coordinates,
+or220 complete width120 banks. This is only the volume calculation: an exact
+block assignment and normalizer/selector invoice are separate required
+admission checks. The resulting five-stage literal stock drop is1,100 and
+the normalized stock drop220 if that tiling closes.
+
+`cleanup_emit.py` freshly checks every new frame's full annihilator, exact cleared
+Gram determinant and nonvanishing modulo the retained prime2^127−1. It
+replays all19,930 formal columns forward, backward with fresh copies in
+place of reversed erasures, and as a complete roundtrip. Omitting one moved
+restoration fails one formal row. It also independently checks the integer
+commutation conditions above. The complete global five-stage, bank, chart,
+and recurrence checks remain the caller's responsibility.
+
+The final all440 output word SHA256 is
+`8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373`.
+The438-helper precursor is preserved separately; the all440 word is the
+intended final candidate under the60-replica normalization.
+
+
+## Portable reproduction
+
+Run from the package root with Python3 and SymPy (validated with SymPy1.14):
+
+```sh
+python code/cleanup.py --source-dir RETIMED --export-dir EXPORT --output CANDIDATE
+```
+
+`RETIMED` is the preceding880-retiming output. `EXPORT` contains the source
+`gen4-states.json` and `frames.json`. The fixed recipe freshly reconstructs
+all440 helper/donor pairs; it rejects a changed input word, changed candidate
+count/geometry, or changed emitted word hash. It preserves the source's COPY
+lifetimes and signed coefficients. No network access, NumPy, SciPy, or native
+compiler is needed for this cleanup step. Global verification remains in the
+package verifier.
+
+The rational basis utilities in `cleanup_reference.py` are derived from
+[PR271's sandwich263.py](https://github.com/CrocSwap/integer-mult-bounds/pull/271).
+This gen4 construction uses a single cleanup gate per retired helper rather
+than PR271's three-gate sandwich selection.
diff --git a/research/gen4-retiming-entrances-target/requirements.txt b/research/gen4-retiming-entrances-target/requirements.txt
new file mode 100644
index 0000000000..1ca5fd0616
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/requirements.txt
@@ -0,0 +1 @@
+sympy==1.14.0
diff --git a/research/gen4-retiming-entrances-target/vendor/json.hpp b/research/gen4-retiming-entrances-target/vendor/json.hpp
new file mode 100644
index 0000000000..82d69f7c5d
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/json.hpp
@@ -0,0 +1,25526 @@
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+/****************************************************************************\
+ * Note on documentation: The source files contain links to the online      *
+ * documentation of the public API at https://json.nlohmann.me. This URL    *
+ * contains the most recent documentation and should also be applicable to  *
+ * previous versions; documentation for deprecated functions is not         *
+ * removed, but marked deprecated. See "Generate documentation" section in  *
+ * file docs/README.md.                                                     *
+\****************************************************************************/
+
+#ifndef INCLUDE_NLOHMANN_JSON_HPP_
+#define INCLUDE_NLOHMANN_JSON_HPP_
+
+#include <algorithm> // all_of, find, for_each
+#include <cstddef> // nullptr_t, ptrdiff_t, size_t
+#include <functional> // hash, less
+#include <initializer_list> // initializer_list
+#ifndef JSON_NO_IO
+    #include <iosfwd> // istream, ostream
+#endif  // JSON_NO_IO
+#include <iterator> // random_access_iterator_tag
+#include <memory> // unique_ptr
+#include <string> // string, stoi, to_string
+#include <utility> // declval, forward, move, pair, swap
+#include <vector> // vector
+
+// #include <nlohmann/adl_serializer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <utility>
+
+// #include <nlohmann/detail/abi_macros.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// This file contains all macro definitions affecting or depending on the ABI
+
+#ifndef JSON_SKIP_LIBRARY_VERSION_CHECK
+    #if defined(NLOHMANN_JSON_VERSION_MAJOR) && defined(NLOHMANN_JSON_VERSION_MINOR) && defined(NLOHMANN_JSON_VERSION_PATCH)
+        #if NLOHMANN_JSON_VERSION_MAJOR != 3 || NLOHMANN_JSON_VERSION_MINOR != 12 || NLOHMANN_JSON_VERSION_PATCH != 0
+            #warning "Already included a different version of the library!"
+        #endif
+    #endif
+#endif
+
+#define NLOHMANN_JSON_VERSION_MAJOR 3   // NOLINT(modernize-macro-to-enum)
+#define NLOHMANN_JSON_VERSION_MINOR 12  // NOLINT(modernize-macro-to-enum)
+#define NLOHMANN_JSON_VERSION_PATCH 0   // NOLINT(modernize-macro-to-enum)
+
+#ifndef JSON_DIAGNOSTICS
+    #define JSON_DIAGNOSTICS 0
+#endif
+
+#ifndef JSON_DIAGNOSTIC_POSITIONS
+    #define JSON_DIAGNOSTIC_POSITIONS 0
+#endif
+
+#ifndef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+    #define JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON 0
+#endif
+
+#if JSON_DIAGNOSTICS
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS _diag
+#else
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS
+#endif
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS _dp
+#else
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS
+#endif
+
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+    #define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON _ldvcmp
+#else
+    #define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_NO_VERSION
+    #define NLOHMANN_JSON_NAMESPACE_NO_VERSION 0
+#endif
+
+// Construct the namespace ABI tags component
+#define NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b, c) json_abi ## a ## b ## c
+#define NLOHMANN_JSON_ABI_TAGS_CONCAT(a, b, c) \
+    NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b, c)
+
+#define NLOHMANN_JSON_ABI_TAGS                                       \
+    NLOHMANN_JSON_ABI_TAGS_CONCAT(                                   \
+            NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS,                       \
+            NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON, \
+            NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS)
+
+// Construct the namespace version component
+#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch) \
+    _v ## major ## _ ## minor ## _ ## patch
+#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(major, minor, patch) \
+    NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch)
+
+#if NLOHMANN_JSON_NAMESPACE_NO_VERSION
+#define NLOHMANN_JSON_NAMESPACE_VERSION
+#else
+#define NLOHMANN_JSON_NAMESPACE_VERSION                                 \
+    NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(NLOHMANN_JSON_VERSION_MAJOR, \
+                                           NLOHMANN_JSON_VERSION_MINOR, \
+                                           NLOHMANN_JSON_VERSION_PATCH)
+#endif
+
+// Combine namespace components
+#define NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b) a ## b
+#define NLOHMANN_JSON_NAMESPACE_CONCAT(a, b) \
+    NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b)
+
+#ifndef NLOHMANN_JSON_NAMESPACE
+#define NLOHMANN_JSON_NAMESPACE               \
+    nlohmann::NLOHMANN_JSON_NAMESPACE_CONCAT( \
+            NLOHMANN_JSON_ABI_TAGS,           \
+            NLOHMANN_JSON_NAMESPACE_VERSION)
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_BEGIN
+#define NLOHMANN_JSON_NAMESPACE_BEGIN                \
+    namespace nlohmann                               \
+    {                                                \
+    inline namespace NLOHMANN_JSON_NAMESPACE_CONCAT( \
+                NLOHMANN_JSON_ABI_TAGS,              \
+                NLOHMANN_JSON_NAMESPACE_VERSION)     \
+    {
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_END
+#define NLOHMANN_JSON_NAMESPACE_END                                     \
+    }  /* namespace (inline namespace) NOLINT(readability/namespace) */ \
+    }  // namespace nlohmann
+#endif
+
+// #include <nlohmann/detail/conversions/from_json.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // transform
+#include <array> // array
+#include <forward_list> // forward_list
+#include <iterator> // inserter, front_inserter, end
+#include <map> // map
+#ifdef JSON_HAS_CPP_17
+    #include <optional> // optional
+#endif
+#include <string> // string
+#include <tuple> // tuple, make_tuple
+#include <type_traits> // is_arithmetic, is_same, is_enum, underlying_type, is_convertible
+#include <unordered_map> // unordered_map
+#include <utility> // pair, declval
+#include <valarray> // valarray
+
+// #include <nlohmann/detail/exceptions.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // nullptr_t
+#include <exception> // exception
+#if JSON_DIAGNOSTICS
+    #include <numeric> // accumulate
+#endif
+#include <stdexcept> // runtime_error
+#include <string> // to_string
+#include <vector> // vector
+
+// #include <nlohmann/detail/value_t.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstddef> // size_t
+#include <cstdint> // uint8_t
+#include <string> // string
+
+// #include <nlohmann/detail/macro_scope.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <utility> // declval, pair
+// #include <nlohmann/detail/meta/detected.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <type_traits>
+
+// #include <nlohmann/detail/meta/void_t.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename ...Ts> struct make_void
+{
+    using type = void;
+};
+template<typename ...Ts> using void_t = typename make_void<Ts...>::type;
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// https://en.cppreference.com/w/cpp/experimental/is_detected
+struct nonesuch
+{
+    nonesuch() = delete;
+    ~nonesuch() = delete;
+    nonesuch(nonesuch const&) = delete;
+    nonesuch(nonesuch const&&) = delete;
+    void operator=(nonesuch const&) = delete;
+    void operator=(nonesuch&&) = delete;
+};
+
+template<class Default,
+         class AlwaysVoid,
+         template<class...> class Op,
+         class... Args>
+struct detector
+{
+    using value_t = std::false_type;
+    using type = Default;
+};
+
+template<class Default, template<class...> class Op, class... Args>
+struct detector<Default, void_t<Op<Args...>>, Op, Args...>
+{
+    using value_t = std::true_type;
+    using type = Op<Args...>;
+};
+
+template<template<class...> class Op, class... Args>
+using is_detected = typename detector<nonesuch, void, Op, Args...>::value_t;
+
+template<template<class...> class Op, class... Args>
+struct is_detected_lazy : is_detected<Op, Args...> { };
+
+template<template<class...> class Op, class... Args>
+using detected_t = typename detector<nonesuch, void, Op, Args...>::type;
+
+template<class Default, template<class...> class Op, class... Args>
+using detected_or = detector<Default, void, Op, Args...>;
+
+template<class Default, template<class...> class Op, class... Args>
+using detected_or_t = typename detected_or<Default, Op, Args...>::type;
+
+template<class Expected, template<class...> class Op, class... Args>
+using is_detected_exact = std::is_same<Expected, detected_t<Op, Args...>>;
+
+template<class To, template<class...> class Op, class... Args>
+using is_detected_convertible =
+    std::is_convertible<detected_t<Op, Args...>, To>;
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/thirdparty/hedley/hedley.hpp>
+
+
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-FileCopyrightText: 2016 - 2021 Evan Nemerson <evan@nemerson.com>
+// SPDX-License-Identifier: MIT
+
+/* Hedley - https://nemequ.github.io/hedley
+ * Created by Evan Nemerson <evan@nemerson.com>
+ */
+
+#if !defined(JSON_HEDLEY_VERSION) || (JSON_HEDLEY_VERSION < 15)
+#if defined(JSON_HEDLEY_VERSION)
+    #undef JSON_HEDLEY_VERSION
+#endif
+#define JSON_HEDLEY_VERSION 15
+
+#if defined(JSON_HEDLEY_STRINGIFY_EX)
+    #undef JSON_HEDLEY_STRINGIFY_EX
+#endif
+#define JSON_HEDLEY_STRINGIFY_EX(x) #x
+
+#if defined(JSON_HEDLEY_STRINGIFY)
+    #undef JSON_HEDLEY_STRINGIFY
+#endif
+#define JSON_HEDLEY_STRINGIFY(x) JSON_HEDLEY_STRINGIFY_EX(x)
+
+#if defined(JSON_HEDLEY_CONCAT_EX)
+    #undef JSON_HEDLEY_CONCAT_EX
+#endif
+#define JSON_HEDLEY_CONCAT_EX(a,b) a##b
+
+#if defined(JSON_HEDLEY_CONCAT)
+    #undef JSON_HEDLEY_CONCAT
+#endif
+#define JSON_HEDLEY_CONCAT(a,b) JSON_HEDLEY_CONCAT_EX(a,b)
+
+#if defined(JSON_HEDLEY_CONCAT3_EX)
+    #undef JSON_HEDLEY_CONCAT3_EX
+#endif
+#define JSON_HEDLEY_CONCAT3_EX(a,b,c) a##b##c
+
+#if defined(JSON_HEDLEY_CONCAT3)
+    #undef JSON_HEDLEY_CONCAT3
+#endif
+#define JSON_HEDLEY_CONCAT3(a,b,c) JSON_HEDLEY_CONCAT3_EX(a,b,c)
+
+#if defined(JSON_HEDLEY_VERSION_ENCODE)
+    #undef JSON_HEDLEY_VERSION_ENCODE
+#endif
+#define JSON_HEDLEY_VERSION_ENCODE(major,minor,revision) (((major) * 1000000) + ((minor) * 1000) + (revision))
+
+#if defined(JSON_HEDLEY_VERSION_DECODE_MAJOR)
+    #undef JSON_HEDLEY_VERSION_DECODE_MAJOR
+#endif
+#define JSON_HEDLEY_VERSION_DECODE_MAJOR(version) ((version) / 1000000)
+
+#if defined(JSON_HEDLEY_VERSION_DECODE_MINOR)
+    #undef JSON_HEDLEY_VERSION_DECODE_MINOR
+#endif
+#define JSON_HEDLEY_VERSION_DECODE_MINOR(version) (((version) % 1000000) / 1000)
+
+#if defined(JSON_HEDLEY_VERSION_DECODE_REVISION)
+    #undef JSON_HEDLEY_VERSION_DECODE_REVISION
+#endif
+#define JSON_HEDLEY_VERSION_DECODE_REVISION(version) ((version) % 1000)
+
+#if defined(JSON_HEDLEY_GNUC_VERSION)
+    #undef JSON_HEDLEY_GNUC_VERSION
+#endif
+#if defined(__GNUC__) && defined(__GNUC_PATCHLEVEL__)
+    #define JSON_HEDLEY_GNUC_VERSION JSON_HEDLEY_VERSION_ENCODE(__GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__)
+#elif defined(__GNUC__)
+    #define JSON_HEDLEY_GNUC_VERSION JSON_HEDLEY_VERSION_ENCODE(__GNUC__, __GNUC_MINOR__, 0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_VERSION_CHECK)
+    #undef JSON_HEDLEY_GNUC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_GNUC_VERSION)
+    #define JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_GNUC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_MSVC_VERSION)
+    #undef JSON_HEDLEY_MSVC_VERSION
+#endif
+#if defined(_MSC_FULL_VER) && (_MSC_FULL_VER >= 140000000) && !defined(__ICL)
+    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_FULL_VER / 10000000, (_MSC_FULL_VER % 10000000) / 100000, (_MSC_FULL_VER % 100000) / 100)
+#elif defined(_MSC_FULL_VER) && !defined(__ICL)
+    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_FULL_VER / 1000000, (_MSC_FULL_VER % 1000000) / 10000, (_MSC_FULL_VER % 10000) / 10)
+#elif defined(_MSC_VER) && !defined(__ICL)
+    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_VER / 100, _MSC_VER % 100, 0)
+#endif
+
+#if defined(JSON_HEDLEY_MSVC_VERSION_CHECK)
+    #undef JSON_HEDLEY_MSVC_VERSION_CHECK
+#endif
+#if !defined(JSON_HEDLEY_MSVC_VERSION)
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (0)
+#elif defined(_MSC_VER) && (_MSC_VER >= 1400)
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_FULL_VER >= ((major * 10000000) + (minor * 100000) + (patch)))
+#elif defined(_MSC_VER) && (_MSC_VER >= 1200)
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_FULL_VER >= ((major * 1000000) + (minor * 10000) + (patch)))
+#else
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_VER >= ((major * 100) + (minor)))
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_VERSION)
+    #undef JSON_HEDLEY_INTEL_VERSION
+#endif
+#if defined(__INTEL_COMPILER) && defined(__INTEL_COMPILER_UPDATE) && !defined(__ICL)
+    #define JSON_HEDLEY_INTEL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER / 100, __INTEL_COMPILER % 100, __INTEL_COMPILER_UPDATE)
+#elif defined(__INTEL_COMPILER) && !defined(__ICL)
+    #define JSON_HEDLEY_INTEL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER / 100, __INTEL_COMPILER % 100, 0)
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_VERSION_CHECK)
+    #undef JSON_HEDLEY_INTEL_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_INTEL_VERSION)
+    #define JSON_HEDLEY_INTEL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_INTEL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_INTEL_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_CL_VERSION)
+    #undef JSON_HEDLEY_INTEL_CL_VERSION
+#endif
+#if defined(__INTEL_COMPILER) && defined(__INTEL_COMPILER_UPDATE) && defined(__ICL)
+    #define JSON_HEDLEY_INTEL_CL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER, __INTEL_COMPILER_UPDATE, 0)
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_CL_VERSION_CHECK)
+    #undef JSON_HEDLEY_INTEL_CL_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_INTEL_CL_VERSION)
+    #define JSON_HEDLEY_INTEL_CL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_INTEL_CL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_INTEL_CL_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_PGI_VERSION)
+    #undef JSON_HEDLEY_PGI_VERSION
+#endif
+#if defined(__PGI) && defined(__PGIC__) && defined(__PGIC_MINOR__) && defined(__PGIC_PATCHLEVEL__)
+    #define JSON_HEDLEY_PGI_VERSION JSON_HEDLEY_VERSION_ENCODE(__PGIC__, __PGIC_MINOR__, __PGIC_PATCHLEVEL__)
+#endif
+
+#if defined(JSON_HEDLEY_PGI_VERSION_CHECK)
+    #undef JSON_HEDLEY_PGI_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_PGI_VERSION)
+    #define JSON_HEDLEY_PGI_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_PGI_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_PGI_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_SUNPRO_VERSION)
+    #undef JSON_HEDLEY_SUNPRO_VERSION
+#endif
+#if defined(__SUNPRO_C) && (__SUNPRO_C > 0x1000)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((((__SUNPRO_C >> 16) & 0xf) * 10) + ((__SUNPRO_C >> 12) & 0xf), (((__SUNPRO_C >> 8) & 0xf) * 10) + ((__SUNPRO_C >> 4) & 0xf), (__SUNPRO_C & 0xf) * 10)
+#elif defined(__SUNPRO_C)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((__SUNPRO_C >> 8) & 0xf, (__SUNPRO_C >> 4) & 0xf, (__SUNPRO_C) & 0xf)
+#elif defined(__SUNPRO_CC) && (__SUNPRO_CC > 0x1000)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((((__SUNPRO_CC >> 16) & 0xf) * 10) + ((__SUNPRO_CC >> 12) & 0xf), (((__SUNPRO_CC >> 8) & 0xf) * 10) + ((__SUNPRO_CC >> 4) & 0xf), (__SUNPRO_CC & 0xf) * 10)
+#elif defined(__SUNPRO_CC)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((__SUNPRO_CC >> 8) & 0xf, (__SUNPRO_CC >> 4) & 0xf, (__SUNPRO_CC) & 0xf)
+#endif
+
+#if defined(JSON_HEDLEY_SUNPRO_VERSION_CHECK)
+    #undef JSON_HEDLEY_SUNPRO_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_SUNPRO_VERSION)
+    #define JSON_HEDLEY_SUNPRO_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_SUNPRO_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_SUNPRO_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION)
+    #undef JSON_HEDLEY_EMSCRIPTEN_VERSION
+#endif
+#if defined(__EMSCRIPTEN__)
+    #define JSON_HEDLEY_EMSCRIPTEN_VERSION JSON_HEDLEY_VERSION_ENCODE(__EMSCRIPTEN_major__, __EMSCRIPTEN_minor__, __EMSCRIPTEN_tiny__)
+#endif
+
+#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK)
+    #undef JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION)
+    #define JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_EMSCRIPTEN_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_ARM_VERSION)
+    #undef JSON_HEDLEY_ARM_VERSION
+#endif
+#if defined(__CC_ARM) && defined(__ARMCOMPILER_VERSION)
+    #define JSON_HEDLEY_ARM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ARMCOMPILER_VERSION / 1000000, (__ARMCOMPILER_VERSION % 1000000) / 10000, (__ARMCOMPILER_VERSION % 10000) / 100)
+#elif defined(__CC_ARM) && defined(__ARMCC_VERSION)
+    #define JSON_HEDLEY_ARM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ARMCC_VERSION / 1000000, (__ARMCC_VERSION % 1000000) / 10000, (__ARMCC_VERSION % 10000) / 100)
+#endif
+
+#if defined(JSON_HEDLEY_ARM_VERSION_CHECK)
+    #undef JSON_HEDLEY_ARM_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_ARM_VERSION)
+    #define JSON_HEDLEY_ARM_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_ARM_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_ARM_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_IBM_VERSION)
+    #undef JSON_HEDLEY_IBM_VERSION
+#endif
+#if defined(__ibmxl__)
+    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ibmxl_version__, __ibmxl_release__, __ibmxl_modification__)
+#elif defined(__xlC__) && defined(__xlC_ver__)
+    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__xlC__ >> 8, __xlC__ & 0xff, (__xlC_ver__ >> 8) & 0xff)
+#elif defined(__xlC__)
+    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__xlC__ >> 8, __xlC__ & 0xff, 0)
+#endif
+
+#if defined(JSON_HEDLEY_IBM_VERSION_CHECK)
+    #undef JSON_HEDLEY_IBM_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_IBM_VERSION)
+    #define JSON_HEDLEY_IBM_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_IBM_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_IBM_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_VERSION)
+    #undef JSON_HEDLEY_TI_VERSION
+#endif
+#if \
+    defined(__TI_COMPILER_VERSION__) && \
+    ( \
+      defined(__TMS470__) || defined(__TI_ARM__) || \
+      defined(__MSP430__) || \
+      defined(__TMS320C2000__) \
+    )
+#if (__TI_COMPILER_VERSION__ >= 16000000)
+    #define JSON_HEDLEY_TI_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+#endif
+
+#if defined(JSON_HEDLEY_TI_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_VERSION)
+    #define JSON_HEDLEY_TI_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL2000_VERSION)
+    #undef JSON_HEDLEY_TI_CL2000_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__TMS320C2000__)
+    #define JSON_HEDLEY_TI_CL2000_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL2000_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL2000_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL2000_VERSION)
+    #define JSON_HEDLEY_TI_CL2000_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL2000_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL2000_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL430_VERSION)
+    #undef JSON_HEDLEY_TI_CL430_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__MSP430__)
+    #define JSON_HEDLEY_TI_CL430_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL430_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL430_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL430_VERSION)
+    #define JSON_HEDLEY_TI_CL430_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL430_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL430_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_ARMCL_VERSION)
+    #undef JSON_HEDLEY_TI_ARMCL_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && (defined(__TMS470__) || defined(__TI_ARM__))
+    #define JSON_HEDLEY_TI_ARMCL_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_ARMCL_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_ARMCL_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_ARMCL_VERSION)
+    #define JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_ARMCL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL6X_VERSION)
+    #undef JSON_HEDLEY_TI_CL6X_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__TMS320C6X__)
+    #define JSON_HEDLEY_TI_CL6X_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL6X_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL6X_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL6X_VERSION)
+    #define JSON_HEDLEY_TI_CL6X_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL6X_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL6X_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL7X_VERSION)
+    #undef JSON_HEDLEY_TI_CL7X_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__C7000__)
+    #define JSON_HEDLEY_TI_CL7X_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL7X_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL7X_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL7X_VERSION)
+    #define JSON_HEDLEY_TI_CL7X_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL7X_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL7X_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CLPRU_VERSION)
+    #undef JSON_HEDLEY_TI_CLPRU_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__PRU__)
+    #define JSON_HEDLEY_TI_CLPRU_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CLPRU_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CLPRU_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CLPRU_VERSION)
+    #define JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CLPRU_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_CRAY_VERSION)
+    #undef JSON_HEDLEY_CRAY_VERSION
+#endif
+#if defined(_CRAYC)
+    #if defined(_RELEASE_PATCHLEVEL)
+        #define JSON_HEDLEY_CRAY_VERSION JSON_HEDLEY_VERSION_ENCODE(_RELEASE_MAJOR, _RELEASE_MINOR, _RELEASE_PATCHLEVEL)
+    #else
+        #define JSON_HEDLEY_CRAY_VERSION JSON_HEDLEY_VERSION_ENCODE(_RELEASE_MAJOR, _RELEASE_MINOR, 0)
+    #endif
+#endif
+
+#if defined(JSON_HEDLEY_CRAY_VERSION_CHECK)
+    #undef JSON_HEDLEY_CRAY_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_CRAY_VERSION)
+    #define JSON_HEDLEY_CRAY_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_CRAY_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_CRAY_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_IAR_VERSION)
+    #undef JSON_HEDLEY_IAR_VERSION
+#endif
+#if defined(__IAR_SYSTEMS_ICC__)
+    #if __VER__ > 1000
+        #define JSON_HEDLEY_IAR_VERSION JSON_HEDLEY_VERSION_ENCODE((__VER__ / 1000000), ((__VER__ / 1000) % 1000), (__VER__ % 1000))
+    #else
+        #define JSON_HEDLEY_IAR_VERSION JSON_HEDLEY_VERSION_ENCODE(__VER__ / 100, __VER__ % 100, 0)
+    #endif
+#endif
+
+#if defined(JSON_HEDLEY_IAR_VERSION_CHECK)
+    #undef JSON_HEDLEY_IAR_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_IAR_VERSION)
+    #define JSON_HEDLEY_IAR_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_IAR_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_IAR_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TINYC_VERSION)
+    #undef JSON_HEDLEY_TINYC_VERSION
+#endif
+#if defined(__TINYC__)
+    #define JSON_HEDLEY_TINYC_VERSION JSON_HEDLEY_VERSION_ENCODE(__TINYC__ / 1000, (__TINYC__ / 100) % 10, __TINYC__ % 100)
+#endif
+
+#if defined(JSON_HEDLEY_TINYC_VERSION_CHECK)
+    #undef JSON_HEDLEY_TINYC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TINYC_VERSION)
+    #define JSON_HEDLEY_TINYC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TINYC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TINYC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_DMC_VERSION)
+    #undef JSON_HEDLEY_DMC_VERSION
+#endif
+#if defined(__DMC__)
+    #define JSON_HEDLEY_DMC_VERSION JSON_HEDLEY_VERSION_ENCODE(__DMC__ >> 8, (__DMC__ >> 4) & 0xf, __DMC__ & 0xf)
+#endif
+
+#if defined(JSON_HEDLEY_DMC_VERSION_CHECK)
+    #undef JSON_HEDLEY_DMC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_DMC_VERSION)
+    #define JSON_HEDLEY_DMC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_DMC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_DMC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_COMPCERT_VERSION)
+    #undef JSON_HEDLEY_COMPCERT_VERSION
+#endif
+#if defined(__COMPCERT_VERSION__)
+    #define JSON_HEDLEY_COMPCERT_VERSION JSON_HEDLEY_VERSION_ENCODE(__COMPCERT_VERSION__ / 10000, (__COMPCERT_VERSION__ / 100) % 100, __COMPCERT_VERSION__ % 100)
+#endif
+
+#if defined(JSON_HEDLEY_COMPCERT_VERSION_CHECK)
+    #undef JSON_HEDLEY_COMPCERT_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_COMPCERT_VERSION)
+    #define JSON_HEDLEY_COMPCERT_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_COMPCERT_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_COMPCERT_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_PELLES_VERSION)
+    #undef JSON_HEDLEY_PELLES_VERSION
+#endif
+#if defined(__POCC__)
+    #define JSON_HEDLEY_PELLES_VERSION JSON_HEDLEY_VERSION_ENCODE(__POCC__ / 100, __POCC__ % 100, 0)
+#endif
+
+#if defined(JSON_HEDLEY_PELLES_VERSION_CHECK)
+    #undef JSON_HEDLEY_PELLES_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_PELLES_VERSION)
+    #define JSON_HEDLEY_PELLES_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_PELLES_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_PELLES_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_MCST_LCC_VERSION)
+    #undef JSON_HEDLEY_MCST_LCC_VERSION
+#endif
+#if defined(__LCC__) && defined(__LCC_MINOR__)
+    #define JSON_HEDLEY_MCST_LCC_VERSION JSON_HEDLEY_VERSION_ENCODE(__LCC__ / 100, __LCC__ % 100, __LCC_MINOR__)
+#endif
+
+#if defined(JSON_HEDLEY_MCST_LCC_VERSION_CHECK)
+    #undef JSON_HEDLEY_MCST_LCC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_MCST_LCC_VERSION)
+    #define JSON_HEDLEY_MCST_LCC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_MCST_LCC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_MCST_LCC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_VERSION)
+    #undef JSON_HEDLEY_GCC_VERSION
+#endif
+#if \
+    defined(JSON_HEDLEY_GNUC_VERSION) && \
+    !defined(__clang__) && \
+    !defined(JSON_HEDLEY_INTEL_VERSION) && \
+    !defined(JSON_HEDLEY_PGI_VERSION) && \
+    !defined(JSON_HEDLEY_ARM_VERSION) && \
+    !defined(JSON_HEDLEY_CRAY_VERSION) && \
+    !defined(JSON_HEDLEY_TI_VERSION) && \
+    !defined(JSON_HEDLEY_TI_ARMCL_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL430_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL2000_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL6X_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL7X_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CLPRU_VERSION) && \
+    !defined(__COMPCERT__) && \
+    !defined(JSON_HEDLEY_MCST_LCC_VERSION)
+    #define JSON_HEDLEY_GCC_VERSION JSON_HEDLEY_GNUC_VERSION
+#endif
+
+#if defined(JSON_HEDLEY_GCC_VERSION_CHECK)
+    #undef JSON_HEDLEY_GCC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_GCC_VERSION)
+    #define JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_GCC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_HAS_ATTRIBUTE
+#endif
+#if \
+  defined(__has_attribute) && \
+  ( \
+    (!defined(JSON_HEDLEY_IAR_VERSION) || JSON_HEDLEY_IAR_VERSION_CHECK(8,5,9)) \
+  )
+#  define JSON_HEDLEY_HAS_ATTRIBUTE(attribute) __has_attribute(attribute)
+#else
+#  define JSON_HEDLEY_HAS_ATTRIBUTE(attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_GNUC_HAS_ATTRIBUTE
+#endif
+#if defined(__has_attribute)
+    #define JSON_HEDLEY_GNUC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_GCC_HAS_ATTRIBUTE
+#endif
+#if defined(__has_attribute)
+    #define JSON_HEDLEY_GCC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)
+#else
+    #define JSON_HEDLEY_GCC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE
+#endif
+#if \
+    defined(__has_cpp_attribute) && \
+    defined(__cplusplus) && \
+    (!defined(JSON_HEDLEY_SUNPRO_VERSION) || JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0))
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute) __has_cpp_attribute(attribute)
+#else
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS)
+    #undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS
+#endif
+#if !defined(__cplusplus) || !defined(__has_cpp_attribute)
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) (0)
+#elif \
+    !defined(JSON_HEDLEY_PGI_VERSION) && \
+    !defined(JSON_HEDLEY_IAR_VERSION) && \
+    (!defined(JSON_HEDLEY_SUNPRO_VERSION) || JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0)) && \
+    (!defined(JSON_HEDLEY_MSVC_VERSION) || JSON_HEDLEY_MSVC_VERSION_CHECK(19,20,0))
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) JSON_HEDLEY_HAS_CPP_ATTRIBUTE(ns::attribute)
+#else
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE
+#endif
+#if defined(__has_cpp_attribute) && defined(__cplusplus)
+    #define JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) __has_cpp_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE
+#endif
+#if defined(__has_cpp_attribute) && defined(__cplusplus)
+    #define JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) __has_cpp_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_BUILTIN)
+    #undef JSON_HEDLEY_HAS_BUILTIN
+#endif
+#if defined(__has_builtin)
+    #define JSON_HEDLEY_HAS_BUILTIN(builtin) __has_builtin(builtin)
+#else
+    #define JSON_HEDLEY_HAS_BUILTIN(builtin) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_BUILTIN)
+    #undef JSON_HEDLEY_GNUC_HAS_BUILTIN
+#endif
+#if defined(__has_builtin)
+    #define JSON_HEDLEY_GNUC_HAS_BUILTIN(builtin,major,minor,patch) __has_builtin(builtin)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_BUILTIN(builtin,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_BUILTIN)
+    #undef JSON_HEDLEY_GCC_HAS_BUILTIN
+#endif
+#if defined(__has_builtin)
+    #define JSON_HEDLEY_GCC_HAS_BUILTIN(builtin,major,minor,patch) __has_builtin(builtin)
+#else
+    #define JSON_HEDLEY_GCC_HAS_BUILTIN(builtin,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_FEATURE)
+    #undef JSON_HEDLEY_HAS_FEATURE
+#endif
+#if defined(__has_feature)
+    #define JSON_HEDLEY_HAS_FEATURE(feature) __has_feature(feature)
+#else
+    #define JSON_HEDLEY_HAS_FEATURE(feature) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_FEATURE)
+    #undef JSON_HEDLEY_GNUC_HAS_FEATURE
+#endif
+#if defined(__has_feature)
+    #define JSON_HEDLEY_GNUC_HAS_FEATURE(feature,major,minor,patch) __has_feature(feature)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_FEATURE(feature,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_FEATURE)
+    #undef JSON_HEDLEY_GCC_HAS_FEATURE
+#endif
+#if defined(__has_feature)
+    #define JSON_HEDLEY_GCC_HAS_FEATURE(feature,major,minor,patch) __has_feature(feature)
+#else
+    #define JSON_HEDLEY_GCC_HAS_FEATURE(feature,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_EXTENSION)
+    #undef JSON_HEDLEY_HAS_EXTENSION
+#endif
+#if defined(__has_extension)
+    #define JSON_HEDLEY_HAS_EXTENSION(extension) __has_extension(extension)
+#else
+    #define JSON_HEDLEY_HAS_EXTENSION(extension) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_EXTENSION)
+    #undef JSON_HEDLEY_GNUC_HAS_EXTENSION
+#endif
+#if defined(__has_extension)
+    #define JSON_HEDLEY_GNUC_HAS_EXTENSION(extension,major,minor,patch) __has_extension(extension)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_EXTENSION(extension,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_EXTENSION)
+    #undef JSON_HEDLEY_GCC_HAS_EXTENSION
+#endif
+#if defined(__has_extension)
+    #define JSON_HEDLEY_GCC_HAS_EXTENSION(extension,major,minor,patch) __has_extension(extension)
+#else
+    #define JSON_HEDLEY_GCC_HAS_EXTENSION(extension,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE
+#endif
+#if defined(__has_declspec_attribute)
+    #define JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute) __has_declspec_attribute(attribute)
+#else
+    #define JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE
+#endif
+#if defined(__has_declspec_attribute)
+    #define JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) __has_declspec_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE
+#endif
+#if defined(__has_declspec_attribute)
+    #define JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) __has_declspec_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_WARNING)
+    #undef JSON_HEDLEY_HAS_WARNING
+#endif
+#if defined(__has_warning)
+    #define JSON_HEDLEY_HAS_WARNING(warning) __has_warning(warning)
+#else
+    #define JSON_HEDLEY_HAS_WARNING(warning) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_WARNING)
+    #undef JSON_HEDLEY_GNUC_HAS_WARNING
+#endif
+#if defined(__has_warning)
+    #define JSON_HEDLEY_GNUC_HAS_WARNING(warning,major,minor,patch) __has_warning(warning)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_WARNING(warning,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_WARNING)
+    #undef JSON_HEDLEY_GCC_HAS_WARNING
+#endif
+#if defined(__has_warning)
+    #define JSON_HEDLEY_GCC_HAS_WARNING(warning,major,minor,patch) __has_warning(warning)
+#else
+    #define JSON_HEDLEY_GCC_HAS_WARNING(warning,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if \
+    (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)) || \
+    defined(__clang__) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(18,4,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,7,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(2,0,1) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,0,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_CRAY_VERSION_CHECK(5,0,0) || \
+    JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,17) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(8,0,0) || \
+    (JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) && defined(__C99_PRAGMA_OPERATOR))
+    #define JSON_HEDLEY_PRAGMA(value) _Pragma(#value)
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)
+    #define JSON_HEDLEY_PRAGMA(value) __pragma(value)
+#else
+    #define JSON_HEDLEY_PRAGMA(value)
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_PUSH)
+    #undef JSON_HEDLEY_DIAGNOSTIC_PUSH
+#endif
+#if defined(JSON_HEDLEY_DIAGNOSTIC_POP)
+    #undef JSON_HEDLEY_DIAGNOSTIC_POP
+#endif
+#if defined(__clang__)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("clang diagnostic push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("clang diagnostic pop")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("warning(push)")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("warning(pop)")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("GCC diagnostic push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("GCC diagnostic pop")
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH __pragma(warning(push))
+    #define JSON_HEDLEY_DIAGNOSTIC_POP __pragma(warning(pop))
+#elif JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("pop")
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,4,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,1,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("diag_push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("diag_pop")
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,90,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("warning(push)")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("warning(pop)")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH
+    #define JSON_HEDLEY_DIAGNOSTIC_POP
+#endif
+
+/* JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_ is for
+   HEDLEY INTERNAL USE ONLY.  API subject to change without notice. */
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_
+#endif
+#if defined(__cplusplus)
+#  if JSON_HEDLEY_HAS_WARNING("-Wc++98-compat")
+#    if JSON_HEDLEY_HAS_WARNING("-Wc++17-extensions")
+#      if JSON_HEDLEY_HAS_WARNING("-Wc++1z-extensions")
+#        define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wc++98-compat\"") \
+    _Pragma("clang diagnostic ignored \"-Wc++17-extensions\"") \
+    _Pragma("clang diagnostic ignored \"-Wc++1z-extensions\"") \
+    xpr \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#      else
+#        define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wc++98-compat\"") \
+    _Pragma("clang diagnostic ignored \"-Wc++17-extensions\"") \
+    xpr \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#      endif
+#    else
+#      define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wc++98-compat\"") \
+    xpr \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#    endif
+#  endif
+#endif
+#if !defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(x) x
+#endif
+
+#if defined(JSON_HEDLEY_CONST_CAST)
+    #undef JSON_HEDLEY_CONST_CAST
+#endif
+#if defined(__cplusplus)
+#  define JSON_HEDLEY_CONST_CAST(T, expr) (const_cast<T>(expr))
+#elif \
+  JSON_HEDLEY_HAS_WARNING("-Wcast-qual") || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+#  define JSON_HEDLEY_CONST_CAST(T, expr) (__extension__ ({ \
+        JSON_HEDLEY_DIAGNOSTIC_PUSH \
+        JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL \
+        ((T) (expr)); \
+        JSON_HEDLEY_DIAGNOSTIC_POP \
+    }))
+#else
+#  define JSON_HEDLEY_CONST_CAST(T, expr) ((T) (expr))
+#endif
+
+#if defined(JSON_HEDLEY_REINTERPRET_CAST)
+    #undef JSON_HEDLEY_REINTERPRET_CAST
+#endif
+#if defined(__cplusplus)
+    #define JSON_HEDLEY_REINTERPRET_CAST(T, expr) (reinterpret_cast<T>(expr))
+#else
+    #define JSON_HEDLEY_REINTERPRET_CAST(T, expr) ((T) (expr))
+#endif
+
+#if defined(JSON_HEDLEY_STATIC_CAST)
+    #undef JSON_HEDLEY_STATIC_CAST
+#endif
+#if defined(__cplusplus)
+    #define JSON_HEDLEY_STATIC_CAST(T, expr) (static_cast<T>(expr))
+#else
+    #define JSON_HEDLEY_STATIC_CAST(T, expr) ((T) (expr))
+#endif
+
+#if defined(JSON_HEDLEY_CPP_CAST)
+    #undef JSON_HEDLEY_CPP_CAST
+#endif
+#if defined(__cplusplus)
+#  if JSON_HEDLEY_HAS_WARNING("-Wold-style-cast")
+#    define JSON_HEDLEY_CPP_CAST(T, expr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wold-style-cast\"") \
+    ((T) (expr)) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#  elif JSON_HEDLEY_IAR_VERSION_CHECK(8,3,0)
+#    define JSON_HEDLEY_CPP_CAST(T, expr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("diag_suppress=Pe137") \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#  else
+#    define JSON_HEDLEY_CPP_CAST(T, expr) ((T) (expr))
+#  endif
+#else
+#  define JSON_HEDLEY_CPP_CAST(T, expr) (expr)
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wdeprecated-declarations")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("clang diagnostic ignored \"-Wdeprecated-declarations\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("warning(disable:1478 1786)")
+#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED __pragma(warning(disable:1478 1786))
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(20,7,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1215,1216,1444,1445")
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1215,1444")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("GCC diagnostic ignored \"-Wdeprecated-declarations\"")
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED __pragma(warning(disable:4996))
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1215,1444")
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1291,1718")
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) && !defined(__cplusplus)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("error_messages(off,E_DEPRECATED_ATT,E_DEPRECATED_ATT_MESS)")
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("error_messages(off,symdeprecated,symdeprecated2)")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress=Pe1444,Pe1215")
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,90,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("warn(disable:2241)")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-pragmas")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("clang diagnostic ignored \"-Wunknown-pragmas\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("warning(disable:161)")
+#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS __pragma(warning(disable:161))
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 1675")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("GCC diagnostic ignored \"-Wunknown-pragmas\"")
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS __pragma(warning(disable:4068))
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(16,9,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,3,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 163")
+#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 163")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress=Pe161")
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 161")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-attributes")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("clang diagnostic ignored \"-Wunknown-attributes\"")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("GCC diagnostic ignored \"-Wdeprecated-declarations\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(17,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("warning(disable:1292)")
+#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES __pragma(warning(disable:1292))
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(19,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES __pragma(warning(disable:5030))
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(20,7,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1097,1098")
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1097")
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,14,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("error_messages(off,attrskipunsup)")
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(18,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,3,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1173")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress=Pe1097")
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1097")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wcast-qual")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma("clang diagnostic ignored \"-Wcast-qual\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma("warning(disable:2203 2331)")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma("GCC diagnostic ignored \"-Wcast-qual\"")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunused-function")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma("clang diagnostic ignored \"-Wunused-function\"")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma("GCC diagnostic ignored \"-Wunused-function\"")
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(1,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION __pragma(warning(disable:4505))
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma("diag_suppress 3142")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION
+#endif
+
+#if defined(JSON_HEDLEY_DEPRECATED)
+    #undef JSON_HEDLEY_DEPRECATED
+#endif
+#if defined(JSON_HEDLEY_DEPRECATED_FOR)
+    #undef JSON_HEDLEY_DEPRECATED_FOR
+#endif
+#if \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DEPRECATED(since) __declspec(deprecated("Since " # since))
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __declspec(deprecated("Since " #since "; use " #replacement))
+#elif \
+    (JSON_HEDLEY_HAS_EXTENSION(attribute_deprecated_with_message) && !defined(JSON_HEDLEY_IAR_VERSION)) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,5,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(18,1,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(18,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,3,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,3,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DEPRECATED(since) __attribute__((__deprecated__("Since " #since)))
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __attribute__((__deprecated__("Since " #since "; use " #replacement)))
+#elif defined(__cplusplus) && (__cplusplus >= 201402L)
+    #define JSON_HEDLEY_DEPRECATED(since) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[deprecated("Since " #since)]])
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[deprecated("Since " #since "; use " #replacement)]])
+#elif \
+    JSON_HEDLEY_HAS_ATTRIBUTE(deprecated) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+    #define JSON_HEDLEY_DEPRECATED(since) __attribute__((__deprecated__))
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __attribute__((__deprecated__))
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_PELLES_VERSION_CHECK(6,50,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DEPRECATED(since) __declspec(deprecated)
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __declspec(deprecated)
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DEPRECATED(since) _Pragma("deprecated")
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) _Pragma("deprecated")
+#else
+    #define JSON_HEDLEY_DEPRECATED(since)
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement)
+#endif
+
+#if defined(JSON_HEDLEY_UNAVAILABLE)
+    #undef JSON_HEDLEY_UNAVAILABLE
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(warning) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_UNAVAILABLE(available_since) __attribute__((__warning__("Not available until " #available_since)))
+#else
+    #define JSON_HEDLEY_UNAVAILABLE(available_since)
+#endif
+
+#if defined(JSON_HEDLEY_WARN_UNUSED_RESULT)
+    #undef JSON_HEDLEY_WARN_UNUSED_RESULT
+#endif
+#if defined(JSON_HEDLEY_WARN_UNUSED_RESULT_MSG)
+    #undef JSON_HEDLEY_WARN_UNUSED_RESULT_MSG
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(warn_unused_result) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0) && defined(__cplusplus)) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT __attribute__((__warn_unused_result__))
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) __attribute__((__warn_unused_result__))
+#elif (JSON_HEDLEY_HAS_CPP_ATTRIBUTE(nodiscard) >= 201907L)
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard(msg)]])
+#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE(nodiscard)
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])
+#elif defined(_Check_return_) /* SAL */
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT _Check_return_
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) _Check_return_
+#else
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg)
+#endif
+
+#if defined(JSON_HEDLEY_SENTINEL)
+    #undef JSON_HEDLEY_SENTINEL
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(sentinel) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(5,4,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_SENTINEL(position) __attribute__((__sentinel__(position)))
+#else
+    #define JSON_HEDLEY_SENTINEL(position)
+#endif
+
+#if defined(JSON_HEDLEY_NO_RETURN)
+    #undef JSON_HEDLEY_NO_RETURN
+#endif
+#if JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_NO_RETURN __noreturn
+#elif \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_NO_RETURN __attribute__((__noreturn__))
+#elif defined(__STDC_VERSION__) && __STDC_VERSION__ >= 201112L
+    #define JSON_HEDLEY_NO_RETURN _Noreturn
+#elif defined(__cplusplus) && (__cplusplus >= 201103L)
+    #define JSON_HEDLEY_NO_RETURN JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[noreturn]])
+#elif \
+    JSON_HEDLEY_HAS_ATTRIBUTE(noreturn) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,2,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+    #define JSON_HEDLEY_NO_RETURN __attribute__((__noreturn__))
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+    #define JSON_HEDLEY_NO_RETURN _Pragma("does_not_return")
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_NO_RETURN __declspec(noreturn)
+#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,0,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_NO_RETURN _Pragma("FUNC_NEVER_RETURNS;")
+#elif JSON_HEDLEY_COMPCERT_VERSION_CHECK(3,2,0)
+    #define JSON_HEDLEY_NO_RETURN __attribute((noreturn))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(9,0,0)
+    #define JSON_HEDLEY_NO_RETURN __declspec(noreturn)
+#else
+    #define JSON_HEDLEY_NO_RETURN
+#endif
+
+#if defined(JSON_HEDLEY_NO_ESCAPE)
+    #undef JSON_HEDLEY_NO_ESCAPE
+#endif
+#if JSON_HEDLEY_HAS_ATTRIBUTE(noescape)
+    #define JSON_HEDLEY_NO_ESCAPE __attribute__((__noescape__))
+#else
+    #define JSON_HEDLEY_NO_ESCAPE
+#endif
+
+#if defined(JSON_HEDLEY_UNREACHABLE)
+    #undef JSON_HEDLEY_UNREACHABLE
+#endif
+#if defined(JSON_HEDLEY_UNREACHABLE_RETURN)
+    #undef JSON_HEDLEY_UNREACHABLE_RETURN
+#endif
+#if defined(JSON_HEDLEY_ASSUME)
+    #undef JSON_HEDLEY_ASSUME
+#endif
+#if \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_ASSUME(expr) __assume(expr)
+#elif JSON_HEDLEY_HAS_BUILTIN(__builtin_assume)
+    #define JSON_HEDLEY_ASSUME(expr) __builtin_assume(expr)
+#elif \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0)
+    #if defined(__cplusplus)
+        #define JSON_HEDLEY_ASSUME(expr) std::_nassert(expr)
+    #else
+        #define JSON_HEDLEY_ASSUME(expr) _nassert(expr)
+    #endif
+#endif
+#if \
+    (JSON_HEDLEY_HAS_BUILTIN(__builtin_unreachable) && (!defined(JSON_HEDLEY_ARM_VERSION))) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,5,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(18,10,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,5) || \
+    JSON_HEDLEY_CRAY_VERSION_CHECK(10,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_UNREACHABLE() __builtin_unreachable()
+#elif defined(JSON_HEDLEY_ASSUME)
+    #define JSON_HEDLEY_UNREACHABLE() JSON_HEDLEY_ASSUME(0)
+#endif
+#if !defined(JSON_HEDLEY_ASSUME)
+    #if defined(JSON_HEDLEY_UNREACHABLE)
+        #define JSON_HEDLEY_ASSUME(expr) JSON_HEDLEY_STATIC_CAST(void, ((expr) ? 1 : (JSON_HEDLEY_UNREACHABLE(), 1)))
+    #else
+        #define JSON_HEDLEY_ASSUME(expr) JSON_HEDLEY_STATIC_CAST(void, expr)
+    #endif
+#endif
+#if defined(JSON_HEDLEY_UNREACHABLE)
+    #if  \
+        JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \
+        JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0)
+        #define JSON_HEDLEY_UNREACHABLE_RETURN(value) return (JSON_HEDLEY_STATIC_CAST(void, JSON_HEDLEY_ASSUME(0)), (value))
+    #else
+        #define JSON_HEDLEY_UNREACHABLE_RETURN(value) JSON_HEDLEY_UNREACHABLE()
+    #endif
+#else
+    #define JSON_HEDLEY_UNREACHABLE_RETURN(value) return (value)
+#endif
+#if !defined(JSON_HEDLEY_UNREACHABLE)
+    #define JSON_HEDLEY_UNREACHABLE() JSON_HEDLEY_ASSUME(0)
+#endif
+
+JSON_HEDLEY_DIAGNOSTIC_PUSH
+#if JSON_HEDLEY_HAS_WARNING("-Wpedantic")
+    #pragma clang diagnostic ignored "-Wpedantic"
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wc++98-compat-pedantic") && defined(__cplusplus)
+    #pragma clang diagnostic ignored "-Wc++98-compat-pedantic"
+#endif
+#if JSON_HEDLEY_GCC_HAS_WARNING("-Wvariadic-macros",4,0,0)
+    #if defined(__clang__)
+        #pragma clang diagnostic ignored "-Wvariadic-macros"
+    #elif defined(JSON_HEDLEY_GCC_VERSION)
+        #pragma GCC diagnostic ignored "-Wvariadic-macros"
+    #endif
+#endif
+#if defined(JSON_HEDLEY_NON_NULL)
+    #undef JSON_HEDLEY_NON_NULL
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(nonnull) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0)
+    #define JSON_HEDLEY_NON_NULL(...) __attribute__((__nonnull__(__VA_ARGS__)))
+#else
+    #define JSON_HEDLEY_NON_NULL(...)
+#endif
+JSON_HEDLEY_DIAGNOSTIC_POP
+
+#if defined(JSON_HEDLEY_PRINTF_FORMAT)
+    #undef JSON_HEDLEY_PRINTF_FORMAT
+#endif
+#if defined(__MINGW32__) && JSON_HEDLEY_GCC_HAS_ATTRIBUTE(format,4,4,0) && !defined(__USE_MINGW_ANSI_STDIO)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(ms_printf, string_idx, first_to_check)))
+#elif defined(__MINGW32__) && JSON_HEDLEY_GCC_HAS_ATTRIBUTE(format,4,4,0) && defined(__USE_MINGW_ANSI_STDIO)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(gnu_printf, string_idx, first_to_check)))
+#elif \
+    JSON_HEDLEY_HAS_ATTRIBUTE(format) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(__printf__, string_idx, first_to_check)))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(6,0,0)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __declspec(vaformat(printf,string_idx,first_to_check))
+#else
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check)
+#endif
+
+#if defined(JSON_HEDLEY_CONSTEXPR)
+    #undef JSON_HEDLEY_CONSTEXPR
+#endif
+#if defined(__cplusplus)
+    #if __cplusplus >= 201103L
+        #define JSON_HEDLEY_CONSTEXPR JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(constexpr)
+    #endif
+#endif
+#if !defined(JSON_HEDLEY_CONSTEXPR)
+    #define JSON_HEDLEY_CONSTEXPR
+#endif
+
+#if defined(JSON_HEDLEY_PREDICT)
+    #undef JSON_HEDLEY_PREDICT
+#endif
+#if defined(JSON_HEDLEY_LIKELY)
+    #undef JSON_HEDLEY_LIKELY
+#endif
+#if defined(JSON_HEDLEY_UNLIKELY)
+    #undef JSON_HEDLEY_UNLIKELY
+#endif
+#if defined(JSON_HEDLEY_UNPREDICTABLE)
+    #undef JSON_HEDLEY_UNPREDICTABLE
+#endif
+#if JSON_HEDLEY_HAS_BUILTIN(__builtin_unpredictable)
+    #define JSON_HEDLEY_UNPREDICTABLE(expr) __builtin_unpredictable((expr))
+#endif
+#if \
+  (JSON_HEDLEY_HAS_BUILTIN(__builtin_expect_with_probability) && !defined(JSON_HEDLEY_PGI_VERSION)) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(9,0,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#  define JSON_HEDLEY_PREDICT(expr, value, probability) __builtin_expect_with_probability(  (expr), (value), (probability))
+#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability)   __builtin_expect_with_probability(!!(expr),    1   , (probability))
+#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability)  __builtin_expect_with_probability(!!(expr),    0   , (probability))
+#  define JSON_HEDLEY_LIKELY(expr)                      __builtin_expect                 (!!(expr),    1                  )
+#  define JSON_HEDLEY_UNLIKELY(expr)                    __builtin_expect                 (!!(expr),    0                  )
+#elif \
+  (JSON_HEDLEY_HAS_BUILTIN(__builtin_expect) && !defined(JSON_HEDLEY_INTEL_CL_VERSION)) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+  (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0) && defined(__cplusplus)) || \
+  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,7,0) || \
+  JSON_HEDLEY_TI_CL430_VERSION_CHECK(3,1,0) || \
+  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,1,0) || \
+  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \
+  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+  JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,27) || \
+  JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#  define JSON_HEDLEY_PREDICT(expr, expected, probability) \
+    (((probability) >= 0.9) ? __builtin_expect((expr), (expected)) : (JSON_HEDLEY_STATIC_CAST(void, expected), (expr)))
+#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability) \
+    (__extension__ ({ \
+        double hedley_probability_ = (probability); \
+        ((hedley_probability_ >= 0.9) ? __builtin_expect(!!(expr), 1) : ((hedley_probability_ <= 0.1) ? __builtin_expect(!!(expr), 0) : !!(expr))); \
+    }))
+#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability) \
+    (__extension__ ({ \
+        double hedley_probability_ = (probability); \
+        ((hedley_probability_ >= 0.9) ? __builtin_expect(!!(expr), 0) : ((hedley_probability_ <= 0.1) ? __builtin_expect(!!(expr), 1) : !!(expr))); \
+    }))
+#  define JSON_HEDLEY_LIKELY(expr)   __builtin_expect(!!(expr), 1)
+#  define JSON_HEDLEY_UNLIKELY(expr) __builtin_expect(!!(expr), 0)
+#else
+#  define JSON_HEDLEY_PREDICT(expr, expected, probability) (JSON_HEDLEY_STATIC_CAST(void, expected), (expr))
+#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability) (!!(expr))
+#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability) (!!(expr))
+#  define JSON_HEDLEY_LIKELY(expr) (!!(expr))
+#  define JSON_HEDLEY_UNLIKELY(expr) (!!(expr))
+#endif
+#if !defined(JSON_HEDLEY_UNPREDICTABLE)
+    #define JSON_HEDLEY_UNPREDICTABLE(expr) JSON_HEDLEY_PREDICT(expr, 1, 0.5)
+#endif
+
+#if defined(JSON_HEDLEY_MALLOC)
+    #undef JSON_HEDLEY_MALLOC
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(malloc) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(12,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_MALLOC __attribute__((__malloc__))
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+    #define JSON_HEDLEY_MALLOC _Pragma("returns_new_memory")
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_MALLOC __declspec(restrict)
+#else
+    #define JSON_HEDLEY_MALLOC
+#endif
+
+#if defined(JSON_HEDLEY_PURE)
+    #undef JSON_HEDLEY_PURE
+#endif
+#if \
+  JSON_HEDLEY_HAS_ATTRIBUTE(pure) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(2,96,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+  JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+  (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+  (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+  (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+  (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+  JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#  define JSON_HEDLEY_PURE __attribute__((__pure__))
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+#  define JSON_HEDLEY_PURE _Pragma("does_not_write_global_data")
+#elif defined(__cplusplus) && \
+    ( \
+      JSON_HEDLEY_TI_CL430_VERSION_CHECK(2,0,1) || \
+      JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0) || \
+      JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) \
+    )
+#  define JSON_HEDLEY_PURE _Pragma("FUNC_IS_PURE;")
+#else
+#  define JSON_HEDLEY_PURE
+#endif
+
+#if defined(JSON_HEDLEY_CONST)
+    #undef JSON_HEDLEY_CONST
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(const) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(2,5,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_CONST __attribute__((__const__))
+#elif \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+    #define JSON_HEDLEY_CONST _Pragma("no_side_effect")
+#else
+    #define JSON_HEDLEY_CONST JSON_HEDLEY_PURE
+#endif
+
+#if defined(JSON_HEDLEY_RESTRICT)
+    #undef JSON_HEDLEY_RESTRICT
+#endif
+#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) && !defined(__cplusplus)
+    #define JSON_HEDLEY_RESTRICT restrict
+#elif \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,4) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,1,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,14,0) && defined(__cplusplus)) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0) || \
+    defined(__clang__) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_RESTRICT __restrict
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,3,0) && !defined(__cplusplus)
+    #define JSON_HEDLEY_RESTRICT _Restrict
+#else
+    #define JSON_HEDLEY_RESTRICT
+#endif
+
+#if defined(JSON_HEDLEY_INLINE)
+    #undef JSON_HEDLEY_INLINE
+#endif
+#if \
+    (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)) || \
+    (defined(__cplusplus) && (__cplusplus >= 199711L))
+    #define JSON_HEDLEY_INLINE inline
+#elif \
+    defined(JSON_HEDLEY_GCC_VERSION) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(6,2,0)
+    #define JSON_HEDLEY_INLINE __inline__
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(12,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,1,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_INLINE __inline
+#else
+    #define JSON_HEDLEY_INLINE
+#endif
+
+#if defined(JSON_HEDLEY_ALWAYS_INLINE)
+    #undef JSON_HEDLEY_ALWAYS_INLINE
+#endif
+#if \
+  JSON_HEDLEY_HAS_ATTRIBUTE(always_inline) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+  JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+  (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+  (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+  (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+  (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \
+  JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+#  define JSON_HEDLEY_ALWAYS_INLINE __attribute__((__always_inline__)) JSON_HEDLEY_INLINE
+#elif \
+  JSON_HEDLEY_MSVC_VERSION_CHECK(12,0,0) || \
+  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+#  define JSON_HEDLEY_ALWAYS_INLINE __forceinline
+#elif defined(__cplusplus) && \
+    ( \
+      JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+      JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+      JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+      JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \
+      JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+      JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) \
+    )
+#  define JSON_HEDLEY_ALWAYS_INLINE _Pragma("FUNC_ALWAYS_INLINE;")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+#  define JSON_HEDLEY_ALWAYS_INLINE _Pragma("inline=forced")
+#else
+#  define JSON_HEDLEY_ALWAYS_INLINE JSON_HEDLEY_INLINE
+#endif
+
+#if defined(JSON_HEDLEY_NEVER_INLINE)
+    #undef JSON_HEDLEY_NEVER_INLINE
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(noinline) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+    #define JSON_HEDLEY_NEVER_INLINE __attribute__((__noinline__))
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_NEVER_INLINE __declspec(noinline)
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(10,2,0)
+    #define JSON_HEDLEY_NEVER_INLINE _Pragma("noinline")
+#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,0,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_NEVER_INLINE _Pragma("FUNC_CANNOT_INLINE;")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_NEVER_INLINE _Pragma("inline=never")
+#elif JSON_HEDLEY_COMPCERT_VERSION_CHECK(3,2,0)
+    #define JSON_HEDLEY_NEVER_INLINE __attribute((noinline))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(9,0,0)
+    #define JSON_HEDLEY_NEVER_INLINE __declspec(noinline)
+#else
+    #define JSON_HEDLEY_NEVER_INLINE
+#endif
+
+#if defined(JSON_HEDLEY_PRIVATE)
+    #undef JSON_HEDLEY_PRIVATE
+#endif
+#if defined(JSON_HEDLEY_PUBLIC)
+    #undef JSON_HEDLEY_PUBLIC
+#endif
+#if defined(JSON_HEDLEY_IMPORT)
+    #undef JSON_HEDLEY_IMPORT
+#endif
+#if defined(_WIN32) || defined(__CYGWIN__)
+#  define JSON_HEDLEY_PRIVATE
+#  define JSON_HEDLEY_PUBLIC   __declspec(dllexport)
+#  define JSON_HEDLEY_IMPORT   __declspec(dllimport)
+#else
+#  if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(visibility) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \
+    ( \
+      defined(__TI_EABI__) && \
+      ( \
+        (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+        JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) \
+      ) \
+    ) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#    define JSON_HEDLEY_PRIVATE __attribute__((__visibility__("hidden")))
+#    define JSON_HEDLEY_PUBLIC  __attribute__((__visibility__("default")))
+#  else
+#    define JSON_HEDLEY_PRIVATE
+#    define JSON_HEDLEY_PUBLIC
+#  endif
+#  define JSON_HEDLEY_IMPORT    extern
+#endif
+
+#if defined(JSON_HEDLEY_NO_THROW)
+    #undef JSON_HEDLEY_NO_THROW
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(nothrow) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_NO_THROW __attribute__((__nothrow__))
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,1,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0)
+    #define JSON_HEDLEY_NO_THROW __declspec(nothrow)
+#else
+    #define JSON_HEDLEY_NO_THROW
+#endif
+
+#if defined(JSON_HEDLEY_FALL_THROUGH)
+    #undef JSON_HEDLEY_FALL_THROUGH
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(fallthrough) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(7,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_FALL_THROUGH __attribute__((__fallthrough__))
+#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(clang,fallthrough)
+    #define JSON_HEDLEY_FALL_THROUGH JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[clang::fallthrough]])
+#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE(fallthrough)
+    #define JSON_HEDLEY_FALL_THROUGH JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[fallthrough]])
+#elif defined(__fallthrough) /* SAL */
+    #define JSON_HEDLEY_FALL_THROUGH __fallthrough
+#else
+    #define JSON_HEDLEY_FALL_THROUGH
+#endif
+
+#if defined(JSON_HEDLEY_RETURNS_NON_NULL)
+    #undef JSON_HEDLEY_RETURNS_NON_NULL
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(returns_nonnull) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_RETURNS_NON_NULL __attribute__((__returns_nonnull__))
+#elif defined(_Ret_notnull_) /* SAL */
+    #define JSON_HEDLEY_RETURNS_NON_NULL _Ret_notnull_
+#else
+    #define JSON_HEDLEY_RETURNS_NON_NULL
+#endif
+
+#if defined(JSON_HEDLEY_ARRAY_PARAM)
+    #undef JSON_HEDLEY_ARRAY_PARAM
+#endif
+#if \
+    defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) && \
+    !defined(__STDC_NO_VLA__) && \
+    !defined(__cplusplus) && \
+    !defined(JSON_HEDLEY_PGI_VERSION) && \
+    !defined(JSON_HEDLEY_TINYC_VERSION)
+    #define JSON_HEDLEY_ARRAY_PARAM(name) (name)
+#else
+    #define JSON_HEDLEY_ARRAY_PARAM(name)
+#endif
+
+#if defined(JSON_HEDLEY_IS_CONSTANT)
+    #undef JSON_HEDLEY_IS_CONSTANT
+#endif
+#if defined(JSON_HEDLEY_REQUIRE_CONSTEXPR)
+    #undef JSON_HEDLEY_REQUIRE_CONSTEXPR
+#endif
+/* JSON_HEDLEY_IS_CONSTEXPR_ is for
+   HEDLEY INTERNAL USE ONLY.  API subject to change without notice. */
+#if defined(JSON_HEDLEY_IS_CONSTEXPR_)
+    #undef JSON_HEDLEY_IS_CONSTEXPR_
+#endif
+#if \
+    JSON_HEDLEY_HAS_BUILTIN(__builtin_constant_p) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,19) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \
+    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0) && !defined(__cplusplus)) || \
+    JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_IS_CONSTANT(expr) __builtin_constant_p(expr)
+#endif
+#if !defined(__cplusplus)
+#  if \
+       JSON_HEDLEY_HAS_BUILTIN(__builtin_types_compatible_p) || \
+       JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \
+       JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+       JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \
+       JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \
+       JSON_HEDLEY_ARM_VERSION_CHECK(5,4,0) || \
+       JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,24)
+#if defined(__INTPTR_TYPE__)
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) __builtin_types_compatible_p(__typeof__((1 ? (void*) ((__INTPTR_TYPE__) ((expr) * 0)) : (int*) 0)), int*)
+#else
+    #include <stdint.h>
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) __builtin_types_compatible_p(__typeof__((1 ? (void*) ((intptr_t) ((expr) * 0)) : (int*) 0)), int*)
+#endif
+#  elif \
+       ( \
+          defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L) && \
+          !defined(JSON_HEDLEY_SUNPRO_VERSION) && \
+          !defined(JSON_HEDLEY_PGI_VERSION) && \
+          !defined(JSON_HEDLEY_IAR_VERSION)) || \
+       (JSON_HEDLEY_HAS_EXTENSION(c_generic_selections) && !defined(JSON_HEDLEY_IAR_VERSION)) || \
+       JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0) || \
+       JSON_HEDLEY_INTEL_VERSION_CHECK(17,0,0) || \
+       JSON_HEDLEY_IBM_VERSION_CHECK(12,1,0) || \
+       JSON_HEDLEY_ARM_VERSION_CHECK(5,3,0)
+#if defined(__INTPTR_TYPE__)
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) _Generic((1 ? (void*) ((__INTPTR_TYPE__) ((expr) * 0)) : (int*) 0), int*: 1, void*: 0)
+#else
+    #include <stdint.h>
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) _Generic((1 ? (void*) ((intptr_t) * 0) : (int*) 0), int*: 1, void*: 0)
+#endif
+#  elif \
+       defined(JSON_HEDLEY_GCC_VERSION) || \
+       defined(JSON_HEDLEY_INTEL_VERSION) || \
+       defined(JSON_HEDLEY_TINYC_VERSION) || \
+       defined(JSON_HEDLEY_TI_ARMCL_VERSION) || \
+       JSON_HEDLEY_TI_CL430_VERSION_CHECK(18,12,0) || \
+       defined(JSON_HEDLEY_TI_CL2000_VERSION) || \
+       defined(JSON_HEDLEY_TI_CL6X_VERSION) || \
+       defined(JSON_HEDLEY_TI_CL7X_VERSION) || \
+       defined(JSON_HEDLEY_TI_CLPRU_VERSION) || \
+       defined(__clang__)
+#    define JSON_HEDLEY_IS_CONSTEXPR_(expr) ( \
+        sizeof(void) != \
+        sizeof(*( \
+                  1 ? \
+                  ((void*) ((expr) * 0L) ) : \
+((struct { char v[sizeof(void) * 2]; } *) 1) \
+                ) \
+              ) \
+                                            )
+#  endif
+#endif
+#if defined(JSON_HEDLEY_IS_CONSTEXPR_)
+    #if !defined(JSON_HEDLEY_IS_CONSTANT)
+        #define JSON_HEDLEY_IS_CONSTANT(expr) JSON_HEDLEY_IS_CONSTEXPR_(expr)
+    #endif
+    #define JSON_HEDLEY_REQUIRE_CONSTEXPR(expr) (JSON_HEDLEY_IS_CONSTEXPR_(expr) ? (expr) : (-1))
+#else
+    #if !defined(JSON_HEDLEY_IS_CONSTANT)
+        #define JSON_HEDLEY_IS_CONSTANT(expr) (0)
+    #endif
+    #define JSON_HEDLEY_REQUIRE_CONSTEXPR(expr) (expr)
+#endif
+
+#if defined(JSON_HEDLEY_BEGIN_C_DECLS)
+    #undef JSON_HEDLEY_BEGIN_C_DECLS
+#endif
+#if defined(JSON_HEDLEY_END_C_DECLS)
+    #undef JSON_HEDLEY_END_C_DECLS
+#endif
+#if defined(JSON_HEDLEY_C_DECL)
+    #undef JSON_HEDLEY_C_DECL
+#endif
+#if defined(__cplusplus)
+    #define JSON_HEDLEY_BEGIN_C_DECLS extern "C" {
+    #define JSON_HEDLEY_END_C_DECLS }
+    #define JSON_HEDLEY_C_DECL extern "C"
+#else
+    #define JSON_HEDLEY_BEGIN_C_DECLS
+    #define JSON_HEDLEY_END_C_DECLS
+    #define JSON_HEDLEY_C_DECL
+#endif
+
+#if defined(JSON_HEDLEY_STATIC_ASSERT)
+    #undef JSON_HEDLEY_STATIC_ASSERT
+#endif
+#if \
+  !defined(__cplusplus) && ( \
+      (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L)) || \
+      (JSON_HEDLEY_HAS_FEATURE(c_static_assert) && !defined(JSON_HEDLEY_INTEL_CL_VERSION)) || \
+      JSON_HEDLEY_GCC_VERSION_CHECK(6,0,0) || \
+      JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+      defined(_Static_assert) \
+    )
+#  define JSON_HEDLEY_STATIC_ASSERT(expr, message) _Static_assert(expr, message)
+#elif \
+  (defined(__cplusplus) && (__cplusplus >= 201103L)) || \
+  JSON_HEDLEY_MSVC_VERSION_CHECK(16,0,0) || \
+  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+#  define JSON_HEDLEY_STATIC_ASSERT(expr, message) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(static_assert(expr, message))
+#else
+#  define JSON_HEDLEY_STATIC_ASSERT(expr, message)
+#endif
+
+#if defined(JSON_HEDLEY_NULL)
+    #undef JSON_HEDLEY_NULL
+#endif
+#if defined(__cplusplus)
+    #if __cplusplus >= 201103L
+        #define JSON_HEDLEY_NULL JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(nullptr)
+    #elif defined(NULL)
+        #define JSON_HEDLEY_NULL NULL
+    #else
+        #define JSON_HEDLEY_NULL JSON_HEDLEY_STATIC_CAST(void*, 0)
+    #endif
+#elif defined(NULL)
+    #define JSON_HEDLEY_NULL NULL
+#else
+    #define JSON_HEDLEY_NULL ((void*) 0)
+#endif
+
+#if defined(JSON_HEDLEY_MESSAGE)
+    #undef JSON_HEDLEY_MESSAGE
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-pragmas")
+#  define JSON_HEDLEY_MESSAGE(msg) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS \
+    JSON_HEDLEY_PRAGMA(message msg) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#elif \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,4,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message msg)
+#elif JSON_HEDLEY_CRAY_VERSION_CHECK(5,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(_CRI message msg)
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message(msg))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message(msg))
+#else
+#  define JSON_HEDLEY_MESSAGE(msg)
+#endif
+
+#if defined(JSON_HEDLEY_WARNING)
+    #undef JSON_HEDLEY_WARNING
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-pragmas")
+#  define JSON_HEDLEY_WARNING(msg) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS \
+    JSON_HEDLEY_PRAGMA(clang warning msg) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#elif \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,8,0) || \
+  JSON_HEDLEY_PGI_VERSION_CHECK(18,4,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_PRAGMA(GCC warning msg)
+#elif \
+  JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0) || \
+  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_PRAGMA(message(msg))
+#else
+#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_MESSAGE(msg)
+#endif
+
+#if defined(JSON_HEDLEY_REQUIRE)
+    #undef JSON_HEDLEY_REQUIRE
+#endif
+#if defined(JSON_HEDLEY_REQUIRE_MSG)
+    #undef JSON_HEDLEY_REQUIRE_MSG
+#endif
+#if JSON_HEDLEY_HAS_ATTRIBUTE(diagnose_if)
+#  if JSON_HEDLEY_HAS_WARNING("-Wgcc-compat")
+#    define JSON_HEDLEY_REQUIRE(expr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wgcc-compat\"") \
+    __attribute__((diagnose_if(!(expr), #expr, "error"))) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#    define JSON_HEDLEY_REQUIRE_MSG(expr,msg) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wgcc-compat\"") \
+    __attribute__((diagnose_if(!(expr), msg, "error"))) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#  else
+#    define JSON_HEDLEY_REQUIRE(expr) __attribute__((diagnose_if(!(expr), #expr, "error")))
+#    define JSON_HEDLEY_REQUIRE_MSG(expr,msg) __attribute__((diagnose_if(!(expr), msg, "error")))
+#  endif
+#else
+#  define JSON_HEDLEY_REQUIRE(expr)
+#  define JSON_HEDLEY_REQUIRE_MSG(expr,msg)
+#endif
+
+#if defined(JSON_HEDLEY_FLAGS)
+    #undef JSON_HEDLEY_FLAGS
+#endif
+#if JSON_HEDLEY_HAS_ATTRIBUTE(flag_enum) && (!defined(__cplusplus) || JSON_HEDLEY_HAS_WARNING("-Wbitfield-enum-conversion"))
+    #define JSON_HEDLEY_FLAGS __attribute__((__flag_enum__))
+#else
+    #define JSON_HEDLEY_FLAGS
+#endif
+
+#if defined(JSON_HEDLEY_FLAGS_CAST)
+    #undef JSON_HEDLEY_FLAGS_CAST
+#endif
+#if JSON_HEDLEY_INTEL_VERSION_CHECK(19,0,0)
+#  define JSON_HEDLEY_FLAGS_CAST(T, expr) (__extension__ ({ \
+        JSON_HEDLEY_DIAGNOSTIC_PUSH \
+        _Pragma("warning(disable:188)") \
+        ((T) (expr)); \
+        JSON_HEDLEY_DIAGNOSTIC_POP \
+    }))
+#else
+#  define JSON_HEDLEY_FLAGS_CAST(T, expr) JSON_HEDLEY_STATIC_CAST(T, expr)
+#endif
+
+#if defined(JSON_HEDLEY_EMPTY_BASES)
+    #undef JSON_HEDLEY_EMPTY_BASES
+#endif
+#if \
+    (JSON_HEDLEY_MSVC_VERSION_CHECK(19,0,23918) && !JSON_HEDLEY_MSVC_VERSION_CHECK(20,0,0)) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_EMPTY_BASES __declspec(empty_bases)
+#else
+    #define JSON_HEDLEY_EMPTY_BASES
+#endif
+
+/* Remaining macros are deprecated. */
+
+#if defined(JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK)
+    #undef JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK
+#endif
+#if defined(__clang__)
+    #define JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK(major,minor,patch) (0)
+#else
+    #define JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK(major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_CLANG_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_CLANG_HAS_ATTRIBUTE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_BUILTIN)
+    #undef JSON_HEDLEY_CLANG_HAS_BUILTIN
+#endif
+#define JSON_HEDLEY_CLANG_HAS_BUILTIN(builtin) JSON_HEDLEY_HAS_BUILTIN(builtin)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_FEATURE)
+    #undef JSON_HEDLEY_CLANG_HAS_FEATURE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_FEATURE(feature) JSON_HEDLEY_HAS_FEATURE(feature)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_EXTENSION)
+    #undef JSON_HEDLEY_CLANG_HAS_EXTENSION
+#endif
+#define JSON_HEDLEY_CLANG_HAS_EXTENSION(extension) JSON_HEDLEY_HAS_EXTENSION(extension)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_DECLSPEC_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_WARNING)
+    #undef JSON_HEDLEY_CLANG_HAS_WARNING
+#endif
+#define JSON_HEDLEY_CLANG_HAS_WARNING(warning) JSON_HEDLEY_HAS_WARNING(warning)
+
+#endif /* !defined(JSON_HEDLEY_VERSION) || (JSON_HEDLEY_VERSION < X) */
+
+
+// This file contains all internal macro definitions (except those affecting ABI)
+// You MUST include macro_unscope.hpp at the end of json.hpp to undef all of them
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+// exclude unsupported compilers
+#if !defined(JSON_SKIP_UNSUPPORTED_COMPILER_CHECK)
+    #if defined(__clang__)
+        #if (__clang_major__ * 10000 + __clang_minor__ * 100 + __clang_patchlevel__) < 30400
+            #error "unsupported Clang version - see https://github.com/nlohmann/json#supported-compilers"
+        #endif
+    #elif defined(__GNUC__) && !(defined(__ICC) || defined(__INTEL_COMPILER))
+        #if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) < 40800
+            #error "unsupported GCC version - see https://github.com/nlohmann/json#supported-compilers"
+        #endif
+    #endif
+#endif
+
+// C++ language standard detection
+// if the user manually specified the used c++ version this is skipped
+#if !defined(JSON_HAS_CPP_23) && !defined(JSON_HAS_CPP_20) && !defined(JSON_HAS_CPP_17) && !defined(JSON_HAS_CPP_14) && !defined(JSON_HAS_CPP_11)
+    #if (defined(__cplusplus) && __cplusplus > 202002L) || (defined(_MSVC_LANG) && _MSVC_LANG > 202002L)
+        #define JSON_HAS_CPP_23
+        #define JSON_HAS_CPP_20
+        #define JSON_HAS_CPP_17
+        #define JSON_HAS_CPP_14
+    #elif (defined(__cplusplus) && __cplusplus > 201703L) || (defined(_MSVC_LANG) && _MSVC_LANG > 201703L)
+        #define JSON_HAS_CPP_20
+        #define JSON_HAS_CPP_17
+        #define JSON_HAS_CPP_14
+    #elif (defined(__cplusplus) && __cplusplus > 201402L) || (defined(_HAS_CXX17) && _HAS_CXX17 == 1) // fix for issue #464
+        #define JSON_HAS_CPP_17
+        #define JSON_HAS_CPP_14
+    #elif (defined(__cplusplus) && __cplusplus > 201103L) || (defined(_HAS_CXX14) && _HAS_CXX14 == 1)
+        #define JSON_HAS_CPP_14
+    #endif
+    // the cpp 11 flag is always specified because it is the minimal required version
+    #define JSON_HAS_CPP_11
+#endif
+
+#ifdef __has_include
+    #if __has_include(<version>)
+        #include <version>
+    #endif
+#endif
+
+#if !defined(JSON_HAS_FILESYSTEM) && !defined(JSON_HAS_EXPERIMENTAL_FILESYSTEM)
+    #ifdef JSON_HAS_CPP_17
+        #if defined(__cpp_lib_filesystem)
+            #define JSON_HAS_FILESYSTEM 1
+        #elif defined(__cpp_lib_experimental_filesystem)
+            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1
+        #elif !defined(__has_include)
+            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1
+        #elif __has_include(<filesystem>)
+            #define JSON_HAS_FILESYSTEM 1
+        #elif __has_include(<experimental/filesystem>)
+            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1
+        #endif
+
+        // std::filesystem does not work on MinGW GCC 8: https://sourceforge.net/p/mingw-w64/bugs/737/
+        #if defined(__MINGW32__) && defined(__GNUC__) && __GNUC__ == 8
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before GCC 8: https://en.cppreference.com/w/cpp/compiler_support
+        #if defined(__GNUC__) && !defined(__clang__) && __GNUC__ < 8
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before Clang 7: https://en.cppreference.com/w/cpp/compiler_support
+        #if defined(__clang_major__) && __clang_major__ < 7
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before MSVC 19.14: https://en.cppreference.com/w/cpp/compiler_support
+        #if defined(_MSC_VER) && _MSC_VER < 1914
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before iOS 13
+        #if defined(__IPHONE_OS_VERSION_MIN_REQUIRED) && __IPHONE_OS_VERSION_MIN_REQUIRED < 130000
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before macOS Catalina
+        #if defined(__MAC_OS_X_VERSION_MIN_REQUIRED) && __MAC_OS_X_VERSION_MIN_REQUIRED < 101500
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+    #endif
+#endif
+
+#ifndef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+    #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 0
+#endif
+
+#ifndef JSON_HAS_FILESYSTEM
+    #define JSON_HAS_FILESYSTEM 0
+#endif
+
+#ifndef JSON_HAS_THREE_WAY_COMPARISON
+    #if defined(__cpp_impl_three_way_comparison) && __cpp_impl_three_way_comparison >= 201907L \
+        && defined(__cpp_lib_three_way_comparison) && __cpp_lib_three_way_comparison >= 201907L
+        #define JSON_HAS_THREE_WAY_COMPARISON 1
+    #else
+        #define JSON_HAS_THREE_WAY_COMPARISON 0
+    #endif
+#endif
+
+#ifndef JSON_HAS_RANGES
+    // ranges header shipping in GCC 11.1.0 (released 2021-04-27) has syntax error
+    #if defined(__GLIBCXX__) && __GLIBCXX__ == 20210427
+        #define JSON_HAS_RANGES 0
+    #elif defined(__cpp_lib_ranges)
+        #define JSON_HAS_RANGES 1
+    #else
+        #define JSON_HAS_RANGES 0
+    #endif
+#endif
+
+#ifndef JSON_HAS_STATIC_RTTI
+    #if !defined(_HAS_STATIC_RTTI) || _HAS_STATIC_RTTI != 0
+        #define JSON_HAS_STATIC_RTTI 1
+    #else
+        #define JSON_HAS_STATIC_RTTI 0
+    #endif
+#endif
+
+#ifdef JSON_HAS_CPP_17
+    #define JSON_INLINE_VARIABLE inline
+#else
+    #define JSON_INLINE_VARIABLE
+#endif
+
+#if JSON_HEDLEY_HAS_ATTRIBUTE(no_unique_address)
+    #define JSON_NO_UNIQUE_ADDRESS [[no_unique_address]]
+#else
+    #define JSON_NO_UNIQUE_ADDRESS
+#endif
+
+// disable documentation warnings on clang
+#if defined(__clang__)
+    #pragma clang diagnostic push
+    #pragma clang diagnostic ignored "-Wdocumentation"
+    #pragma clang diagnostic ignored "-Wdocumentation-unknown-command"
+#endif
+
+// allow disabling exceptions
+#if (defined(__cpp_exceptions) || defined(__EXCEPTIONS) || defined(_CPPUNWIND)) && !defined(JSON_NOEXCEPTION)
+    #define JSON_THROW(exception) throw exception
+    #define JSON_TRY try
+    #define JSON_CATCH(exception) catch(exception)
+    #define JSON_INTERNAL_CATCH(exception) catch(exception)
+#else
+    #include <cstdlib>
+    #define JSON_THROW(exception) std::abort()
+    #define JSON_TRY if(true)
+    #define JSON_CATCH(exception) if(false)
+    #define JSON_INTERNAL_CATCH(exception) if(false)
+#endif
+
+// override exception macros
+#if defined(JSON_THROW_USER)
+    #undef JSON_THROW
+    #define JSON_THROW JSON_THROW_USER
+#endif
+#if defined(JSON_TRY_USER)
+    #undef JSON_TRY
+    #define JSON_TRY JSON_TRY_USER
+#endif
+#if defined(JSON_CATCH_USER)
+    #undef JSON_CATCH
+    #define JSON_CATCH JSON_CATCH_USER
+    #undef JSON_INTERNAL_CATCH
+    #define JSON_INTERNAL_CATCH JSON_CATCH_USER
+#endif
+#if defined(JSON_INTERNAL_CATCH_USER)
+    #undef JSON_INTERNAL_CATCH
+    #define JSON_INTERNAL_CATCH JSON_INTERNAL_CATCH_USER
+#endif
+
+// allow overriding assert
+#if !defined(JSON_ASSERT)
+    #include <cassert> // assert
+    #define JSON_ASSERT(x) assert(x)
+#endif
+
+// allow to access some private functions (needed by the test suite)
+#if defined(JSON_TESTS_PRIVATE)
+    #define JSON_PRIVATE_UNLESS_TESTED public
+#else
+    #define JSON_PRIVATE_UNLESS_TESTED private
+#endif
+
+/*!
+@brief macro to briefly define a mapping between an enum and JSON
+@def NLOHMANN_JSON_SERIALIZE_ENUM
+@since version 3.4.0
+*/
+#define NLOHMANN_JSON_SERIALIZE_ENUM(ENUM_TYPE, ...)                                            \
+    template<typename BasicJsonType>                                                            \
+    inline void to_json(BasicJsonType& j, const ENUM_TYPE& e)                                   \
+    {                                                                                           \
+        /* NOLINTNEXTLINE(modernize-type-traits) we use C++11 */                                \
+        static_assert(std::is_enum<ENUM_TYPE>::value, #ENUM_TYPE " must be an enum!");          \
+        /* NOLINTNEXTLINE(modernize-avoid-c-arrays) we don't want to depend on <array> */       \
+        static const std::pair<ENUM_TYPE, BasicJsonType> m[] = __VA_ARGS__;                     \
+        auto it = std::find_if(std::begin(m), std::end(m),                                      \
+                               [e](const std::pair<ENUM_TYPE, BasicJsonType>& ej_pair) -> bool  \
+        {                                                                                       \
+            return ej_pair.first == e;                                                          \
+        });                                                                                     \
+        j = ((it != std::end(m)) ? it : std::begin(m))->second;                                 \
+    }                                                                                           \
+    template<typename BasicJsonType>                                                            \
+    inline void from_json(const BasicJsonType& j, ENUM_TYPE& e)                                 \
+    {                                                                                           \
+        /* NOLINTNEXTLINE(modernize-type-traits) we use C++11 */                                \
+        static_assert(std::is_enum<ENUM_TYPE>::value, #ENUM_TYPE " must be an enum!");          \
+        /* NOLINTNEXTLINE(modernize-avoid-c-arrays) we don't want to depend on <array> */       \
+        static const std::pair<ENUM_TYPE, BasicJsonType> m[] = __VA_ARGS__;                     \
+        auto it = std::find_if(std::begin(m), std::end(m),                                      \
+                               [&j](const std::pair<ENUM_TYPE, BasicJsonType>& ej_pair) -> bool \
+        {                                                                                       \
+            return ej_pair.second == j;                                                         \
+        });                                                                                     \
+        e = ((it != std::end(m)) ? it : std::begin(m))->first;                                  \
+    }
+
+// Ugly macros to avoid uglier copy-paste when specializing basic_json. They
+// may be removed in the future once the class is split.
+
+#define NLOHMANN_BASIC_JSON_TPL_DECLARATION                                \
+    template<template<typename, typename, typename...> class ObjectType,   \
+             template<typename, typename...> class ArrayType,              \
+             class StringType, class BooleanType, class NumberIntegerType, \
+             class NumberUnsignedType, class NumberFloatType,              \
+             template<typename> class AllocatorType,                       \
+             template<typename, typename = void> class JSONSerializer,     \
+             class BinaryType,                                             \
+             class CustomBaseClass>
+
+#define NLOHMANN_BASIC_JSON_TPL                                            \
+    basic_json<ObjectType, ArrayType, StringType, BooleanType,             \
+    NumberIntegerType, NumberUnsignedType, NumberFloatType,                \
+    AllocatorType, JSONSerializer, BinaryType, CustomBaseClass>
+
+// Macros to simplify conversion from/to types
+
+#define NLOHMANN_JSON_EXPAND( x ) x
+#define NLOHMANN_JSON_GET_MACRO(_1, _2, _3, _4, _5, _6, _7, _8, _9, _10, _11, _12, _13, _14, _15, _16, _17, _18, _19, _20, _21, _22, _23, _24, _25, _26, _27, _28, _29, _30, _31, _32, _33, _34, _35, _36, _37, _38, _39, _40, _41, _42, _43, _44, _45, _46, _47, _48, _49, _50, _51, _52, _53, _54, _55, _56, _57, _58, _59, _60, _61, _62, _63, _64, NAME,...) NAME
+#define NLOHMANN_JSON_PASTE(...) NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_GET_MACRO(__VA_ARGS__, \
+        NLOHMANN_JSON_PASTE64, \
+        NLOHMANN_JSON_PASTE63, \
+        NLOHMANN_JSON_PASTE62, \
+        NLOHMANN_JSON_PASTE61, \
+        NLOHMANN_JSON_PASTE60, \
+        NLOHMANN_JSON_PASTE59, \
+        NLOHMANN_JSON_PASTE58, \
+        NLOHMANN_JSON_PASTE57, \
+        NLOHMANN_JSON_PASTE56, \
+        NLOHMANN_JSON_PASTE55, \
+        NLOHMANN_JSON_PASTE54, \
+        NLOHMANN_JSON_PASTE53, \
+        NLOHMANN_JSON_PASTE52, \
+        NLOHMANN_JSON_PASTE51, \
+        NLOHMANN_JSON_PASTE50, \
+        NLOHMANN_JSON_PASTE49, \
+        NLOHMANN_JSON_PASTE48, \
+        NLOHMANN_JSON_PASTE47, \
+        NLOHMANN_JSON_PASTE46, \
+        NLOHMANN_JSON_PASTE45, \
+        NLOHMANN_JSON_PASTE44, \
+        NLOHMANN_JSON_PASTE43, \
+        NLOHMANN_JSON_PASTE42, \
+        NLOHMANN_JSON_PASTE41, \
+        NLOHMANN_JSON_PASTE40, \
+        NLOHMANN_JSON_PASTE39, \
+        NLOHMANN_JSON_PASTE38, \
+        NLOHMANN_JSON_PASTE37, \
+        NLOHMANN_JSON_PASTE36, \
+        NLOHMANN_JSON_PASTE35, \
+        NLOHMANN_JSON_PASTE34, \
+        NLOHMANN_JSON_PASTE33, \
+        NLOHMANN_JSON_PASTE32, \
+        NLOHMANN_JSON_PASTE31, \
+        NLOHMANN_JSON_PASTE30, \
+        NLOHMANN_JSON_PASTE29, \
+        NLOHMANN_JSON_PASTE28, \
+        NLOHMANN_JSON_PASTE27, \
+        NLOHMANN_JSON_PASTE26, \
+        NLOHMANN_JSON_PASTE25, \
+        NLOHMANN_JSON_PASTE24, \
+        NLOHMANN_JSON_PASTE23, \
+        NLOHMANN_JSON_PASTE22, \
+        NLOHMANN_JSON_PASTE21, \
+        NLOHMANN_JSON_PASTE20, \
+        NLOHMANN_JSON_PASTE19, \
+        NLOHMANN_JSON_PASTE18, \
+        NLOHMANN_JSON_PASTE17, \
+        NLOHMANN_JSON_PASTE16, \
+        NLOHMANN_JSON_PASTE15, \
+        NLOHMANN_JSON_PASTE14, \
+        NLOHMANN_JSON_PASTE13, \
+        NLOHMANN_JSON_PASTE12, \
+        NLOHMANN_JSON_PASTE11, \
+        NLOHMANN_JSON_PASTE10, \
+        NLOHMANN_JSON_PASTE9, \
+        NLOHMANN_JSON_PASTE8, \
+        NLOHMANN_JSON_PASTE7, \
+        NLOHMANN_JSON_PASTE6, \
+        NLOHMANN_JSON_PASTE5, \
+        NLOHMANN_JSON_PASTE4, \
+        NLOHMANN_JSON_PASTE3, \
+        NLOHMANN_JSON_PASTE2, \
+        NLOHMANN_JSON_PASTE1)(__VA_ARGS__))
+#define NLOHMANN_JSON_PASTE2(func, v1) func(v1)
+#define NLOHMANN_JSON_PASTE3(func, v1, v2) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE2(func, v2)
+#define NLOHMANN_JSON_PASTE4(func, v1, v2, v3) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE3(func, v2, v3)
+#define NLOHMANN_JSON_PASTE5(func, v1, v2, v3, v4) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE4(func, v2, v3, v4)
+#define NLOHMANN_JSON_PASTE6(func, v1, v2, v3, v4, v5) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE5(func, v2, v3, v4, v5)
+#define NLOHMANN_JSON_PASTE7(func, v1, v2, v3, v4, v5, v6) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE6(func, v2, v3, v4, v5, v6)
+#define NLOHMANN_JSON_PASTE8(func, v1, v2, v3, v4, v5, v6, v7) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE7(func, v2, v3, v4, v5, v6, v7)
+#define NLOHMANN_JSON_PASTE9(func, v1, v2, v3, v4, v5, v6, v7, v8) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE8(func, v2, v3, v4, v5, v6, v7, v8)
+#define NLOHMANN_JSON_PASTE10(func, v1, v2, v3, v4, v5, v6, v7, v8, v9) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE9(func, v2, v3, v4, v5, v6, v7, v8, v9)
+#define NLOHMANN_JSON_PASTE11(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE10(func, v2, v3, v4, v5, v6, v7, v8, v9, v10)
+#define NLOHMANN_JSON_PASTE12(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE11(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11)
+#define NLOHMANN_JSON_PASTE13(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE12(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12)
+#define NLOHMANN_JSON_PASTE14(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE13(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13)
+#define NLOHMANN_JSON_PASTE15(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE14(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14)
+#define NLOHMANN_JSON_PASTE16(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE15(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15)
+#define NLOHMANN_JSON_PASTE17(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE16(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16)
+#define NLOHMANN_JSON_PASTE18(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE17(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17)
+#define NLOHMANN_JSON_PASTE19(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE18(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18)
+#define NLOHMANN_JSON_PASTE20(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE19(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19)
+#define NLOHMANN_JSON_PASTE21(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE20(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20)
+#define NLOHMANN_JSON_PASTE22(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE21(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21)
+#define NLOHMANN_JSON_PASTE23(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE22(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22)
+#define NLOHMANN_JSON_PASTE24(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE23(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23)
+#define NLOHMANN_JSON_PASTE25(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE24(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24)
+#define NLOHMANN_JSON_PASTE26(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE25(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25)
+#define NLOHMANN_JSON_PASTE27(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE26(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26)
+#define NLOHMANN_JSON_PASTE28(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE27(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27)
+#define NLOHMANN_JSON_PASTE29(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE28(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28)
+#define NLOHMANN_JSON_PASTE30(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE29(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29)
+#define NLOHMANN_JSON_PASTE31(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE30(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30)
+#define NLOHMANN_JSON_PASTE32(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE31(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31)
+#define NLOHMANN_JSON_PASTE33(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE32(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32)
+#define NLOHMANN_JSON_PASTE34(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE33(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33)
+#define NLOHMANN_JSON_PASTE35(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE34(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34)
+#define NLOHMANN_JSON_PASTE36(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE35(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35)
+#define NLOHMANN_JSON_PASTE37(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE36(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36)
+#define NLOHMANN_JSON_PASTE38(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE37(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37)
+#define NLOHMANN_JSON_PASTE39(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE38(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38)
+#define NLOHMANN_JSON_PASTE40(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE39(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39)
+#define NLOHMANN_JSON_PASTE41(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE40(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40)
+#define NLOHMANN_JSON_PASTE42(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE41(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41)
+#define NLOHMANN_JSON_PASTE43(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE42(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42)
+#define NLOHMANN_JSON_PASTE44(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE43(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43)
+#define NLOHMANN_JSON_PASTE45(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE44(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44)
+#define NLOHMANN_JSON_PASTE46(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE45(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45)
+#define NLOHMANN_JSON_PASTE47(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE46(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46)
+#define NLOHMANN_JSON_PASTE48(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE47(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47)
+#define NLOHMANN_JSON_PASTE49(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE48(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48)
+#define NLOHMANN_JSON_PASTE50(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE49(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49)
+#define NLOHMANN_JSON_PASTE51(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE50(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50)
+#define NLOHMANN_JSON_PASTE52(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE51(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51)
+#define NLOHMANN_JSON_PASTE53(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE52(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52)
+#define NLOHMANN_JSON_PASTE54(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE53(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53)
+#define NLOHMANN_JSON_PASTE55(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE54(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54)
+#define NLOHMANN_JSON_PASTE56(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE55(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55)
+#define NLOHMANN_JSON_PASTE57(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE56(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56)
+#define NLOHMANN_JSON_PASTE58(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE57(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57)
+#define NLOHMANN_JSON_PASTE59(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE58(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58)
+#define NLOHMANN_JSON_PASTE60(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE59(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59)
+#define NLOHMANN_JSON_PASTE61(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE60(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60)
+#define NLOHMANN_JSON_PASTE62(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE61(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61)
+#define NLOHMANN_JSON_PASTE63(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE62(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62)
+#define NLOHMANN_JSON_PASTE64(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE63(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63)
+
+#define NLOHMANN_JSON_TO(v1) nlohmann_json_j[#v1] = nlohmann_json_t.v1;
+#define NLOHMANN_JSON_FROM(v1) nlohmann_json_j.at(#v1).get_to(nlohmann_json_t.v1);
+#define NLOHMANN_JSON_FROM_WITH_DEFAULT(v1) nlohmann_json_t.v1 = !nlohmann_json_j.is_null() ? nlohmann_json_j.value(#v1, nlohmann_json_default_obj.v1) : nlohmann_json_default_obj.v1;
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_INTRUSIVE
+@since version 3.9.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_INTRUSIVE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_INTRUSIVE_WITH_DEFAULT
+@since version 3.11.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_INTRUSIVE_WITH_DEFAULT(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.11.3
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_INTRUSIVE_ONLY_SERIALIZE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE
+@since version 3.9.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_non_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_WITH_DEFAULT
+@since version 3.11.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_non_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_WITH_DEFAULT(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.11.3
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_non_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_WITH_DEFAULT
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_WITH_DEFAULT(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType&>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_ONLY_SERIALIZE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_WITH_DEFAULT
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_WITH_DEFAULT(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+// inspired from https://stackoverflow.com/a/26745591
+// allows calling any std function as if (e.g., with begin):
+// using std::begin; begin(x);
+//
+// it allows using the detected idiom to retrieve the return type
+// of such an expression
+#define NLOHMANN_CAN_CALL_STD_FUNC_IMPL(std_name)                                 \
+    namespace detail {                                                            \
+    using std::std_name;                                                          \
+    \
+    template<typename... T>                                                       \
+    using result_of_##std_name = decltype(std_name(std::declval<T>()...));        \
+    }                                                                             \
+    \
+    namespace detail2 {                                                           \
+    struct std_name##_tag                                                         \
+    {                                                                             \
+    };                                                                            \
+    \
+    template<typename... T>                                                       \
+    std_name##_tag std_name(T&&...);                                              \
+    \
+    template<typename... T>                                                       \
+    using result_of_##std_name = decltype(std_name(std::declval<T>()...));        \
+    \
+    template<typename... T>                                                       \
+    struct would_call_std_##std_name                                              \
+    {                                                                             \
+        static constexpr auto const value = ::nlohmann::detail::                  \
+                                            is_detected_exact<std_name##_tag, result_of_##std_name, T...>::value; \
+    };                                                                            \
+    } /* namespace detail2 */ \
+    \
+    template<typename... T>                                                       \
+    struct would_call_std_##std_name : detail2::would_call_std_##std_name<T...>   \
+    {                                                                             \
+    }
+
+#ifndef JSON_USE_IMPLICIT_CONVERSIONS
+    #define JSON_USE_IMPLICIT_CONVERSIONS 1
+#endif
+
+#if JSON_USE_IMPLICIT_CONVERSIONS
+    #define JSON_EXPLICIT
+#else
+    #define JSON_EXPLICIT explicit
+#endif
+
+#ifndef JSON_DISABLE_ENUM_SERIALIZATION
+    #define JSON_DISABLE_ENUM_SERIALIZATION 0
+#endif
+
+#ifndef JSON_USE_GLOBAL_UDLS
+    #define JSON_USE_GLOBAL_UDLS 1
+#endif
+
+#if JSON_HAS_THREE_WAY_COMPARISON
+    #include <compare> // partial_ordering
+#endif
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+///////////////////////////
+// JSON type enumeration //
+///////////////////////////
+
+/*!
+@brief the JSON type enumeration
+
+This enumeration collects the different JSON types. It is internally used to
+distinguish the stored values, and the functions @ref basic_json::is_null(),
+@ref basic_json::is_object(), @ref basic_json::is_array(),
+@ref basic_json::is_string(), @ref basic_json::is_boolean(),
+@ref basic_json::is_number() (with @ref basic_json::is_number_integer(),
+@ref basic_json::is_number_unsigned(), and @ref basic_json::is_number_float()),
+@ref basic_json::is_discarded(), @ref basic_json::is_primitive(), and
+@ref basic_json::is_structured() rely on it.
+
+@note There are three enumeration entries (number_integer, number_unsigned, and
+number_float), because the library distinguishes these three types for numbers:
+@ref basic_json::number_unsigned_t is used for unsigned integers,
+@ref basic_json::number_integer_t is used for signed integers, and
+@ref basic_json::number_float_t is used for floating-point numbers or to
+approximate integers which do not fit in the limits of their respective type.
+
+@sa see @ref basic_json::basic_json(const value_t value_type) -- create a JSON
+value with the default value for a given type
+
+@since version 1.0.0
+*/
+enum class value_t : std::uint8_t
+{
+    null,             ///< null value
+    object,           ///< object (unordered set of name/value pairs)
+    array,            ///< array (ordered collection of values)
+    string,           ///< string value
+    boolean,          ///< boolean value
+    number_integer,   ///< number value (signed integer)
+    number_unsigned,  ///< number value (unsigned integer)
+    number_float,     ///< number value (floating-point)
+    binary,           ///< binary array (ordered collection of bytes)
+    discarded         ///< discarded by the parser callback function
+};
+
+/*!
+@brief comparison operator for JSON types
+
+Returns an ordering that is similar to Python:
+- order: null < boolean < number < object < array < string < binary
+- furthermore, each type is not smaller than itself
+- discarded values are not comparable
+- binary is represented as a b"" string in python and directly comparable to a
+  string; however, making a binary array directly comparable with a string would
+  be surprising behavior in a JSON file.
+
+@since version 1.0.0
+*/
+#if JSON_HAS_THREE_WAY_COMPARISON
+    inline std::partial_ordering operator<=>(const value_t lhs, const value_t rhs) noexcept // *NOPAD*
+#else
+    inline bool operator<(const value_t lhs, const value_t rhs) noexcept
+#endif
+{
+    static constexpr std::array<std::uint8_t, 9> order = {{
+            0 /* null */, 3 /* object */, 4 /* array */, 5 /* string */,
+            1 /* boolean */, 2 /* integer */, 2 /* unsigned */, 2 /* float */,
+            6 /* binary */
+        }
+    };
+
+    const auto l_index = static_cast<std::size_t>(lhs);
+    const auto r_index = static_cast<std::size_t>(rhs);
+#if JSON_HAS_THREE_WAY_COMPARISON
+    if (l_index < order.size() && r_index < order.size())
+    {
+        return order[l_index] <=> order[r_index]; // *NOPAD*
+    }
+    return std::partial_ordering::unordered;
+#else
+    return l_index < order.size() && r_index < order.size() && order[l_index] < order[r_index];
+#endif
+}
+
+// GCC selects the built-in operator< over an operator rewritten from
+// a user-defined spaceship operator
+// Clang, MSVC, and ICC select the rewritten candidate
+// (see GCC bug https://gcc.gnu.org/bugzilla/show_bug.cgi?id=105200)
+#if JSON_HAS_THREE_WAY_COMPARISON && defined(__GNUC__)
+inline bool operator<(const value_t lhs, const value_t rhs) noexcept
+{
+    return std::is_lt(lhs <=> rhs); // *NOPAD*
+}
+#endif
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/string_escape.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief replace all occurrences of a substring by another string
+
+@param[in,out] s  the string to manipulate; changed so that all
+               occurrences of @a f are replaced with @a t
+@param[in]     f  the substring to replace with @a t
+@param[in]     t  the string to replace @a f
+
+@pre The search string @a f must not be empty. **This precondition is
+enforced with an assertion.**
+
+@since version 2.0.0
+*/
+template<typename StringType>
+inline void replace_substring(StringType& s, const StringType& f,
+                              const StringType& t)
+{
+    JSON_ASSERT(!f.empty());
+    for (auto pos = s.find(f);                // find first occurrence of f
+            pos != StringType::npos;          // make sure f was found
+            s.replace(pos, f.size(), t),      // replace with t, and
+            pos = s.find(f, pos + t.size()))  // find next occurrence of f
+    {}
+}
+
+/*!
+ * @brief string escaping as described in RFC 6901 (Sect. 4)
+ * @param[in] s string to escape
+ * @return    escaped string
+ *
+ * Note the order of escaping "~" to "~0" and "/" to "~1" is important.
+ */
+template<typename StringType>
+inline StringType escape(StringType s)
+{
+    replace_substring(s, StringType{"~"}, StringType{"~0"});
+    replace_substring(s, StringType{"/"}, StringType{"~1"});
+    return s;
+}
+
+/*!
+ * @brief string unescaping as described in RFC 6901 (Sect. 4)
+ * @param[in] s string to unescape
+ * @return    unescaped string
+ *
+ * Note the order of escaping "~1" to "/" and "~0" to "~" is important.
+ */
+template<typename StringType>
+static void unescape(StringType& s)
+{
+    replace_substring(s, StringType{"~1"}, StringType{"/"});
+    replace_substring(s, StringType{"~0"}, StringType{"~"});
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/position_t.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // size_t
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// struct to capture the start position of the current token
+struct position_t
+{
+    /// the total number of characters read
+    std::size_t chars_read_total = 0;
+    /// the number of characters read in the current line
+    std::size_t chars_read_current_line = 0;
+    /// the number of lines read
+    std::size_t lines_read = 0;
+
+    /// conversion to size_t to preserve SAX interface
+    constexpr operator size_t() const
+    {
+        return chars_read_total;
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-FileCopyrightText: 2018 The Abseil Authors
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstddef> // size_t
+#include <type_traits> // conditional, enable_if, false_type, integral_constant, is_constructible, is_integral, is_same, remove_cv, remove_reference, true_type
+#include <utility> // index_sequence, make_index_sequence, index_sequence_for
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename T>
+using uncvref_t = typename std::remove_cv<typename std::remove_reference<T>::type>::type;
+
+#ifdef JSON_HAS_CPP_14
+
+// the following utilities are natively available in C++14
+using std::enable_if_t;
+using std::index_sequence;
+using std::make_index_sequence;
+using std::index_sequence_for;
+
+#else
+
+// alias templates to reduce boilerplate
+template<bool B, typename T = void>
+using enable_if_t = typename std::enable_if<B, T>::type;
+
+// The following code is taken from https://github.com/abseil/abseil-cpp/blob/10cb35e459f5ecca5b2ff107635da0bfa41011b4/absl/utility/utility.h
+// which is part of Google Abseil (https://github.com/abseil/abseil-cpp), licensed under the Apache License 2.0.
+
+//// START OF CODE FROM GOOGLE ABSEIL
+
+// integer_sequence
+//
+// Class template representing a compile-time integer sequence. An instantiation
+// of `integer_sequence<T, Ints...>` has a sequence of integers encoded in its
+// type through its template arguments (which is a common need when
+// working with C++11 variadic templates). `absl::integer_sequence` is designed
+// to be a drop-in replacement for C++14's `std::integer_sequence`.
+//
+// Example:
+//
+//   template< class T, T... Ints >
+//   void user_function(integer_sequence<T, Ints...>);
+//
+//   int main()
+//   {
+//     // user_function's `T` will be deduced to `int` and `Ints...`
+//     // will be deduced to `0, 1, 2, 3, 4`.
+//     user_function(make_integer_sequence<int, 5>());
+//   }
+template <typename T, T... Ints>
+struct integer_sequence
+{
+    using value_type = T;
+    static constexpr std::size_t size() noexcept
+    {
+        return sizeof...(Ints);
+    }
+};
+
+// index_sequence
+//
+// A helper template for an `integer_sequence` of `size_t`,
+// `absl::index_sequence` is designed to be a drop-in replacement for C++14's
+// `std::index_sequence`.
+template <size_t... Ints>
+using index_sequence = integer_sequence<size_t, Ints...>;
+
+namespace utility_internal
+{
+
+template <typename Seq, size_t SeqSize, size_t Rem>
+struct Extend;
+
+// Note that SeqSize == sizeof...(Ints). It's passed explicitly for efficiency.
+template <typename T, T... Ints, size_t SeqSize>
+struct Extend<integer_sequence<T, Ints...>, SeqSize, 0>
+{
+    using type = integer_sequence < T, Ints..., (Ints + SeqSize)... >;
+};
+
+template <typename T, T... Ints, size_t SeqSize>
+struct Extend<integer_sequence<T, Ints...>, SeqSize, 1>
+{
+    using type = integer_sequence < T, Ints..., (Ints + SeqSize)..., 2 * SeqSize >;
+};
+
+// Recursion helper for 'make_integer_sequence<T, N>'.
+// 'Gen<T, N>::type' is an alias for 'integer_sequence<T, 0, 1, ... N-1>'.
+template <typename T, size_t N>
+struct Gen
+{
+    using type =
+        typename Extend < typename Gen < T, N / 2 >::type, N / 2, N % 2 >::type;
+};
+
+template <typename T>
+struct Gen<T, 0>
+{
+    using type = integer_sequence<T>;
+};
+
+}  // namespace utility_internal
+
+// Compile-time sequences of integers
+
+// make_integer_sequence
+//
+// This template alias is equivalent to
+// `integer_sequence<int, 0, 1, ..., N-1>`, and is designed to be a drop-in
+// replacement for C++14's `std::make_integer_sequence`.
+template <typename T, T N>
+using make_integer_sequence = typename utility_internal::Gen<T, N>::type;
+
+// make_index_sequence
+//
+// This template alias is equivalent to `index_sequence<0, 1, ..., N-1>`,
+// and is designed to be a drop-in replacement for C++14's
+// `std::make_index_sequence`.
+template <size_t N>
+using make_index_sequence = make_integer_sequence<size_t, N>;
+
+// index_sequence_for
+//
+// Converts a typename pack into an index sequence of the same length, and
+// is designed to be a drop-in replacement for C++14's
+// `std::index_sequence_for()`
+template <typename... Ts>
+using index_sequence_for = make_index_sequence<sizeof...(Ts)>;
+
+//// END OF CODE FROM GOOGLE ABSEIL
+
+#endif
+
+// dispatch utility (taken from ranges-v3)
+template<unsigned N> struct priority_tag : priority_tag < N - 1 > {};
+template<> struct priority_tag<0> {};
+
+// taken from ranges-v3
+template<typename T>
+struct static_const
+{
+    static JSON_INLINE_VARIABLE constexpr T value{};
+};
+
+#ifndef JSON_HAS_CPP_17
+    template<typename T>
+    constexpr T static_const<T>::value;
+#endif
+
+template<typename T, typename... Args>
+constexpr std::array<T, sizeof...(Args)> make_array(Args&& ... args)
+{
+    return std::array<T, sizeof...(Args)> {{static_cast<T>(std::forward<Args>(args))...}};
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <limits> // numeric_limits
+#include <string> // char_traits
+#include <tuple> // tuple
+#include <type_traits> // false_type, is_constructible, is_integral, is_same, true_type
+#include <utility> // declval
+
+// #include <nlohmann/detail/iterators/iterator_traits.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <iterator> // random_access_iterator_tag
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/void_t.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename It, typename = void>
+struct iterator_types {};
+
+template<typename It>
+struct iterator_types <
+    It,
+    void_t<typename It::difference_type, typename It::value_type, typename It::pointer,
+    typename It::reference, typename It::iterator_category >>
+{
+    using difference_type = typename It::difference_type;
+    using value_type = typename It::value_type;
+    using pointer = typename It::pointer;
+    using reference = typename It::reference;
+    using iterator_category = typename It::iterator_category;
+};
+
+// This is required as some compilers implement std::iterator_traits in a way that
+// doesn't work with SFINAE. See https://github.com/nlohmann/json/issues/1341.
+template<typename T, typename = void>
+struct iterator_traits
+{
+};
+
+template<typename T>
+struct iterator_traits < T, enable_if_t < !std::is_pointer<T>::value >>
+    : iterator_types<T>
+{
+};
+
+template<typename T>
+struct iterator_traits<T*, enable_if_t<std::is_object<T>::value>>
+{
+    using iterator_category = std::random_access_iterator_tag;
+    using value_type = T;
+    using difference_type = ptrdiff_t;
+    using pointer = T*;
+    using reference = T&;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/call_std/begin.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+NLOHMANN_CAN_CALL_STD_FUNC_IMPL(begin);
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/call_std/end.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+NLOHMANN_CAN_CALL_STD_FUNC_IMPL(end);
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/detected.hpp>
+
+// #include <nlohmann/json_fwd.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+#ifndef INCLUDE_NLOHMANN_JSON_FWD_HPP_
+    #define INCLUDE_NLOHMANN_JSON_FWD_HPP_
+
+    #include <cstdint> // int64_t, uint64_t
+    #include <map> // map
+    #include <memory> // allocator
+    #include <string> // string
+    #include <vector> // vector
+
+    // #include <nlohmann/detail/abi_macros.hpp>
+
+
+    /*!
+    @brief namespace for Niels Lohmann
+    @see https://github.com/nlohmann
+    @since version 1.0.0
+    */
+    NLOHMANN_JSON_NAMESPACE_BEGIN
+
+    /*!
+    @brief default JSONSerializer template argument
+
+    This serializer ignores the template arguments and uses ADL
+    ([argument-dependent lookup](https://en.cppreference.com/w/cpp/language/adl))
+    for serialization.
+    */
+    template<typename T = void, typename SFINAE = void>
+    struct adl_serializer;
+
+    /// a class to store JSON values
+    /// @sa https://json.nlohmann.me/api/basic_json/
+    template<template<typename U, typename V, typename... Args> class ObjectType =
+    std::map,
+    template<typename U, typename... Args> class ArrayType = std::vector,
+    class StringType = std::string, class BooleanType = bool,
+    class NumberIntegerType = std::int64_t,
+    class NumberUnsignedType = std::uint64_t,
+    class NumberFloatType = double,
+    template<typename U> class AllocatorType = std::allocator,
+    template<typename T, typename SFINAE = void> class JSONSerializer =
+    adl_serializer,
+    class BinaryType = std::vector<std::uint8_t>, // cppcheck-suppress syntaxError
+    class CustomBaseClass = void>
+    class basic_json;
+
+    /// @brief JSON Pointer defines a string syntax for identifying a specific value within a JSON document
+    /// @sa https://json.nlohmann.me/api/json_pointer/
+    template<typename RefStringType>
+    class json_pointer;
+
+    /*!
+    @brief default specialization
+    @sa https://json.nlohmann.me/api/json/
+    */
+    using json = basic_json<>;
+
+    /// @brief a minimal map-like container that preserves insertion order
+    /// @sa https://json.nlohmann.me/api/ordered_map/
+    template<class Key, class T, class IgnoredLess, class Allocator>
+    struct ordered_map;
+
+    /// @brief specialization that maintains the insertion order of object keys
+    /// @sa https://json.nlohmann.me/api/ordered_json/
+    using ordered_json = basic_json<nlohmann::ordered_map>;
+
+    NLOHMANN_JSON_NAMESPACE_END
+
+#endif  // INCLUDE_NLOHMANN_JSON_FWD_HPP_
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+/*!
+@brief detail namespace with internal helper functions
+
+This namespace collects functions that should not be exposed,
+implementations of some @ref basic_json methods, and meta-programming helpers.
+
+@since version 2.1.0
+*/
+namespace detail
+{
+
+/////////////
+// helpers //
+/////////////
+
+// Note to maintainers:
+//
+// Every trait in this file expects a non CV-qualified type.
+// The only exceptions are in the 'aliases for detected' section
+// (i.e. those of the form: decltype(T::member_function(std::declval<T>())))
+//
+// In this case, T has to be properly CV-qualified to constraint the function arguments
+// (e.g. to_json(BasicJsonType&, const T&))
+
+template<typename> struct is_basic_json : std::false_type {};
+
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+struct is_basic_json<NLOHMANN_BASIC_JSON_TPL> : std::true_type {};
+
+// used by exceptions create() member functions
+// true_type for pointer to possibly cv-qualified basic_json or std::nullptr_t
+// false_type otherwise
+template<typename BasicJsonContext>
+struct is_basic_json_context :
+    std::integral_constant < bool,
+    is_basic_json<typename std::remove_cv<typename std::remove_pointer<BasicJsonContext>::type>::type>::value
+    || std::is_same<BasicJsonContext, std::nullptr_t>::value >
+{};
+
+//////////////////////
+// json_ref helpers //
+//////////////////////
+
+template<typename>
+class json_ref;
+
+template<typename>
+struct is_json_ref : std::false_type {};
+
+template<typename T>
+struct is_json_ref<json_ref<T>> : std::true_type {};
+
+//////////////////////////
+// aliases for detected //
+//////////////////////////
+
+template<typename T>
+using mapped_type_t = typename T::mapped_type;
+
+template<typename T>
+using key_type_t = typename T::key_type;
+
+template<typename T>
+using value_type_t = typename T::value_type;
+
+template<typename T>
+using difference_type_t = typename T::difference_type;
+
+template<typename T>
+using pointer_t = typename T::pointer;
+
+template<typename T>
+using reference_t = typename T::reference;
+
+template<typename T>
+using iterator_category_t = typename T::iterator_category;
+
+template<typename T, typename... Args>
+using to_json_function = decltype(T::to_json(std::declval<Args>()...));
+
+template<typename T, typename... Args>
+using from_json_function = decltype(T::from_json(std::declval<Args>()...));
+
+template<typename T, typename U>
+using get_template_function = decltype(std::declval<T>().template get<U>());
+
+// trait checking if JSONSerializer<T>::from_json(json const&, udt&) exists
+template<typename BasicJsonType, typename T, typename = void>
+struct has_from_json : std::false_type {};
+
+// trait checking if j.get<T> is valid
+// use this trait instead of std::is_constructible or std::is_convertible,
+// both rely on, or make use of implicit conversions, and thus fail when T
+// has several constructors/operator= (see https://github.com/nlohmann/json/issues/958)
+template <typename BasicJsonType, typename T>
+struct is_getable
+{
+    static constexpr bool value = is_detected<get_template_function, const BasicJsonType&, T>::value;
+};
+
+template<typename BasicJsonType, typename T>
+struct has_from_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>
+{
+    using serializer = typename BasicJsonType::template json_serializer<T, void>;
+
+    static constexpr bool value =
+        is_detected_exact<void, from_json_function, serializer,
+        const BasicJsonType&, T&>::value;
+};
+
+// This trait checks if JSONSerializer<T>::from_json(json const&) exists
+// this overload is used for non-default-constructible user-defined-types
+template<typename BasicJsonType, typename T, typename = void>
+struct has_non_default_from_json : std::false_type {};
+
+template<typename BasicJsonType, typename T>
+struct has_non_default_from_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>
+{
+    using serializer = typename BasicJsonType::template json_serializer<T, void>;
+
+    static constexpr bool value =
+        is_detected_exact<T, from_json_function, serializer,
+        const BasicJsonType&>::value;
+};
+
+// This trait checks if BasicJsonType::json_serializer<T>::to_json exists
+// Do not evaluate the trait when T is a basic_json type, to avoid template instantiation infinite recursion.
+template<typename BasicJsonType, typename T, typename = void>
+struct has_to_json : std::false_type {};
+
+template<typename BasicJsonType, typename T>
+struct has_to_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>
+{
+    using serializer = typename BasicJsonType::template json_serializer<T, void>;
+
+    static constexpr bool value =
+        is_detected_exact<void, to_json_function, serializer, BasicJsonType&,
+        T>::value;
+};
+
+template<typename T>
+using detect_key_compare = typename T::key_compare;
+
+template<typename T>
+struct has_key_compare : std::integral_constant<bool, is_detected<detect_key_compare, T>::value> {};
+
+// obtains the actual object key comparator
+template<typename BasicJsonType>
+struct actual_object_comparator
+{
+    using object_t = typename BasicJsonType::object_t;
+    using object_comparator_t = typename BasicJsonType::default_object_comparator_t;
+    using type = typename std::conditional < has_key_compare<object_t>::value,
+          typename object_t::key_compare, object_comparator_t>::type;
+};
+
+template<typename BasicJsonType>
+using actual_object_comparator_t = typename actual_object_comparator<BasicJsonType>::type;
+
+/////////////////
+// char_traits //
+/////////////////
+
+// Primary template of char_traits calls std char_traits
+template<typename T>
+struct char_traits : std::char_traits<T>
+{};
+
+// Explicitly define char traits for unsigned char since it is not standard
+template<>
+struct char_traits<unsigned char> : std::char_traits<char>
+{
+    using char_type = unsigned char;
+    using int_type = uint64_t;
+
+    // Redefine to_int_type function
+    static int_type to_int_type(char_type c) noexcept
+    {
+        return static_cast<int_type>(c);
+    }
+
+    static char_type to_char_type(int_type i) noexcept
+    {
+        return static_cast<char_type>(i);
+    }
+
+    static constexpr int_type eof() noexcept
+    {
+        return static_cast<int_type>(std::char_traits<char>::eof());
+    }
+};
+
+// Explicitly define char traits for signed char since it is not standard
+template<>
+struct char_traits<signed char> : std::char_traits<char>
+{
+    using char_type = signed char;
+    using int_type = uint64_t;
+
+    // Redefine to_int_type function
+    static int_type to_int_type(char_type c) noexcept
+    {
+        return static_cast<int_type>(c);
+    }
+
+    static char_type to_char_type(int_type i) noexcept
+    {
+        return static_cast<char_type>(i);
+    }
+
+    static constexpr int_type eof() noexcept
+    {
+        return static_cast<int_type>(std::char_traits<char>::eof());
+    }
+};
+
+///////////////////
+// is_ functions //
+///////////////////
+
+// https://en.cppreference.com/w/cpp/types/conjunction
+template<class...> struct conjunction : std::true_type { };
+template<class B> struct conjunction<B> : B { };
+template<class B, class... Bn>
+struct conjunction<B, Bn...>
+: std::conditional<static_cast<bool>(B::value), conjunction<Bn...>, B>::type {};
+
+// https://en.cppreference.com/w/cpp/types/negation
+template<class B> struct negation : std::integral_constant < bool, !B::value > { };
+
+// Reimplementation of is_constructible and is_default_constructible, due to them being broken for
+// std::pair and std::tuple until LWG 2367 fix (see https://cplusplus.github.io/LWG/lwg-defects.html#2367).
+// This causes compile errors in e.g. clang 3.5 or gcc 4.9.
+template <typename T>
+struct is_default_constructible : std::is_default_constructible<T> {};
+
+template <typename T1, typename T2>
+struct is_default_constructible<std::pair<T1, T2>>
+    : conjunction<is_default_constructible<T1>, is_default_constructible<T2>> {};
+
+template <typename T1, typename T2>
+struct is_default_constructible<const std::pair<T1, T2>>
+    : conjunction<is_default_constructible<T1>, is_default_constructible<T2>> {};
+
+template <typename... Ts>
+struct is_default_constructible<std::tuple<Ts...>>
+    : conjunction<is_default_constructible<Ts>...> {};
+
+template <typename... Ts>
+struct is_default_constructible<const std::tuple<Ts...>>
+    : conjunction<is_default_constructible<Ts>...> {};
+
+template <typename T, typename... Args>
+struct is_constructible : std::is_constructible<T, Args...> {};
+
+template <typename T1, typename T2>
+struct is_constructible<std::pair<T1, T2>> : is_default_constructible<std::pair<T1, T2>> {};
+
+template <typename T1, typename T2>
+struct is_constructible<const std::pair<T1, T2>> : is_default_constructible<const std::pair<T1, T2>> {};
+
+template <typename... Ts>
+struct is_constructible<std::tuple<Ts...>> : is_default_constructible<std::tuple<Ts...>> {};
+
+template <typename... Ts>
+struct is_constructible<const std::tuple<Ts...>> : is_default_constructible<const std::tuple<Ts...>> {};
+
+template<typename T, typename = void>
+struct is_iterator_traits : std::false_type {};
+
+template<typename T>
+struct is_iterator_traits<iterator_traits<T>>
+{
+  private:
+    using traits = iterator_traits<T>;
+
+  public:
+    static constexpr auto value =
+        is_detected<value_type_t, traits>::value &&
+        is_detected<difference_type_t, traits>::value &&
+        is_detected<pointer_t, traits>::value &&
+        is_detected<iterator_category_t, traits>::value &&
+        is_detected<reference_t, traits>::value;
+};
+
+template<typename T>
+struct is_range
+{
+  private:
+    using t_ref = typename std::add_lvalue_reference<T>::type;
+
+    using iterator = detected_t<result_of_begin, t_ref>;
+    using sentinel = detected_t<result_of_end, t_ref>;
+
+    // to be 100% correct, it should use https://en.cppreference.com/w/cpp/iterator/input_or_output_iterator
+    // and https://en.cppreference.com/w/cpp/iterator/sentinel_for
+    // but reimplementing these would be too much work, as a lot of other concepts are used underneath
+    static constexpr auto is_iterator_begin =
+        is_iterator_traits<iterator_traits<iterator>>::value;
+
+  public:
+    static constexpr bool value = !std::is_same<iterator, nonesuch>::value && !std::is_same<sentinel, nonesuch>::value && is_iterator_begin;
+};
+
+template<typename R>
+using iterator_t = enable_if_t<is_range<R>::value, result_of_begin<decltype(std::declval<R&>())>>;
+
+template<typename T>
+using range_value_t = value_type_t<iterator_traits<iterator_t<T>>>;
+
+// The following implementation of is_complete_type is taken from
+// https://blogs.msdn.microsoft.com/vcblog/2015/12/02/partial-support-for-expression-sfinae-in-vs-2015-update-1/
+// and is written by Xiang Fan who agreed to using it in this library.
+
+template<typename T, typename = void>
+struct is_complete_type : std::false_type {};
+
+template<typename T>
+struct is_complete_type<T, decltype(void(sizeof(T)))> : std::true_type {};
+
+template<typename BasicJsonType, typename CompatibleObjectType,
+         typename = void>
+struct is_compatible_object_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename CompatibleObjectType>
+struct is_compatible_object_type_impl <
+    BasicJsonType, CompatibleObjectType,
+    enable_if_t < is_detected<mapped_type_t, CompatibleObjectType>::value&&
+    is_detected<key_type_t, CompatibleObjectType>::value >>
+{
+    using object_t = typename BasicJsonType::object_t;
+
+    // macOS's is_constructible does not play well with nonesuch...
+    static constexpr bool value =
+        is_constructible<typename object_t::key_type,
+        typename CompatibleObjectType::key_type>::value &&
+        is_constructible<typename object_t::mapped_type,
+        typename CompatibleObjectType::mapped_type>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleObjectType>
+struct is_compatible_object_type
+    : is_compatible_object_type_impl<BasicJsonType, CompatibleObjectType> {};
+
+template<typename BasicJsonType, typename ConstructibleObjectType,
+         typename = void>
+struct is_constructible_object_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename ConstructibleObjectType>
+struct is_constructible_object_type_impl <
+    BasicJsonType, ConstructibleObjectType,
+    enable_if_t < is_detected<mapped_type_t, ConstructibleObjectType>::value&&
+    is_detected<key_type_t, ConstructibleObjectType>::value >>
+{
+    using object_t = typename BasicJsonType::object_t;
+
+    static constexpr bool value =
+        (is_default_constructible<ConstructibleObjectType>::value &&
+         (std::is_move_assignable<ConstructibleObjectType>::value ||
+          std::is_copy_assignable<ConstructibleObjectType>::value) &&
+         (is_constructible<typename ConstructibleObjectType::key_type,
+          typename object_t::key_type>::value &&
+          std::is_same <
+          typename object_t::mapped_type,
+          typename ConstructibleObjectType::mapped_type >::value)) ||
+        (has_from_json<BasicJsonType,
+         typename ConstructibleObjectType::mapped_type>::value ||
+         has_non_default_from_json <
+         BasicJsonType,
+         typename ConstructibleObjectType::mapped_type >::value);
+};
+
+template<typename BasicJsonType, typename ConstructibleObjectType>
+struct is_constructible_object_type
+    : is_constructible_object_type_impl<BasicJsonType,
+      ConstructibleObjectType> {};
+
+template<typename BasicJsonType, typename CompatibleStringType>
+struct is_compatible_string_type
+{
+    static constexpr auto value =
+        is_constructible<typename BasicJsonType::string_t, CompatibleStringType>::value;
+};
+
+template<typename BasicJsonType, typename ConstructibleStringType>
+struct is_constructible_string_type
+{
+    // launder type through decltype() to fix compilation failure on ICPC
+#ifdef __INTEL_COMPILER
+    using laundered_type = decltype(std::declval<ConstructibleStringType>());
+#else
+    using laundered_type = ConstructibleStringType;
+#endif
+
+    static constexpr auto value =
+        conjunction <
+        is_constructible<laundered_type, typename BasicJsonType::string_t>,
+        is_detected_exact<typename BasicJsonType::string_t::value_type,
+        value_type_t, laundered_type >>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleArrayType, typename = void>
+struct is_compatible_array_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename CompatibleArrayType>
+struct is_compatible_array_type_impl <
+    BasicJsonType, CompatibleArrayType,
+    enable_if_t <
+    is_detected<iterator_t, CompatibleArrayType>::value&&
+    is_iterator_traits<iterator_traits<detected_t<iterator_t, CompatibleArrayType>>>::value&&
+// special case for types like std::filesystem::path whose iterator's value_type are themselves
+// c.f. https://github.com/nlohmann/json/pull/3073
+    !std::is_same<CompatibleArrayType, detected_t<range_value_t, CompatibleArrayType>>::value >>
+{
+    static constexpr bool value =
+        is_constructible<BasicJsonType,
+        range_value_t<CompatibleArrayType>>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleArrayType>
+struct is_compatible_array_type
+    : is_compatible_array_type_impl<BasicJsonType, CompatibleArrayType> {};
+
+template<typename BasicJsonType, typename ConstructibleArrayType, typename = void>
+struct is_constructible_array_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename ConstructibleArrayType>
+struct is_constructible_array_type_impl <
+    BasicJsonType, ConstructibleArrayType,
+    enable_if_t<std::is_same<ConstructibleArrayType,
+    typename BasicJsonType::value_type>::value >>
+            : std::true_type {};
+
+template<typename BasicJsonType, typename ConstructibleArrayType>
+struct is_constructible_array_type_impl <
+    BasicJsonType, ConstructibleArrayType,
+    enable_if_t < !std::is_same<ConstructibleArrayType,
+    typename BasicJsonType::value_type>::value&&
+    !is_compatible_string_type<BasicJsonType, ConstructibleArrayType>::value&&
+    is_default_constructible<ConstructibleArrayType>::value&&
+(std::is_move_assignable<ConstructibleArrayType>::value ||
+ std::is_copy_assignable<ConstructibleArrayType>::value)&&
+is_detected<iterator_t, ConstructibleArrayType>::value&&
+is_iterator_traits<iterator_traits<detected_t<iterator_t, ConstructibleArrayType>>>::value&&
+is_detected<range_value_t, ConstructibleArrayType>::value&&
+// special case for types like std::filesystem::path whose iterator's value_type are themselves
+// c.f. https://github.com/nlohmann/json/pull/3073
+!std::is_same<ConstructibleArrayType, detected_t<range_value_t, ConstructibleArrayType>>::value&&
+is_complete_type <
+detected_t<range_value_t, ConstructibleArrayType >>::value >>
+{
+    using value_type = range_value_t<ConstructibleArrayType>;
+
+    static constexpr bool value =
+        std::is_same<value_type,
+        typename BasicJsonType::array_t::value_type>::value ||
+        has_from_json<BasicJsonType,
+        value_type>::value ||
+        has_non_default_from_json <
+        BasicJsonType,
+        value_type >::value;
+};
+
+template<typename BasicJsonType, typename ConstructibleArrayType>
+struct is_constructible_array_type
+    : is_constructible_array_type_impl<BasicJsonType, ConstructibleArrayType> {};
+
+template<typename RealIntegerType, typename CompatibleNumberIntegerType,
+         typename = void>
+struct is_compatible_integer_type_impl : std::false_type {};
+
+template<typename RealIntegerType, typename CompatibleNumberIntegerType>
+struct is_compatible_integer_type_impl <
+    RealIntegerType, CompatibleNumberIntegerType,
+    enable_if_t < std::is_integral<RealIntegerType>::value&&
+    std::is_integral<CompatibleNumberIntegerType>::value&&
+    !std::is_same<bool, CompatibleNumberIntegerType>::value >>
+{
+    // is there an assert somewhere on overflows?
+    using RealLimits = std::numeric_limits<RealIntegerType>;
+    using CompatibleLimits = std::numeric_limits<CompatibleNumberIntegerType>;
+
+    static constexpr auto value =
+        is_constructible<RealIntegerType,
+        CompatibleNumberIntegerType>::value &&
+        CompatibleLimits::is_integer &&
+        RealLimits::is_signed == CompatibleLimits::is_signed;
+};
+
+template<typename RealIntegerType, typename CompatibleNumberIntegerType>
+struct is_compatible_integer_type
+    : is_compatible_integer_type_impl<RealIntegerType,
+      CompatibleNumberIntegerType> {};
+
+template<typename BasicJsonType, typename CompatibleType, typename = void>
+struct is_compatible_type_impl: std::false_type {};
+
+template<typename BasicJsonType, typename CompatibleType>
+struct is_compatible_type_impl <
+    BasicJsonType, CompatibleType,
+    enable_if_t<is_complete_type<CompatibleType>::value >>
+{
+    static constexpr bool value =
+        has_to_json<BasicJsonType, CompatibleType>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleType>
+struct is_compatible_type
+    : is_compatible_type_impl<BasicJsonType, CompatibleType> {};
+
+template<typename T1, typename T2>
+struct is_constructible_tuple : std::false_type {};
+
+template<typename T1, typename... Args>
+struct is_constructible_tuple<T1, std::tuple<Args...>> : conjunction<is_constructible<T1, Args>...> {};
+
+template<typename BasicJsonType, typename T>
+struct is_json_iterator_of : std::false_type {};
+
+template<typename BasicJsonType>
+struct is_json_iterator_of<BasicJsonType, typename BasicJsonType::iterator> : std::true_type {};
+
+template<typename BasicJsonType>
+struct is_json_iterator_of<BasicJsonType, typename BasicJsonType::const_iterator> : std::true_type
+{};
+
+// checks if a given type T is a template specialization of Primary
+template<template <typename...> class Primary, typename T>
+struct is_specialization_of : std::false_type {};
+
+template<template <typename...> class Primary, typename... Args>
+struct is_specialization_of<Primary, Primary<Args...>> : std::true_type {};
+
+template<typename T>
+using is_json_pointer = is_specialization_of<::nlohmann::json_pointer, uncvref_t<T>>;
+
+// checks if A and B are comparable using Compare functor
+template<typename Compare, typename A, typename B, typename = void>
+struct is_comparable : std::false_type {};
+
+template<typename Compare, typename A, typename B>
+struct is_comparable<Compare, A, B, void_t<
+decltype(std::declval<Compare>()(std::declval<A>(), std::declval<B>())),
+decltype(std::declval<Compare>()(std::declval<B>(), std::declval<A>()))
+>> : std::true_type {};
+
+template<typename T>
+using detect_is_transparent = typename T::is_transparent;
+
+// type trait to check if KeyType can be used as object key (without a BasicJsonType)
+// see is_usable_as_basic_json_key_type below
+template<typename Comparator, typename ObjectKeyType, typename KeyTypeCVRef, bool RequireTransparentComparator = true,
+         bool ExcludeObjectKeyType = RequireTransparentComparator, typename KeyType = uncvref_t<KeyTypeCVRef>>
+using is_usable_as_key_type = typename std::conditional <
+                              is_comparable<Comparator, ObjectKeyType, KeyTypeCVRef>::value
+                              && !(ExcludeObjectKeyType && std::is_same<KeyType,
+                                   ObjectKeyType>::value)
+                              && (!RequireTransparentComparator
+                                  || is_detected <detect_is_transparent, Comparator>::value)
+                              && !is_json_pointer<KeyType>::value,
+                              std::true_type,
+                              std::false_type >::type;
+
+// type trait to check if KeyType can be used as object key
+// true if:
+//   - KeyType is comparable with BasicJsonType::object_t::key_type
+//   - if ExcludeObjectKeyType is true, KeyType is not BasicJsonType::object_t::key_type
+//   - the comparator is transparent or RequireTransparentComparator is false
+//   - KeyType is not a JSON iterator or json_pointer
+template<typename BasicJsonType, typename KeyTypeCVRef, bool RequireTransparentComparator = true,
+         bool ExcludeObjectKeyType = RequireTransparentComparator, typename KeyType = uncvref_t<KeyTypeCVRef>>
+using is_usable_as_basic_json_key_type = typename std::conditional <
+    is_usable_as_key_type<typename BasicJsonType::object_comparator_t,
+    typename BasicJsonType::object_t::key_type, KeyTypeCVRef,
+    RequireTransparentComparator, ExcludeObjectKeyType>::value
+    && !is_json_iterator_of<BasicJsonType, KeyType>::value,
+    std::true_type,
+    std::false_type >::type;
+
+template<typename ObjectType, typename KeyType>
+using detect_erase_with_key_type = decltype(std::declval<ObjectType&>().erase(std::declval<KeyType>()));
+
+// type trait to check if object_t has an erase() member functions accepting KeyType
+template<typename BasicJsonType, typename KeyType>
+using has_erase_with_key_type = typename std::conditional <
+                                is_detected <
+                                detect_erase_with_key_type,
+                                typename BasicJsonType::object_t, KeyType >::value,
+                                std::true_type,
+                                std::false_type >::type;
+
+// a naive helper to check if a type is an ordered_map (exploits the fact that
+// ordered_map inherits capacity() from std::vector)
+template <typename T>
+struct is_ordered_map
+{
+    using one = char;
+
+    struct two
+    {
+        char x[2]; // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+    };
+
+    template <typename C> static one test( decltype(&C::capacity) ) ;
+    template <typename C> static two test(...);
+
+    enum { value = sizeof(test<T>(nullptr)) == sizeof(char) }; // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+};
+
+// to avoid useless casts (see https://github.com/nlohmann/json/issues/2893#issuecomment-889152324)
+template < typename T, typename U, enable_if_t < !std::is_same<T, U>::value, int > = 0 >
+T conditional_static_cast(U value)
+{
+    return static_cast<T>(value);
+}
+
+template<typename T, typename U, enable_if_t<std::is_same<T, U>::value, int> = 0>
+T conditional_static_cast(U value)
+{
+    return value;
+}
+
+template<typename... Types>
+using all_integral = conjunction<std::is_integral<Types>...>;
+
+template<typename... Types>
+using all_signed = conjunction<std::is_signed<Types>...>;
+
+template<typename... Types>
+using all_unsigned = conjunction<std::is_unsigned<Types>...>;
+
+// there's a disjunction trait in another PR; replace when merged
+template<typename... Types>
+using same_sign = std::integral_constant < bool,
+      all_signed<Types...>::value || all_unsigned<Types...>::value >;
+
+template<typename OfType, typename T>
+using never_out_of_range = std::integral_constant < bool,
+      (std::is_signed<OfType>::value && (sizeof(T) < sizeof(OfType)))
+      || (same_sign<OfType, T>::value && sizeof(OfType) == sizeof(T)) >;
+
+template<typename OfType, typename T,
+         bool OfTypeSigned = std::is_signed<OfType>::value,
+         bool TSigned = std::is_signed<T>::value>
+struct value_in_range_of_impl2;
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, false, false>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, true, false>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, false, true>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return val >= 0 && static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, true, true>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return static_cast<CommonType>(val) >= static_cast<CommonType>((std::numeric_limits<OfType>::min)())
+               && static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T,
+         bool NeverOutOfRange = never_out_of_range<OfType, T>::value,
+         typename = detail::enable_if_t<all_integral<OfType, T>::value>>
+struct value_in_range_of_impl1;
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl1<OfType, T, false>
+{
+    static constexpr bool test(T val)
+    {
+        return value_in_range_of_impl2<OfType, T>::test(val);
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl1<OfType, T, true>
+{
+    static constexpr bool test(T /*val*/)
+    {
+        return true;
+    }
+};
+
+template<typename OfType, typename T>
+constexpr bool value_in_range_of(T val)
+{
+    return value_in_range_of_impl1<OfType, T>::test(val);
+}
+
+template<bool Value>
+using bool_constant = std::integral_constant<bool, Value>;
+
+///////////////////////////////////////////////////////////////////////////////
+// is_c_string
+///////////////////////////////////////////////////////////////////////////////
+
+namespace impl
+{
+
+template<typename T>
+constexpr bool is_c_string()
+{
+    using TUnExt = typename std::remove_extent<T>::type;
+    using TUnCVExt = typename std::remove_cv<TUnExt>::type;
+    using TUnPtr = typename std::remove_pointer<T>::type;
+    using TUnCVPtr = typename std::remove_cv<TUnPtr>::type;
+    return
+        (std::is_array<T>::value && std::is_same<TUnCVExt, char>::value)
+        || (std::is_pointer<T>::value && std::is_same<TUnCVPtr, char>::value);
+}
+
+}  // namespace impl
+
+// checks whether T is a [cv] char */[cv] char[] C string
+template<typename T>
+struct is_c_string : bool_constant<impl::is_c_string<T>()> {};
+
+template<typename T>
+using is_c_string_uncvref = is_c_string<uncvref_t<T>>;
+
+///////////////////////////////////////////////////////////////////////////////
+// is_transparent
+///////////////////////////////////////////////////////////////////////////////
+
+namespace impl
+{
+
+template<typename T>
+constexpr bool is_transparent()
+{
+    return is_detected<detect_is_transparent, T>::value;
+}
+
+}  // namespace impl
+
+// checks whether T has a member named is_transparent
+template<typename T>
+struct is_transparent : bool_constant<impl::is_transparent<T>()> {};
+
+///////////////////////////////////////////////////////////////////////////////
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/string_concat.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstring> // strlen
+#include <string> // string
+#include <utility> // forward
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/detected.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+inline std::size_t concat_length()
+{
+    return 0;
+}
+
+template<typename... Args>
+inline std::size_t concat_length(const char* cstr, const Args& ... rest);
+
+template<typename StringType, typename... Args>
+inline std::size_t concat_length(const StringType& str, const Args& ... rest);
+
+template<typename... Args>
+inline std::size_t concat_length(const char /*c*/, const Args& ... rest)
+{
+    return 1 + concat_length(rest...);
+}
+
+template<typename... Args>
+inline std::size_t concat_length(const char* cstr, const Args& ... rest)
+{
+    // cppcheck-suppress ignoredReturnValue
+    return ::strlen(cstr) + concat_length(rest...);
+}
+
+template<typename StringType, typename... Args>
+inline std::size_t concat_length(const StringType& str, const Args& ... rest)
+{
+    return str.size() + concat_length(rest...);
+}
+
+template<typename OutStringType>
+inline void concat_into(OutStringType& /*out*/)
+{}
+
+template<typename StringType, typename Arg>
+using string_can_append = decltype(std::declval<StringType&>().append(std::declval < Arg && > ()));
+
+template<typename StringType, typename Arg>
+using detect_string_can_append = is_detected<string_can_append, StringType, Arg>;
+
+template<typename StringType, typename Arg>
+using string_can_append_op = decltype(std::declval<StringType&>() += std::declval < Arg && > ());
+
+template<typename StringType, typename Arg>
+using detect_string_can_append_op = is_detected<string_can_append_op, StringType, Arg>;
+
+template<typename StringType, typename Arg>
+using string_can_append_iter = decltype(std::declval<StringType&>().append(std::declval<const Arg&>().begin(), std::declval<const Arg&>().end()));
+
+template<typename StringType, typename Arg>
+using detect_string_can_append_iter = is_detected<string_can_append_iter, StringType, Arg>;
+
+template<typename StringType, typename Arg>
+using string_can_append_data = decltype(std::declval<StringType&>().append(std::declval<const Arg&>().data(), std::declval<const Arg&>().size()));
+
+template<typename StringType, typename Arg>
+using detect_string_can_append_data = is_detected<string_can_append_data, StringType, Arg>;
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && detect_string_can_append_op<OutStringType, Arg>::value, int > = 0 >
+inline void concat_into(OutStringType& out, Arg && arg, Args && ... rest);
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && detect_string_can_append_iter<OutStringType, Arg>::value, int > = 0 >
+inline void concat_into(OutStringType& out, const Arg& arg, Args && ... rest);
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && !detect_string_can_append_iter<OutStringType, Arg>::value
+                         && detect_string_can_append_data<OutStringType, Arg>::value, int > = 0 >
+inline void concat_into(OutStringType& out, const Arg& arg, Args && ... rest);
+
+template<typename OutStringType, typename Arg, typename... Args,
+         enable_if_t<detect_string_can_append<OutStringType, Arg>::value, int> = 0>
+inline void concat_into(OutStringType& out, Arg && arg, Args && ... rest)
+{
+    out.append(std::forward<Arg>(arg));
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && detect_string_can_append_op<OutStringType, Arg>::value, int > >
+inline void concat_into(OutStringType& out, Arg&& arg, Args&& ... rest)
+{
+    out += std::forward<Arg>(arg);
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && detect_string_can_append_iter<OutStringType, Arg>::value, int > >
+inline void concat_into(OutStringType& out, const Arg& arg, Args&& ... rest)
+{
+    out.append(arg.begin(), arg.end());
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && !detect_string_can_append_iter<OutStringType, Arg>::value
+                         && detect_string_can_append_data<OutStringType, Arg>::value, int > >
+inline void concat_into(OutStringType& out, const Arg& arg, Args&& ... rest)
+{
+    out.append(arg.data(), arg.size());
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template<typename OutStringType = std::string, typename... Args>
+inline OutStringType concat(Args && ... args)
+{
+    OutStringType str;
+    str.reserve(concat_length(args...));
+    concat_into(str, std::forward<Args>(args)...);
+    return str;
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+
+// With -Wweak-vtables, Clang will complain about the exception classes as they
+// have no out-of-line virtual method definitions and their vtable will be
+// emitted in every translation unit. This issue cannot be fixed with a
+// header-only library as there is no implementation file to move these
+// functions to. As a result, we suppress this warning here to avoid client
+// code to stumble over this. See https://github.com/nlohmann/json/issues/4087
+// for a discussion.
+#if defined(__clang__)
+    #pragma clang diagnostic push
+    #pragma clang diagnostic ignored "-Wweak-vtables"
+#endif
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+////////////////
+// exceptions //
+////////////////
+
+/// @brief general exception of the @ref basic_json class
+/// @sa https://json.nlohmann.me/api/basic_json/exception/
+class exception : public std::exception
+{
+  public:
+    /// returns the explanatory string
+    const char* what() const noexcept override
+    {
+        return m.what();
+    }
+
+    /// the id of the exception
+    const int id; // NOLINT(cppcoreguidelines-non-private-member-variables-in-classes)
+
+  protected:
+    JSON_HEDLEY_NON_NULL(3)
+    exception(int id_, const char* what_arg) : id(id_), m(what_arg) {} // NOLINT(bugprone-throw-keyword-missing)
+
+    static std::string name(const std::string& ename, int id_)
+    {
+        return concat("[json.exception.", ename, '.', std::to_string(id_), "] ");
+    }
+
+    static std::string diagnostics(std::nullptr_t /*leaf_element*/)
+    {
+        return "";
+    }
+
+    template<typename BasicJsonType>
+    static std::string diagnostics(const BasicJsonType* leaf_element)
+    {
+#if JSON_DIAGNOSTICS
+        std::vector<std::string> tokens;
+        for (const auto* current = leaf_element; current != nullptr && current->m_parent != nullptr; current = current->m_parent)
+        {
+            switch (current->m_parent->type())
+            {
+                case value_t::array:
+                {
+                    for (std::size_t i = 0; i < current->m_parent->m_data.m_value.array->size(); ++i)
+                    {
+                        if (&current->m_parent->m_data.m_value.array->operator[](i) == current)
+                        {
+                            tokens.emplace_back(std::to_string(i));
+                            break;
+                        }
+                    }
+                    break;
+                }
+
+                case value_t::object:
+                {
+                    for (const auto& element : *current->m_parent->m_data.m_value.object)
+                    {
+                        if (&element.second == current)
+                        {
+                            tokens.emplace_back(element.first.c_str());
+                            break;
+                        }
+                    }
+                    break;
+                }
+
+                case value_t::null: // LCOV_EXCL_LINE
+                case value_t::string: // LCOV_EXCL_LINE
+                case value_t::boolean: // LCOV_EXCL_LINE
+                case value_t::number_integer: // LCOV_EXCL_LINE
+                case value_t::number_unsigned: // LCOV_EXCL_LINE
+                case value_t::number_float: // LCOV_EXCL_LINE
+                case value_t::binary: // LCOV_EXCL_LINE
+                case value_t::discarded: // LCOV_EXCL_LINE
+                default:   // LCOV_EXCL_LINE
+                    break; // LCOV_EXCL_LINE
+            }
+        }
+
+        if (tokens.empty())
+        {
+            return "";
+        }
+
+        auto str = std::accumulate(tokens.rbegin(), tokens.rend(), std::string{},
+                                   [](const std::string & a, const std::string & b)
+        {
+            return concat(a, '/', detail::escape(b));
+        });
+
+        return concat('(', str, ") ", get_byte_positions(leaf_element));
+#else
+        return get_byte_positions(leaf_element);
+#endif
+    }
+
+  private:
+    /// an exception object as storage for error messages
+    std::runtime_error m;
+#if JSON_DIAGNOSTIC_POSITIONS
+    template<typename BasicJsonType>
+    static std::string get_byte_positions(const BasicJsonType* leaf_element)
+    {
+        if ((leaf_element->start_pos() != std::string::npos) && (leaf_element->end_pos() != std::string::npos))
+        {
+            return concat("(bytes ", std::to_string(leaf_element->start_pos()), "-", std::to_string(leaf_element->end_pos()), ") ");
+        }
+        return "";
+    }
+#else
+    template<typename BasicJsonType>
+    static std::string get_byte_positions(const BasicJsonType* leaf_element)
+    {
+        static_cast<void>(leaf_element);
+        return "";
+    }
+#endif
+};
+
+/// @brief exception indicating a parse error
+/// @sa https://json.nlohmann.me/api/basic_json/parse_error/
+class parse_error : public exception
+{
+  public:
+    /*!
+    @brief create a parse error exception
+    @param[in] id_       the id of the exception
+    @param[in] pos       the position where the error occurred (or with
+                         chars_read_total=0 if the position cannot be
+                         determined)
+    @param[in] what_arg  the explanatory string
+    @return parse_error object
+    */
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static parse_error create(int id_, const position_t& pos, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("parse_error", id_), "parse error",
+                                     position_string(pos), ": ", exception::diagnostics(context), what_arg);
+        return {id_, pos.chars_read_total, w.c_str()};
+    }
+
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static parse_error create(int id_, std::size_t byte_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("parse_error", id_), "parse error",
+                                     (byte_ != 0 ? (concat(" at byte ", std::to_string(byte_))) : ""),
+                                     ": ", exception::diagnostics(context), what_arg);
+        return {id_, byte_, w.c_str()};
+    }
+
+    /*!
+    @brief byte index of the parse error
+
+    The byte index of the last read character in the input file.
+
+    @note For an input with n bytes, 1 is the index of the first character and
+          n+1 is the index of the terminating null byte or the end of file.
+          This also holds true when reading a byte vector (CBOR or MessagePack).
+    */
+    const std::size_t byte;
+
+  private:
+    parse_error(int id_, std::size_t byte_, const char* what_arg)
+        : exception(id_, what_arg), byte(byte_) {}
+
+    static std::string position_string(const position_t& pos)
+    {
+        return concat(" at line ", std::to_string(pos.lines_read + 1),
+                      ", column ", std::to_string(pos.chars_read_current_line));
+    }
+};
+
+/// @brief exception indicating errors with iterators
+/// @sa https://json.nlohmann.me/api/basic_json/invalid_iterator/
+class invalid_iterator : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static invalid_iterator create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("invalid_iterator", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    invalid_iterator(int id_, const char* what_arg)
+        : exception(id_, what_arg) {}
+};
+
+/// @brief exception indicating executing a member function with a wrong type
+/// @sa https://json.nlohmann.me/api/basic_json/type_error/
+class type_error : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static type_error create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("type_error", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    type_error(int id_, const char* what_arg) : exception(id_, what_arg) {}
+};
+
+/// @brief exception indicating access out of the defined range
+/// @sa https://json.nlohmann.me/api/basic_json/out_of_range/
+class out_of_range : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static out_of_range create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("out_of_range", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    out_of_range(int id_, const char* what_arg) : exception(id_, what_arg) {}
+};
+
+/// @brief exception indicating other library errors
+/// @sa https://json.nlohmann.me/api/basic_json/other_error/
+class other_error : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static other_error create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("other_error", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    other_error(int id_, const char* what_arg) : exception(id_, what_arg) {}
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+#if defined(__clang__)
+    #pragma clang diagnostic pop
+#endif
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/identity_tag.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// dispatching helper struct
+template <class T> struct identity_tag {};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/std_fs.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+#if JSON_HAS_EXPERIMENTAL_FILESYSTEM
+#include <experimental/filesystem>
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+namespace std_fs = std::experimental::filesystem;
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+#elif JSON_HAS_FILESYSTEM
+#include <filesystem> // NOLINT(build/c++17)
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+namespace std_fs = std::filesystem;
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+#endif
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename std::nullptr_t& n)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_null()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be null, but is ", j.type_name()), &j));
+    }
+    n = nullptr;
+}
+
+#ifdef JSON_HAS_CPP_17
+#ifndef JSON_USE_IMPLICIT_CONVERSIONS
+template<typename BasicJsonType, typename T>
+void from_json(const BasicJsonType& j, std::optional<T>& opt)
+{
+    if (j.is_null())
+    {
+        opt = std::nullopt;
+    }
+    else
+    {
+        opt.emplace(j.template get<T>());
+    }
+}
+
+#endif // JSON_USE_IMPLICIT_CONVERSIONS
+#endif // JSON_HAS_CPP_17
+
+// overloads for basic_json template parameters
+template < typename BasicJsonType, typename ArithmeticType,
+           enable_if_t < std::is_arithmetic<ArithmeticType>::value&&
+                         !std::is_same<ArithmeticType, typename BasicJsonType::boolean_t>::value,
+                         int > = 0 >
+void get_arithmetic_value(const BasicJsonType& j, ArithmeticType& val)
+{
+    switch (static_cast<value_t>(j))
+    {
+        case value_t::number_unsigned:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_unsigned_t*>());
+            break;
+        }
+        case value_t::number_integer:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_integer_t*>());
+            break;
+        }
+        case value_t::number_float:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_float_t*>());
+            break;
+        }
+
+        case value_t::null:
+        case value_t::object:
+        case value_t::array:
+        case value_t::string:
+        case value_t::boolean:
+        case value_t::binary:
+        case value_t::discarded:
+        default:
+            JSON_THROW(type_error::create(302, concat("type must be number, but is ", j.type_name()), &j));
+    }
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::boolean_t& b)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_boolean()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be boolean, but is ", j.type_name()), &j));
+    }
+    b = *j.template get_ptr<const typename BasicJsonType::boolean_t*>();
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::string_t& s)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be string, but is ", j.type_name()), &j));
+    }
+    s = *j.template get_ptr<const typename BasicJsonType::string_t*>();
+}
+
+template <
+    typename BasicJsonType, typename StringType,
+    enable_if_t <
+        std::is_assignable<StringType&, const typename BasicJsonType::string_t>::value
+        && is_detected_exact<typename BasicJsonType::string_t::value_type, value_type_t, StringType>::value
+        && !std::is_same<typename BasicJsonType::string_t, StringType>::value
+        && !is_json_ref<StringType>::value, int > = 0 >
+inline void from_json(const BasicJsonType& j, StringType& s)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be string, but is ", j.type_name()), &j));
+    }
+
+    s = *j.template get_ptr<const typename BasicJsonType::string_t*>();
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::number_float_t& val)
+{
+    get_arithmetic_value(j, val);
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::number_unsigned_t& val)
+{
+    get_arithmetic_value(j, val);
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::number_integer_t& val)
+{
+    get_arithmetic_value(j, val);
+}
+
+#if !JSON_DISABLE_ENUM_SERIALIZATION
+template<typename BasicJsonType, typename EnumType,
+         enable_if_t<std::is_enum<EnumType>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, EnumType& e)
+{
+    typename std::underlying_type<EnumType>::type val;
+    get_arithmetic_value(j, val);
+    e = static_cast<EnumType>(val);
+}
+#endif  // JSON_DISABLE_ENUM_SERIALIZATION
+
+// forward_list doesn't have an insert method
+template<typename BasicJsonType, typename T, typename Allocator,
+         enable_if_t<is_getable<BasicJsonType, T>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, std::forward_list<T, Allocator>& l)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    l.clear();
+    std::transform(j.rbegin(), j.rend(),
+                   std::front_inserter(l), [](const BasicJsonType & i)
+    {
+        return i.template get<T>();
+    });
+}
+
+// valarray doesn't have an insert method
+template<typename BasicJsonType, typename T,
+         enable_if_t<is_getable<BasicJsonType, T>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, std::valarray<T>& l)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    l.resize(j.size());
+    std::transform(j.begin(), j.end(), std::begin(l),
+                   [](const BasicJsonType & elem)
+    {
+        return elem.template get<T>();
+    });
+}
+
+template<typename BasicJsonType, typename T, std::size_t N>
+auto from_json(const BasicJsonType& j, T (&arr)[N])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i = 0; i < N; ++i)
+    {
+        arr[i] = j.at(i).template get<T>();
+    }
+}
+
+template<typename BasicJsonType, typename T, std::size_t N1, std::size_t N2>
+auto from_json(const BasicJsonType& j, T (&arr)[N1][N2])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i1 = 0; i1 < N1; ++i1)
+    {
+        for (std::size_t i2 = 0; i2 < N2; ++i2)
+        {
+            arr[i1][i2] = j.at(i1).at(i2).template get<T>();
+        }
+    }
+}
+
+template<typename BasicJsonType, typename T, std::size_t N1, std::size_t N2, std::size_t N3>
+auto from_json(const BasicJsonType& j, T (&arr)[N1][N2][N3])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i1 = 0; i1 < N1; ++i1)
+    {
+        for (std::size_t i2 = 0; i2 < N2; ++i2)
+        {
+            for (std::size_t i3 = 0; i3 < N3; ++i3)
+            {
+                arr[i1][i2][i3] = j.at(i1).at(i2).at(i3).template get<T>();
+            }
+        }
+    }
+}
+
+template<typename BasicJsonType, typename T, std::size_t N1, std::size_t N2, std::size_t N3, std::size_t N4>
+auto from_json(const BasicJsonType& j, T (&arr)[N1][N2][N3][N4])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i1 = 0; i1 < N1; ++i1)
+    {
+        for (std::size_t i2 = 0; i2 < N2; ++i2)
+        {
+            for (std::size_t i3 = 0; i3 < N3; ++i3)
+            {
+                for (std::size_t i4 = 0; i4 < N4; ++i4)
+                {
+                    arr[i1][i2][i3][i4] = j.at(i1).at(i2).at(i3).at(i4).template get<T>();
+                }
+            }
+        }
+    }
+}
+
+template<typename BasicJsonType>
+inline void from_json_array_impl(const BasicJsonType& j, typename BasicJsonType::array_t& arr, priority_tag<3> /*unused*/)
+{
+    arr = *j.template get_ptr<const typename BasicJsonType::array_t*>();
+}
+
+template<typename BasicJsonType, typename T, std::size_t N>
+auto from_json_array_impl(const BasicJsonType& j, std::array<T, N>& arr,
+                          priority_tag<2> /*unused*/)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i = 0; i < N; ++i)
+    {
+        arr[i] = j.at(i).template get<T>();
+    }
+}
+
+template<typename BasicJsonType, typename ConstructibleArrayType,
+         enable_if_t<
+             std::is_assignable<ConstructibleArrayType&, ConstructibleArrayType>::value,
+             int> = 0>
+auto from_json_array_impl(const BasicJsonType& j, ConstructibleArrayType& arr, priority_tag<1> /*unused*/)
+-> decltype(
+    arr.reserve(std::declval<typename ConstructibleArrayType::size_type>()),
+    j.template get<typename ConstructibleArrayType::value_type>(),
+    void())
+{
+    using std::end;
+
+    ConstructibleArrayType ret;
+    ret.reserve(j.size());
+    std::transform(j.begin(), j.end(),
+                   std::inserter(ret, end(ret)), [](const BasicJsonType & i)
+    {
+        // get<BasicJsonType>() returns *this, this won't call a from_json
+        // method when value_type is BasicJsonType
+        return i.template get<typename ConstructibleArrayType::value_type>();
+    });
+    arr = std::move(ret);
+}
+
+template<typename BasicJsonType, typename ConstructibleArrayType,
+         enable_if_t<
+             std::is_assignable<ConstructibleArrayType&, ConstructibleArrayType>::value,
+             int> = 0>
+inline void from_json_array_impl(const BasicJsonType& j, ConstructibleArrayType& arr,
+                                 priority_tag<0> /*unused*/)
+{
+    using std::end;
+
+    ConstructibleArrayType ret;
+    std::transform(
+        j.begin(), j.end(), std::inserter(ret, end(ret)),
+        [](const BasicJsonType & i)
+    {
+        // get<BasicJsonType>() returns *this, this won't call a from_json
+        // method when value_type is BasicJsonType
+        return i.template get<typename ConstructibleArrayType::value_type>();
+    });
+    arr = std::move(ret);
+}
+
+template < typename BasicJsonType, typename ConstructibleArrayType,
+           enable_if_t <
+               is_constructible_array_type<BasicJsonType, ConstructibleArrayType>::value&&
+               !is_constructible_object_type<BasicJsonType, ConstructibleArrayType>::value&&
+               !is_constructible_string_type<BasicJsonType, ConstructibleArrayType>::value&&
+               !std::is_same<ConstructibleArrayType, typename BasicJsonType::binary_t>::value&&
+               !is_basic_json<ConstructibleArrayType>::value,
+               int > = 0 >
+auto from_json(const BasicJsonType& j, ConstructibleArrayType& arr)
+-> decltype(from_json_array_impl(j, arr, priority_tag<3> {}),
+j.template get<typename ConstructibleArrayType::value_type>(),
+void())
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+
+    from_json_array_impl(j, arr, priority_tag<3> {});
+}
+
+template < typename BasicJsonType, typename T, std::size_t... Idx >
+std::array<T, sizeof...(Idx)> from_json_inplace_array_impl(BasicJsonType&& j,
+                     identity_tag<std::array<T, sizeof...(Idx)>> /*unused*/, index_sequence<Idx...> /*unused*/)
+{
+    return { { std::forward<BasicJsonType>(j).at(Idx).template get<T>()... } };
+}
+
+template < typename BasicJsonType, typename T, std::size_t N >
+auto from_json(BasicJsonType&& j, identity_tag<std::array<T, N>> tag)
+-> decltype(from_json_inplace_array_impl(std::forward<BasicJsonType>(j), tag, make_index_sequence<N> {}))
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+
+    return from_json_inplace_array_impl(std::forward<BasicJsonType>(j), tag, make_index_sequence<N> {});
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::binary_t& bin)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_binary()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be binary, but is ", j.type_name()), &j));
+    }
+
+    bin = *j.template get_ptr<const typename BasicJsonType::binary_t*>();
+}
+
+template<typename BasicJsonType, typename ConstructibleObjectType,
+         enable_if_t<is_constructible_object_type<BasicJsonType, ConstructibleObjectType>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, ConstructibleObjectType& obj)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_object()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be object, but is ", j.type_name()), &j));
+    }
+
+    ConstructibleObjectType ret;
+    const auto* inner_object = j.template get_ptr<const typename BasicJsonType::object_t*>();
+    using value_type = typename ConstructibleObjectType::value_type;
+    std::transform(
+        inner_object->begin(), inner_object->end(),
+        std::inserter(ret, ret.begin()),
+        [](typename BasicJsonType::object_t::value_type const & p)
+    {
+        return value_type(p.first, p.second.template get<typename ConstructibleObjectType::mapped_type>());
+    });
+    obj = std::move(ret);
+}
+
+// overload for arithmetic types, not chosen for basic_json template arguments
+// (BooleanType, etc..); note: Is it really necessary to provide explicit
+// overloads for boolean_t etc. in case of a custom BooleanType which is not
+// an arithmetic type?
+template < typename BasicJsonType, typename ArithmeticType,
+           enable_if_t <
+               std::is_arithmetic<ArithmeticType>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::number_unsigned_t>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::number_integer_t>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::number_float_t>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::boolean_t>::value,
+               int > = 0 >
+inline void from_json(const BasicJsonType& j, ArithmeticType& val)
+{
+    switch (static_cast<value_t>(j))
+    {
+        case value_t::number_unsigned:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_unsigned_t*>());
+            break;
+        }
+        case value_t::number_integer:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_integer_t*>());
+            break;
+        }
+        case value_t::number_float:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_float_t*>());
+            break;
+        }
+        case value_t::boolean:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::boolean_t*>());
+            break;
+        }
+
+        case value_t::null:
+        case value_t::object:
+        case value_t::array:
+        case value_t::string:
+        case value_t::binary:
+        case value_t::discarded:
+        default:
+            JSON_THROW(type_error::create(302, concat("type must be number, but is ", j.type_name()), &j));
+    }
+}
+
+template<typename BasicJsonType, typename... Args, std::size_t... Idx>
+std::tuple<Args...> from_json_tuple_impl_base(BasicJsonType&& j, index_sequence<Idx...> /*unused*/)
+{
+    return std::make_tuple(std::forward<BasicJsonType>(j).at(Idx).template get<Args>()...);
+}
+
+template<typename BasicJsonType>
+std::tuple<> from_json_tuple_impl_base(BasicJsonType& /*unused*/, index_sequence<> /*unused*/)
+{
+    return {};
+}
+
+template < typename BasicJsonType, class A1, class A2 >
+std::pair<A1, A2> from_json_tuple_impl(BasicJsonType&& j, identity_tag<std::pair<A1, A2>> /*unused*/, priority_tag<0> /*unused*/)
+{
+    return {std::forward<BasicJsonType>(j).at(0).template get<A1>(),
+            std::forward<BasicJsonType>(j).at(1).template get<A2>()};
+}
+
+template<typename BasicJsonType, typename A1, typename A2>
+inline void from_json_tuple_impl(BasicJsonType&& j, std::pair<A1, A2>& p, priority_tag<1> /*unused*/)
+{
+    p = from_json_tuple_impl(std::forward<BasicJsonType>(j), identity_tag<std::pair<A1, A2>> {}, priority_tag<0> {});
+}
+
+template<typename BasicJsonType, typename... Args>
+std::tuple<Args...> from_json_tuple_impl(BasicJsonType&& j, identity_tag<std::tuple<Args...>> /*unused*/, priority_tag<2> /*unused*/)
+{
+    return from_json_tuple_impl_base<BasicJsonType, Args...>(std::forward<BasicJsonType>(j), index_sequence_for<Args...> {});
+}
+
+template<typename BasicJsonType, typename... Args>
+inline void from_json_tuple_impl(BasicJsonType&& j, std::tuple<Args...>& t, priority_tag<3> /*unused*/)
+{
+    t = from_json_tuple_impl_base<BasicJsonType, Args...>(std::forward<BasicJsonType>(j), index_sequence_for<Args...> {});
+}
+
+template<typename BasicJsonType, typename TupleRelated>
+auto from_json(BasicJsonType&& j, TupleRelated&& t)
+-> decltype(from_json_tuple_impl(std::forward<BasicJsonType>(j), std::forward<TupleRelated>(t), priority_tag<3> {}))
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+
+    return from_json_tuple_impl(std::forward<BasicJsonType>(j), std::forward<TupleRelated>(t), priority_tag<3> {});
+}
+
+template < typename BasicJsonType, typename Key, typename Value, typename Compare, typename Allocator,
+           typename = enable_if_t < !std::is_constructible <
+                                        typename BasicJsonType::string_t, Key >::value >>
+inline void from_json(const BasicJsonType& j, std::map<Key, Value, Compare, Allocator>& m)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    m.clear();
+    for (const auto& p : j)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!p.is_array()))
+        {
+            JSON_THROW(type_error::create(302, concat("type must be array, but is ", p.type_name()), &j));
+        }
+        m.emplace(p.at(0).template get<Key>(), p.at(1).template get<Value>());
+    }
+}
+
+template < typename BasicJsonType, typename Key, typename Value, typename Hash, typename KeyEqual, typename Allocator,
+           typename = enable_if_t < !std::is_constructible <
+                                        typename BasicJsonType::string_t, Key >::value >>
+inline void from_json(const BasicJsonType& j, std::unordered_map<Key, Value, Hash, KeyEqual, Allocator>& m)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    m.clear();
+    for (const auto& p : j)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!p.is_array()))
+        {
+            JSON_THROW(type_error::create(302, concat("type must be array, but is ", p.type_name()), &j));
+        }
+        m.emplace(p.at(0).template get<Key>(), p.at(1).template get<Value>());
+    }
+}
+
+#if JSON_HAS_FILESYSTEM || JSON_HAS_EXPERIMENTAL_FILESYSTEM
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, std_fs::path& p)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be string, but is ", j.type_name()), &j));
+    }
+    const auto& s = *j.template get_ptr<const typename BasicJsonType::string_t*>();
+#ifdef JSON_HAS_CPP_20
+    p = std_fs::path(std::u8string_view(reinterpret_cast<const char8_t*>(s.data()), s.size()));
+#else
+    p = std_fs::u8path(s); // accepts UTF-8 encoded std::string in C++17, deprecated in C++20
+#endif
+}
+#endif
+
+struct from_json_fn
+{
+    template<typename BasicJsonType, typename T>
+    auto operator()(const BasicJsonType& j, T&& val) const
+    noexcept(noexcept(from_json(j, std::forward<T>(val))))
+    -> decltype(from_json(j, std::forward<T>(val)))
+    {
+        return from_json(j, std::forward<T>(val));
+    }
+};
+
+}  // namespace detail
+
+#ifndef JSON_HAS_CPP_17
+/// namespace to hold default `from_json` function
+/// to see why this is required:
+/// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/n4381.html
+namespace // NOLINT(cert-dcl59-cpp,fuchsia-header-anon-namespaces,google-build-namespaces)
+{
+#endif
+JSON_INLINE_VARIABLE constexpr const auto& from_json = // NOLINT(misc-definitions-in-headers)
+    detail::static_const<detail::from_json_fn>::value;
+#ifndef JSON_HAS_CPP_17
+}  // namespace
+#endif
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/conversions/to_json.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+// JSON_HAS_CPP_17
+#ifdef JSON_HAS_CPP_17
+    #include <optional> // optional
+#endif
+
+#include <algorithm> // copy
+#include <iterator> // begin, end
+#include <string> // string
+#include <tuple> // tuple, get
+#include <type_traits> // is_same, is_constructible, is_floating_point, is_enum, underlying_type
+#include <utility> // move, forward, declval, pair
+#include <valarray> // valarray
+#include <vector> // vector
+
+// #include <nlohmann/detail/iterators/iteration_proxy.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // size_t
+#include <iterator> // forward_iterator_tag
+#include <tuple> // tuple_size, get, tuple_element
+#include <utility> // move
+
+#if JSON_HAS_RANGES
+    #include <ranges> // enable_borrowed_range
+#endif
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/string_utils.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // size_t
+#include <string> // string, to_string
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename StringType>
+void int_to_string(StringType& target, std::size_t value)
+{
+    // For ADL
+    using std::to_string;
+    target = to_string(value);
+}
+
+template<typename StringType>
+StringType to_string(std::size_t value)
+{
+    StringType result;
+    int_to_string(result, value);
+    return result;
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename IteratorType> class iteration_proxy_value
+{
+  public:
+    using difference_type = std::ptrdiff_t;
+    using value_type = iteration_proxy_value;
+    using pointer = value_type *;
+    using reference = value_type &;
+    using iterator_category = std::forward_iterator_tag;
+    using string_type = typename std::remove_cv< typename std::remove_reference<decltype( std::declval<IteratorType>().key() ) >::type >::type;
+
+  private:
+    /// the iterator
+    IteratorType anchor{};
+    /// an index for arrays (used to create key names)
+    std::size_t array_index = 0;
+    /// last stringified array index
+    mutable std::size_t array_index_last = 0;
+    /// a string representation of the array index
+    mutable string_type array_index_str = "0";
+    /// an empty string (to return a reference for primitive values)
+    string_type empty_str{};
+
+  public:
+    explicit iteration_proxy_value() = default;
+    explicit iteration_proxy_value(IteratorType it, std::size_t array_index_ = 0)
+    noexcept(std::is_nothrow_move_constructible<IteratorType>::value
+             && std::is_nothrow_default_constructible<string_type>::value)
+        : anchor(std::move(it))
+        , array_index(array_index_)
+    {}
+
+    iteration_proxy_value(iteration_proxy_value const&) = default;
+    iteration_proxy_value& operator=(iteration_proxy_value const&) = default;
+    // older GCCs are a bit fussy and require explicit noexcept specifiers on defaulted functions
+    iteration_proxy_value(iteration_proxy_value&&)
+    noexcept(std::is_nothrow_move_constructible<IteratorType>::value
+             && std::is_nothrow_move_constructible<string_type>::value) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor,cppcoreguidelines-noexcept-move-operations)
+    iteration_proxy_value& operator=(iteration_proxy_value&&)
+    noexcept(std::is_nothrow_move_assignable<IteratorType>::value
+             && std::is_nothrow_move_assignable<string_type>::value) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor,cppcoreguidelines-noexcept-move-operations)
+    ~iteration_proxy_value() = default;
+
+    /// dereference operator (needed for range-based for)
+    const iteration_proxy_value& operator*() const
+    {
+        return *this;
+    }
+
+    /// increment operator (needed for range-based for)
+    iteration_proxy_value& operator++()
+    {
+        ++anchor;
+        ++array_index;
+
+        return *this;
+    }
+
+    iteration_proxy_value operator++(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        auto tmp = iteration_proxy_value(anchor, array_index);
+        ++anchor;
+        ++array_index;
+        return tmp;
+    }
+
+    /// equality operator (needed for InputIterator)
+    bool operator==(const iteration_proxy_value& o) const
+    {
+        return anchor == o.anchor;
+    }
+
+    /// inequality operator (needed for range-based for)
+    bool operator!=(const iteration_proxy_value& o) const
+    {
+        return anchor != o.anchor;
+    }
+
+    /// return key of the iterator
+    const string_type& key() const
+    {
+        JSON_ASSERT(anchor.m_object != nullptr);
+
+        switch (anchor.m_object->type())
+        {
+            // use integer array index as key
+            case value_t::array:
+            {
+                if (array_index != array_index_last)
+                {
+                    int_to_string( array_index_str, array_index );
+                    array_index_last = array_index;
+                }
+                return array_index_str;
+            }
+
+            // use key from the object
+            case value_t::object:
+                return anchor.key();
+
+            // use an empty key for all primitive types
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return empty_str;
+        }
+    }
+
+    /// return value of the iterator
+    typename IteratorType::reference value() const
+    {
+        return anchor.value();
+    }
+};
+
+/// proxy class for the items() function
+template<typename IteratorType> class iteration_proxy
+{
+  private:
+    /// the container to iterate
+    typename IteratorType::pointer container = nullptr;
+
+  public:
+    explicit iteration_proxy() = default;
+
+    /// construct iteration proxy from a container
+    explicit iteration_proxy(typename IteratorType::reference cont) noexcept
+        : container(&cont) {}
+
+    iteration_proxy(iteration_proxy const&) = default;
+    iteration_proxy& operator=(iteration_proxy const&) = default;
+    iteration_proxy(iteration_proxy&&) noexcept = default;
+    iteration_proxy& operator=(iteration_proxy&&) noexcept = default;
+    ~iteration_proxy() = default;
+
+    /// return iterator begin (needed for range-based for)
+    iteration_proxy_value<IteratorType> begin() const noexcept
+    {
+        return iteration_proxy_value<IteratorType>(container->begin());
+    }
+
+    /// return iterator end (needed for range-based for)
+    iteration_proxy_value<IteratorType> end() const noexcept
+    {
+        return iteration_proxy_value<IteratorType>(container->end());
+    }
+};
+
+// Structured Bindings Support
+// For further reference see https://blog.tartanllama.xyz/structured-bindings/
+// And see https://github.com/nlohmann/json/pull/1391
+template<std::size_t N, typename IteratorType, enable_if_t<N == 0, int> = 0>
+auto get(const nlohmann::detail::iteration_proxy_value<IteratorType>& i) -> decltype(i.key())
+{
+    return i.key();
+}
+// Structured Bindings Support
+// For further reference see https://blog.tartanllama.xyz/structured-bindings/
+// And see https://github.com/nlohmann/json/pull/1391
+template<std::size_t N, typename IteratorType, enable_if_t<N == 1, int> = 0>
+auto get(const nlohmann::detail::iteration_proxy_value<IteratorType>& i) -> decltype(i.value())
+{
+    return i.value();
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// The Addition to the STD Namespace is required to add
+// Structured Bindings Support to the iteration_proxy_value class
+// For further reference see https://blog.tartanllama.xyz/structured-bindings/
+// And see https://github.com/nlohmann/json/pull/1391
+namespace std
+{
+
+#if defined(__clang__)
+    // Fix: https://github.com/nlohmann/json/issues/1401
+    #pragma clang diagnostic push
+    #pragma clang diagnostic ignored "-Wmismatched-tags"
+#endif
+template<typename IteratorType>
+class tuple_size<::nlohmann::detail::iteration_proxy_value<IteratorType>> // NOLINT(cert-dcl58-cpp)
+    : public std::integral_constant<std::size_t, 2> {};
+
+template<std::size_t N, typename IteratorType>
+class tuple_element<N, ::nlohmann::detail::iteration_proxy_value<IteratorType >> // NOLINT(cert-dcl58-cpp)
+{
+  public:
+    using type = decltype(
+                     get<N>(std::declval <
+                            ::nlohmann::detail::iteration_proxy_value<IteratorType >> ()));
+};
+#if defined(__clang__)
+    #pragma clang diagnostic pop
+#endif
+
+}  // namespace std
+
+#if JSON_HAS_RANGES
+    template <typename IteratorType>
+    inline constexpr bool ::std::ranges::enable_borrowed_range<::nlohmann::detail::iteration_proxy<IteratorType>> = true;
+#endif
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/std_fs.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+//////////////////
+// constructors //
+//////////////////
+
+/*
+ * Note all external_constructor<>::construct functions need to call
+ * j.m_data.m_value.destroy(j.m_data.m_type) to avoid a memory leak in case j contains an
+ * allocated value (e.g., a string). See bug issue
+ * https://github.com/nlohmann/json/issues/2865 for more information.
+ */
+
+template<value_t> struct external_constructor;
+
+template<>
+struct external_constructor<value_t::boolean>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::boolean_t b) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::boolean;
+        j.m_data.m_value = b;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::string>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::string_t& s)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::string;
+        j.m_data.m_value = s;
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::string_t&& s)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::string;
+        j.m_data.m_value = std::move(s);
+        j.assert_invariant();
+    }
+
+    template < typename BasicJsonType, typename CompatibleStringType,
+               enable_if_t < !std::is_same<CompatibleStringType, typename BasicJsonType::string_t>::value,
+                             int > = 0 >
+    static void construct(BasicJsonType& j, const CompatibleStringType& str)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::string;
+        j.m_data.m_value.string = j.template create<typename BasicJsonType::string_t>(str);
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::binary>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::binary_t& b)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::binary;
+        j.m_data.m_value = typename BasicJsonType::binary_t(b);
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::binary_t&& b)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::binary;
+        j.m_data.m_value = typename BasicJsonType::binary_t(std::move(b));
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::number_float>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::number_float_t val) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::number_float;
+        j.m_data.m_value = val;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::number_unsigned>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::number_unsigned_t val) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::number_unsigned;
+        j.m_data.m_value = val;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::number_integer>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::number_integer_t val) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::number_integer;
+        j.m_data.m_value = val;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::array>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::array_t& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = arr;
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::array_t&& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = std::move(arr);
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template < typename BasicJsonType, typename CompatibleArrayType,
+               enable_if_t < !std::is_same<CompatibleArrayType, typename BasicJsonType::array_t>::value,
+                             int > = 0 >
+    static void construct(BasicJsonType& j, const CompatibleArrayType& arr)
+    {
+        using std::begin;
+        using std::end;
+
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value.array = j.template create<typename BasicJsonType::array_t>(begin(arr), end(arr));
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const std::vector<bool>& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = value_t::array;
+        j.m_data.m_value.array->reserve(arr.size());
+        for (const bool x : arr)
+        {
+            j.m_data.m_value.array->push_back(x);
+            j.set_parent(j.m_data.m_value.array->back());
+        }
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType, typename T,
+             enable_if_t<std::is_convertible<T, BasicJsonType>::value, int> = 0>
+    static void construct(BasicJsonType& j, const std::valarray<T>& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = value_t::array;
+        j.m_data.m_value.array->resize(arr.size());
+        if (arr.size() > 0)
+        {
+            std::copy(std::begin(arr), std::end(arr), j.m_data.m_value.array->begin());
+        }
+        j.set_parents();
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::object>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::object_t& obj)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::object;
+        j.m_data.m_value = obj;
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::object_t&& obj)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::object;
+        j.m_data.m_value = std::move(obj);
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template < typename BasicJsonType, typename CompatibleObjectType,
+               enable_if_t < !std::is_same<CompatibleObjectType, typename BasicJsonType::object_t>::value, int > = 0 >
+    static void construct(BasicJsonType& j, const CompatibleObjectType& obj)
+    {
+        using std::begin;
+        using std::end;
+
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::object;
+        j.m_data.m_value.object = j.template create<typename BasicJsonType::object_t>(begin(obj), end(obj));
+        j.set_parents();
+        j.assert_invariant();
+    }
+};
+
+/////////////
+// to_json //
+/////////////
+
+#ifdef JSON_HAS_CPP_17
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_constructible<BasicJsonType, T>::value, int> = 0>
+void to_json(BasicJsonType& j, const std::optional<T>& opt)
+{
+    if (opt.has_value())
+    {
+        j = *opt;
+    }
+    else
+    {
+        j = nullptr;
+    }
+}
+#endif
+
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_same<T, typename BasicJsonType::boolean_t>::value, int> = 0>
+inline void to_json(BasicJsonType& j, T b) noexcept
+{
+    external_constructor<value_t::boolean>::construct(j, b);
+}
+
+template < typename BasicJsonType, typename BoolRef,
+           enable_if_t <
+               ((std::is_same<std::vector<bool>::reference, BoolRef>::value
+                 && !std::is_same <std::vector<bool>::reference, typename BasicJsonType::boolean_t&>::value)
+                || (std::is_same<std::vector<bool>::const_reference, BoolRef>::value
+                    && !std::is_same <detail::uncvref_t<std::vector<bool>::const_reference>,
+                                      typename BasicJsonType::boolean_t >::value))
+               && std::is_convertible<const BoolRef&, typename BasicJsonType::boolean_t>::value, int > = 0 >
+inline void to_json(BasicJsonType& j, const BoolRef& b) noexcept
+{
+    external_constructor<value_t::boolean>::construct(j, static_cast<typename BasicJsonType::boolean_t>(b));
+}
+
+template<typename BasicJsonType, typename CompatibleString,
+         enable_if_t<std::is_constructible<typename BasicJsonType::string_t, CompatibleString>::value, int> = 0>
+inline void to_json(BasicJsonType& j, const CompatibleString& s)
+{
+    external_constructor<value_t::string>::construct(j, s);
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, typename BasicJsonType::string_t&& s)
+{
+    external_constructor<value_t::string>::construct(j, std::move(s));
+}
+
+template<typename BasicJsonType, typename FloatType,
+         enable_if_t<std::is_floating_point<FloatType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, FloatType val) noexcept
+{
+    external_constructor<value_t::number_float>::construct(j, static_cast<typename BasicJsonType::number_float_t>(val));
+}
+
+template<typename BasicJsonType, typename CompatibleNumberUnsignedType,
+         enable_if_t<is_compatible_integer_type<typename BasicJsonType::number_unsigned_t, CompatibleNumberUnsignedType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, CompatibleNumberUnsignedType val) noexcept
+{
+    external_constructor<value_t::number_unsigned>::construct(j, static_cast<typename BasicJsonType::number_unsigned_t>(val));
+}
+
+template<typename BasicJsonType, typename CompatibleNumberIntegerType,
+         enable_if_t<is_compatible_integer_type<typename BasicJsonType::number_integer_t, CompatibleNumberIntegerType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, CompatibleNumberIntegerType val) noexcept
+{
+    external_constructor<value_t::number_integer>::construct(j, static_cast<typename BasicJsonType::number_integer_t>(val));
+}
+
+#if !JSON_DISABLE_ENUM_SERIALIZATION
+template<typename BasicJsonType, typename EnumType,
+         enable_if_t<std::is_enum<EnumType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, EnumType e) noexcept
+{
+    using underlying_type = typename std::underlying_type<EnumType>::type;
+    static constexpr value_t integral_value_t = std::is_unsigned<underlying_type>::value ? value_t::number_unsigned : value_t::number_integer;
+    external_constructor<integral_value_t>::construct(j, static_cast<underlying_type>(e));
+}
+#endif  // JSON_DISABLE_ENUM_SERIALIZATION
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, const std::vector<bool>& e)
+{
+    external_constructor<value_t::array>::construct(j, e);
+}
+
+template < typename BasicJsonType, typename CompatibleArrayType,
+           enable_if_t < is_compatible_array_type<BasicJsonType,
+                         CompatibleArrayType>::value&&
+                         !is_compatible_object_type<BasicJsonType, CompatibleArrayType>::value&&
+                         !is_compatible_string_type<BasicJsonType, CompatibleArrayType>::value&&
+                         !std::is_same<typename BasicJsonType::binary_t, CompatibleArrayType>::value&&
+                         !is_basic_json<CompatibleArrayType>::value,
+                         int > = 0 >
+inline void to_json(BasicJsonType& j, const CompatibleArrayType& arr)
+{
+    external_constructor<value_t::array>::construct(j, arr);
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, const typename BasicJsonType::binary_t& bin)
+{
+    external_constructor<value_t::binary>::construct(j, bin);
+}
+
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_convertible<T, BasicJsonType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, const std::valarray<T>& arr)
+{
+    external_constructor<value_t::array>::construct(j, std::move(arr));
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, typename BasicJsonType::array_t&& arr)
+{
+    external_constructor<value_t::array>::construct(j, std::move(arr));
+}
+
+template < typename BasicJsonType, typename CompatibleObjectType,
+           enable_if_t < is_compatible_object_type<BasicJsonType, CompatibleObjectType>::value&& !is_basic_json<CompatibleObjectType>::value, int > = 0 >
+inline void to_json(BasicJsonType& j, const CompatibleObjectType& obj)
+{
+    external_constructor<value_t::object>::construct(j, obj);
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, typename BasicJsonType::object_t&& obj)
+{
+    external_constructor<value_t::object>::construct(j, std::move(obj));
+}
+
+template <
+    typename BasicJsonType, typename T, std::size_t N,
+    enable_if_t < !std::is_constructible<typename BasicJsonType::string_t,
+                  const T(&)[N]>::value, // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+                  int > = 0 >
+inline void to_json(BasicJsonType& j, const T(&arr)[N]) // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+{
+    external_constructor<value_t::array>::construct(j, arr);
+}
+
+template < typename BasicJsonType, typename T1, typename T2, enable_if_t < std::is_constructible<BasicJsonType, T1>::value&& std::is_constructible<BasicJsonType, T2>::value, int > = 0 >
+inline void to_json(BasicJsonType& j, const std::pair<T1, T2>& p)
+{
+    j = { p.first, p.second };
+}
+
+// for https://github.com/nlohmann/json/pull/1134
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_same<T, iteration_proxy_value<typename BasicJsonType::iterator>>::value, int> = 0>
+inline void to_json(BasicJsonType& j, const T& b)
+{
+    j = { {b.key(), b.value()} };
+}
+
+template<typename BasicJsonType, typename Tuple, std::size_t... Idx>
+inline void to_json_tuple_impl(BasicJsonType& j, const Tuple& t, index_sequence<Idx...> /*unused*/)
+{
+    j = { std::get<Idx>(t)... };
+}
+
+template<typename BasicJsonType, typename Tuple>
+inline void to_json_tuple_impl(BasicJsonType& j, const Tuple& /*unused*/, index_sequence<> /*unused*/)
+{
+    using array_t = typename BasicJsonType::array_t;
+    j = array_t();
+}
+
+template<typename BasicJsonType, typename T, enable_if_t<is_constructible_tuple<BasicJsonType, T>::value, int > = 0>
+inline void to_json(BasicJsonType& j, const T& t)
+{
+    to_json_tuple_impl(j, t, make_index_sequence<std::tuple_size<T>::value> {});
+}
+
+#if JSON_HAS_FILESYSTEM || JSON_HAS_EXPERIMENTAL_FILESYSTEM
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, const std_fs::path& p)
+{
+#ifdef JSON_HAS_CPP_20
+    const std::u8string s = p.u8string();
+    j = std::string(s.begin(), s.end());
+#else
+    j = p.u8string(); // returns std::string in C++17
+#endif
+}
+#endif
+
+struct to_json_fn
+{
+    template<typename BasicJsonType, typename T>
+    auto operator()(BasicJsonType& j, T&& val) const noexcept(noexcept(to_json(j, std::forward<T>(val))))
+    -> decltype(to_json(j, std::forward<T>(val)), void())
+    {
+        return to_json(j, std::forward<T>(val));
+    }
+};
+}  // namespace detail
+
+#ifndef JSON_HAS_CPP_17
+/// namespace to hold default `to_json` function
+/// to see why this is required:
+/// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/n4381.html
+namespace // NOLINT(cert-dcl59-cpp,fuchsia-header-anon-namespaces,google-build-namespaces)
+{
+#endif
+JSON_INLINE_VARIABLE constexpr const auto& to_json = // NOLINT(misc-definitions-in-headers)
+    detail::static_const<detail::to_json_fn>::value;
+#ifndef JSON_HAS_CPP_17
+}  // namespace
+#endif
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/identity_tag.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// @sa https://json.nlohmann.me/api/adl_serializer/
+template<typename ValueType, typename>
+struct adl_serializer
+{
+    /// @brief convert a JSON value to any value type
+    /// @sa https://json.nlohmann.me/api/adl_serializer/from_json/
+    template<typename BasicJsonType, typename TargetType = ValueType>
+    static auto from_json(BasicJsonType && j, TargetType& val) noexcept(
+        noexcept(::nlohmann::from_json(std::forward<BasicJsonType>(j), val)))
+    -> decltype(::nlohmann::from_json(std::forward<BasicJsonType>(j), val), void())
+    {
+        ::nlohmann::from_json(std::forward<BasicJsonType>(j), val);
+    }
+
+    /// @brief convert a JSON value to any value type
+    /// @sa https://json.nlohmann.me/api/adl_serializer/from_json/
+    template<typename BasicJsonType, typename TargetType = ValueType>
+    static auto from_json(BasicJsonType && j) noexcept(
+    noexcept(::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {})))
+    -> decltype(::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {}))
+    {
+        return ::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {});
+    }
+
+    /// @brief convert any value type to a JSON value
+    /// @sa https://json.nlohmann.me/api/adl_serializer/to_json/
+    template<typename BasicJsonType, typename TargetType = ValueType>
+    static auto to_json(BasicJsonType& j, TargetType && val) noexcept(
+        noexcept(::nlohmann::to_json(j, std::forward<TargetType>(val))))
+    -> decltype(::nlohmann::to_json(j, std::forward<TargetType>(val)), void())
+    {
+        ::nlohmann::to_json(j, std::forward<TargetType>(val));
+    }
+};
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/byte_container_with_subtype.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // uint8_t, uint64_t
+#include <tuple> // tie
+#include <utility> // move
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// @brief an internal type for a backed binary type
+/// @sa https://json.nlohmann.me/api/byte_container_with_subtype/
+template<typename BinaryType>
+class byte_container_with_subtype : public BinaryType
+{
+  public:
+    using container_type = BinaryType;
+    using subtype_type = std::uint64_t;
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype() noexcept(noexcept(container_type()))
+        : container_type()
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(const container_type& b) noexcept(noexcept(container_type(b)))
+        : container_type(b)
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(container_type&& b) noexcept(noexcept(container_type(std::move(b))))
+        : container_type(std::move(b))
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(const container_type& b, subtype_type subtype_) noexcept(noexcept(container_type(b)))
+        : container_type(b)
+        , m_subtype(subtype_)
+        , m_has_subtype(true)
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(container_type&& b, subtype_type subtype_) noexcept(noexcept(container_type(std::move(b))))
+        : container_type(std::move(b))
+        , m_subtype(subtype_)
+        , m_has_subtype(true)
+    {}
+
+    bool operator==(const byte_container_with_subtype& rhs) const
+    {
+        return std::tie(static_cast<const BinaryType&>(*this), m_subtype, m_has_subtype) ==
+               std::tie(static_cast<const BinaryType&>(rhs), rhs.m_subtype, rhs.m_has_subtype);
+    }
+
+    bool operator!=(const byte_container_with_subtype& rhs) const
+    {
+        return !(rhs == *this);
+    }
+
+    /// @brief sets the binary subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/set_subtype/
+    void set_subtype(subtype_type subtype_) noexcept
+    {
+        m_subtype = subtype_;
+        m_has_subtype = true;
+    }
+
+    /// @brief return the binary subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/subtype/
+    constexpr subtype_type subtype() const noexcept
+    {
+        return m_has_subtype ? m_subtype : static_cast<subtype_type>(-1);
+    }
+
+    /// @brief return whether the value has a subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/has_subtype/
+    constexpr bool has_subtype() const noexcept
+    {
+        return m_has_subtype;
+    }
+
+    /// @brief clears the binary subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/clear_subtype/
+    void clear_subtype() noexcept
+    {
+        m_subtype = 0;
+        m_has_subtype = false;
+    }
+
+  private:
+    subtype_type m_subtype = 0;
+    bool m_has_subtype = false;
+};
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/conversions/from_json.hpp>
+
+// #include <nlohmann/detail/conversions/to_json.hpp>
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/hash.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // uint8_t
+#include <cstddef> // size_t
+#include <functional> // hash
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// boost::hash_combine
+inline std::size_t combine(std::size_t seed, std::size_t h) noexcept
+{
+    seed ^= h + 0x9e3779b9 + (seed << 6U) + (seed >> 2U);
+    return seed;
+}
+
+/*!
+@brief hash a JSON value
+
+The hash function tries to rely on std::hash where possible. Furthermore, the
+type of the JSON value is taken into account to have different hash values for
+null, 0, 0U, and false, etc.
+
+@tparam BasicJsonType basic_json specialization
+@param j JSON value to hash
+@return hash value of j
+*/
+template<typename BasicJsonType>
+std::size_t hash(const BasicJsonType& j)
+{
+    using string_t = typename BasicJsonType::string_t;
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+
+    const auto type = static_cast<std::size_t>(j.type());
+    switch (j.type())
+    {
+        case BasicJsonType::value_t::null:
+        case BasicJsonType::value_t::discarded:
+        {
+            return combine(type, 0);
+        }
+
+        case BasicJsonType::value_t::object:
+        {
+            auto seed = combine(type, j.size());
+            for (const auto& element : j.items())
+            {
+                const auto h = std::hash<string_t> {}(element.key());
+                seed = combine(seed, h);
+                seed = combine(seed, hash(element.value()));
+            }
+            return seed;
+        }
+
+        case BasicJsonType::value_t::array:
+        {
+            auto seed = combine(type, j.size());
+            for (const auto& element : j)
+            {
+                seed = combine(seed, hash(element));
+            }
+            return seed;
+        }
+
+        case BasicJsonType::value_t::string:
+        {
+            const auto h = std::hash<string_t> {}(j.template get_ref<const string_t&>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::boolean:
+        {
+            const auto h = std::hash<bool> {}(j.template get<bool>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::number_integer:
+        {
+            const auto h = std::hash<number_integer_t> {}(j.template get<number_integer_t>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::number_unsigned:
+        {
+            const auto h = std::hash<number_unsigned_t> {}(j.template get<number_unsigned_t>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::number_float:
+        {
+            const auto h = std::hash<number_float_t> {}(j.template get<number_float_t>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::binary:
+        {
+            auto seed = combine(type, j.get_binary().size());
+            const auto h = std::hash<bool> {}(j.get_binary().has_subtype());
+            seed = combine(seed, h);
+            seed = combine(seed, static_cast<std::size_t>(j.get_binary().subtype()));
+            for (const auto byte : j.get_binary())
+            {
+                seed = combine(seed, std::hash<std::uint8_t> {}(byte));
+            }
+            return seed;
+        }
+
+        default:                   // LCOV_EXCL_LINE
+            JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+            return 0;              // LCOV_EXCL_LINE
+    }
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/binary_reader.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // generate_n
+#include <array> // array
+#include <cmath> // ldexp
+#include <cstddef> // size_t
+#include <cstdint> // uint8_t, uint16_t, uint32_t, uint64_t
+#include <cstdio> // snprintf
+#include <cstring> // memcpy
+#include <iterator> // back_inserter
+#include <limits> // numeric_limits
+#include <string> // char_traits, string
+#include <utility> // make_pair, move
+#include <vector> // vector
+#ifdef __cpp_lib_byteswap
+    #include <bit>  //byteswap
+#endif
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstddef> // size_t
+#include <cstring> // strlen
+#include <iterator> // begin, end, iterator_traits, random_access_iterator_tag, distance, next
+#include <memory> // shared_ptr, make_shared, addressof
+#include <numeric> // accumulate
+#include <string> // string, char_traits
+#include <type_traits> // enable_if, is_base_of, is_pointer, is_integral, remove_pointer
+#include <utility> // pair, declval
+
+#ifndef JSON_NO_IO
+    #include <cstdio>   // FILE *
+    #include <istream>  // istream
+#endif                  // JSON_NO_IO
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/iterators/iterator_traits.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// the supported input formats
+enum class input_format_t { json, cbor, msgpack, ubjson, bson, bjdata };
+
+////////////////////
+// input adapters //
+////////////////////
+
+#ifndef JSON_NO_IO
+/*!
+Input adapter for stdio file access. This adapter read only 1 byte and do not use any
+ buffer. This adapter is a very low level adapter.
+*/
+class file_input_adapter
+{
+  public:
+    using char_type = char;
+
+    JSON_HEDLEY_NON_NULL(2)
+    explicit file_input_adapter(std::FILE* f) noexcept
+        : m_file(f)
+    {
+        JSON_ASSERT(m_file != nullptr);
+    }
+
+    // make class move-only
+    file_input_adapter(const file_input_adapter&) = delete;
+    file_input_adapter(file_input_adapter&&) noexcept = default;
+    file_input_adapter& operator=(const file_input_adapter&) = delete;
+    file_input_adapter& operator=(file_input_adapter&&) = delete;
+    ~file_input_adapter() = default;
+
+    std::char_traits<char>::int_type get_character() noexcept
+    {
+        return std::fgetc(m_file);
+    }
+
+    // returns the number of characters successfully read
+    template<class T>
+    std::size_t get_elements(T* dest, std::size_t count = 1)
+    {
+        return fread(dest, 1, sizeof(T) * count, m_file);
+    }
+
+  private:
+    /// the file pointer to read from
+    std::FILE* m_file;
+};
+
+/*!
+Input adapter for a (caching) istream. Ignores a UFT Byte Order Mark at
+beginning of input. Does not support changing the underlying std::streambuf
+in mid-input. Maintains underlying std::istream and std::streambuf to support
+subsequent use of standard std::istream operations to process any input
+characters following those used in parsing the JSON input.  Clears the
+std::istream flags; any input errors (e.g., EOF) will be detected by the first
+subsequent call for input from the std::istream.
+*/
+class input_stream_adapter
+{
+  public:
+    using char_type = char;
+
+    ~input_stream_adapter()
+    {
+        // clear stream flags; we use underlying streambuf I/O, do not
+        // maintain ifstream flags, except eof
+        if (is != nullptr)
+        {
+            is->clear(is->rdstate() & std::ios::eofbit);
+        }
+    }
+
+    explicit input_stream_adapter(std::istream& i)
+        : is(&i), sb(i.rdbuf())
+    {}
+
+    // delete because of pointer members
+    input_stream_adapter(const input_stream_adapter&) = delete;
+    input_stream_adapter& operator=(input_stream_adapter&) = delete;
+    input_stream_adapter& operator=(input_stream_adapter&&) = delete;
+
+    input_stream_adapter(input_stream_adapter&& rhs) noexcept
+        : is(rhs.is), sb(rhs.sb)
+    {
+        rhs.is = nullptr;
+        rhs.sb = nullptr;
+    }
+
+    // std::istream/std::streambuf use std::char_traits<char>::to_int_type, to
+    // ensure that std::char_traits<char>::eof() and the character 0xFF do not
+    // end up as the same value, e.g. 0xFFFFFFFF.
+    std::char_traits<char>::int_type get_character()
+    {
+        auto res = sb->sbumpc();
+        // set eof manually, as we don't use the istream interface.
+        if (JSON_HEDLEY_UNLIKELY(res == std::char_traits<char>::eof()))
+        {
+            is->clear(is->rdstate() | std::ios::eofbit);
+        }
+        return res;
+    }
+
+    template<class T>
+    std::size_t get_elements(T* dest, std::size_t count = 1)
+    {
+        auto res = static_cast<std::size_t>(sb->sgetn(reinterpret_cast<char*>(dest), static_cast<std::streamsize>(count * sizeof(T))));
+        if (JSON_HEDLEY_UNLIKELY(res < count * sizeof(T)))
+        {
+            is->clear(is->rdstate() | std::ios::eofbit);
+        }
+        return res;
+    }
+
+  private:
+    /// the associated input stream
+    std::istream* is = nullptr;
+    std::streambuf* sb = nullptr;
+};
+#endif  // JSON_NO_IO
+
+// General-purpose iterator-based adapter. It might not be as fast as
+// theoretically possible for some containers, but it is extremely versatile.
+template<typename IteratorType>
+class iterator_input_adapter
+{
+  public:
+    using char_type = typename std::iterator_traits<IteratorType>::value_type;
+
+    iterator_input_adapter(IteratorType first, IteratorType last)
+        : current(std::move(first)), end(std::move(last))
+    {}
+
+    typename char_traits<char_type>::int_type get_character()
+    {
+        if (JSON_HEDLEY_LIKELY(current != end))
+        {
+            auto result = char_traits<char_type>::to_int_type(*current);
+            std::advance(current, 1);
+            return result;
+        }
+
+        return char_traits<char_type>::eof();
+    }
+
+    // for general iterators, we cannot really do something better than falling back to processing the range one-by-one
+    template<class T>
+    std::size_t get_elements(T* dest, std::size_t count = 1)
+    {
+        auto* ptr = reinterpret_cast<char*>(dest);
+        for (std::size_t read_index = 0; read_index < count * sizeof(T); ++read_index)
+        {
+            if (JSON_HEDLEY_LIKELY(current != end))
+            {
+                ptr[read_index] = static_cast<char>(*current);
+                std::advance(current, 1);
+            }
+            else
+            {
+                return read_index;
+            }
+        }
+        return count * sizeof(T);
+    }
+
+  private:
+    IteratorType current;
+    IteratorType end;
+
+    template<typename BaseInputAdapter, size_t T>
+    friend struct wide_string_input_helper;
+
+    bool empty() const
+    {
+        return current == end;
+    }
+};
+
+template<typename BaseInputAdapter, size_t T>
+struct wide_string_input_helper;
+
+template<typename BaseInputAdapter>
+struct wide_string_input_helper<BaseInputAdapter, 4>
+{
+    // UTF-32
+    static void fill_buffer(BaseInputAdapter& input,
+                            std::array<std::char_traits<char>::int_type, 4>& utf8_bytes,
+                            size_t& utf8_bytes_index,
+                            size_t& utf8_bytes_filled)
+    {
+        utf8_bytes_index = 0;
+
+        if (JSON_HEDLEY_UNLIKELY(input.empty()))
+        {
+            utf8_bytes[0] = std::char_traits<char>::eof();
+            utf8_bytes_filled = 1;
+        }
+        else
+        {
+            // get the current character
+            const auto wc = input.get_character();
+
+            // UTF-32 to UTF-8 encoding
+            if (wc < 0x80)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                utf8_bytes_filled = 1;
+            }
+            else if (wc <= 0x7FF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xC0u | ((static_cast<unsigned int>(wc) >> 6u) & 0x1Fu));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 2;
+            }
+            else if (wc <= 0xFFFF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xE0u | ((static_cast<unsigned int>(wc) >> 12u) & 0x0Fu));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));
+                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 3;
+            }
+            else if (wc <= 0x10FFFF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xF0u | ((static_cast<unsigned int>(wc) >> 18u) & 0x07u));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 12u) & 0x3Fu));
+                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));
+                utf8_bytes[3] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 4;
+            }
+            else
+            {
+                // unknown character
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                utf8_bytes_filled = 1;
+            }
+        }
+    }
+};
+
+template<typename BaseInputAdapter>
+struct wide_string_input_helper<BaseInputAdapter, 2>
+{
+    // UTF-16
+    static void fill_buffer(BaseInputAdapter& input,
+                            std::array<std::char_traits<char>::int_type, 4>& utf8_bytes,
+                            size_t& utf8_bytes_index,
+                            size_t& utf8_bytes_filled)
+    {
+        utf8_bytes_index = 0;
+
+        if (JSON_HEDLEY_UNLIKELY(input.empty()))
+        {
+            utf8_bytes[0] = std::char_traits<char>::eof();
+            utf8_bytes_filled = 1;
+        }
+        else
+        {
+            // get the current character
+            const auto wc = input.get_character();
+
+            // UTF-16 to UTF-8 encoding
+            if (wc < 0x80)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                utf8_bytes_filled = 1;
+            }
+            else if (wc <= 0x7FF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xC0u | ((static_cast<unsigned int>(wc) >> 6u)));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 2;
+            }
+            else if (0xD800 > wc || wc >= 0xE000)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xE0u | ((static_cast<unsigned int>(wc) >> 12u)));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));
+                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 3;
+            }
+            else
+            {
+                if (JSON_HEDLEY_UNLIKELY(!input.empty()))
+                {
+                    const auto wc2 = static_cast<unsigned int>(input.get_character());
+                    const auto charcode = 0x10000u + (((static_cast<unsigned int>(wc) & 0x3FFu) << 10u) | (wc2 & 0x3FFu));
+                    utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xF0u | (charcode >> 18u));
+                    utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((charcode >> 12u) & 0x3Fu));
+                    utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | ((charcode >> 6u) & 0x3Fu));
+                    utf8_bytes[3] = static_cast<std::char_traits<char>::int_type>(0x80u | (charcode & 0x3Fu));
+                    utf8_bytes_filled = 4;
+                }
+                else
+                {
+                    utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                    utf8_bytes_filled = 1;
+                }
+            }
+        }
+    }
+};
+
+// Wraps another input adapter to convert wide character types into individual bytes.
+template<typename BaseInputAdapter, typename WideCharType>
+class wide_string_input_adapter
+{
+  public:
+    using char_type = char;
+
+    wide_string_input_adapter(BaseInputAdapter base)
+        : base_adapter(base) {}
+
+    typename std::char_traits<char>::int_type get_character() noexcept
+    {
+        // check if buffer needs to be filled
+        if (utf8_bytes_index == utf8_bytes_filled)
+        {
+            fill_buffer<sizeof(WideCharType)>();
+
+            JSON_ASSERT(utf8_bytes_filled > 0);
+            JSON_ASSERT(utf8_bytes_index == 0);
+        }
+
+        // use buffer
+        JSON_ASSERT(utf8_bytes_filled > 0);
+        JSON_ASSERT(utf8_bytes_index < utf8_bytes_filled);
+        return utf8_bytes[utf8_bytes_index++];
+    }
+
+    // parsing binary with wchar doesn't make sense, but since the parsing mode can be runtime, we need something here
+    template<class T>
+    std::size_t get_elements(T* /*dest*/, std::size_t /*count*/ = 1)
+    {
+        JSON_THROW(parse_error::create(112, 1, "wide string type cannot be interpreted as binary data", nullptr));
+    }
+
+  private:
+    BaseInputAdapter base_adapter;
+
+    template<size_t T>
+    void fill_buffer()
+    {
+        wide_string_input_helper<BaseInputAdapter, T>::fill_buffer(base_adapter, utf8_bytes, utf8_bytes_index, utf8_bytes_filled);
+    }
+
+    /// a buffer for UTF-8 bytes
+    std::array<std::char_traits<char>::int_type, 4> utf8_bytes = {{0, 0, 0, 0}};
+
+    /// index to the utf8_codes array for the next valid byte
+    std::size_t utf8_bytes_index = 0;
+    /// number of valid bytes in the utf8_codes array
+    std::size_t utf8_bytes_filled = 0;
+};
+
+template<typename IteratorType, typename Enable = void>
+struct iterator_input_adapter_factory
+{
+    using iterator_type = IteratorType;
+    using char_type = typename std::iterator_traits<iterator_type>::value_type;
+    using adapter_type = iterator_input_adapter<iterator_type>;
+
+    static adapter_type create(IteratorType first, IteratorType last)
+    {
+        return adapter_type(std::move(first), std::move(last));
+    }
+};
+
+template<typename T>
+struct is_iterator_of_multibyte
+{
+    using value_type = typename std::iterator_traits<T>::value_type;
+    enum
+    {
+        value = sizeof(value_type) > 1
+    };
+};
+
+template<typename IteratorType>
+struct iterator_input_adapter_factory<IteratorType, enable_if_t<is_iterator_of_multibyte<IteratorType>::value>>
+{
+    using iterator_type = IteratorType;
+    using char_type = typename std::iterator_traits<iterator_type>::value_type;
+    using base_adapter_type = iterator_input_adapter<iterator_type>;
+    using adapter_type = wide_string_input_adapter<base_adapter_type, char_type>;
+
+    static adapter_type create(IteratorType first, IteratorType last)
+    {
+        return adapter_type(base_adapter_type(std::move(first), std::move(last)));
+    }
+};
+
+// General purpose iterator-based input
+template<typename IteratorType>
+typename iterator_input_adapter_factory<IteratorType>::adapter_type input_adapter(IteratorType first, IteratorType last)
+{
+    using factory_type = iterator_input_adapter_factory<IteratorType>;
+    return factory_type::create(first, last);
+}
+
+// Convenience shorthand from container to iterator
+// Enables ADL on begin(container) and end(container)
+// Encloses the using declarations in namespace for not to leak them to outside scope
+
+namespace container_input_adapter_factory_impl
+{
+
+using std::begin;
+using std::end;
+
+template<typename ContainerType, typename Enable = void>
+struct container_input_adapter_factory {};
+
+template<typename ContainerType>
+struct container_input_adapter_factory< ContainerType,
+       void_t<decltype(begin(std::declval<ContainerType>()), end(std::declval<ContainerType>()))>>
+       {
+           using adapter_type = decltype(input_adapter(begin(std::declval<ContainerType>()), end(std::declval<ContainerType>())));
+
+           static adapter_type create(const ContainerType& container)
+{
+    return input_adapter(begin(container), end(container));
+}
+       };
+
+}  // namespace container_input_adapter_factory_impl
+
+template<typename ContainerType>
+typename container_input_adapter_factory_impl::container_input_adapter_factory<ContainerType>::adapter_type input_adapter(const ContainerType& container)
+{
+    return container_input_adapter_factory_impl::container_input_adapter_factory<ContainerType>::create(container);
+}
+
+// specialization for std::string
+using string_input_adapter_type = decltype(input_adapter(std::declval<std::string>()));
+
+#ifndef JSON_NO_IO
+// Special cases with fast paths
+inline file_input_adapter input_adapter(std::FILE* file)
+{
+    if (file == nullptr)
+    {
+        JSON_THROW(parse_error::create(101, 0, "attempting to parse an empty input; check that your input string or stream contains the expected JSON", nullptr));
+    }
+    return file_input_adapter(file);
+}
+
+inline input_stream_adapter input_adapter(std::istream& stream)
+{
+    return input_stream_adapter(stream);
+}
+
+inline input_stream_adapter input_adapter(std::istream&& stream)
+{
+    return input_stream_adapter(stream);
+}
+#endif  // JSON_NO_IO
+
+using contiguous_bytes_input_adapter = decltype(input_adapter(std::declval<const char*>(), std::declval<const char*>()));
+
+// Null-delimited strings, and the like.
+template < typename CharT,
+           typename std::enable_if <
+               std::is_pointer<CharT>::value&&
+               !std::is_array<CharT>::value&&
+               std::is_integral<typename std::remove_pointer<CharT>::type>::value&&
+               sizeof(typename std::remove_pointer<CharT>::type) == 1,
+               int >::type = 0 >
+contiguous_bytes_input_adapter input_adapter(CharT b)
+{
+    if (b == nullptr)
+    {
+        JSON_THROW(parse_error::create(101, 0, "attempting to parse an empty input; check that your input string or stream contains the expected JSON", nullptr));
+    }
+    auto length = std::strlen(reinterpret_cast<const char*>(b));
+    const auto* ptr = reinterpret_cast<const char*>(b);
+    return input_adapter(ptr, ptr + length); // cppcheck-suppress[nullPointerArithmeticRedundantCheck]
+}
+
+template<typename T, std::size_t N>
+auto input_adapter(T (&array)[N]) -> decltype(input_adapter(array, array + N)) // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+{
+    return input_adapter(array, array + N);
+}
+
+// This class only handles inputs of input_buffer_adapter type.
+// It's required so that expressions like {ptr, len} can be implicitly cast
+// to the correct adapter.
+class span_input_adapter
+{
+  public:
+    template < typename CharT,
+               typename std::enable_if <
+                   std::is_pointer<CharT>::value&&
+                   std::is_integral<typename std::remove_pointer<CharT>::type>::value&&
+                   sizeof(typename std::remove_pointer<CharT>::type) == 1,
+                   int >::type = 0 >
+    span_input_adapter(CharT b, std::size_t l)
+        : ia(reinterpret_cast<const char*>(b), reinterpret_cast<const char*>(b) + l) {}
+
+    template<class IteratorType,
+             typename std::enable_if<
+                 std::is_same<typename iterator_traits<IteratorType>::iterator_category, std::random_access_iterator_tag>::value,
+                 int>::type = 0>
+    span_input_adapter(IteratorType first, IteratorType last)
+        : ia(input_adapter(first, last)) {}
+
+    contiguous_bytes_input_adapter&& get()
+    {
+        return std::move(ia); // NOLINT(hicpp-move-const-arg,performance-move-const-arg)
+    }
+
+  private:
+    contiguous_bytes_input_adapter ia;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/json_sax.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef>
+#include <string> // string
+#include <type_traits> // enable_if_t
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/input/lexer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <clocale> // localeconv
+#include <cstddef> // size_t
+#include <cstdio> // snprintf
+#include <cstdlib> // strtof, strtod, strtold, strtoll, strtoull
+#include <initializer_list> // initializer_list
+#include <string> // char_traits, string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+
+// #include <nlohmann/detail/input/position_t.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+///////////
+// lexer //
+///////////
+
+template<typename BasicJsonType>
+class lexer_base
+{
+  public:
+    /// token types for the parser
+    enum class token_type
+    {
+        uninitialized,    ///< indicating the scanner is uninitialized
+        literal_true,     ///< the `true` literal
+        literal_false,    ///< the `false` literal
+        literal_null,     ///< the `null` literal
+        value_string,     ///< a string -- use get_string() for actual value
+        value_unsigned,   ///< an unsigned integer -- use get_number_unsigned() for actual value
+        value_integer,    ///< a signed integer -- use get_number_integer() for actual value
+        value_float,      ///< an floating point number -- use get_number_float() for actual value
+        begin_array,      ///< the character for array begin `[`
+        begin_object,     ///< the character for object begin `{`
+        end_array,        ///< the character for array end `]`
+        end_object,       ///< the character for object end `}`
+        name_separator,   ///< the name separator `:`
+        value_separator,  ///< the value separator `,`
+        parse_error,      ///< indicating a parse error
+        end_of_input,     ///< indicating the end of the input buffer
+        literal_or_value  ///< a literal or the begin of a value (only for diagnostics)
+    };
+
+    /// return name of values of type token_type (only used for errors)
+    JSON_HEDLEY_RETURNS_NON_NULL
+    JSON_HEDLEY_CONST
+    static const char* token_type_name(const token_type t) noexcept
+    {
+        switch (t)
+        {
+            case token_type::uninitialized:
+                return "<uninitialized>";
+            case token_type::literal_true:
+                return "true literal";
+            case token_type::literal_false:
+                return "false literal";
+            case token_type::literal_null:
+                return "null literal";
+            case token_type::value_string:
+                return "string literal";
+            case token_type::value_unsigned:
+            case token_type::value_integer:
+            case token_type::value_float:
+                return "number literal";
+            case token_type::begin_array:
+                return "'['";
+            case token_type::begin_object:
+                return "'{'";
+            case token_type::end_array:
+                return "']'";
+            case token_type::end_object:
+                return "'}'";
+            case token_type::name_separator:
+                return "':'";
+            case token_type::value_separator:
+                return "','";
+            case token_type::parse_error:
+                return "<parse error>";
+            case token_type::end_of_input:
+                return "end of input";
+            case token_type::literal_or_value:
+                return "'[', '{', or a literal";
+            // LCOV_EXCL_START
+            default: // catch non-enum values
+                return "unknown token";
+                // LCOV_EXCL_STOP
+        }
+    }
+};
+/*!
+@brief lexical analysis
+
+This class organizes the lexical analysis during JSON deserialization.
+*/
+template<typename BasicJsonType, typename InputAdapterType>
+class lexer : public lexer_base<BasicJsonType>
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using char_type = typename InputAdapterType::char_type;
+    using char_int_type = typename char_traits<char_type>::int_type;
+
+  public:
+    using token_type = typename lexer_base<BasicJsonType>::token_type;
+
+    explicit lexer(InputAdapterType&& adapter, bool ignore_comments_ = false) noexcept
+        : ia(std::move(adapter))
+        , ignore_comments(ignore_comments_)
+        , decimal_point_char(static_cast<char_int_type>(get_decimal_point()))
+    {}
+
+    // delete because of pointer members
+    lexer(const lexer&) = delete;
+    lexer(lexer&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    lexer& operator=(lexer&) = delete;
+    lexer& operator=(lexer&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~lexer() = default;
+
+  private:
+    /////////////////////
+    // locales
+    /////////////////////
+
+    /// return the locale-dependent decimal point
+    JSON_HEDLEY_PURE
+    static char get_decimal_point() noexcept
+    {
+        const auto* loc = localeconv();
+        JSON_ASSERT(loc != nullptr);
+        return (loc->decimal_point == nullptr) ? '.' : *(loc->decimal_point);
+    }
+
+    /////////////////////
+    // scan functions
+    /////////////////////
+
+    /*!
+    @brief get codepoint from 4 hex characters following `\u`
+
+    For input "\u c1 c2 c3 c4" the codepoint is:
+      (c1 * 0x1000) + (c2 * 0x0100) + (c3 * 0x0010) + c4
+    = (c1 << 12) + (c2 << 8) + (c3 << 4) + (c4 << 0)
+
+    Furthermore, the possible characters '0'..'9', 'A'..'F', and 'a'..'f'
+    must be converted to the integers 0x0..0x9, 0xA..0xF, 0xA..0xF, resp. The
+    conversion is done by subtracting the offset (0x30, 0x37, and 0x57)
+    between the ASCII value of the character and the desired integer value.
+
+    @return codepoint (0x0000..0xFFFF) or -1 in case of an error (e.g. EOF or
+            non-hex character)
+    */
+    int get_codepoint()
+    {
+        // this function only makes sense after reading `\u`
+        JSON_ASSERT(current == 'u');
+        int codepoint = 0;
+
+        const auto factors = { 12u, 8u, 4u, 0u };
+        for (const auto factor : factors)
+        {
+            get();
+
+            if (current >= '0' && current <= '9')
+            {
+                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x30u) << factor);
+            }
+            else if (current >= 'A' && current <= 'F')
+            {
+                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x37u) << factor);
+            }
+            else if (current >= 'a' && current <= 'f')
+            {
+                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x57u) << factor);
+            }
+            else
+            {
+                return -1;
+            }
+        }
+
+        JSON_ASSERT(0x0000 <= codepoint && codepoint <= 0xFFFF);
+        return codepoint;
+    }
+
+    /*!
+    @brief check if the next byte(s) are inside a given range
+
+    Adds the current byte and, for each passed range, reads a new byte and
+    checks if it is inside the range. If a violation was detected, set up an
+    error message and return false. Otherwise, return true.
+
+    @param[in] ranges  list of integers; interpreted as list of pairs of
+                       inclusive lower and upper bound, respectively
+
+    @pre The passed list @a ranges must have 2, 4, or 6 elements; that is,
+         1, 2, or 3 pairs. This precondition is enforced by an assertion.
+
+    @return true if and only if no range violation was detected
+    */
+    bool next_byte_in_range(std::initializer_list<char_int_type> ranges)
+    {
+        JSON_ASSERT(ranges.size() == 2 || ranges.size() == 4 || ranges.size() == 6);
+        add(current);
+
+        for (auto range = ranges.begin(); range != ranges.end(); ++range)
+        {
+            get();
+            if (JSON_HEDLEY_LIKELY(*range <= current && current <= *(++range))) // NOLINT(bugprone-inc-dec-in-conditions)
+            {
+                add(current);
+            }
+            else
+            {
+                error_message = "invalid string: ill-formed UTF-8 byte";
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    /*!
+    @brief scan a string literal
+
+    This function scans a string according to Sect. 7 of RFC 8259. While
+    scanning, bytes are escaped and copied into buffer token_buffer. Then the
+    function returns successfully, token_buffer is *not* null-terminated (as it
+    may contain \0 bytes), and token_buffer.size() is the number of bytes in the
+    string.
+
+    @return token_type::value_string if string could be successfully scanned,
+            token_type::parse_error otherwise
+
+    @note In case of errors, variable error_message contains a textual
+          description.
+    */
+    token_type scan_string()
+    {
+        // reset token_buffer (ignore opening quote)
+        reset();
+
+        // we entered the function by reading an open quote
+        JSON_ASSERT(current == '\"');
+
+        while (true)
+        {
+            // get next character
+            switch (get())
+            {
+                // end of file while parsing string
+                case char_traits<char_type>::eof():
+                {
+                    error_message = "invalid string: missing closing quote";
+                    return token_type::parse_error;
+                }
+
+                // closing quote
+                case '\"':
+                {
+                    return token_type::value_string;
+                }
+
+                // escapes
+                case '\\':
+                {
+                    switch (get())
+                    {
+                        // quotation mark
+                        case '\"':
+                            add('\"');
+                            break;
+                        // reverse solidus
+                        case '\\':
+                            add('\\');
+                            break;
+                        // solidus
+                        case '/':
+                            add('/');
+                            break;
+                        // backspace
+                        case 'b':
+                            add('\b');
+                            break;
+                        // form feed
+                        case 'f':
+                            add('\f');
+                            break;
+                        // line feed
+                        case 'n':
+                            add('\n');
+                            break;
+                        // carriage return
+                        case 'r':
+                            add('\r');
+                            break;
+                        // tab
+                        case 't':
+                            add('\t');
+                            break;
+
+                        // unicode escapes
+                        case 'u':
+                        {
+                            const int codepoint1 = get_codepoint();
+                            int codepoint = codepoint1; // start with codepoint1
+
+                            if (JSON_HEDLEY_UNLIKELY(codepoint1 == -1))
+                            {
+                                error_message = "invalid string: '\\u' must be followed by 4 hex digits";
+                                return token_type::parse_error;
+                            }
+
+                            // check if code point is a high surrogate
+                            if (0xD800 <= codepoint1 && codepoint1 <= 0xDBFF)
+                            {
+                                // expect next \uxxxx entry
+                                if (JSON_HEDLEY_LIKELY(get() == '\\' && get() == 'u'))
+                                {
+                                    const int codepoint2 = get_codepoint();
+
+                                    if (JSON_HEDLEY_UNLIKELY(codepoint2 == -1))
+                                    {
+                                        error_message = "invalid string: '\\u' must be followed by 4 hex digits";
+                                        return token_type::parse_error;
+                                    }
+
+                                    // check if codepoint2 is a low surrogate
+                                    if (JSON_HEDLEY_LIKELY(0xDC00 <= codepoint2 && codepoint2 <= 0xDFFF))
+                                    {
+                                        // overwrite codepoint
+                                        codepoint = static_cast<int>(
+                                                        // high surrogate occupies the most significant 22 bits
+                                                        (static_cast<unsigned int>(codepoint1) << 10u)
+                                                        // low surrogate occupies the least significant 15 bits
+                                                        + static_cast<unsigned int>(codepoint2)
+                                                        // there is still the 0xD800, 0xDC00 and 0x10000 noise
+                                                        // in the result, so we have to subtract with:
+                                                        // (0xD800 << 10) + DC00 - 0x10000 = 0x35FDC00
+                                                        - 0x35FDC00u);
+                                    }
+                                    else
+                                    {
+                                        error_message = "invalid string: surrogate U+D800..U+DBFF must be followed by U+DC00..U+DFFF";
+                                        return token_type::parse_error;
+                                    }
+                                }
+                                else
+                                {
+                                    error_message = "invalid string: surrogate U+D800..U+DBFF must be followed by U+DC00..U+DFFF";
+                                    return token_type::parse_error;
+                                }
+                            }
+                            else
+                            {
+                                if (JSON_HEDLEY_UNLIKELY(0xDC00 <= codepoint1 && codepoint1 <= 0xDFFF))
+                                {
+                                    error_message = "invalid string: surrogate U+DC00..U+DFFF must follow U+D800..U+DBFF";
+                                    return token_type::parse_error;
+                                }
+                            }
+
+                            // result of the above calculation yields a proper codepoint
+                            JSON_ASSERT(0x00 <= codepoint && codepoint <= 0x10FFFF);
+
+                            // translate codepoint into bytes
+                            if (codepoint < 0x80)
+                            {
+                                // 1-byte characters: 0xxxxxxx (ASCII)
+                                add(static_cast<char_int_type>(codepoint));
+                            }
+                            else if (codepoint <= 0x7FF)
+                            {
+                                // 2-byte characters: 110xxxxx 10xxxxxx
+                                add(static_cast<char_int_type>(0xC0u | (static_cast<unsigned int>(codepoint) >> 6u)));
+                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));
+                            }
+                            else if (codepoint <= 0xFFFF)
+                            {
+                                // 3-byte characters: 1110xxxx 10xxxxxx 10xxxxxx
+                                add(static_cast<char_int_type>(0xE0u | (static_cast<unsigned int>(codepoint) >> 12u)));
+                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 6u) & 0x3Fu)));
+                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));
+                            }
+                            else
+                            {
+                                // 4-byte characters: 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx
+                                add(static_cast<char_int_type>(0xF0u | (static_cast<unsigned int>(codepoint) >> 18u)));
+                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 12u) & 0x3Fu)));
+                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 6u) & 0x3Fu)));
+                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));
+                            }
+
+                            break;
+                        }
+
+                        // other characters after escape
+                        default:
+                            error_message = "invalid string: forbidden character after backslash";
+                            return token_type::parse_error;
+                    }
+
+                    break;
+                }
+
+                // invalid control characters
+                case 0x00:
+                {
+                    error_message = "invalid string: control character U+0000 (NUL) must be escaped to \\u0000";
+                    return token_type::parse_error;
+                }
+
+                case 0x01:
+                {
+                    error_message = "invalid string: control character U+0001 (SOH) must be escaped to \\u0001";
+                    return token_type::parse_error;
+                }
+
+                case 0x02:
+                {
+                    error_message = "invalid string: control character U+0002 (STX) must be escaped to \\u0002";
+                    return token_type::parse_error;
+                }
+
+                case 0x03:
+                {
+                    error_message = "invalid string: control character U+0003 (ETX) must be escaped to \\u0003";
+                    return token_type::parse_error;
+                }
+
+                case 0x04:
+                {
+                    error_message = "invalid string: control character U+0004 (EOT) must be escaped to \\u0004";
+                    return token_type::parse_error;
+                }
+
+                case 0x05:
+                {
+                    error_message = "invalid string: control character U+0005 (ENQ) must be escaped to \\u0005";
+                    return token_type::parse_error;
+                }
+
+                case 0x06:
+                {
+                    error_message = "invalid string: control character U+0006 (ACK) must be escaped to \\u0006";
+                    return token_type::parse_error;
+                }
+
+                case 0x07:
+                {
+                    error_message = "invalid string: control character U+0007 (BEL) must be escaped to \\u0007";
+                    return token_type::parse_error;
+                }
+
+                case 0x08:
+                {
+                    error_message = "invalid string: control character U+0008 (BS) must be escaped to \\u0008 or \\b";
+                    return token_type::parse_error;
+                }
+
+                case 0x09:
+                {
+                    error_message = "invalid string: control character U+0009 (HT) must be escaped to \\u0009 or \\t";
+                    return token_type::parse_error;
+                }
+
+                case 0x0A:
+                {
+                    error_message = "invalid string: control character U+000A (LF) must be escaped to \\u000A or \\n";
+                    return token_type::parse_error;
+                }
+
+                case 0x0B:
+                {
+                    error_message = "invalid string: control character U+000B (VT) must be escaped to \\u000B";
+                    return token_type::parse_error;
+                }
+
+                case 0x0C:
+                {
+                    error_message = "invalid string: control character U+000C (FF) must be escaped to \\u000C or \\f";
+                    return token_type::parse_error;
+                }
+
+                case 0x0D:
+                {
+                    error_message = "invalid string: control character U+000D (CR) must be escaped to \\u000D or \\r";
+                    return token_type::parse_error;
+                }
+
+                case 0x0E:
+                {
+                    error_message = "invalid string: control character U+000E (SO) must be escaped to \\u000E";
+                    return token_type::parse_error;
+                }
+
+                case 0x0F:
+                {
+                    error_message = "invalid string: control character U+000F (SI) must be escaped to \\u000F";
+                    return token_type::parse_error;
+                }
+
+                case 0x10:
+                {
+                    error_message = "invalid string: control character U+0010 (DLE) must be escaped to \\u0010";
+                    return token_type::parse_error;
+                }
+
+                case 0x11:
+                {
+                    error_message = "invalid string: control character U+0011 (DC1) must be escaped to \\u0011";
+                    return token_type::parse_error;
+                }
+
+                case 0x12:
+                {
+                    error_message = "invalid string: control character U+0012 (DC2) must be escaped to \\u0012";
+                    return token_type::parse_error;
+                }
+
+                case 0x13:
+                {
+                    error_message = "invalid string: control character U+0013 (DC3) must be escaped to \\u0013";
+                    return token_type::parse_error;
+                }
+
+                case 0x14:
+                {
+                    error_message = "invalid string: control character U+0014 (DC4) must be escaped to \\u0014";
+                    return token_type::parse_error;
+                }
+
+                case 0x15:
+                {
+                    error_message = "invalid string: control character U+0015 (NAK) must be escaped to \\u0015";
+                    return token_type::parse_error;
+                }
+
+                case 0x16:
+                {
+                    error_message = "invalid string: control character U+0016 (SYN) must be escaped to \\u0016";
+                    return token_type::parse_error;
+                }
+
+                case 0x17:
+                {
+                    error_message = "invalid string: control character U+0017 (ETB) must be escaped to \\u0017";
+                    return token_type::parse_error;
+                }
+
+                case 0x18:
+                {
+                    error_message = "invalid string: control character U+0018 (CAN) must be escaped to \\u0018";
+                    return token_type::parse_error;
+                }
+
+                case 0x19:
+                {
+                    error_message = "invalid string: control character U+0019 (EM) must be escaped to \\u0019";
+                    return token_type::parse_error;
+                }
+
+                case 0x1A:
+                {
+                    error_message = "invalid string: control character U+001A (SUB) must be escaped to \\u001A";
+                    return token_type::parse_error;
+                }
+
+                case 0x1B:
+                {
+                    error_message = "invalid string: control character U+001B (ESC) must be escaped to \\u001B";
+                    return token_type::parse_error;
+                }
+
+                case 0x1C:
+                {
+                    error_message = "invalid string: control character U+001C (FS) must be escaped to \\u001C";
+                    return token_type::parse_error;
+                }
+
+                case 0x1D:
+                {
+                    error_message = "invalid string: control character U+001D (GS) must be escaped to \\u001D";
+                    return token_type::parse_error;
+                }
+
+                case 0x1E:
+                {
+                    error_message = "invalid string: control character U+001E (RS) must be escaped to \\u001E";
+                    return token_type::parse_error;
+                }
+
+                case 0x1F:
+                {
+                    error_message = "invalid string: control character U+001F (US) must be escaped to \\u001F";
+                    return token_type::parse_error;
+                }
+
+                // U+0020..U+007F (except U+0022 (quote) and U+005C (backspace))
+                case 0x20:
+                case 0x21:
+                case 0x23:
+                case 0x24:
+                case 0x25:
+                case 0x26:
+                case 0x27:
+                case 0x28:
+                case 0x29:
+                case 0x2A:
+                case 0x2B:
+                case 0x2C:
+                case 0x2D:
+                case 0x2E:
+                case 0x2F:
+                case 0x30:
+                case 0x31:
+                case 0x32:
+                case 0x33:
+                case 0x34:
+                case 0x35:
+                case 0x36:
+                case 0x37:
+                case 0x38:
+                case 0x39:
+                case 0x3A:
+                case 0x3B:
+                case 0x3C:
+                case 0x3D:
+                case 0x3E:
+                case 0x3F:
+                case 0x40:
+                case 0x41:
+                case 0x42:
+                case 0x43:
+                case 0x44:
+                case 0x45:
+                case 0x46:
+                case 0x47:
+                case 0x48:
+                case 0x49:
+                case 0x4A:
+                case 0x4B:
+                case 0x4C:
+                case 0x4D:
+                case 0x4E:
+                case 0x4F:
+                case 0x50:
+                case 0x51:
+                case 0x52:
+                case 0x53:
+                case 0x54:
+                case 0x55:
+                case 0x56:
+                case 0x57:
+                case 0x58:
+                case 0x59:
+                case 0x5A:
+                case 0x5B:
+                case 0x5D:
+                case 0x5E:
+                case 0x5F:
+                case 0x60:
+                case 0x61:
+                case 0x62:
+                case 0x63:
+                case 0x64:
+                case 0x65:
+                case 0x66:
+                case 0x67:
+                case 0x68:
+                case 0x69:
+                case 0x6A:
+                case 0x6B:
+                case 0x6C:
+                case 0x6D:
+                case 0x6E:
+                case 0x6F:
+                case 0x70:
+                case 0x71:
+                case 0x72:
+                case 0x73:
+                case 0x74:
+                case 0x75:
+                case 0x76:
+                case 0x77:
+                case 0x78:
+                case 0x79:
+                case 0x7A:
+                case 0x7B:
+                case 0x7C:
+                case 0x7D:
+                case 0x7E:
+                case 0x7F:
+                {
+                    add(current);
+                    break;
+                }
+
+                // U+0080..U+07FF: bytes C2..DF 80..BF
+                case 0xC2:
+                case 0xC3:
+                case 0xC4:
+                case 0xC5:
+                case 0xC6:
+                case 0xC7:
+                case 0xC8:
+                case 0xC9:
+                case 0xCA:
+                case 0xCB:
+                case 0xCC:
+                case 0xCD:
+                case 0xCE:
+                case 0xCF:
+                case 0xD0:
+                case 0xD1:
+                case 0xD2:
+                case 0xD3:
+                case 0xD4:
+                case 0xD5:
+                case 0xD6:
+                case 0xD7:
+                case 0xD8:
+                case 0xD9:
+                case 0xDA:
+                case 0xDB:
+                case 0xDC:
+                case 0xDD:
+                case 0xDE:
+                case 0xDF:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!next_byte_in_range({0x80, 0xBF})))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+0800..U+0FFF: bytes E0 A0..BF 80..BF
+                case 0xE0:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0xA0, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+1000..U+CFFF: bytes E1..EC 80..BF 80..BF
+                // U+E000..U+FFFF: bytes EE..EF 80..BF 80..BF
+                case 0xE1:
+                case 0xE2:
+                case 0xE3:
+                case 0xE4:
+                case 0xE5:
+                case 0xE6:
+                case 0xE7:
+                case 0xE8:
+                case 0xE9:
+                case 0xEA:
+                case 0xEB:
+                case 0xEC:
+                case 0xEE:
+                case 0xEF:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+D000..U+D7FF: bytes ED 80..9F 80..BF
+                case 0xED:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0x9F, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+10000..U+3FFFF F0 90..BF 80..BF 80..BF
+                case 0xF0:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x90, 0xBF, 0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+40000..U+FFFFF F1..F3 80..BF 80..BF 80..BF
+                case 0xF1:
+                case 0xF2:
+                case 0xF3:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0xBF, 0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+100000..U+10FFFF F4 80..8F 80..BF 80..BF
+                case 0xF4:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0x8F, 0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // remaining bytes (80..C1 and F5..FF) are ill-formed
+                default:
+                {
+                    error_message = "invalid string: ill-formed UTF-8 byte";
+                    return token_type::parse_error;
+                }
+            }
+        }
+    }
+
+    /*!
+     * @brief scan a comment
+     * @return whether comment could be scanned successfully
+     */
+    bool scan_comment()
+    {
+        switch (get())
+        {
+            // single-line comments skip input until a newline or EOF is read
+            case '/':
+            {
+                while (true)
+                {
+                    switch (get())
+                    {
+                        case '\n':
+                        case '\r':
+                        case char_traits<char_type>::eof():
+                        case '\0':
+                            return true;
+
+                        default:
+                            break;
+                    }
+                }
+            }
+
+            // multi-line comments skip input until */ is read
+            case '*':
+            {
+                while (true)
+                {
+                    switch (get())
+                    {
+                        case char_traits<char_type>::eof():
+                        case '\0':
+                        {
+                            error_message = "invalid comment; missing closing '*/'";
+                            return false;
+                        }
+
+                        case '*':
+                        {
+                            switch (get())
+                            {
+                                case '/':
+                                    return true;
+
+                                default:
+                                {
+                                    unget();
+                                    continue;
+                                }
+                            }
+                        }
+
+                        default:
+                            continue;
+                    }
+                }
+            }
+
+            // unexpected character after reading '/'
+            default:
+            {
+                error_message = "invalid comment; expecting '/' or '*' after '/'";
+                return false;
+            }
+        }
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    static void strtof(float& f, const char* str, char** endptr) noexcept
+    {
+        f = std::strtof(str, endptr);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    static void strtof(double& f, const char* str, char** endptr) noexcept
+    {
+        f = std::strtod(str, endptr);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    static void strtof(long double& f, const char* str, char** endptr) noexcept
+    {
+        f = std::strtold(str, endptr);
+    }
+
+    /*!
+    @brief scan a number literal
+
+    This function scans a string according to Sect. 6 of RFC 8259.
+
+    The function is realized with a deterministic finite state machine derived
+    from the grammar described in RFC 8259. Starting in state "init", the
+    input is read and used to determined the next state. Only state "done"
+    accepts the number. State "error" is a trap state to model errors. In the
+    table below, "anything" means any character but the ones listed before.
+
+    state    | 0        | 1-9      | e E      | +       | -       | .        | anything
+    ---------|----------|----------|----------|---------|---------|----------|-----------
+    init     | zero     | any1     | [error]  | [error] | minus   | [error]  | [error]
+    minus    | zero     | any1     | [error]  | [error] | [error] | [error]  | [error]
+    zero     | done     | done     | exponent | done    | done    | decimal1 | done
+    any1     | any1     | any1     | exponent | done    | done    | decimal1 | done
+    decimal1 | decimal2 | decimal2 | [error]  | [error] | [error] | [error]  | [error]
+    decimal2 | decimal2 | decimal2 | exponent | done    | done    | done     | done
+    exponent | any2     | any2     | [error]  | sign    | sign    | [error]  | [error]
+    sign     | any2     | any2     | [error]  | [error] | [error] | [error]  | [error]
+    any2     | any2     | any2     | done     | done    | done    | done     | done
+
+    The state machine is realized with one label per state (prefixed with
+    "scan_number_") and `goto` statements between them. The state machine
+    contains cycles, but any cycle can be left when EOF is read. Therefore,
+    the function is guaranteed to terminate.
+
+    During scanning, the read bytes are stored in token_buffer. This string is
+    then converted to a signed integer, an unsigned integer, or a
+    floating-point number.
+
+    @return token_type::value_unsigned, token_type::value_integer, or
+            token_type::value_float if number could be successfully scanned,
+            token_type::parse_error otherwise
+
+    @note The scanner is independent of the current locale. Internally, the
+          locale's decimal point is used instead of `.` to work with the
+          locale-dependent converters.
+    */
+    token_type scan_number()  // lgtm [cpp/use-of-goto] `goto` is used in this function to implement the number-parsing state machine described above. By design, any finite input will eventually reach the "done" state or return token_type::parse_error. In each intermediate state, 1 byte of the input is appended to the token_buffer vector, and only the already initialized variables token_buffer, number_type, and error_message are manipulated.
+    {
+        // reset token_buffer to store the number's bytes
+        reset();
+
+        // the type of the parsed number; initially set to unsigned; will be
+        // changed if minus sign, decimal point or exponent is read
+        token_type number_type = token_type::value_unsigned;
+
+        // state (init): we just found out we need to scan a number
+        switch (current)
+        {
+            case '-':
+            {
+                add(current);
+                goto scan_number_minus;
+            }
+
+            case '0':
+            {
+                add(current);
+                goto scan_number_zero;
+            }
+
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any1;
+            }
+
+            // all other characters are rejected outside scan_number()
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+
+scan_number_minus:
+        // state: we just parsed a leading minus sign
+        number_type = token_type::value_integer;
+        switch (get())
+        {
+            case '0':
+            {
+                add(current);
+                goto scan_number_zero;
+            }
+
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any1;
+            }
+
+            default:
+            {
+                error_message = "invalid number; expected digit after '-'";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_zero:
+        // state: we just parse a zero (maybe with a leading minus sign)
+        switch (get())
+        {
+            case '.':
+            {
+                add(decimal_point_char);
+                decimal_point_position = token_buffer.size() - 1;
+                goto scan_number_decimal1;
+            }
+
+            case 'e':
+            case 'E':
+            {
+                add(current);
+                goto scan_number_exponent;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_any1:
+        // state: we just parsed a number 0-9 (maybe with a leading minus sign)
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any1;
+            }
+
+            case '.':
+            {
+                add(decimal_point_char);
+                decimal_point_position = token_buffer.size() - 1;
+                goto scan_number_decimal1;
+            }
+
+            case 'e':
+            case 'E':
+            {
+                add(current);
+                goto scan_number_exponent;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_decimal1:
+        // state: we just parsed a decimal point
+        number_type = token_type::value_float;
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_decimal2;
+            }
+
+            default:
+            {
+                error_message = "invalid number; expected digit after '.'";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_decimal2:
+        // we just parsed at least one number after a decimal point
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_decimal2;
+            }
+
+            case 'e':
+            case 'E':
+            {
+                add(current);
+                goto scan_number_exponent;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_exponent:
+        // we just parsed an exponent
+        number_type = token_type::value_float;
+        switch (get())
+        {
+            case '+':
+            case '-':
+            {
+                add(current);
+                goto scan_number_sign;
+            }
+
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any2;
+            }
+
+            default:
+            {
+                error_message =
+                    "invalid number; expected '+', '-', or digit after exponent";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_sign:
+        // we just parsed an exponent sign
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any2;
+            }
+
+            default:
+            {
+                error_message = "invalid number; expected digit after exponent sign";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_any2:
+        // we just parsed a number after the exponent or exponent sign
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any2;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_done:
+        // unget the character after the number (we only read it to know that
+        // we are done scanning a number)
+        unget();
+
+        char* endptr = nullptr; // NOLINT(misc-const-correctness,cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+        errno = 0;
+
+        // try to parse integers first and fall back to floats
+        if (number_type == token_type::value_unsigned)
+        {
+            const auto x = std::strtoull(token_buffer.data(), &endptr, 10);
+
+            // we checked the number format before
+            JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());
+
+            if (errno != ERANGE)
+            {
+                value_unsigned = static_cast<number_unsigned_t>(x);
+                if (value_unsigned == x)
+                {
+                    return token_type::value_unsigned;
+                }
+            }
+        }
+        else if (number_type == token_type::value_integer)
+        {
+            const auto x = std::strtoll(token_buffer.data(), &endptr, 10);
+
+            // we checked the number format before
+            JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());
+
+            if (errno != ERANGE)
+            {
+                value_integer = static_cast<number_integer_t>(x);
+                if (value_integer == x)
+                {
+                    return token_type::value_integer;
+                }
+            }
+        }
+
+        // this code is reached if we parse a floating-point number or if an
+        // integer conversion above failed
+        strtof(value_float, token_buffer.data(), &endptr);
+
+        // we checked the number format before
+        JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());
+
+        return token_type::value_float;
+    }
+
+    /*!
+    @param[in] literal_text  the literal text to expect
+    @param[in] length        the length of the passed literal text
+    @param[in] return_type   the token type to return on success
+    */
+    JSON_HEDLEY_NON_NULL(2)
+    token_type scan_literal(const char_type* literal_text, const std::size_t length,
+                            token_type return_type)
+    {
+        JSON_ASSERT(char_traits<char_type>::to_char_type(current) == literal_text[0]);
+        for (std::size_t i = 1; i < length; ++i)
+        {
+            if (JSON_HEDLEY_UNLIKELY(char_traits<char_type>::to_char_type(get()) != literal_text[i]))
+            {
+                error_message = "invalid literal";
+                return token_type::parse_error;
+            }
+        }
+        return return_type;
+    }
+
+    /////////////////////
+    // input management
+    /////////////////////
+
+    /// reset token_buffer; current character is beginning of token
+    void reset() noexcept
+    {
+        token_buffer.clear();
+        token_string.clear();
+        decimal_point_position = std::string::npos;
+        token_string.push_back(char_traits<char_type>::to_char_type(current));
+    }
+
+    /*
+    @brief get next character from the input
+
+    This function provides the interface to the used input adapter. It does
+    not throw in case the input reached EOF, but returns a
+    `char_traits<char>::eof()` in that case.  Stores the scanned characters
+    for use in error messages.
+
+    @return character read from the input
+    */
+    char_int_type get()
+    {
+        ++position.chars_read_total;
+        ++position.chars_read_current_line;
+
+        if (next_unget)
+        {
+            // just reset the next_unget variable and work with current
+            next_unget = false;
+        }
+        else
+        {
+            current = ia.get_character();
+        }
+
+        if (JSON_HEDLEY_LIKELY(current != char_traits<char_type>::eof()))
+        {
+            token_string.push_back(char_traits<char_type>::to_char_type(current));
+        }
+
+        if (current == '\n')
+        {
+            ++position.lines_read;
+            position.chars_read_current_line = 0;
+        }
+
+        return current;
+    }
+
+    /*!
+    @brief unget current character (read it again on next get)
+
+    We implement unget by setting variable next_unget to true. The input is not
+    changed - we just simulate ungetting by modifying chars_read_total,
+    chars_read_current_line, and token_string. The next call to get() will
+    behave as if the unget character is read again.
+    */
+    void unget()
+    {
+        next_unget = true;
+
+        --position.chars_read_total;
+
+        // in case we "unget" a newline, we have to also decrement the lines_read
+        if (position.chars_read_current_line == 0)
+        {
+            if (position.lines_read > 0)
+            {
+                --position.lines_read;
+            }
+        }
+        else
+        {
+            --position.chars_read_current_line;
+        }
+
+        if (JSON_HEDLEY_LIKELY(current != char_traits<char_type>::eof()))
+        {
+            JSON_ASSERT(!token_string.empty());
+            token_string.pop_back();
+        }
+    }
+
+    /// add a character to token_buffer
+    void add(char_int_type c)
+    {
+        token_buffer.push_back(static_cast<typename string_t::value_type>(c));
+    }
+
+  public:
+    /////////////////////
+    // value getters
+    /////////////////////
+
+    /// return integer value
+    constexpr number_integer_t get_number_integer() const noexcept
+    {
+        return value_integer;
+    }
+
+    /// return unsigned integer value
+    constexpr number_unsigned_t get_number_unsigned() const noexcept
+    {
+        return value_unsigned;
+    }
+
+    /// return floating-point value
+    constexpr number_float_t get_number_float() const noexcept
+    {
+        return value_float;
+    }
+
+    /// return current string value (implicitly resets the token; useful only once)
+    string_t& get_string()
+    {
+        // translate decimal points from locale back to '.' (#4084)
+        if (decimal_point_char != '.' && decimal_point_position != std::string::npos)
+        {
+            token_buffer[decimal_point_position] = '.';
+        }
+        return token_buffer;
+    }
+
+    /////////////////////
+    // diagnostics
+    /////////////////////
+
+    /// return position of last read token
+    constexpr position_t get_position() const noexcept
+    {
+        return position;
+    }
+
+    /// return the last read token (for errors only).  Will never contain EOF
+    /// (an arbitrary value that is not a valid char value, often -1), because
+    /// 255 may legitimately occur.  May contain NUL, which should be escaped.
+    std::string get_token_string() const
+    {
+        // escape control characters
+        std::string result;
+        for (const auto c : token_string)
+        {
+            if (static_cast<unsigned char>(c) <= '\x1F')
+            {
+                // escape control characters
+                std::array<char, 9> cs{{}};
+                static_cast<void>((std::snprintf)(cs.data(), cs.size(), "<U+%.4X>", static_cast<unsigned char>(c))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                result += cs.data();
+            }
+            else
+            {
+                // add character as is
+                result.push_back(static_cast<std::string::value_type>(c));
+            }
+        }
+
+        return result;
+    }
+
+    /// return syntax error message
+    JSON_HEDLEY_RETURNS_NON_NULL
+    constexpr const char* get_error_message() const noexcept
+    {
+        return error_message;
+    }
+
+    /////////////////////
+    // actual scanner
+    /////////////////////
+
+    /*!
+    @brief skip the UTF-8 byte order mark
+    @return true iff there is no BOM or the correct BOM has been skipped
+    */
+    bool skip_bom()
+    {
+        if (get() == 0xEF)
+        {
+            // check if we completely parse the BOM
+            return get() == 0xBB && get() == 0xBF;
+        }
+
+        // the first character is not the beginning of the BOM; unget it to
+        // process is later
+        unget();
+        return true;
+    }
+
+    void skip_whitespace()
+    {
+        do
+        {
+            get();
+        }
+        while (current == ' ' || current == '\t' || current == '\n' || current == '\r');
+    }
+
+    token_type scan()
+    {
+        // initially, skip the BOM
+        if (position.chars_read_total == 0 && !skip_bom())
+        {
+            error_message = "invalid BOM; must be 0xEF 0xBB 0xBF if given";
+            return token_type::parse_error;
+        }
+
+        // read next character and ignore whitespace
+        skip_whitespace();
+
+        // ignore comments
+        while (ignore_comments && current == '/')
+        {
+            if (!scan_comment())
+            {
+                return token_type::parse_error;
+            }
+
+            // skip following whitespace
+            skip_whitespace();
+        }
+
+        switch (current)
+        {
+            // structural characters
+            case '[':
+                return token_type::begin_array;
+            case ']':
+                return token_type::end_array;
+            case '{':
+                return token_type::begin_object;
+            case '}':
+                return token_type::end_object;
+            case ':':
+                return token_type::name_separator;
+            case ',':
+                return token_type::value_separator;
+
+            // literals
+            case 't':
+            {
+                std::array<char_type, 4> true_literal = {{static_cast<char_type>('t'), static_cast<char_type>('r'), static_cast<char_type>('u'), static_cast<char_type>('e')}};
+                return scan_literal(true_literal.data(), true_literal.size(), token_type::literal_true);
+            }
+            case 'f':
+            {
+                std::array<char_type, 5> false_literal = {{static_cast<char_type>('f'), static_cast<char_type>('a'), static_cast<char_type>('l'), static_cast<char_type>('s'), static_cast<char_type>('e')}};
+                return scan_literal(false_literal.data(), false_literal.size(), token_type::literal_false);
+            }
+            case 'n':
+            {
+                std::array<char_type, 4> null_literal = {{static_cast<char_type>('n'), static_cast<char_type>('u'), static_cast<char_type>('l'), static_cast<char_type>('l')}};
+                return scan_literal(null_literal.data(), null_literal.size(), token_type::literal_null);
+            }
+
+            // string
+            case '\"':
+                return scan_string();
+
+            // number
+            case '-':
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+                return scan_number();
+
+            // end of input (the null byte is needed when parsing from
+            // string literals)
+            case '\0':
+            case char_traits<char_type>::eof():
+                return token_type::end_of_input;
+
+            // error
+            default:
+                error_message = "invalid literal";
+                return token_type::parse_error;
+        }
+    }
+
+  private:
+    /// input adapter
+    InputAdapterType ia;
+
+    /// whether comments should be ignored (true) or signaled as errors (false)
+    const bool ignore_comments = false;
+
+    /// the current character
+    char_int_type current = char_traits<char_type>::eof();
+
+    /// whether the next get() call should just return current
+    bool next_unget = false;
+
+    /// the start position of the current token
+    position_t position {};
+
+    /// raw input token string (for error messages)
+    std::vector<char_type> token_string {};
+
+    /// buffer for variable-length tokens (numbers, strings)
+    string_t token_buffer {};
+
+    /// a description of occurred lexer errors
+    const char* error_message = "";
+
+    // number values
+    number_integer_t value_integer = 0;
+    number_unsigned_t value_unsigned = 0;
+    number_float_t value_float = 0;
+
+    /// the decimal point
+    const char_int_type decimal_point_char = '.';
+    /// the position of the decimal point in the input
+    std::size_t decimal_point_position = std::string::npos;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/*!
+@brief SAX interface
+
+This class describes the SAX interface used by @ref nlohmann::json::sax_parse.
+Each function is called in different situations while the input is parsed. The
+boolean return value informs the parser whether to continue processing the
+input.
+*/
+template<typename BasicJsonType>
+struct json_sax
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+
+    /*!
+    @brief a null value was read
+    @return whether parsing should proceed
+    */
+    virtual bool null() = 0;
+
+    /*!
+    @brief a boolean value was read
+    @param[in] val  boolean value
+    @return whether parsing should proceed
+    */
+    virtual bool boolean(bool val) = 0;
+
+    /*!
+    @brief an integer number was read
+    @param[in] val  integer value
+    @return whether parsing should proceed
+    */
+    virtual bool number_integer(number_integer_t val) = 0;
+
+    /*!
+    @brief an unsigned integer number was read
+    @param[in] val  unsigned integer value
+    @return whether parsing should proceed
+    */
+    virtual bool number_unsigned(number_unsigned_t val) = 0;
+
+    /*!
+    @brief a floating-point number was read
+    @param[in] val  floating-point value
+    @param[in] s    raw token value
+    @return whether parsing should proceed
+    */
+    virtual bool number_float(number_float_t val, const string_t& s) = 0;
+
+    /*!
+    @brief a string value was read
+    @param[in] val  string value
+    @return whether parsing should proceed
+    @note It is safe to move the passed string value.
+    */
+    virtual bool string(string_t& val) = 0;
+
+    /*!
+    @brief a binary value was read
+    @param[in] val  binary value
+    @return whether parsing should proceed
+    @note It is safe to move the passed binary value.
+    */
+    virtual bool binary(binary_t& val) = 0;
+
+    /*!
+    @brief the beginning of an object was read
+    @param[in] elements  number of object elements or -1 if unknown
+    @return whether parsing should proceed
+    @note binary formats may report the number of elements
+    */
+    virtual bool start_object(std::size_t elements) = 0;
+
+    /*!
+    @brief an object key was read
+    @param[in] val  object key
+    @return whether parsing should proceed
+    @note It is safe to move the passed string.
+    */
+    virtual bool key(string_t& val) = 0;
+
+    /*!
+    @brief the end of an object was read
+    @return whether parsing should proceed
+    */
+    virtual bool end_object() = 0;
+
+    /*!
+    @brief the beginning of an array was read
+    @param[in] elements  number of array elements or -1 if unknown
+    @return whether parsing should proceed
+    @note binary formats may report the number of elements
+    */
+    virtual bool start_array(std::size_t elements) = 0;
+
+    /*!
+    @brief the end of an array was read
+    @return whether parsing should proceed
+    */
+    virtual bool end_array() = 0;
+
+    /*!
+    @brief a parse error occurred
+    @param[in] position    the position in the input where the error occurs
+    @param[in] last_token  the last read token
+    @param[in] ex          an exception object describing the error
+    @return whether parsing should proceed (must return false)
+    */
+    virtual bool parse_error(std::size_t position,
+                             const std::string& last_token,
+                             const detail::exception& ex) = 0;
+
+    json_sax() = default;
+    json_sax(const json_sax&) = default;
+    json_sax(json_sax&&) noexcept = default;
+    json_sax& operator=(const json_sax&) = default;
+    json_sax& operator=(json_sax&&) noexcept = default;
+    virtual ~json_sax() = default;
+};
+
+namespace detail
+{
+constexpr std::size_t unknown_size()
+{
+    return (std::numeric_limits<std::size_t>::max)();
+}
+
+/*!
+@brief SAX implementation to create a JSON value from SAX events
+
+This class implements the @ref json_sax interface and processes the SAX events
+to create a JSON value which makes it basically a DOM parser. The structure or
+hierarchy of the JSON value is managed by the stack `ref_stack` which contains
+a pointer to the respective array or object for each recursion depth.
+
+After successful parsing, the value that is passed by reference to the
+constructor contains the parsed value.
+
+@tparam BasicJsonType  the JSON type
+*/
+template<typename BasicJsonType, typename InputAdapterType>
+class json_sax_dom_parser
+{
+  public:
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using lexer_t = lexer<BasicJsonType, InputAdapterType>;
+
+    /*!
+    @param[in,out] r  reference to a JSON value that is manipulated while
+                       parsing
+    @param[in] allow_exceptions_  whether parse errors yield exceptions
+    */
+    explicit json_sax_dom_parser(BasicJsonType& r, const bool allow_exceptions_ = true, lexer_t* lexer_ = nullptr)
+        : root(r), allow_exceptions(allow_exceptions_), m_lexer_ref(lexer_)
+    {}
+
+    // make class move-only
+    json_sax_dom_parser(const json_sax_dom_parser&) = delete;
+    json_sax_dom_parser(json_sax_dom_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    json_sax_dom_parser& operator=(const json_sax_dom_parser&) = delete;
+    json_sax_dom_parser& operator=(json_sax_dom_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~json_sax_dom_parser() = default;
+
+    bool null()
+    {
+        handle_value(nullptr);
+        return true;
+    }
+
+    bool boolean(bool val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_integer(number_integer_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_unsigned(number_unsigned_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_float(number_float_t val, const string_t& /*unused*/)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool string(string_t& val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool binary(binary_t& val)
+    {
+        handle_value(std::move(val));
+        return true;
+    }
+
+    bool start_object(std::size_t len)
+    {
+        ref_stack.push_back(handle_value(BasicJsonType::value_t::object));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        // Manually set the start position of the object here.
+        // Ensure this is after the call to handle_value to ensure correct start position.
+        if (m_lexer_ref)
+        {
+            // Lexer has read the first character of the object, so
+            // subtract 1 from the position to get the correct start position.
+            ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+        }
+#endif
+
+        if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+        {
+            JSON_THROW(out_of_range::create(408, concat("excessive object size: ", std::to_string(len)), ref_stack.back()));
+        }
+
+        return true;
+    }
+
+    bool key(string_t& val)
+    {
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(ref_stack.back()->is_object());
+
+        // add null at given key and store the reference for later
+        object_element = &(ref_stack.back()->m_data.m_value.object->operator[](val));
+        return true;
+    }
+
+    bool end_object()
+    {
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(ref_stack.back()->is_object());
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        if (m_lexer_ref)
+        {
+            // Lexer's position is past the closing brace, so set that as the end position.
+            ref_stack.back()->end_position = m_lexer_ref->get_position();
+        }
+#endif
+
+        ref_stack.back()->set_parents();
+        ref_stack.pop_back();
+        return true;
+    }
+
+    bool start_array(std::size_t len)
+    {
+        ref_stack.push_back(handle_value(BasicJsonType::value_t::array));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        // Manually set the start position of the array here.
+        // Ensure this is after the call to handle_value to ensure correct start position.
+        if (m_lexer_ref)
+        {
+            ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+        }
+#endif
+
+        if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+        {
+            JSON_THROW(out_of_range::create(408, concat("excessive array size: ", std::to_string(len)), ref_stack.back()));
+        }
+
+        return true;
+    }
+
+    bool end_array()
+    {
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(ref_stack.back()->is_array());
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        if (m_lexer_ref)
+        {
+            // Lexer's position is past the closing bracket, so set that as the end position.
+            ref_stack.back()->end_position = m_lexer_ref->get_position();
+        }
+#endif
+
+        ref_stack.back()->set_parents();
+        ref_stack.pop_back();
+        return true;
+    }
+
+    template<class Exception>
+    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/,
+                     const Exception& ex)
+    {
+        errored = true;
+        static_cast<void>(ex);
+        if (allow_exceptions)
+        {
+            JSON_THROW(ex);
+        }
+        return false;
+    }
+
+    constexpr bool is_errored() const
+    {
+        return errored;
+    }
+
+  private:
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    void handle_diagnostic_positions_for_json_value(BasicJsonType& v)
+    {
+        if (m_lexer_ref)
+        {
+            // Lexer has read past the current field value, so set the end position to the current position.
+            // The start position will be set below based on the length of the string representation
+            // of the value.
+            v.end_position = m_lexer_ref->get_position();
+
+            switch (v.type())
+            {
+                case value_t::boolean:
+                {
+                    // 4 and 5 are the string length of "true" and "false"
+                    v.start_position = v.end_position - (v.m_data.m_value.boolean ? 4 : 5);
+                    break;
+                }
+
+                case value_t::null:
+                {
+                    // 4 is the string length of "null"
+                    v.start_position = v.end_position - 4;
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    // include the length of the quotes, which is 2
+                    v.start_position = v.end_position - v.m_data.m_value.string->size() - 2;
+                    break;
+                }
+
+                // As we handle the start and end positions for values created during parsing,
+                // we do not expect the following value type to be called. Regardless, set the positions
+                // in case this is created manually or through a different constructor. Exclude from lcov
+                // since the exact condition of this switch is esoteric.
+                // LCOV_EXCL_START
+                case value_t::discarded:
+                {
+                    v.end_position = std::string::npos;
+                    v.start_position = v.end_position;
+                    break;
+                }
+                // LCOV_EXCL_STOP
+                case value_t::binary:
+                case value_t::number_integer:
+                case value_t::number_unsigned:
+                case value_t::number_float:
+                {
+                    v.start_position = v.end_position - m_lexer_ref->get_string().size();
+                    break;
+                }
+                case value_t::object:
+                case value_t::array:
+                {
+                    // object and array are handled in start_object() and start_array() handlers
+                    // skip setting the values here.
+                    break;
+                }
+                default: // LCOV_EXCL_LINE
+                    // Handle all possible types discretely, default handler should never be reached.
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert,-warnings-as-errors) LCOV_EXCL_LINE
+            }
+        }
+    }
+#endif
+
+    /*!
+    @invariant If the ref stack is empty, then the passed value will be the new
+               root.
+    @invariant If the ref stack contains a value, then it is an array or an
+               object to which we can add elements
+    */
+    template<typename Value>
+    JSON_HEDLEY_RETURNS_NON_NULL
+    BasicJsonType* handle_value(Value&& v)
+    {
+        if (ref_stack.empty())
+        {
+            root = BasicJsonType(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            handle_diagnostic_positions_for_json_value(root);
+#endif
+
+            return &root;
+        }
+
+        JSON_ASSERT(ref_stack.back()->is_array() || ref_stack.back()->is_object());
+
+        if (ref_stack.back()->is_array())
+        {
+            ref_stack.back()->m_data.m_value.array->emplace_back(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            handle_diagnostic_positions_for_json_value(ref_stack.back()->m_data.m_value.array->back());
+#endif
+
+            return &(ref_stack.back()->m_data.m_value.array->back());
+        }
+
+        JSON_ASSERT(ref_stack.back()->is_object());
+        JSON_ASSERT(object_element);
+        *object_element = BasicJsonType(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        handle_diagnostic_positions_for_json_value(*object_element);
+#endif
+
+        return object_element;
+    }
+
+    /// the parsed JSON value
+    BasicJsonType& root;
+    /// stack to model hierarchy of values
+    std::vector<BasicJsonType*> ref_stack {};
+    /// helper to hold the reference for the next object element
+    BasicJsonType* object_element = nullptr;
+    /// whether a syntax error occurred
+    bool errored = false;
+    /// whether to throw exceptions in case of errors
+    const bool allow_exceptions = true;
+    /// the lexer reference to obtain the current position
+    lexer_t* m_lexer_ref = nullptr;
+};
+
+template<typename BasicJsonType, typename InputAdapterType>
+class json_sax_dom_callback_parser
+{
+  public:
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using parser_callback_t = typename BasicJsonType::parser_callback_t;
+    using parse_event_t = typename BasicJsonType::parse_event_t;
+    using lexer_t = lexer<BasicJsonType, InputAdapterType>;
+
+    json_sax_dom_callback_parser(BasicJsonType& r,
+                                 parser_callback_t cb,
+                                 const bool allow_exceptions_ = true,
+                                 lexer_t* lexer_ = nullptr)
+        : root(r), callback(std::move(cb)), allow_exceptions(allow_exceptions_), m_lexer_ref(lexer_)
+    {
+        keep_stack.push_back(true);
+    }
+
+    // make class move-only
+    json_sax_dom_callback_parser(const json_sax_dom_callback_parser&) = delete;
+    json_sax_dom_callback_parser(json_sax_dom_callback_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    json_sax_dom_callback_parser& operator=(const json_sax_dom_callback_parser&) = delete;
+    json_sax_dom_callback_parser& operator=(json_sax_dom_callback_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~json_sax_dom_callback_parser() = default;
+
+    bool null()
+    {
+        handle_value(nullptr);
+        return true;
+    }
+
+    bool boolean(bool val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_integer(number_integer_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_unsigned(number_unsigned_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_float(number_float_t val, const string_t& /*unused*/)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool string(string_t& val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool binary(binary_t& val)
+    {
+        handle_value(std::move(val));
+        return true;
+    }
+
+    bool start_object(std::size_t len)
+    {
+        // check callback for object start
+        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::object_start, discarded);
+        keep_stack.push_back(keep);
+
+        auto val = handle_value(BasicJsonType::value_t::object, true);
+        ref_stack.push_back(val.second);
+
+        if (ref_stack.back())
+        {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            // Manually set the start position of the object here.
+            // Ensure this is after the call to handle_value to ensure correct start position.
+            if (m_lexer_ref)
+            {
+                // Lexer has read the first character of the object, so
+                // subtract 1 from the position to get the correct start position.
+                ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+            }
+#endif
+
+            // check object limit
+            if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+            {
+                JSON_THROW(out_of_range::create(408, concat("excessive object size: ", std::to_string(len)), ref_stack.back()));
+            }
+        }
+        return true;
+    }
+
+    bool key(string_t& val)
+    {
+        BasicJsonType k = BasicJsonType(val);
+
+        // check callback for key
+        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::key, k);
+        key_keep_stack.push_back(keep);
+
+        // add discarded value at given key and store the reference for later
+        if (keep && ref_stack.back())
+        {
+            object_element = &(ref_stack.back()->m_data.m_value.object->operator[](val) = discarded);
+        }
+
+        return true;
+    }
+
+    bool end_object()
+    {
+        if (ref_stack.back())
+        {
+            if (!callback(static_cast<int>(ref_stack.size()) - 1, parse_event_t::object_end, *ref_stack.back()))
+            {
+                // discard object
+                *ref_stack.back() = discarded;
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                // Set start/end positions for discarded object.
+                handle_diagnostic_positions_for_json_value(*ref_stack.back());
+#endif
+            }
+            else
+            {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                if (m_lexer_ref)
+                {
+                    // Lexer's position is past the closing brace, so set that as the end position.
+                    ref_stack.back()->end_position = m_lexer_ref->get_position();
+                }
+#endif
+
+                ref_stack.back()->set_parents();
+            }
+        }
+
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(!keep_stack.empty());
+        ref_stack.pop_back();
+        keep_stack.pop_back();
+
+        if (!ref_stack.empty() && ref_stack.back() && ref_stack.back()->is_structured())
+        {
+            // remove discarded value
+            for (auto it = ref_stack.back()->begin(); it != ref_stack.back()->end(); ++it)
+            {
+                if (it->is_discarded())
+                {
+                    ref_stack.back()->erase(it);
+                    break;
+                }
+            }
+        }
+
+        return true;
+    }
+
+    bool start_array(std::size_t len)
+    {
+        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::array_start, discarded);
+        keep_stack.push_back(keep);
+
+        auto val = handle_value(BasicJsonType::value_t::array, true);
+        ref_stack.push_back(val.second);
+
+        if (ref_stack.back())
+        {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            // Manually set the start position of the array here.
+            // Ensure this is after the call to handle_value to ensure correct start position.
+            if (m_lexer_ref)
+            {
+                // Lexer has read the first character of the array, so
+                // subtract 1 from the position to get the correct start position.
+                ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+            }
+#endif
+
+            // check array limit
+            if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+            {
+                JSON_THROW(out_of_range::create(408, concat("excessive array size: ", std::to_string(len)), ref_stack.back()));
+            }
+        }
+
+        return true;
+    }
+
+    bool end_array()
+    {
+        bool keep = true;
+
+        if (ref_stack.back())
+        {
+            keep = callback(static_cast<int>(ref_stack.size()) - 1, parse_event_t::array_end, *ref_stack.back());
+            if (keep)
+            {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                if (m_lexer_ref)
+                {
+                    // Lexer's position is past the closing bracket, so set that as the end position.
+                    ref_stack.back()->end_position = m_lexer_ref->get_position();
+                }
+#endif
+
+                ref_stack.back()->set_parents();
+            }
+            else
+            {
+                // discard array
+                *ref_stack.back() = discarded;
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                // Set start/end positions for discarded array.
+                handle_diagnostic_positions_for_json_value(*ref_stack.back());
+#endif
+            }
+        }
+
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(!keep_stack.empty());
+        ref_stack.pop_back();
+        keep_stack.pop_back();
+
+        // remove discarded value
+        if (!keep && !ref_stack.empty() && ref_stack.back()->is_array())
+        {
+            ref_stack.back()->m_data.m_value.array->pop_back();
+        }
+
+        return true;
+    }
+
+    template<class Exception>
+    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/,
+                     const Exception& ex)
+    {
+        errored = true;
+        static_cast<void>(ex);
+        if (allow_exceptions)
+        {
+            JSON_THROW(ex);
+        }
+        return false;
+    }
+
+    constexpr bool is_errored() const
+    {
+        return errored;
+    }
+
+  private:
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    void handle_diagnostic_positions_for_json_value(BasicJsonType& v)
+    {
+        if (m_lexer_ref)
+        {
+            // Lexer has read past the current field value, so set the end position to the current position.
+            // The start position will be set below based on the length of the string representation
+            // of the value.
+            v.end_position = m_lexer_ref->get_position();
+
+            switch (v.type())
+            {
+                case value_t::boolean:
+                {
+                    // 4 and 5 are the string length of "true" and "false"
+                    v.start_position = v.end_position - (v.m_data.m_value.boolean ? 4 : 5);
+                    break;
+                }
+
+                case value_t::null:
+                {
+                    // 4 is the string length of "null"
+                    v.start_position = v.end_position - 4;
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    // include the length of the quotes, which is 2
+                    v.start_position = v.end_position - v.m_data.m_value.string->size() - 2;
+                    break;
+                }
+
+                case value_t::discarded:
+                {
+                    v.end_position = std::string::npos;
+                    v.start_position = v.end_position;
+                    break;
+                }
+
+                case value_t::binary:
+                case value_t::number_integer:
+                case value_t::number_unsigned:
+                case value_t::number_float:
+                {
+                    v.start_position = v.end_position - m_lexer_ref->get_string().size();
+                    break;
+                }
+
+                case value_t::object:
+                case value_t::array:
+                {
+                    // object and array are handled in start_object() and start_array() handlers
+                    // skip setting the values here.
+                    break;
+                }
+                default: // LCOV_EXCL_LINE
+                    // Handle all possible types discretely, default handler should never be reached.
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert,-warnings-as-errors) LCOV_EXCL_LINE
+            }
+        }
+    }
+#endif
+
+    /*!
+    @param[in] v  value to add to the JSON value we build during parsing
+    @param[in] skip_callback  whether we should skip calling the callback
+               function; this is required after start_array() and
+               start_object() SAX events, because otherwise we would call the
+               callback function with an empty array or object, respectively.
+
+    @invariant If the ref stack is empty, then the passed value will be the new
+               root.
+    @invariant If the ref stack contains a value, then it is an array or an
+               object to which we can add elements
+
+    @return pair of boolean (whether value should be kept) and pointer (to the
+            passed value in the ref_stack hierarchy; nullptr if not kept)
+    */
+    template<typename Value>
+    std::pair<bool, BasicJsonType*> handle_value(Value&& v, const bool skip_callback = false)
+    {
+        JSON_ASSERT(!keep_stack.empty());
+
+        // do not handle this value if we know it would be added to a discarded
+        // container
+        if (!keep_stack.back())
+        {
+            return {false, nullptr};
+        }
+
+        // create value
+        auto value = BasicJsonType(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        handle_diagnostic_positions_for_json_value(value);
+#endif
+
+        // check callback
+        const bool keep = skip_callback || callback(static_cast<int>(ref_stack.size()), parse_event_t::value, value);
+
+        // do not handle this value if we just learnt it shall be discarded
+        if (!keep)
+        {
+            return {false, nullptr};
+        }
+
+        if (ref_stack.empty())
+        {
+            root = std::move(value);
+            return {true, & root};
+        }
+
+        // skip this value if we already decided to skip the parent
+        // (https://github.com/nlohmann/json/issues/971#issuecomment-413678360)
+        if (!ref_stack.back())
+        {
+            return {false, nullptr};
+        }
+
+        // we now only expect arrays and objects
+        JSON_ASSERT(ref_stack.back()->is_array() || ref_stack.back()->is_object());
+
+        // array
+        if (ref_stack.back()->is_array())
+        {
+            ref_stack.back()->m_data.m_value.array->emplace_back(std::move(value));
+            return {true, & (ref_stack.back()->m_data.m_value.array->back())};
+        }
+
+        // object
+        JSON_ASSERT(ref_stack.back()->is_object());
+        // check if we should store an element for the current key
+        JSON_ASSERT(!key_keep_stack.empty());
+        const bool store_element = key_keep_stack.back();
+        key_keep_stack.pop_back();
+
+        if (!store_element)
+        {
+            return {false, nullptr};
+        }
+
+        JSON_ASSERT(object_element);
+        *object_element = std::move(value);
+        return {true, object_element};
+    }
+
+    /// the parsed JSON value
+    BasicJsonType& root;
+    /// stack to model hierarchy of values
+    std::vector<BasicJsonType*> ref_stack {};
+    /// stack to manage which values to keep
+    std::vector<bool> keep_stack {}; // NOLINT(readability-redundant-member-init)
+    /// stack to manage which object keys to keep
+    std::vector<bool> key_keep_stack {}; // NOLINT(readability-redundant-member-init)
+    /// helper to hold the reference for the next object element
+    BasicJsonType* object_element = nullptr;
+    /// whether a syntax error occurred
+    bool errored = false;
+    /// callback function
+    const parser_callback_t callback = nullptr;
+    /// whether to throw exceptions in case of errors
+    const bool allow_exceptions = true;
+    /// a discarded value for the callback
+    BasicJsonType discarded = BasicJsonType::value_t::discarded;
+    /// the lexer reference to obtain the current position
+    lexer_t* m_lexer_ref = nullptr;
+};
+
+template<typename BasicJsonType>
+class json_sax_acceptor
+{
+  public:
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+
+    bool null()
+    {
+        return true;
+    }
+
+    bool boolean(bool /*unused*/)
+    {
+        return true;
+    }
+
+    bool number_integer(number_integer_t /*unused*/)
+    {
+        return true;
+    }
+
+    bool number_unsigned(number_unsigned_t /*unused*/)
+    {
+        return true;
+    }
+
+    bool number_float(number_float_t /*unused*/, const string_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool string(string_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool binary(binary_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool start_object(std::size_t /*unused*/ = detail::unknown_size())
+    {
+        return true;
+    }
+
+    bool key(string_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool end_object()
+    {
+        return true;
+    }
+
+    bool start_array(std::size_t /*unused*/ = detail::unknown_size())
+    {
+        return true;
+    }
+
+    bool end_array()
+    {
+        return true;
+    }
+
+    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/, const detail::exception& /*unused*/)
+    {
+        return false;
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/lexer.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/is_sax.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // size_t
+#include <utility> // declval
+#include <string> // string
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/detected.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename T>
+using null_function_t = decltype(std::declval<T&>().null());
+
+template<typename T>
+using boolean_function_t =
+    decltype(std::declval<T&>().boolean(std::declval<bool>()));
+
+template<typename T, typename Integer>
+using number_integer_function_t =
+    decltype(std::declval<T&>().number_integer(std::declval<Integer>()));
+
+template<typename T, typename Unsigned>
+using number_unsigned_function_t =
+    decltype(std::declval<T&>().number_unsigned(std::declval<Unsigned>()));
+
+template<typename T, typename Float, typename String>
+using number_float_function_t = decltype(std::declval<T&>().number_float(
+                                    std::declval<Float>(), std::declval<const String&>()));
+
+template<typename T, typename String>
+using string_function_t =
+    decltype(std::declval<T&>().string(std::declval<String&>()));
+
+template<typename T, typename Binary>
+using binary_function_t =
+    decltype(std::declval<T&>().binary(std::declval<Binary&>()));
+
+template<typename T>
+using start_object_function_t =
+    decltype(std::declval<T&>().start_object(std::declval<std::size_t>()));
+
+template<typename T, typename String>
+using key_function_t =
+    decltype(std::declval<T&>().key(std::declval<String&>()));
+
+template<typename T>
+using end_object_function_t = decltype(std::declval<T&>().end_object());
+
+template<typename T>
+using start_array_function_t =
+    decltype(std::declval<T&>().start_array(std::declval<std::size_t>()));
+
+template<typename T>
+using end_array_function_t = decltype(std::declval<T&>().end_array());
+
+template<typename T, typename Exception>
+using parse_error_function_t = decltype(std::declval<T&>().parse_error(
+        std::declval<std::size_t>(), std::declval<const std::string&>(),
+        std::declval<const Exception&>()));
+
+template<typename SAX, typename BasicJsonType>
+struct is_sax
+{
+  private:
+    static_assert(is_basic_json<BasicJsonType>::value,
+                  "BasicJsonType must be of type basic_json<...>");
+
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using exception_t = typename BasicJsonType::exception;
+
+  public:
+    static constexpr bool value =
+        is_detected_exact<bool, null_function_t, SAX>::value &&
+        is_detected_exact<bool, boolean_function_t, SAX>::value &&
+        is_detected_exact<bool, number_integer_function_t, SAX, number_integer_t>::value &&
+        is_detected_exact<bool, number_unsigned_function_t, SAX, number_unsigned_t>::value &&
+        is_detected_exact<bool, number_float_function_t, SAX, number_float_t, string_t>::value &&
+        is_detected_exact<bool, string_function_t, SAX, string_t>::value &&
+        is_detected_exact<bool, binary_function_t, SAX, binary_t>::value &&
+        is_detected_exact<bool, start_object_function_t, SAX>::value &&
+        is_detected_exact<bool, key_function_t, SAX, string_t>::value &&
+        is_detected_exact<bool, end_object_function_t, SAX>::value &&
+        is_detected_exact<bool, start_array_function_t, SAX>::value &&
+        is_detected_exact<bool, end_array_function_t, SAX>::value &&
+        is_detected_exact<bool, parse_error_function_t, SAX, exception_t>::value;
+};
+
+template<typename SAX, typename BasicJsonType>
+struct is_sax_static_asserts
+{
+  private:
+    static_assert(is_basic_json<BasicJsonType>::value,
+                  "BasicJsonType must be of type basic_json<...>");
+
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using exception_t = typename BasicJsonType::exception;
+
+  public:
+    static_assert(is_detected_exact<bool, null_function_t, SAX>::value,
+                  "Missing/invalid function: bool null()");
+    static_assert(is_detected_exact<bool, boolean_function_t, SAX>::value,
+                  "Missing/invalid function: bool boolean(bool)");
+    static_assert(is_detected_exact<bool, boolean_function_t, SAX>::value,
+                  "Missing/invalid function: bool boolean(bool)");
+    static_assert(
+        is_detected_exact<bool, number_integer_function_t, SAX,
+        number_integer_t>::value,
+        "Missing/invalid function: bool number_integer(number_integer_t)");
+    static_assert(
+        is_detected_exact<bool, number_unsigned_function_t, SAX,
+        number_unsigned_t>::value,
+        "Missing/invalid function: bool number_unsigned(number_unsigned_t)");
+    static_assert(is_detected_exact<bool, number_float_function_t, SAX,
+                  number_float_t, string_t>::value,
+                  "Missing/invalid function: bool number_float(number_float_t, const string_t&)");
+    static_assert(
+        is_detected_exact<bool, string_function_t, SAX, string_t>::value,
+        "Missing/invalid function: bool string(string_t&)");
+    static_assert(
+        is_detected_exact<bool, binary_function_t, SAX, binary_t>::value,
+        "Missing/invalid function: bool binary(binary_t&)");
+    static_assert(is_detected_exact<bool, start_object_function_t, SAX>::value,
+                  "Missing/invalid function: bool start_object(std::size_t)");
+    static_assert(is_detected_exact<bool, key_function_t, SAX, string_t>::value,
+                  "Missing/invalid function: bool key(string_t&)");
+    static_assert(is_detected_exact<bool, end_object_function_t, SAX>::value,
+                  "Missing/invalid function: bool end_object()");
+    static_assert(is_detected_exact<bool, start_array_function_t, SAX>::value,
+                  "Missing/invalid function: bool start_array(std::size_t)");
+    static_assert(is_detected_exact<bool, end_array_function_t, SAX>::value,
+                  "Missing/invalid function: bool end_array()");
+    static_assert(
+        is_detected_exact<bool, parse_error_function_t, SAX, exception_t>::value,
+        "Missing/invalid function: bool parse_error(std::size_t, const "
+        "std::string&, const exception&)");
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// how to treat CBOR tags
+enum class cbor_tag_handler_t
+{
+    error,   ///< throw a parse_error exception in case of a tag
+    ignore,  ///< ignore tags
+    store    ///< store tags as binary type
+};
+
+/*!
+@brief determine system byte order
+
+@return true if and only if system's byte order is little endian
+
+@note from https://stackoverflow.com/a/1001328/266378
+*/
+static inline bool little_endianness(int num = 1) noexcept
+{
+    return *reinterpret_cast<char*>(&num) == 1;
+}
+
+///////////////////
+// binary reader //
+///////////////////
+
+/*!
+@brief deserialization of CBOR, MessagePack, and UBJSON values
+*/
+template<typename BasicJsonType, typename InputAdapterType, typename SAX = json_sax_dom_parser<BasicJsonType, InputAdapterType>>
+class binary_reader
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using json_sax_t = SAX;
+    using char_type = typename InputAdapterType::char_type;
+    using char_int_type = typename char_traits<char_type>::int_type;
+
+  public:
+    /*!
+    @brief create a binary reader
+
+    @param[in] adapter  input adapter to read from
+    */
+    explicit binary_reader(InputAdapterType&& adapter, const input_format_t format = input_format_t::json) noexcept : ia(std::move(adapter)), input_format(format)
+    {
+        (void)detail::is_sax_static_asserts<SAX, BasicJsonType> {};
+    }
+
+    // make class move-only
+    binary_reader(const binary_reader&) = delete;
+    binary_reader(binary_reader&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    binary_reader& operator=(const binary_reader&) = delete;
+    binary_reader& operator=(binary_reader&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~binary_reader() = default;
+
+    /*!
+    @param[in] format  the binary format to parse
+    @param[in] sax_    a SAX event processor
+    @param[in] strict  whether to expect the input to be consumed completed
+    @param[in] tag_handler  how to treat CBOR tags
+
+    @return whether parsing was successful
+    */
+    JSON_HEDLEY_NON_NULL(3)
+    bool sax_parse(const input_format_t format,
+                   json_sax_t* sax_,
+                   const bool strict = true,
+                   const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        sax = sax_;
+        bool result = false;
+
+        switch (format)
+        {
+            case input_format_t::bson:
+                result = parse_bson_internal();
+                break;
+
+            case input_format_t::cbor:
+                result = parse_cbor_internal(true, tag_handler);
+                break;
+
+            case input_format_t::msgpack:
+                result = parse_msgpack_internal();
+                break;
+
+            case input_format_t::ubjson:
+            case input_format_t::bjdata:
+                result = parse_ubjson_internal();
+                break;
+
+            case input_format_t::json: // LCOV_EXCL_LINE
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+
+        // strict mode: next byte must be EOF
+        if (result && strict)
+        {
+            if (input_format == input_format_t::ubjson || input_format == input_format_t::bjdata)
+            {
+                get_ignore_noop();
+            }
+            else
+            {
+                get();
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(current != char_traits<char_type>::eof()))
+            {
+                return sax->parse_error(chars_read, get_token_string(), parse_error::create(110, chars_read,
+                                        exception_message(input_format, concat("expected end of input; last byte: 0x", get_token_string()), "value"), nullptr));
+            }
+        }
+
+        return result;
+    }
+
+  private:
+    //////////
+    // BSON //
+    //////////
+
+    /*!
+    @brief Reads in a BSON-object and passes it to the SAX-parser.
+    @return whether a valid BSON-value was passed to the SAX parser
+    */
+    bool parse_bson_internal()
+    {
+        std::int32_t document_size{};
+        get_number<std::int32_t, true>(input_format_t::bson, document_size);
+
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(detail::unknown_size())))
+        {
+            return false;
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_list(/*is_array*/false)))
+        {
+            return false;
+        }
+
+        return sax->end_object();
+    }
+
+    /*!
+    @brief Parses a C-style string from the BSON input.
+    @param[in,out] result  A reference to the string variable where the read
+                            string is to be stored.
+    @return `true` if the \x00-byte indicating the end of the string was
+             encountered before the EOF; false` indicates an unexpected EOF.
+    */
+    bool get_bson_cstr(string_t& result)
+    {
+        auto out = std::back_inserter(result);
+        while (true)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::bson, "cstring")))
+            {
+                return false;
+            }
+            if (current == 0x00)
+            {
+                return true;
+            }
+            *out++ = static_cast<typename string_t::value_type>(current);
+        }
+    }
+
+    /*!
+    @brief Parses a zero-terminated string of length @a len from the BSON
+           input.
+    @param[in] len  The length (including the zero-byte at the end) of the
+                    string to be read.
+    @param[in,out] result  A reference to the string variable where the read
+                            string is to be stored.
+    @tparam NumberType The type of the length @a len
+    @pre len >= 1
+    @return `true` if the string was successfully parsed
+    */
+    template<typename NumberType>
+    bool get_bson_string(const NumberType len, string_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(len < 1))
+        {
+            auto last_token = get_token_string();
+            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                    exception_message(input_format_t::bson, concat("string length must be at least 1, is ", std::to_string(len)), "string"), nullptr));
+        }
+
+        return get_string(input_format_t::bson, len - static_cast<NumberType>(1), result) && get() != char_traits<char_type>::eof();
+    }
+
+    /*!
+    @brief Parses a byte array input of length @a len from the BSON input.
+    @param[in] len  The length of the byte array to be read.
+    @param[in,out] result  A reference to the binary variable where the read
+                            array is to be stored.
+    @tparam NumberType The type of the length @a len
+    @pre len >= 0
+    @return `true` if the byte array was successfully parsed
+    */
+    template<typename NumberType>
+    bool get_bson_binary(const NumberType len, binary_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(len < 0))
+        {
+            auto last_token = get_token_string();
+            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                    exception_message(input_format_t::bson, concat("byte array length cannot be negative, is ", std::to_string(len)), "binary"), nullptr));
+        }
+
+        // All BSON binary values have a subtype
+        std::uint8_t subtype{};
+        get_number<std::uint8_t>(input_format_t::bson, subtype);
+        result.set_subtype(subtype);
+
+        return get_binary(input_format_t::bson, len, result);
+    }
+
+    /*!
+    @brief Read a BSON document element of the given @a element_type.
+    @param[in] element_type The BSON element type, c.f. http://bsonspec.org/spec.html
+    @param[in] element_type_parse_position The position in the input stream,
+               where the `element_type` was read.
+    @warning Not all BSON element types are supported yet. An unsupported
+             @a element_type will give rise to a parse_error.114:
+             Unsupported BSON record type 0x...
+    @return whether a valid BSON-object/array was passed to the SAX parser
+    */
+    bool parse_bson_element_internal(const char_int_type element_type,
+                                     const std::size_t element_type_parse_position)
+    {
+        switch (element_type)
+        {
+            case 0x01: // double
+            {
+                double number{};
+                return get_number<double, true>(input_format_t::bson, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0x02: // string
+            {
+                std::int32_t len{};
+                string_t value;
+                return get_number<std::int32_t, true>(input_format_t::bson, len) && get_bson_string(len, value) && sax->string(value);
+            }
+
+            case 0x03: // object
+            {
+                return parse_bson_internal();
+            }
+
+            case 0x04: // array
+            {
+                return parse_bson_array();
+            }
+
+            case 0x05: // binary
+            {
+                std::int32_t len{};
+                binary_t value;
+                return get_number<std::int32_t, true>(input_format_t::bson, len) && get_bson_binary(len, value) && sax->binary(value);
+            }
+
+            case 0x08: // boolean
+            {
+                return sax->boolean(get() != 0);
+            }
+
+            case 0x0A: // null
+            {
+                return sax->null();
+            }
+
+            case 0x10: // int32
+            {
+                std::int32_t value{};
+                return get_number<std::int32_t, true>(input_format_t::bson, value) && sax->number_integer(value);
+            }
+
+            case 0x12: // int64
+            {
+                std::int64_t value{};
+                return get_number<std::int64_t, true>(input_format_t::bson, value) && sax->number_integer(value);
+            }
+
+            case 0x11: // uint64
+            {
+                std::uint64_t value{};
+                return get_number<std::uint64_t, true>(input_format_t::bson, value) && sax->number_unsigned(value);
+            }
+
+            default: // anything else not supported (yet)
+            {
+                std::array<char, 3> cr{{}};
+                static_cast<void>((std::snprintf)(cr.data(), cr.size(), "%.2hhX", static_cast<unsigned char>(element_type))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                const std::string cr_str{cr.data()};
+                return sax->parse_error(element_type_parse_position, cr_str,
+                                        parse_error::create(114, element_type_parse_position, concat("Unsupported BSON record type 0x", cr_str), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief Read a BSON element list (as specified in the BSON-spec)
+
+    The same binary layout is used for objects and arrays, hence it must be
+    indicated with the argument @a is_array which one is expected
+    (true --> array, false --> object).
+
+    @param[in] is_array Determines if the element list being read is to be
+                        treated as an object (@a is_array == false), or as an
+                        array (@a is_array == true).
+    @return whether a valid BSON-object/array was passed to the SAX parser
+    */
+    bool parse_bson_element_list(const bool is_array)
+    {
+        string_t key;
+
+        while (auto element_type = get())
+        {
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::bson, "element list")))
+            {
+                return false;
+            }
+
+            const std::size_t element_type_parse_position = chars_read;
+            if (JSON_HEDLEY_UNLIKELY(!get_bson_cstr(key)))
+            {
+                return false;
+            }
+
+            if (!is_array && !sax->key(key))
+            {
+                return false;
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_internal(element_type, element_type_parse_position)))
+            {
+                return false;
+            }
+
+            // get_bson_cstr only appends
+            key.clear();
+        }
+
+        return true;
+    }
+
+    /*!
+    @brief Reads an array from the BSON input and passes it to the SAX-parser.
+    @return whether a valid BSON-array was passed to the SAX parser
+    */
+    bool parse_bson_array()
+    {
+        std::int32_t document_size{};
+        get_number<std::int32_t, true>(input_format_t::bson, document_size);
+
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(detail::unknown_size())))
+        {
+            return false;
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_list(/*is_array*/true)))
+        {
+            return false;
+        }
+
+        return sax->end_array();
+    }
+
+    //////////
+    // CBOR //
+    //////////
+
+    /*!
+    @param[in] get_char  whether a new character should be retrieved from the
+                         input (true) or whether the last read character should
+                         be considered instead (false)
+    @param[in] tag_handler how CBOR tags should be treated
+
+    @return whether a valid CBOR value was passed to the SAX parser
+    */
+    bool parse_cbor_internal(const bool get_char,
+                             const cbor_tag_handler_t tag_handler)
+    {
+        switch (get_char ? get() : current)
+        {
+            // EOF
+            case char_traits<char_type>::eof():
+                return unexpect_eof(input_format_t::cbor, "value");
+
+            // Integer 0x00..0x17 (0..23)
+            case 0x00:
+            case 0x01:
+            case 0x02:
+            case 0x03:
+            case 0x04:
+            case 0x05:
+            case 0x06:
+            case 0x07:
+            case 0x08:
+            case 0x09:
+            case 0x0A:
+            case 0x0B:
+            case 0x0C:
+            case 0x0D:
+            case 0x0E:
+            case 0x0F:
+            case 0x10:
+            case 0x11:
+            case 0x12:
+            case 0x13:
+            case 0x14:
+            case 0x15:
+            case 0x16:
+            case 0x17:
+                return sax->number_unsigned(static_cast<number_unsigned_t>(current));
+
+            case 0x18: // Unsigned integer (one-byte uint8_t follows)
+            {
+                std::uint8_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            case 0x19: // Unsigned integer (two-byte uint16_t follows)
+            {
+                std::uint16_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            case 0x1A: // Unsigned integer (four-byte uint32_t follows)
+            {
+                std::uint32_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            case 0x1B: // Unsigned integer (eight-byte uint64_t follows)
+            {
+                std::uint64_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            // Negative integer -1-0x00..-1-0x17 (-1..-24)
+            case 0x20:
+            case 0x21:
+            case 0x22:
+            case 0x23:
+            case 0x24:
+            case 0x25:
+            case 0x26:
+            case 0x27:
+            case 0x28:
+            case 0x29:
+            case 0x2A:
+            case 0x2B:
+            case 0x2C:
+            case 0x2D:
+            case 0x2E:
+            case 0x2F:
+            case 0x30:
+            case 0x31:
+            case 0x32:
+            case 0x33:
+            case 0x34:
+            case 0x35:
+            case 0x36:
+            case 0x37:
+                return sax->number_integer(static_cast<std::int8_t>(0x20 - 1 - current));
+
+            case 0x38: // Negative integer (one-byte uint8_t follows)
+            {
+                std::uint8_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);
+            }
+
+            case 0x39: // Negative integer -1-n (two-byte uint16_t follows)
+            {
+                std::uint16_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);
+            }
+
+            case 0x3A: // Negative integer -1-n (four-byte uint32_t follows)
+            {
+                std::uint32_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);
+            }
+
+            case 0x3B: // Negative integer -1-n (eight-byte uint64_t follows)
+            {
+                std::uint64_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1)
+                        - static_cast<number_integer_t>(number));
+            }
+
+            // Binary data (0x00..0x17 bytes follow)
+            case 0x40:
+            case 0x41:
+            case 0x42:
+            case 0x43:
+            case 0x44:
+            case 0x45:
+            case 0x46:
+            case 0x47:
+            case 0x48:
+            case 0x49:
+            case 0x4A:
+            case 0x4B:
+            case 0x4C:
+            case 0x4D:
+            case 0x4E:
+            case 0x4F:
+            case 0x50:
+            case 0x51:
+            case 0x52:
+            case 0x53:
+            case 0x54:
+            case 0x55:
+            case 0x56:
+            case 0x57:
+            case 0x58: // Binary data (one-byte uint8_t for n follows)
+            case 0x59: // Binary data (two-byte uint16_t for n follow)
+            case 0x5A: // Binary data (four-byte uint32_t for n follow)
+            case 0x5B: // Binary data (eight-byte uint64_t for n follow)
+            case 0x5F: // Binary data (indefinite length)
+            {
+                binary_t b;
+                return get_cbor_binary(b) && sax->binary(b);
+            }
+
+            // UTF-8 string (0x00..0x17 bytes follow)
+            case 0x60:
+            case 0x61:
+            case 0x62:
+            case 0x63:
+            case 0x64:
+            case 0x65:
+            case 0x66:
+            case 0x67:
+            case 0x68:
+            case 0x69:
+            case 0x6A:
+            case 0x6B:
+            case 0x6C:
+            case 0x6D:
+            case 0x6E:
+            case 0x6F:
+            case 0x70:
+            case 0x71:
+            case 0x72:
+            case 0x73:
+            case 0x74:
+            case 0x75:
+            case 0x76:
+            case 0x77:
+            case 0x78: // UTF-8 string (one-byte uint8_t for n follows)
+            case 0x79: // UTF-8 string (two-byte uint16_t for n follow)
+            case 0x7A: // UTF-8 string (four-byte uint32_t for n follow)
+            case 0x7B: // UTF-8 string (eight-byte uint64_t for n follow)
+            case 0x7F: // UTF-8 string (indefinite length)
+            {
+                string_t s;
+                return get_cbor_string(s) && sax->string(s);
+            }
+
+            // array (0x00..0x17 data items follow)
+            case 0x80:
+            case 0x81:
+            case 0x82:
+            case 0x83:
+            case 0x84:
+            case 0x85:
+            case 0x86:
+            case 0x87:
+            case 0x88:
+            case 0x89:
+            case 0x8A:
+            case 0x8B:
+            case 0x8C:
+            case 0x8D:
+            case 0x8E:
+            case 0x8F:
+            case 0x90:
+            case 0x91:
+            case 0x92:
+            case 0x93:
+            case 0x94:
+            case 0x95:
+            case 0x96:
+            case 0x97:
+                return get_cbor_array(
+                           conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x1Fu), tag_handler);
+
+            case 0x98: // array (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x99: // array (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x9A: // array (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x9B: // array (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x9F: // array (indefinite length)
+                return get_cbor_array(detail::unknown_size(), tag_handler);
+
+            // map (0x00..0x17 pairs of data items follow)
+            case 0xA0:
+            case 0xA1:
+            case 0xA2:
+            case 0xA3:
+            case 0xA4:
+            case 0xA5:
+            case 0xA6:
+            case 0xA7:
+            case 0xA8:
+            case 0xA9:
+            case 0xAA:
+            case 0xAB:
+            case 0xAC:
+            case 0xAD:
+            case 0xAE:
+            case 0xAF:
+            case 0xB0:
+            case 0xB1:
+            case 0xB2:
+            case 0xB3:
+            case 0xB4:
+            case 0xB5:
+            case 0xB6:
+            case 0xB7:
+                return get_cbor_object(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x1Fu), tag_handler);
+
+            case 0xB8: // map (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xB9: // map (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xBA: // map (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xBB: // map (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xBF: // map (indefinite length)
+                return get_cbor_object(detail::unknown_size(), tag_handler);
+
+            case 0xC6: // tagged item
+            case 0xC7:
+            case 0xC8:
+            case 0xC9:
+            case 0xCA:
+            case 0xCB:
+            case 0xCC:
+            case 0xCD:
+            case 0xCE:
+            case 0xCF:
+            case 0xD0:
+            case 0xD1:
+            case 0xD2:
+            case 0xD3:
+            case 0xD4:
+            case 0xD8: // tagged item (1 bytes follow)
+            case 0xD9: // tagged item (2 bytes follow)
+            case 0xDA: // tagged item (4 bytes follow)
+            case 0xDB: // tagged item (8 bytes follow)
+            {
+                switch (tag_handler)
+                {
+                    case cbor_tag_handler_t::error:
+                    {
+                        auto last_token = get_token_string();
+                        return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                                exception_message(input_format_t::cbor, concat("invalid byte: 0x", last_token), "value"), nullptr));
+                    }
+
+                    case cbor_tag_handler_t::ignore:
+                    {
+                        // ignore binary subtype
+                        switch (current)
+                        {
+                            case 0xD8:
+                            {
+                                std::uint8_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            case 0xD9:
+                            {
+                                std::uint16_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            case 0xDA:
+                            {
+                                std::uint32_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            case 0xDB:
+                            {
+                                std::uint64_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            default:
+                                break;
+                        }
+                        return parse_cbor_internal(true, tag_handler);
+                    }
+
+                    case cbor_tag_handler_t::store:
+                    {
+                        binary_t b;
+                        // use binary subtype and store in binary container
+                        switch (current)
+                        {
+                            case 0xD8:
+                            {
+                                std::uint8_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            case 0xD9:
+                            {
+                                std::uint16_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            case 0xDA:
+                            {
+                                std::uint32_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            case 0xDB:
+                            {
+                                std::uint64_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            default:
+                                return parse_cbor_internal(true, tag_handler);
+                        }
+                        get();
+                        return get_cbor_binary(b) && sax->binary(b);
+                    }
+
+                    default:                 // LCOV_EXCL_LINE
+                        JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+                        return false;        // LCOV_EXCL_LINE
+                }
+            }
+
+            case 0xF4: // false
+                return sax->boolean(false);
+
+            case 0xF5: // true
+                return sax->boolean(true);
+
+            case 0xF6: // null
+                return sax->null();
+
+            case 0xF9: // Half-Precision Float (two-byte IEEE 754)
+            {
+                const auto byte1_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "number")))
+                {
+                    return false;
+                }
+                const auto byte2_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "number")))
+                {
+                    return false;
+                }
+
+                const auto byte1 = static_cast<unsigned char>(byte1_raw);
+                const auto byte2 = static_cast<unsigned char>(byte2_raw);
+
+                // code from RFC 7049, Appendix D, Figure 3:
+                // As half-precision floating-point numbers were only added
+                // to IEEE 754 in 2008, today's programming platforms often
+                // still only have limited support for them. It is very
+                // easy to include at least decoding support for them even
+                // without such support. An example of a small decoder for
+                // half-precision floating-point numbers in the C language
+                // is shown in Fig. 3.
+                const auto half = static_cast<unsigned int>((byte1 << 8u) + byte2);
+                const double val = [&half]
+                {
+                    const int exp = (half >> 10u) & 0x1Fu;
+                    const unsigned int mant = half & 0x3FFu;
+                    JSON_ASSERT(0 <= exp&& exp <= 32);
+                    JSON_ASSERT(mant <= 1024);
+                    switch (exp)
+                    {
+                        case 0:
+                            return std::ldexp(mant, -24);
+                        case 31:
+                            return (mant == 0)
+                            ? std::numeric_limits<double>::infinity()
+                            : std::numeric_limits<double>::quiet_NaN();
+                        default:
+                            return std::ldexp(mant + 1024, exp - 25);
+                    }
+                }();
+                return sax->number_float((half & 0x8000u) != 0
+                                         ? static_cast<number_float_t>(-val)
+                                         : static_cast<number_float_t>(val), "");
+            }
+
+            case 0xFA: // Single-Precision Float (four-byte IEEE 754)
+            {
+                float number{};
+                return get_number(input_format_t::cbor, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0xFB: // Double-Precision Float (eight-byte IEEE 754)
+            {
+                double number{};
+                return get_number(input_format_t::cbor, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            default: // anything else (0xFF is handled inside the other types)
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format_t::cbor, concat("invalid byte: 0x", last_token), "value"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a CBOR string
+
+    This function first reads starting bytes to determine the expected
+    string length and then copies this number of bytes into a string.
+    Additionally, CBOR's strings with indefinite lengths are supported.
+
+    @param[out] result  created string
+
+    @return whether string creation completed
+    */
+    bool get_cbor_string(string_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "string")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            // UTF-8 string (0x00..0x17 bytes follow)
+            case 0x60:
+            case 0x61:
+            case 0x62:
+            case 0x63:
+            case 0x64:
+            case 0x65:
+            case 0x66:
+            case 0x67:
+            case 0x68:
+            case 0x69:
+            case 0x6A:
+            case 0x6B:
+            case 0x6C:
+            case 0x6D:
+            case 0x6E:
+            case 0x6F:
+            case 0x70:
+            case 0x71:
+            case 0x72:
+            case 0x73:
+            case 0x74:
+            case 0x75:
+            case 0x76:
+            case 0x77:
+            {
+                return get_string(input_format_t::cbor, static_cast<unsigned int>(current) & 0x1Fu, result);
+            }
+
+            case 0x78: // UTF-8 string (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x79: // UTF-8 string (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x7A: // UTF-8 string (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x7B: // UTF-8 string (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x7F: // UTF-8 string (indefinite length)
+            {
+                while (get() != 0xFF)
+                {
+                    string_t chunk;
+                    if (!get_cbor_string(chunk))
+                    {
+                        return false;
+                    }
+                    result.append(chunk);
+                }
+                return true;
+            }
+
+            default:
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                        exception_message(input_format_t::cbor, concat("expected length specification (0x60-0x7B) or indefinite string type (0x7F); last byte: 0x", last_token), "string"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a CBOR byte array
+
+    This function first reads starting bytes to determine the expected
+    byte array length and then copies this number of bytes into the byte array.
+    Additionally, CBOR's byte arrays with indefinite lengths are supported.
+
+    @param[out] result  created byte array
+
+    @return whether byte array creation completed
+    */
+    bool get_cbor_binary(binary_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "binary")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            // Binary data (0x00..0x17 bytes follow)
+            case 0x40:
+            case 0x41:
+            case 0x42:
+            case 0x43:
+            case 0x44:
+            case 0x45:
+            case 0x46:
+            case 0x47:
+            case 0x48:
+            case 0x49:
+            case 0x4A:
+            case 0x4B:
+            case 0x4C:
+            case 0x4D:
+            case 0x4E:
+            case 0x4F:
+            case 0x50:
+            case 0x51:
+            case 0x52:
+            case 0x53:
+            case 0x54:
+            case 0x55:
+            case 0x56:
+            case 0x57:
+            {
+                return get_binary(input_format_t::cbor, static_cast<unsigned int>(current) & 0x1Fu, result);
+            }
+
+            case 0x58: // Binary data (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x59: // Binary data (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x5A: // Binary data (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x5B: // Binary data (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x5F: // Binary data (indefinite length)
+            {
+                while (get() != 0xFF)
+                {
+                    binary_t chunk;
+                    if (!get_cbor_binary(chunk))
+                    {
+                        return false;
+                    }
+                    result.insert(result.end(), chunk.begin(), chunk.end());
+                }
+                return true;
+            }
+
+            default:
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                        exception_message(input_format_t::cbor, concat("expected length specification (0x40-0x5B) or indefinite binary array type (0x5F); last byte: 0x", last_token), "binary"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @param[in] len  the length of the array or detail::unknown_size() for an
+                    array of indefinite size
+    @param[in] tag_handler how CBOR tags should be treated
+    @return whether array creation completed
+    */
+    bool get_cbor_array(const std::size_t len,
+                        const cbor_tag_handler_t tag_handler)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(len)))
+        {
+            return false;
+        }
+
+        if (len != detail::unknown_size())
+        {
+            for (std::size_t i = 0; i < len; ++i)
+            {
+                if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))
+                {
+                    return false;
+                }
+            }
+        }
+        else
+        {
+            while (get() != 0xFF)
+            {
+                if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(false, tag_handler)))
+                {
+                    return false;
+                }
+            }
+        }
+
+        return sax->end_array();
+    }
+
+    /*!
+    @param[in] len  the length of the object or detail::unknown_size() for an
+                    object of indefinite size
+    @param[in] tag_handler how CBOR tags should be treated
+    @return whether object creation completed
+    */
+    bool get_cbor_object(const std::size_t len,
+                         const cbor_tag_handler_t tag_handler)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(len)))
+        {
+            return false;
+        }
+
+        if (len != 0)
+        {
+            string_t key;
+            if (len != detail::unknown_size())
+            {
+                for (std::size_t i = 0; i < len; ++i)
+                {
+                    get();
+                    if (JSON_HEDLEY_UNLIKELY(!get_cbor_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+
+                    if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+            else
+            {
+                while (get() != 0xFF)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_cbor_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+
+                    if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+        }
+
+        return sax->end_object();
+    }
+
+    /////////////
+    // MsgPack //
+    /////////////
+
+    /*!
+    @return whether a valid MessagePack value was passed to the SAX parser
+    */
+    bool parse_msgpack_internal()
+    {
+        switch (get())
+        {
+            // EOF
+            case char_traits<char_type>::eof():
+                return unexpect_eof(input_format_t::msgpack, "value");
+
+            // positive fixint
+            case 0x00:
+            case 0x01:
+            case 0x02:
+            case 0x03:
+            case 0x04:
+            case 0x05:
+            case 0x06:
+            case 0x07:
+            case 0x08:
+            case 0x09:
+            case 0x0A:
+            case 0x0B:
+            case 0x0C:
+            case 0x0D:
+            case 0x0E:
+            case 0x0F:
+            case 0x10:
+            case 0x11:
+            case 0x12:
+            case 0x13:
+            case 0x14:
+            case 0x15:
+            case 0x16:
+            case 0x17:
+            case 0x18:
+            case 0x19:
+            case 0x1A:
+            case 0x1B:
+            case 0x1C:
+            case 0x1D:
+            case 0x1E:
+            case 0x1F:
+            case 0x20:
+            case 0x21:
+            case 0x22:
+            case 0x23:
+            case 0x24:
+            case 0x25:
+            case 0x26:
+            case 0x27:
+            case 0x28:
+            case 0x29:
+            case 0x2A:
+            case 0x2B:
+            case 0x2C:
+            case 0x2D:
+            case 0x2E:
+            case 0x2F:
+            case 0x30:
+            case 0x31:
+            case 0x32:
+            case 0x33:
+            case 0x34:
+            case 0x35:
+            case 0x36:
+            case 0x37:
+            case 0x38:
+            case 0x39:
+            case 0x3A:
+            case 0x3B:
+            case 0x3C:
+            case 0x3D:
+            case 0x3E:
+            case 0x3F:
+            case 0x40:
+            case 0x41:
+            case 0x42:
+            case 0x43:
+            case 0x44:
+            case 0x45:
+            case 0x46:
+            case 0x47:
+            case 0x48:
+            case 0x49:
+            case 0x4A:
+            case 0x4B:
+            case 0x4C:
+            case 0x4D:
+            case 0x4E:
+            case 0x4F:
+            case 0x50:
+            case 0x51:
+            case 0x52:
+            case 0x53:
+            case 0x54:
+            case 0x55:
+            case 0x56:
+            case 0x57:
+            case 0x58:
+            case 0x59:
+            case 0x5A:
+            case 0x5B:
+            case 0x5C:
+            case 0x5D:
+            case 0x5E:
+            case 0x5F:
+            case 0x60:
+            case 0x61:
+            case 0x62:
+            case 0x63:
+            case 0x64:
+            case 0x65:
+            case 0x66:
+            case 0x67:
+            case 0x68:
+            case 0x69:
+            case 0x6A:
+            case 0x6B:
+            case 0x6C:
+            case 0x6D:
+            case 0x6E:
+            case 0x6F:
+            case 0x70:
+            case 0x71:
+            case 0x72:
+            case 0x73:
+            case 0x74:
+            case 0x75:
+            case 0x76:
+            case 0x77:
+            case 0x78:
+            case 0x79:
+            case 0x7A:
+            case 0x7B:
+            case 0x7C:
+            case 0x7D:
+            case 0x7E:
+            case 0x7F:
+                return sax->number_unsigned(static_cast<number_unsigned_t>(current));
+
+            // fixmap
+            case 0x80:
+            case 0x81:
+            case 0x82:
+            case 0x83:
+            case 0x84:
+            case 0x85:
+            case 0x86:
+            case 0x87:
+            case 0x88:
+            case 0x89:
+            case 0x8A:
+            case 0x8B:
+            case 0x8C:
+            case 0x8D:
+            case 0x8E:
+            case 0x8F:
+                return get_msgpack_object(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x0Fu));
+
+            // fixarray
+            case 0x90:
+            case 0x91:
+            case 0x92:
+            case 0x93:
+            case 0x94:
+            case 0x95:
+            case 0x96:
+            case 0x97:
+            case 0x98:
+            case 0x99:
+            case 0x9A:
+            case 0x9B:
+            case 0x9C:
+            case 0x9D:
+            case 0x9E:
+            case 0x9F:
+                return get_msgpack_array(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x0Fu));
+
+            // fixstr
+            case 0xA0:
+            case 0xA1:
+            case 0xA2:
+            case 0xA3:
+            case 0xA4:
+            case 0xA5:
+            case 0xA6:
+            case 0xA7:
+            case 0xA8:
+            case 0xA9:
+            case 0xAA:
+            case 0xAB:
+            case 0xAC:
+            case 0xAD:
+            case 0xAE:
+            case 0xAF:
+            case 0xB0:
+            case 0xB1:
+            case 0xB2:
+            case 0xB3:
+            case 0xB4:
+            case 0xB5:
+            case 0xB6:
+            case 0xB7:
+            case 0xB8:
+            case 0xB9:
+            case 0xBA:
+            case 0xBB:
+            case 0xBC:
+            case 0xBD:
+            case 0xBE:
+            case 0xBF:
+            case 0xD9: // str 8
+            case 0xDA: // str 16
+            case 0xDB: // str 32
+            {
+                string_t s;
+                return get_msgpack_string(s) && sax->string(s);
+            }
+
+            case 0xC0: // nil
+                return sax->null();
+
+            case 0xC2: // false
+                return sax->boolean(false);
+
+            case 0xC3: // true
+                return sax->boolean(true);
+
+            case 0xC4: // bin 8
+            case 0xC5: // bin 16
+            case 0xC6: // bin 32
+            case 0xC7: // ext 8
+            case 0xC8: // ext 16
+            case 0xC9: // ext 32
+            case 0xD4: // fixext 1
+            case 0xD5: // fixext 2
+            case 0xD6: // fixext 4
+            case 0xD7: // fixext 8
+            case 0xD8: // fixext 16
+            {
+                binary_t b;
+                return get_msgpack_binary(b) && sax->binary(b);
+            }
+
+            case 0xCA: // float 32
+            {
+                float number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0xCB: // float 64
+            {
+                double number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0xCC: // uint 8
+            {
+                std::uint8_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xCD: // uint 16
+            {
+                std::uint16_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xCE: // uint 32
+            {
+                std::uint32_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xCF: // uint 64
+            {
+                std::uint64_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xD0: // int 8
+            {
+                std::int8_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xD1: // int 16
+            {
+                std::int16_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xD2: // int 32
+            {
+                std::int32_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xD3: // int 64
+            {
+                std::int64_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xDC: // array 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_array(static_cast<std::size_t>(len));
+            }
+
+            case 0xDD: // array 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_array(conditional_static_cast<std::size_t>(len));
+            }
+
+            case 0xDE: // map 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_object(static_cast<std::size_t>(len));
+            }
+
+            case 0xDF: // map 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_object(conditional_static_cast<std::size_t>(len));
+            }
+
+            // negative fixint
+            case 0xE0:
+            case 0xE1:
+            case 0xE2:
+            case 0xE3:
+            case 0xE4:
+            case 0xE5:
+            case 0xE6:
+            case 0xE7:
+            case 0xE8:
+            case 0xE9:
+            case 0xEA:
+            case 0xEB:
+            case 0xEC:
+            case 0xED:
+            case 0xEE:
+            case 0xEF:
+            case 0xF0:
+            case 0xF1:
+            case 0xF2:
+            case 0xF3:
+            case 0xF4:
+            case 0xF5:
+            case 0xF6:
+            case 0xF7:
+            case 0xF8:
+            case 0xF9:
+            case 0xFA:
+            case 0xFB:
+            case 0xFC:
+            case 0xFD:
+            case 0xFE:
+            case 0xFF:
+                return sax->number_integer(static_cast<std::int8_t>(current));
+
+            default: // anything else
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format_t::msgpack, concat("invalid byte: 0x", last_token), "value"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a MessagePack string
+
+    This function first reads starting bytes to determine the expected
+    string length and then copies this number of bytes into a string.
+
+    @param[out] result  created string
+
+    @return whether string creation completed
+    */
+    bool get_msgpack_string(string_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::msgpack, "string")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            // fixstr
+            case 0xA0:
+            case 0xA1:
+            case 0xA2:
+            case 0xA3:
+            case 0xA4:
+            case 0xA5:
+            case 0xA6:
+            case 0xA7:
+            case 0xA8:
+            case 0xA9:
+            case 0xAA:
+            case 0xAB:
+            case 0xAC:
+            case 0xAD:
+            case 0xAE:
+            case 0xAF:
+            case 0xB0:
+            case 0xB1:
+            case 0xB2:
+            case 0xB3:
+            case 0xB4:
+            case 0xB5:
+            case 0xB6:
+            case 0xB7:
+            case 0xB8:
+            case 0xB9:
+            case 0xBA:
+            case 0xBB:
+            case 0xBC:
+            case 0xBD:
+            case 0xBE:
+            case 0xBF:
+            {
+                return get_string(input_format_t::msgpack, static_cast<unsigned int>(current) & 0x1Fu, result);
+            }
+
+            case 0xD9: // str 8
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);
+            }
+
+            case 0xDA: // str 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);
+            }
+
+            case 0xDB: // str 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);
+            }
+
+            default:
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                        exception_message(input_format_t::msgpack, concat("expected length specification (0xA0-0xBF, 0xD9-0xDB); last byte: 0x", last_token), "string"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a MessagePack byte array
+
+    This function first reads starting bytes to determine the expected
+    byte array length and then copies this number of bytes into a byte array.
+
+    @param[out] result  created byte array
+
+    @return whether byte array creation completed
+    */
+    bool get_msgpack_binary(binary_t& result)
+    {
+        // helper function to set the subtype
+        auto assign_and_return_true = [&result](std::int8_t subtype)
+        {
+            result.set_subtype(static_cast<std::uint8_t>(subtype));
+            return true;
+        };
+
+        switch (current)
+        {
+            case 0xC4: // bin 8
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_binary(input_format_t::msgpack, len, result);
+            }
+
+            case 0xC5: // bin 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_binary(input_format_t::msgpack, len, result);
+            }
+
+            case 0xC6: // bin 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_binary(input_format_t::msgpack, len, result);
+            }
+
+            case 0xC7: // ext 8
+            {
+                std::uint8_t len{};
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, len, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xC8: // ext 16
+            {
+                std::uint16_t len{};
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, len, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xC9: // ext 32
+            {
+                std::uint32_t len{};
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, len, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD4: // fixext 1
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 1, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD5: // fixext 2
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 2, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD6: // fixext 4
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 4, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD7: // fixext 8
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 8, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD8: // fixext 16
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 16, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            default:           // LCOV_EXCL_LINE
+                return false;  // LCOV_EXCL_LINE
+        }
+    }
+
+    /*!
+    @param[in] len  the length of the array
+    @return whether array creation completed
+    */
+    bool get_msgpack_array(const std::size_t len)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(len)))
+        {
+            return false;
+        }
+
+        for (std::size_t i = 0; i < len; ++i)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!parse_msgpack_internal()))
+            {
+                return false;
+            }
+        }
+
+        return sax->end_array();
+    }
+
+    /*!
+    @param[in] len  the length of the object
+    @return whether object creation completed
+    */
+    bool get_msgpack_object(const std::size_t len)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(len)))
+        {
+            return false;
+        }
+
+        string_t key;
+        for (std::size_t i = 0; i < len; ++i)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!get_msgpack_string(key) || !sax->key(key)))
+            {
+                return false;
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(!parse_msgpack_internal()))
+            {
+                return false;
+            }
+            key.clear();
+        }
+
+        return sax->end_object();
+    }
+
+    ////////////
+    // UBJSON //
+    ////////////
+
+    /*!
+    @param[in] get_char  whether a new character should be retrieved from the
+                         input (true, default) or whether the last read
+                         character should be considered instead
+
+    @return whether a valid UBJSON value was passed to the SAX parser
+    */
+    bool parse_ubjson_internal(const bool get_char = true)
+    {
+        return get_ubjson_value(get_char ? get_ignore_noop() : current);
+    }
+
+    /*!
+    @brief reads a UBJSON string
+
+    This function is either called after reading the 'S' byte explicitly
+    indicating a string, or in case of an object key where the 'S' byte can be
+    left out.
+
+    @param[out] result   created string
+    @param[in] get_char  whether a new character should be retrieved from the
+                         input (true, default) or whether the last read
+                         character should be considered instead
+
+    @return whether string creation completed
+    */
+    bool get_ubjson_string(string_t& result, const bool get_char = true)
+    {
+        if (get_char)
+        {
+            get();  // TODO(niels): may we ignore N here?
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "value")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            case 'U':
+            {
+                std::uint8_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'i':
+            {
+                std::int8_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'I':
+            {
+                std::int16_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'l':
+            {
+                std::int32_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'L':
+            {
+                std::int64_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'u':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint16_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'm':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint32_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'M':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint64_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            default:
+                break;
+        }
+        auto last_token = get_token_string();
+        std::string message;
+
+        if (input_format != input_format_t::bjdata)
+        {
+            message = "expected length type specification (U, i, I, l, L); last byte: 0x" + last_token;
+        }
+        else
+        {
+            message = "expected length type specification (U, i, u, I, m, l, M, L); last byte: 0x" + last_token;
+        }
+        return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read, exception_message(input_format, message, "string"), nullptr));
+    }
+
+    /*!
+    @param[out] dim  an integer vector storing the ND array dimensions
+    @return whether reading ND array size vector is successful
+    */
+    bool get_ubjson_ndarray_size(std::vector<size_t>& dim)
+    {
+        std::pair<std::size_t, char_int_type> size_and_type;
+        size_t dimlen = 0;
+        bool no_ndarray = true;
+
+        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type, no_ndarray)))
+        {
+            return false;
+        }
+
+        if (size_and_type.first != npos)
+        {
+            if (size_and_type.second != 0)
+            {
+                if (size_and_type.second != 'N')
+                {
+                    for (std::size_t i = 0; i < size_and_type.first; ++i)
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray, size_and_type.second)))
+                        {
+                            return false;
+                        }
+                        dim.push_back(dimlen);
+                    }
+                }
+            }
+            else
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray)))
+                    {
+                        return false;
+                    }
+                    dim.push_back(dimlen);
+                }
+            }
+        }
+        else
+        {
+            while (current != ']')
+            {
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray, current)))
+                {
+                    return false;
+                }
+                dim.push_back(dimlen);
+                get_ignore_noop();
+            }
+        }
+        return true;
+    }
+
+    /*!
+    @param[out] result  determined size
+    @param[in,out] is_ndarray  for input, `true` means already inside an ndarray vector
+                               or ndarray dimension is not allowed; `false` means ndarray
+                               is allowed; for output, `true` means an ndarray is found;
+                               is_ndarray can only return `true` when its initial value
+                               is `false`
+    @param[in] prefix  type marker if already read, otherwise set to 0
+
+    @return whether size determination completed
+    */
+    bool get_ubjson_size_value(std::size_t& result, bool& is_ndarray, char_int_type prefix = 0)
+    {
+        if (prefix == 0)
+        {
+            prefix = get_ignore_noop();
+        }
+
+        switch (prefix)
+        {
+            case 'U':
+            {
+                std::uint8_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'i':
+            {
+                std::int8_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number); // NOLINT(bugprone-signed-char-misuse,cert-str34-c): number is not a char
+                return true;
+            }
+
+            case 'I':
+            {
+                std::int16_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'l':
+            {
+                std::int32_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'L':
+            {
+                std::int64_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                if (!value_in_range_of<std::size_t>(number))
+                {
+                    return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408,
+                                            exception_message(input_format, "integer value overflow", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'u':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint16_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'm':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint32_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                result = conditional_static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'M':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint64_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (!value_in_range_of<std::size_t>(number))
+                {
+                    return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408,
+                                            exception_message(input_format, "integer value overflow", "size"), nullptr));
+                }
+                result = detail::conditional_static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case '[':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                if (is_ndarray) // ndarray dimensional vector can only contain integers, and can not embed another array
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read, exception_message(input_format, "ndarray dimensional vector is not allowed", "size"), nullptr));
+                }
+                std::vector<size_t> dim;
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_ndarray_size(dim)))
+                {
+                    return false;
+                }
+                if (dim.size() == 1 || (dim.size() == 2 && dim.at(0) == 1)) // return normal array size if 1D row vector
+                {
+                    result = dim.at(dim.size() - 1);
+                    return true;
+                }
+                if (!dim.empty())  // if ndarray, convert to an object in JData annotated array format
+                {
+                    for (auto i : dim) // test if any dimension in an ndarray is 0, if so, return a 1D empty container
+                    {
+                        if ( i == 0 )
+                        {
+                            result = 0;
+                            return true;
+                        }
+                    }
+
+                    string_t key = "_ArraySize_";
+                    if (JSON_HEDLEY_UNLIKELY(!sax->start_object(3) || !sax->key(key) || !sax->start_array(dim.size())))
+                    {
+                        return false;
+                    }
+                    result = 1;
+                    for (auto i : dim)
+                    {
+                        result *= i;
+                        if (result == 0 || result == npos) // because dim elements shall not have zeros, result = 0 means overflow happened; it also can't be npos as it is used to initialize size in get_ubjson_size_type()
+                        {
+                            return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408, exception_message(input_format, "excessive ndarray size caused overflow", "size"), nullptr));
+                        }
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_unsigned(static_cast<number_unsigned_t>(i))))
+                        {
+                            return false;
+                        }
+                    }
+                    is_ndarray = true;
+                    return sax->end_array();
+                }
+                result = 0;
+                return true;
+            }
+
+            default:
+                break;
+        }
+        auto last_token = get_token_string();
+        std::string message;
+
+        if (input_format != input_format_t::bjdata)
+        {
+            message = "expected length type specification (U, i, I, l, L) after '#'; last byte: 0x" + last_token;
+        }
+        else
+        {
+            message = "expected length type specification (U, i, u, I, m, l, M, L) after '#'; last byte: 0x" + last_token;
+        }
+        return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read, exception_message(input_format, message, "size"), nullptr));
+    }
+
+    /*!
+    @brief determine the type and size for a container
+
+    In the optimized UBJSON format, a type and a size can be provided to allow
+    for a more compact representation.
+
+    @param[out] result  pair of the size and the type
+    @param[in] inside_ndarray  whether the parser is parsing an ND array dimensional vector
+
+    @return whether pair creation completed
+    */
+    bool get_ubjson_size_type(std::pair<std::size_t, char_int_type>& result, bool inside_ndarray = false)
+    {
+        result.first = npos; // size
+        result.second = 0; // type
+        bool is_ndarray = false;
+
+        get_ignore_noop();
+
+        if (current == '$')
+        {
+            result.second = get();  // must not ignore 'N', because 'N' maybe the type
+            if (input_format == input_format_t::bjdata
+                    && JSON_HEDLEY_UNLIKELY(std::binary_search(bjd_optimized_type_markers.begin(), bjd_optimized_type_markers.end(), result.second)))
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format, concat("marker 0x", last_token, " is not a permitted optimized array type"), "type"), nullptr));
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "type")))
+            {
+                return false;
+            }
+
+            get_ignore_noop();
+            if (JSON_HEDLEY_UNLIKELY(current != '#'))
+            {
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "value")))
+                {
+                    return false;
+                }
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format, concat("expected '#' after type information; last byte: 0x", last_token), "size"), nullptr));
+            }
+
+            const bool is_error = get_ubjson_size_value(result.first, is_ndarray);
+            if (input_format == input_format_t::bjdata && is_ndarray)
+            {
+                if (inside_ndarray)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(112, chars_read,
+                                            exception_message(input_format, "ndarray can not be recursive", "size"), nullptr));
+                }
+                result.second |= (1 << 8); // use bit 8 to indicate ndarray, all UBJSON and BJData markers should be ASCII letters
+            }
+            return is_error;
+        }
+
+        if (current == '#')
+        {
+            const bool is_error = get_ubjson_size_value(result.first, is_ndarray);
+            if (input_format == input_format_t::bjdata && is_ndarray)
+            {
+                return sax->parse_error(chars_read, get_token_string(), parse_error::create(112, chars_read,
+                                        exception_message(input_format, "ndarray requires both type and size", "size"), nullptr));
+            }
+            return is_error;
+        }
+
+        return true;
+    }
+
+    /*!
+    @param prefix  the previously read or set type prefix
+    @return whether value creation completed
+    */
+    bool get_ubjson_value(const char_int_type prefix)
+    {
+        switch (prefix)
+        {
+            case char_traits<char_type>::eof():  // EOF
+                return unexpect_eof(input_format, "value");
+
+            case 'T':  // true
+                return sax->boolean(true);
+            case 'F':  // false
+                return sax->boolean(false);
+
+            case 'Z':  // null
+                return sax->null();
+
+            case 'B':  // byte
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint8_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'U':
+            {
+                std::uint8_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'i':
+            {
+                std::int8_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'I':
+            {
+                std::int16_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'l':
+            {
+                std::int32_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'L':
+            {
+                std::int64_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'u':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint16_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'm':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint32_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'M':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint64_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'h':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                const auto byte1_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "number")))
+                {
+                    return false;
+                }
+                const auto byte2_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "number")))
+                {
+                    return false;
+                }
+
+                const auto byte1 = static_cast<unsigned char>(byte1_raw);
+                const auto byte2 = static_cast<unsigned char>(byte2_raw);
+
+                // code from RFC 7049, Appendix D, Figure 3:
+                // As half-precision floating-point numbers were only added
+                // to IEEE 754 in 2008, today's programming platforms often
+                // still only have limited support for them. It is very
+                // easy to include at least decoding support for them even
+                // without such support. An example of a small decoder for
+                // half-precision floating-point numbers in the C language
+                // is shown in Fig. 3.
+                const auto half = static_cast<unsigned int>((byte2 << 8u) + byte1);
+                const double val = [&half]
+                {
+                    const int exp = (half >> 10u) & 0x1Fu;
+                    const unsigned int mant = half & 0x3FFu;
+                    JSON_ASSERT(0 <= exp&& exp <= 32);
+                    JSON_ASSERT(mant <= 1024);
+                    switch (exp)
+                    {
+                        case 0:
+                            return std::ldexp(mant, -24);
+                        case 31:
+                            return (mant == 0)
+                            ? std::numeric_limits<double>::infinity()
+                            : std::numeric_limits<double>::quiet_NaN();
+                        default:
+                            return std::ldexp(mant + 1024, exp - 25);
+                    }
+                }();
+                return sax->number_float((half & 0x8000u) != 0
+                                         ? static_cast<number_float_t>(-val)
+                                         : static_cast<number_float_t>(val), "");
+            }
+
+            case 'd':
+            {
+                float number{};
+                return get_number(input_format, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 'D':
+            {
+                double number{};
+                return get_number(input_format, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 'H':
+            {
+                return get_ubjson_high_precision_number();
+            }
+
+            case 'C':  // char
+            {
+                get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "char")))
+                {
+                    return false;
+                }
+                if (JSON_HEDLEY_UNLIKELY(current > 127))
+                {
+                    auto last_token = get_token_string();
+                    return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                            exception_message(input_format, concat("byte after 'C' must be in range 0x00..0x7F; last byte: 0x", last_token), "char"), nullptr));
+                }
+                string_t s(1, static_cast<typename string_t::value_type>(current));
+                return sax->string(s);
+            }
+
+            case 'S':  // string
+            {
+                string_t s;
+                return get_ubjson_string(s) && sax->string(s);
+            }
+
+            case '[':  // array
+                return get_ubjson_array();
+
+            case '{':  // object
+                return get_ubjson_object();
+
+            default: // anything else
+                break;
+        }
+        auto last_token = get_token_string();
+        return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read, exception_message(input_format, "invalid byte: 0x" + last_token, "value"), nullptr));
+    }
+
+    /*!
+    @return whether array creation completed
+    */
+    bool get_ubjson_array()
+    {
+        std::pair<std::size_t, char_int_type> size_and_type;
+        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type)))
+        {
+            return false;
+        }
+
+        // if bit-8 of size_and_type.second is set to 1, encode bjdata ndarray as an object in JData annotated array format (https://github.com/NeuroJSON/jdata):
+        // {"_ArrayType_" : "typeid", "_ArraySize_" : [n1, n2, ...], "_ArrayData_" : [v1, v2, ...]}
+
+        if (input_format == input_format_t::bjdata && size_and_type.first != npos && (size_and_type.second & (1 << 8)) != 0)
+        {
+            size_and_type.second &= ~(static_cast<char_int_type>(1) << 8);  // use bit 8 to indicate ndarray, here we remove the bit to restore the type marker
+            auto it = std::lower_bound(bjd_types_map.begin(), bjd_types_map.end(), size_and_type.second, [](const bjd_type & p, char_int_type t)
+            {
+                return p.first < t;
+            });
+            string_t key = "_ArrayType_";
+            if (JSON_HEDLEY_UNLIKELY(it == bjd_types_map.end() || it->first != size_and_type.second))
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format, "invalid byte: 0x" + last_token, "type"), nullptr));
+            }
+
+            string_t type = it->second; // sax->string() takes a reference
+            if (JSON_HEDLEY_UNLIKELY(!sax->key(key) || !sax->string(type)))
+            {
+                return false;
+            }
+
+            if (size_and_type.second == 'C' || size_and_type.second == 'B')
+            {
+                size_and_type.second = 'U';
+            }
+
+            key = "_ArrayData_";
+            if (JSON_HEDLEY_UNLIKELY(!sax->key(key) || !sax->start_array(size_and_type.first) ))
+            {
+                return false;
+            }
+
+            for (std::size_t i = 0; i < size_and_type.first; ++i)
+            {
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))
+                {
+                    return false;
+                }
+            }
+
+            return (sax->end_array() && sax->end_object());
+        }
+
+        // If BJData type marker is 'B' decode as binary
+        if (input_format == input_format_t::bjdata && size_and_type.first != npos && size_and_type.second == 'B')
+        {
+            binary_t result;
+            return get_binary(input_format, size_and_type.first, result) && sax->binary(result);
+        }
+
+        if (size_and_type.first != npos)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_array(size_and_type.first)))
+            {
+                return false;
+            }
+
+            if (size_and_type.second != 0)
+            {
+                if (size_and_type.second != 'N')
+                {
+                    for (std::size_t i = 0; i < size_and_type.first; ++i)
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))
+                        {
+                            return false;
+                        }
+                    }
+                }
+            }
+            else
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))
+                    {
+                        return false;
+                    }
+                }
+            }
+        }
+        else
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_array(detail::unknown_size())))
+            {
+                return false;
+            }
+
+            while (current != ']')
+            {
+                if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal(false)))
+                {
+                    return false;
+                }
+                get_ignore_noop();
+            }
+        }
+
+        return sax->end_array();
+    }
+
+    /*!
+    @return whether object creation completed
+    */
+    bool get_ubjson_object()
+    {
+        std::pair<std::size_t, char_int_type> size_and_type;
+        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type)))
+        {
+            return false;
+        }
+
+        // do not accept ND-array size in objects in BJData
+        if (input_format == input_format_t::bjdata && size_and_type.first != npos && (size_and_type.second & (1 << 8)) != 0)
+        {
+            auto last_token = get_token_string();
+            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                    exception_message(input_format, "BJData object does not support ND-array size in optimized format", "object"), nullptr));
+        }
+
+        string_t key;
+        if (size_and_type.first != npos)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_object(size_and_type.first)))
+            {
+                return false;
+            }
+
+            if (size_and_type.second != 0)
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+            else
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+        }
+        else
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_object(detail::unknown_size())))
+            {
+                return false;
+            }
+
+            while (current != '}')
+            {
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key, false) || !sax->key(key)))
+                {
+                    return false;
+                }
+                if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))
+                {
+                    return false;
+                }
+                get_ignore_noop();
+                key.clear();
+            }
+        }
+
+        return sax->end_object();
+    }
+
+    // Note, no reader for UBJSON binary types is implemented because they do
+    // not exist
+
+    bool get_ubjson_high_precision_number()
+    {
+        // get size of following number string
+        std::size_t size{};
+        bool no_ndarray = true;
+        auto res = get_ubjson_size_value(size, no_ndarray);
+        if (JSON_HEDLEY_UNLIKELY(!res))
+        {
+            return res;
+        }
+
+        // get number string
+        std::vector<char> number_vector;
+        for (std::size_t i = 0; i < size; ++i)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "number")))
+            {
+                return false;
+            }
+            number_vector.push_back(static_cast<char>(current));
+        }
+
+        // parse number string
+        using ia_type = decltype(detail::input_adapter(number_vector));
+        auto number_lexer = detail::lexer<BasicJsonType, ia_type>(detail::input_adapter(number_vector), false);
+        const auto result_number = number_lexer.scan();
+        const auto number_string = number_lexer.get_token_string();
+        const auto result_remainder = number_lexer.scan();
+
+        using token_type = typename detail::lexer_base<BasicJsonType>::token_type;
+
+        if (JSON_HEDLEY_UNLIKELY(result_remainder != token_type::end_of_input))
+        {
+            return sax->parse_error(chars_read, number_string, parse_error::create(115, chars_read,
+                                    exception_message(input_format, concat("invalid number text: ", number_lexer.get_token_string()), "high-precision number"), nullptr));
+        }
+
+        switch (result_number)
+        {
+            case token_type::value_integer:
+                return sax->number_integer(number_lexer.get_number_integer());
+            case token_type::value_unsigned:
+                return sax->number_unsigned(number_lexer.get_number_unsigned());
+            case token_type::value_float:
+                return sax->number_float(number_lexer.get_number_float(), std::move(number_string));
+            case token_type::uninitialized:
+            case token_type::literal_true:
+            case token_type::literal_false:
+            case token_type::literal_null:
+            case token_type::value_string:
+            case token_type::begin_array:
+            case token_type::begin_object:
+            case token_type::end_array:
+            case token_type::end_object:
+            case token_type::name_separator:
+            case token_type::value_separator:
+            case token_type::parse_error:
+            case token_type::end_of_input:
+            case token_type::literal_or_value:
+            default:
+                return sax->parse_error(chars_read, number_string, parse_error::create(115, chars_read,
+                                        exception_message(input_format, concat("invalid number text: ", number_lexer.get_token_string()), "high-precision number"), nullptr));
+        }
+    }
+
+    ///////////////////////
+    // Utility functions //
+    ///////////////////////
+
+    /*!
+    @brief get next character from the input
+
+    This function provides the interface to the used input adapter. It does
+    not throw in case the input reached EOF, but returns a -'ve valued
+    `char_traits<char_type>::eof()` in that case.
+
+    @return character read from the input
+    */
+    char_int_type get()
+    {
+        ++chars_read;
+        return current = ia.get_character();
+    }
+
+    /*!
+    @brief get_to read into a primitive type
+
+    This function provides the interface to the used input adapter. It does
+    not throw in case the input reached EOF, but returns false instead
+
+    @return bool, whether the read was successful
+    */
+    template<class T>
+    bool get_to(T& dest, const input_format_t format, const char* context)
+    {
+        auto new_chars_read = ia.get_elements(&dest);
+        chars_read += new_chars_read;
+        if (JSON_HEDLEY_UNLIKELY(new_chars_read < sizeof(T)))
+        {
+            // in case of failure, advance position by 1 to report failing location
+            ++chars_read;
+            sax->parse_error(chars_read, "<end of file>", parse_error::create(110, chars_read, exception_message(format, "unexpected end of input", context), nullptr));
+            return false;
+        }
+        return true;
+    }
+
+    /*!
+    @return character read from the input after ignoring all 'N' entries
+    */
+    char_int_type get_ignore_noop()
+    {
+        do
+        {
+            get();
+        }
+        while (current == 'N');
+
+        return current;
+    }
+
+    template<class NumberType>
+    static void byte_swap(NumberType& number)
+    {
+        constexpr std::size_t sz = sizeof(number);
+#ifdef __cpp_lib_byteswap
+        if constexpr (sz == 1)
+        {
+            return;
+        }
+        if constexpr(std::is_integral_v<NumberType>)
+        {
+            number = std::byteswap(number);
+            return;
+        }
+#endif
+        auto* ptr = reinterpret_cast<std::uint8_t*>(&number);
+        for (std::size_t i = 0; i < sz / 2; ++i)
+        {
+            std::swap(ptr[i], ptr[sz - i - 1]);
+        }
+    }
+
+    /*
+    @brief read a number from the input
+
+    @tparam NumberType the type of the number
+    @param[in] format   the current format (for diagnostics)
+    @param[out] result  number of type @a NumberType
+
+    @return whether conversion completed
+
+    @note This function needs to respect the system's endianness, because
+          bytes in CBOR, MessagePack, and UBJSON are stored in network order
+          (big endian) and therefore need reordering on little endian systems.
+          On the other hand, BSON and BJData use little endian and should reorder
+          on big endian systems.
+    */
+    template<typename NumberType, bool InputIsLittleEndian = false>
+    bool get_number(const input_format_t format, NumberType& result)
+    {
+        // read in the original format
+
+        if (JSON_HEDLEY_UNLIKELY(!get_to(result, format, "number")))
+        {
+            return false;
+        }
+        if (is_little_endian != (InputIsLittleEndian || format == input_format_t::bjdata))
+        {
+            byte_swap(result);
+        }
+        return true;
+    }
+
+    /*!
+    @brief create a string by reading characters from the input
+
+    @tparam NumberType the type of the number
+    @param[in] format the current format (for diagnostics)
+    @param[in] len number of characters to read
+    @param[out] result string created by reading @a len bytes
+
+    @return whether string creation completed
+
+    @note We can not reserve @a len bytes for the result, because @a len
+          may be too large. Usually, @ref unexpect_eof() detects the end of
+          the input before we run out of string memory.
+    */
+    template<typename NumberType>
+    bool get_string(const input_format_t format,
+                    const NumberType len,
+                    string_t& result)
+    {
+        bool success = true;
+        for (NumberType i = 0; i < len; i++)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, "string")))
+            {
+                success = false;
+                break;
+            }
+            result.push_back(static_cast<typename string_t::value_type>(current));
+        }
+        return success;
+    }
+
+    /*!
+    @brief create a byte array by reading bytes from the input
+
+    @tparam NumberType the type of the number
+    @param[in] format the current format (for diagnostics)
+    @param[in] len number of bytes to read
+    @param[out] result byte array created by reading @a len bytes
+
+    @return whether byte array creation completed
+
+    @note We can not reserve @a len bytes for the result, because @a len
+          may be too large. Usually, @ref unexpect_eof() detects the end of
+          the input before we run out of memory.
+    */
+    template<typename NumberType>
+    bool get_binary(const input_format_t format,
+                    const NumberType len,
+                    binary_t& result)
+    {
+        bool success = true;
+        for (NumberType i = 0; i < len; i++)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, "binary")))
+            {
+                success = false;
+                break;
+            }
+            result.push_back(static_cast<std::uint8_t>(current));
+        }
+        return success;
+    }
+
+    /*!
+    @param[in] format   the current format (for diagnostics)
+    @param[in] context  further context information (for diagnostics)
+    @return whether the last read character is not EOF
+    */
+    JSON_HEDLEY_NON_NULL(3)
+    bool unexpect_eof(const input_format_t format, const char* context) const
+    {
+        if (JSON_HEDLEY_UNLIKELY(current == char_traits<char_type>::eof()))
+        {
+            return sax->parse_error(chars_read, "<end of file>",
+                                    parse_error::create(110, chars_read, exception_message(format, "unexpected end of input", context), nullptr));
+        }
+        return true;
+    }
+
+    /*!
+    @return a string representation of the last read byte
+    */
+    std::string get_token_string() const
+    {
+        std::array<char, 3> cr{{}};
+        static_cast<void>((std::snprintf)(cr.data(), cr.size(), "%.2hhX", static_cast<unsigned char>(current))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+        return std::string{cr.data()};
+    }
+
+    /*!
+    @param[in] format   the current format
+    @param[in] detail   a detailed error message
+    @param[in] context  further context information
+    @return a message string to use in the parse_error exceptions
+    */
+    std::string exception_message(const input_format_t format,
+                                  const std::string& detail,
+                                  const std::string& context) const
+    {
+        std::string error_msg = "syntax error while parsing ";
+
+        switch (format)
+        {
+            case input_format_t::cbor:
+                error_msg += "CBOR";
+                break;
+
+            case input_format_t::msgpack:
+                error_msg += "MessagePack";
+                break;
+
+            case input_format_t::ubjson:
+                error_msg += "UBJSON";
+                break;
+
+            case input_format_t::bson:
+                error_msg += "BSON";
+                break;
+
+            case input_format_t::bjdata:
+                error_msg += "BJData";
+                break;
+
+            case input_format_t::json: // LCOV_EXCL_LINE
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+
+        return concat(error_msg, ' ', context, ": ", detail);
+    }
+
+  private:
+    static JSON_INLINE_VARIABLE constexpr std::size_t npos = detail::unknown_size();
+
+    /// input adapter
+    InputAdapterType ia;
+
+    /// the current character
+    char_int_type current = char_traits<char_type>::eof();
+
+    /// the number of characters read
+    std::size_t chars_read = 0;
+
+    /// whether we can assume little endianness
+    const bool is_little_endian = little_endianness();
+
+    /// input format
+    const input_format_t input_format = input_format_t::json;
+
+    /// the SAX parser
+    json_sax_t* sax = nullptr;
+
+    // excluded markers in bjdata optimized type
+#define JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_ \
+    make_array<char_int_type>('F', 'H', 'N', 'S', 'T', 'Z', '[', '{')
+
+#define JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_ \
+    make_array<bjd_type>(                      \
+    bjd_type{'B', "byte"},                     \
+    bjd_type{'C', "char"},                     \
+    bjd_type{'D', "double"},                   \
+    bjd_type{'I', "int16"},                    \
+    bjd_type{'L', "int64"},                    \
+    bjd_type{'M', "uint64"},                   \
+    bjd_type{'U', "uint8"},                    \
+    bjd_type{'d', "single"},                   \
+    bjd_type{'i', "int8"},                     \
+    bjd_type{'l', "int32"},                    \
+    bjd_type{'m', "uint32"},                   \
+    bjd_type{'u', "uint16"})
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    // lookup tables
+    // NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
+    const decltype(JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_) bjd_optimized_type_markers =
+        JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_;
+
+    using bjd_type = std::pair<char_int_type, string_t>;
+    // NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
+    const decltype(JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_) bjd_types_map =
+        JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_;
+
+#undef JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_
+#undef JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_
+};
+
+#ifndef JSON_HAS_CPP_17
+    template<typename BasicJsonType, typename InputAdapterType, typename SAX>
+    constexpr std::size_t binary_reader<BasicJsonType, InputAdapterType, SAX>::npos;
+#endif
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+
+// #include <nlohmann/detail/input/lexer.hpp>
+
+// #include <nlohmann/detail/input/parser.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cmath> // isfinite
+#include <cstdint> // uint8_t
+#include <functional> // function
+#include <string> // string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+
+// #include <nlohmann/detail/input/json_sax.hpp>
+
+// #include <nlohmann/detail/input/lexer.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/is_sax.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+////////////
+// parser //
+////////////
+
+enum class parse_event_t : std::uint8_t
+{
+    /// the parser read `{` and started to process a JSON object
+    object_start,
+    /// the parser read `}` and finished processing a JSON object
+    object_end,
+    /// the parser read `[` and started to process a JSON array
+    array_start,
+    /// the parser read `]` and finished processing a JSON array
+    array_end,
+    /// the parser read a key of a value in an object
+    key,
+    /// the parser finished reading a JSON value
+    value
+};
+
+template<typename BasicJsonType>
+using parser_callback_t =
+    std::function<bool(int /*depth*/, parse_event_t /*event*/, BasicJsonType& /*parsed*/)>;
+
+/*!
+@brief syntax analysis
+
+This class implements a recursive descent parser.
+*/
+template<typename BasicJsonType, typename InputAdapterType>
+class parser
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using lexer_t = lexer<BasicJsonType, InputAdapterType>;
+    using token_type = typename lexer_t::token_type;
+
+  public:
+    /// a parser reading from an input adapter
+    explicit parser(InputAdapterType&& adapter,
+                    parser_callback_t<BasicJsonType> cb = nullptr,
+                    const bool allow_exceptions_ = true,
+                    const bool skip_comments = false)
+        : callback(std::move(cb))
+        , m_lexer(std::move(adapter), skip_comments)
+        , allow_exceptions(allow_exceptions_)
+    {
+        // read first token
+        get_token();
+    }
+
+    /*!
+    @brief public parser interface
+
+    @param[in] strict      whether to expect the last token to be EOF
+    @param[in,out] result  parsed JSON value
+
+    @throw parse_error.101 in case of an unexpected token
+    @throw parse_error.102 if to_unicode fails or surrogate error
+    @throw parse_error.103 if to_unicode fails
+    */
+    void parse(const bool strict, BasicJsonType& result)
+    {
+        if (callback)
+        {
+            json_sax_dom_callback_parser<BasicJsonType, InputAdapterType> sdp(result, callback, allow_exceptions, &m_lexer);
+            sax_parse_internal(&sdp);
+
+            // in strict mode, input must be completely read
+            if (strict && (get_token() != token_type::end_of_input))
+            {
+                sdp.parse_error(m_lexer.get_position(),
+                                m_lexer.get_token_string(),
+                                parse_error::create(101, m_lexer.get_position(),
+                                                    exception_message(token_type::end_of_input, "value"), nullptr));
+            }
+
+            // in case of an error, return discarded value
+            if (sdp.is_errored())
+            {
+                result = value_t::discarded;
+                return;
+            }
+
+            // set top-level value to null if it was discarded by the callback
+            // function
+            if (result.is_discarded())
+            {
+                result = nullptr;
+            }
+        }
+        else
+        {
+            json_sax_dom_parser<BasicJsonType, InputAdapterType> sdp(result, allow_exceptions, &m_lexer);
+            sax_parse_internal(&sdp);
+
+            // in strict mode, input must be completely read
+            if (strict && (get_token() != token_type::end_of_input))
+            {
+                sdp.parse_error(m_lexer.get_position(),
+                                m_lexer.get_token_string(),
+                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_of_input, "value"), nullptr));
+            }
+
+            // in case of an error, return discarded value
+            if (sdp.is_errored())
+            {
+                result = value_t::discarded;
+                return;
+            }
+        }
+
+        result.assert_invariant();
+    }
+
+    /*!
+    @brief public accept interface
+
+    @param[in] strict  whether to expect the last token to be EOF
+    @return whether the input is a proper JSON text
+    */
+    bool accept(const bool strict = true)
+    {
+        json_sax_acceptor<BasicJsonType> sax_acceptor;
+        return sax_parse(&sax_acceptor, strict);
+    }
+
+    template<typename SAX>
+    JSON_HEDLEY_NON_NULL(2)
+    bool sax_parse(SAX* sax, const bool strict = true)
+    {
+        (void)detail::is_sax_static_asserts<SAX, BasicJsonType> {};
+        const bool result = sax_parse_internal(sax);
+
+        // strict mode: next byte must be EOF
+        if (result && strict && (get_token() != token_type::end_of_input))
+        {
+            return sax->parse_error(m_lexer.get_position(),
+                                    m_lexer.get_token_string(),
+                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_of_input, "value"), nullptr));
+        }
+
+        return result;
+    }
+
+  private:
+    template<typename SAX>
+    JSON_HEDLEY_NON_NULL(2)
+    bool sax_parse_internal(SAX* sax)
+    {
+        // stack to remember the hierarchy of structured values we are parsing
+        // true = array; false = object
+        std::vector<bool> states;
+        // value to avoid a goto (see comment where set to true)
+        bool skip_to_state_evaluation = false;
+
+        while (true)
+        {
+            if (!skip_to_state_evaluation)
+            {
+                // invariant: get_token() was called before each iteration
+                switch (last_token)
+                {
+                    case token_type::begin_object:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(detail::unknown_size())))
+                        {
+                            return false;
+                        }
+
+                        // closing } -> we are done
+                        if (get_token() == token_type::end_object)
+                        {
+                            if (JSON_HEDLEY_UNLIKELY(!sax->end_object()))
+                            {
+                                return false;
+                            }
+                            break;
+                        }
+
+                        // parse key
+                        if (JSON_HEDLEY_UNLIKELY(last_token != token_type::value_string))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::value_string, "object key"), nullptr));
+                        }
+                        if (JSON_HEDLEY_UNLIKELY(!sax->key(m_lexer.get_string())))
+                        {
+                            return false;
+                        }
+
+                        // parse separator (:)
+                        if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::name_separator))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::name_separator, "object separator"), nullptr));
+                        }
+
+                        // remember we are now inside an object
+                        states.push_back(false);
+
+                        // parse values
+                        get_token();
+                        continue;
+                    }
+
+                    case token_type::begin_array:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(detail::unknown_size())))
+                        {
+                            return false;
+                        }
+
+                        // closing ] -> we are done
+                        if (get_token() == token_type::end_array)
+                        {
+                            if (JSON_HEDLEY_UNLIKELY(!sax->end_array()))
+                            {
+                                return false;
+                            }
+                            break;
+                        }
+
+                        // remember we are now inside an array
+                        states.push_back(true);
+
+                        // parse values (no need to call get_token)
+                        continue;
+                    }
+
+                    case token_type::value_float:
+                    {
+                        const auto res = m_lexer.get_number_float();
+
+                        if (JSON_HEDLEY_UNLIKELY(!std::isfinite(res)))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    out_of_range::create(406, concat("number overflow parsing '", m_lexer.get_token_string(), '\''), nullptr));
+                        }
+
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_float(res, m_lexer.get_string())))
+                        {
+                            return false;
+                        }
+
+                        break;
+                    }
+
+                    case token_type::literal_false:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->boolean(false)))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::literal_null:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->null()))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::literal_true:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->boolean(true)))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::value_integer:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_integer(m_lexer.get_number_integer())))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::value_string:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->string(m_lexer.get_string())))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::value_unsigned:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_unsigned(m_lexer.get_number_unsigned())))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::parse_error:
+                    {
+                        // using "uninitialized" to avoid "expected" message
+                        return sax->parse_error(m_lexer.get_position(),
+                                                m_lexer.get_token_string(),
+                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::uninitialized, "value"), nullptr));
+                    }
+                    case token_type::end_of_input:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(m_lexer.get_position().chars_read_total == 1))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    parse_error::create(101, m_lexer.get_position(),
+                                                            "attempting to parse an empty input; check that your input string or stream contains the expected JSON", nullptr));
+                        }
+
+                        return sax->parse_error(m_lexer.get_position(),
+                                                m_lexer.get_token_string(),
+                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::literal_or_value, "value"), nullptr));
+                    }
+                    case token_type::uninitialized:
+                    case token_type::end_array:
+                    case token_type::end_object:
+                    case token_type::name_separator:
+                    case token_type::value_separator:
+                    case token_type::literal_or_value:
+                    default: // the last token was unexpected
+                    {
+                        return sax->parse_error(m_lexer.get_position(),
+                                                m_lexer.get_token_string(),
+                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::literal_or_value, "value"), nullptr));
+                    }
+                }
+            }
+            else
+            {
+                skip_to_state_evaluation = false;
+            }
+
+            // we reached this line after we successfully parsed a value
+            if (states.empty())
+            {
+                // empty stack: we reached the end of the hierarchy: done
+                return true;
+            }
+
+            if (states.back())  // array
+            {
+                // comma -> next value
+                if (get_token() == token_type::value_separator)
+                {
+                    // parse a new value
+                    get_token();
+                    continue;
+                }
+
+                // closing ]
+                if (JSON_HEDLEY_LIKELY(last_token == token_type::end_array))
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!sax->end_array()))
+                    {
+                        return false;
+                    }
+
+                    // We are done with this array. Before we can parse a
+                    // new value, we need to evaluate the new state first.
+                    // By setting skip_to_state_evaluation to false, we
+                    // are effectively jumping to the beginning of this if.
+                    JSON_ASSERT(!states.empty());
+                    states.pop_back();
+                    skip_to_state_evaluation = true;
+                    continue;
+                }
+
+                return sax->parse_error(m_lexer.get_position(),
+                                        m_lexer.get_token_string(),
+                                        parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_array, "array"), nullptr));
+            }
+
+            // states.back() is false -> object
+
+            // comma -> next value
+            if (get_token() == token_type::value_separator)
+            {
+                // parse key
+                if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::value_string))
+                {
+                    return sax->parse_error(m_lexer.get_position(),
+                                            m_lexer.get_token_string(),
+                                            parse_error::create(101, m_lexer.get_position(), exception_message(token_type::value_string, "object key"), nullptr));
+                }
+
+                if (JSON_HEDLEY_UNLIKELY(!sax->key(m_lexer.get_string())))
+                {
+                    return false;
+                }
+
+                // parse separator (:)
+                if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::name_separator))
+                {
+                    return sax->parse_error(m_lexer.get_position(),
+                                            m_lexer.get_token_string(),
+                                            parse_error::create(101, m_lexer.get_position(), exception_message(token_type::name_separator, "object separator"), nullptr));
+                }
+
+                // parse values
+                get_token();
+                continue;
+            }
+
+            // closing }
+            if (JSON_HEDLEY_LIKELY(last_token == token_type::end_object))
+            {
+                if (JSON_HEDLEY_UNLIKELY(!sax->end_object()))
+                {
+                    return false;
+                }
+
+                // We are done with this object. Before we can parse a
+                // new value, we need to evaluate the new state first.
+                // By setting skip_to_state_evaluation to false, we
+                // are effectively jumping to the beginning of this if.
+                JSON_ASSERT(!states.empty());
+                states.pop_back();
+                skip_to_state_evaluation = true;
+                continue;
+            }
+
+            return sax->parse_error(m_lexer.get_position(),
+                                    m_lexer.get_token_string(),
+                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_object, "object"), nullptr));
+        }
+    }
+
+    /// get next token from lexer
+    token_type get_token()
+    {
+        return last_token = m_lexer.scan();
+    }
+
+    std::string exception_message(const token_type expected, const std::string& context)
+    {
+        std::string error_msg = "syntax error ";
+
+        if (!context.empty())
+        {
+            error_msg += concat("while parsing ", context, ' ');
+        }
+
+        error_msg += "- ";
+
+        if (last_token == token_type::parse_error)
+        {
+            error_msg += concat(m_lexer.get_error_message(), "; last read: '",
+                                m_lexer.get_token_string(), '\'');
+        }
+        else
+        {
+            error_msg += concat("unexpected ", lexer_t::token_type_name(last_token));
+        }
+
+        if (expected != token_type::uninitialized)
+        {
+            error_msg += concat("; expected ", lexer_t::token_type_name(expected));
+        }
+
+        return error_msg;
+    }
+
+  private:
+    /// callback function
+    const parser_callback_t<BasicJsonType> callback = nullptr;
+    /// the type of the last read token
+    token_type last_token = token_type::uninitialized;
+    /// the lexer
+    lexer_t m_lexer;
+    /// whether to throw exceptions in case of errors
+    const bool allow_exceptions = true;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/internal_iterator.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/iterators/primitive_iterator.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // ptrdiff_t
+#include <limits>  // numeric_limits
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*
+@brief an iterator for primitive JSON types
+
+This class models an iterator for primitive JSON types (boolean, number,
+string). It's only purpose is to allow the iterator/const_iterator classes
+to "iterate" over primitive values. Internally, the iterator is modeled by
+a `difference_type` variable. Value begin_value (`0`) models the begin,
+end_value (`1`) models past the end.
+*/
+class primitive_iterator_t
+{
+  private:
+    using difference_type = std::ptrdiff_t;
+    static constexpr difference_type begin_value = 0;
+    static constexpr difference_type end_value = begin_value + 1;
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /// iterator as signed integer type
+    difference_type m_it = (std::numeric_limits<std::ptrdiff_t>::min)();
+
+  public:
+    constexpr difference_type get_value() const noexcept
+    {
+        return m_it;
+    }
+
+    /// set iterator to a defined beginning
+    void set_begin() noexcept
+    {
+        m_it = begin_value;
+    }
+
+    /// set iterator to a defined past the end
+    void set_end() noexcept
+    {
+        m_it = end_value;
+    }
+
+    /// return whether the iterator can be dereferenced
+    constexpr bool is_begin() const noexcept
+    {
+        return m_it == begin_value;
+    }
+
+    /// return whether the iterator is at end
+    constexpr bool is_end() const noexcept
+    {
+        return m_it == end_value;
+    }
+
+    friend constexpr bool operator==(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept
+    {
+        return lhs.m_it == rhs.m_it;
+    }
+
+    friend constexpr bool operator<(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept
+    {
+        return lhs.m_it < rhs.m_it;
+    }
+
+    primitive_iterator_t operator+(difference_type n) noexcept
+    {
+        auto result = *this;
+        result += n;
+        return result;
+    }
+
+    friend constexpr difference_type operator-(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept
+    {
+        return lhs.m_it - rhs.m_it;
+    }
+
+    primitive_iterator_t& operator++() noexcept
+    {
+        ++m_it;
+        return *this;
+    }
+
+    primitive_iterator_t operator++(int)& noexcept // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        ++m_it;
+        return result;
+    }
+
+    primitive_iterator_t& operator--() noexcept
+    {
+        --m_it;
+        return *this;
+    }
+
+    primitive_iterator_t operator--(int)& noexcept // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        --m_it;
+        return result;
+    }
+
+    primitive_iterator_t& operator+=(difference_type n) noexcept
+    {
+        m_it += n;
+        return *this;
+    }
+
+    primitive_iterator_t& operator-=(difference_type n) noexcept
+    {
+        m_it -= n;
+        return *this;
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief an iterator value
+
+@note This structure could easily be a union, but MSVC currently does not allow
+unions members with complex constructors, see https://github.com/nlohmann/json/pull/105.
+*/
+template<typename BasicJsonType> struct internal_iterator
+{
+    /// iterator for JSON objects
+    typename BasicJsonType::object_t::iterator object_iterator {};
+    /// iterator for JSON arrays
+    typename BasicJsonType::array_t::iterator array_iterator {};
+    /// generic iterator for all other types
+    primitive_iterator_t primitive_iterator {};
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/iter_impl.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <iterator> // iterator, random_access_iterator_tag, bidirectional_iterator_tag, advance, next
+#include <type_traits> // conditional, is_const, remove_const
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/iterators/internal_iterator.hpp>
+
+// #include <nlohmann/detail/iterators/primitive_iterator.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// forward declare, to be able to friend it later on
+template<typename IteratorType> class iteration_proxy;
+template<typename IteratorType> class iteration_proxy_value;
+
+/*!
+@brief a template for a bidirectional iterator for the @ref basic_json class
+This class implements a both iterators (iterator and const_iterator) for the
+@ref basic_json class.
+@note An iterator is called *initialized* when a pointer to a JSON value has
+      been set (e.g., by a constructor or a copy assignment). If the iterator is
+      default-constructed, it is *uninitialized* and most methods are undefined.
+      **The library uses assertions to detect calls on uninitialized iterators.**
+@requirement The class satisfies the following concept requirements:
+-
+[BidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator):
+  The iterator that can be moved can be moved in both directions (i.e.
+  incremented and decremented).
+@since version 1.0.0, simplified in version 2.0.9, change to bidirectional
+       iterators in version 3.0.0 (see https://github.com/nlohmann/json/issues/593)
+*/
+template<typename BasicJsonType>
+class iter_impl // NOLINT(cppcoreguidelines-special-member-functions,hicpp-special-member-functions)
+{
+    /// the iterator with BasicJsonType of different const-ness
+    using other_iter_impl = iter_impl<typename std::conditional<std::is_const<BasicJsonType>::value, typename std::remove_const<BasicJsonType>::type, const BasicJsonType>::type>;
+    /// allow basic_json to access private members
+    friend other_iter_impl;
+    friend BasicJsonType;
+    friend iteration_proxy<iter_impl>;
+    friend iteration_proxy_value<iter_impl>;
+
+    using object_t = typename BasicJsonType::object_t;
+    using array_t = typename BasicJsonType::array_t;
+    // make sure BasicJsonType is basic_json or const basic_json
+    static_assert(is_basic_json<typename std::remove_const<BasicJsonType>::type>::value,
+                  "iter_impl only accepts (const) basic_json");
+    // superficial check for the LegacyBidirectionalIterator named requirement
+    static_assert(std::is_base_of<std::bidirectional_iterator_tag, std::bidirectional_iterator_tag>::value
+                  &&  std::is_base_of<std::bidirectional_iterator_tag, typename std::iterator_traits<typename array_t::iterator>::iterator_category>::value,
+                  "basic_json iterator assumes array and object type iterators satisfy the LegacyBidirectionalIterator named requirement.");
+
+  public:
+    /// The std::iterator class template (used as a base class to provide typedefs) is deprecated in C++17.
+    /// The C++ Standard has never required user-defined iterators to derive from std::iterator.
+    /// A user-defined iterator should provide publicly accessible typedefs named
+    /// iterator_category, value_type, difference_type, pointer, and reference.
+    /// Note that value_type is required to be non-const, even for constant iterators.
+    using iterator_category = std::bidirectional_iterator_tag;
+
+    /// the type of the values when the iterator is dereferenced
+    using value_type = typename BasicJsonType::value_type;
+    /// a type to represent differences between iterators
+    using difference_type = typename BasicJsonType::difference_type;
+    /// defines a pointer to the type iterated over (value_type)
+    using pointer = typename std::conditional<std::is_const<BasicJsonType>::value,
+          typename BasicJsonType::const_pointer,
+          typename BasicJsonType::pointer>::type;
+    /// defines a reference to the type iterated over (value_type)
+    using reference =
+        typename std::conditional<std::is_const<BasicJsonType>::value,
+        typename BasicJsonType::const_reference,
+        typename BasicJsonType::reference>::type;
+
+    iter_impl() = default;
+    ~iter_impl() = default;
+    iter_impl(iter_impl&&) noexcept = default;
+    iter_impl& operator=(iter_impl&&) noexcept = default;
+
+    /*!
+    @brief constructor for a given JSON instance
+    @param[in] object  pointer to a JSON object for this iterator
+    @pre object != nullptr
+    @post The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    explicit iter_impl(pointer object) noexcept : m_object(object)
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_it.object_iterator = typename object_t::iterator();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_it.array_iterator = typename array_t::iterator();
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator = primitive_iterator_t();
+                break;
+            }
+        }
+    }
+
+    /*!
+    @note The conventional copy constructor and copy assignment are implicitly
+          defined. Combined with the following converting constructor and
+          assignment, they support: (1) copy from iterator to iterator, (2)
+          copy from const iterator to const iterator, and (3) conversion from
+          iterator to const iterator. However conversion from const iterator
+          to iterator is not defined.
+    */
+
+    /*!
+    @brief const copy constructor
+    @param[in] other const iterator to copy from
+    @note This copy constructor had to be defined explicitly to circumvent a bug
+          occurring on msvc v19.0 compiler (VS 2015) debug build. For more
+          information refer to: https://github.com/nlohmann/json/issues/1608
+    */
+    iter_impl(const iter_impl<const BasicJsonType>& other) noexcept
+        : m_object(other.m_object), m_it(other.m_it)
+    {}
+
+    /*!
+    @brief converting assignment
+    @param[in] other const iterator to copy from
+    @return const/non-const iterator
+    @note It is not checked whether @a other is initialized.
+    */
+    iter_impl& operator=(const iter_impl<const BasicJsonType>& other) noexcept
+    {
+        if (&other != this)
+        {
+            m_object = other.m_object;
+            m_it = other.m_it;
+        }
+        return *this;
+    }
+
+    /*!
+    @brief converting constructor
+    @param[in] other  non-const iterator to copy from
+    @note It is not checked whether @a other is initialized.
+    */
+    iter_impl(const iter_impl<typename std::remove_const<BasicJsonType>::type>& other) noexcept
+        : m_object(other.m_object), m_it(other.m_it)
+    {}
+
+    /*!
+    @brief converting assignment
+    @param[in] other  non-const iterator to copy from
+    @return const/non-const iterator
+    @note It is not checked whether @a other is initialized.
+    */
+    iter_impl& operator=(const iter_impl<typename std::remove_const<BasicJsonType>::type>& other) noexcept // NOLINT(cert-oop54-cpp)
+    {
+        m_object = other.m_object;
+        m_it = other.m_it;
+        return *this;
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /*!
+    @brief set the iterator to the first value
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    void set_begin() noexcept
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_it.object_iterator = m_object->m_data.m_value.object->begin();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_it.array_iterator = m_object->m_data.m_value.array->begin();
+                break;
+            }
+
+            case value_t::null:
+            {
+                // set to end so begin()==end() is true: null is empty
+                m_it.primitive_iterator.set_end();
+                break;
+            }
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator.set_begin();
+                break;
+            }
+        }
+    }
+
+    /*!
+    @brief set the iterator past the last value
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    void set_end() noexcept
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_it.object_iterator = m_object->m_data.m_value.object->end();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_it.array_iterator = m_object->m_data.m_value.array->end();
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator.set_end();
+                break;
+            }
+        }
+    }
+
+  public:
+    /*!
+    @brief return a reference to the value pointed to by the iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    reference operator*() const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                JSON_ASSERT(m_it.object_iterator != m_object->m_data.m_value.object->end());
+                return m_it.object_iterator->second;
+            }
+
+            case value_t::array:
+            {
+                JSON_ASSERT(m_it.array_iterator != m_object->m_data.m_value.array->end());
+                return *m_it.array_iterator;
+            }
+
+            case value_t::null:
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.is_begin()))
+                {
+                    return *m_object;
+                }
+
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+            }
+        }
+    }
+
+    /*!
+    @brief dereference the iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    pointer operator->() const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                JSON_ASSERT(m_it.object_iterator != m_object->m_data.m_value.object->end());
+                return &(m_it.object_iterator->second);
+            }
+
+            case value_t::array:
+            {
+                JSON_ASSERT(m_it.array_iterator != m_object->m_data.m_value.array->end());
+                return &*m_it.array_iterator;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.is_begin()))
+                {
+                    return m_object;
+                }
+
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+            }
+        }
+    }
+
+    /*!
+    @brief post-increment (it++)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator++(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        ++(*this);
+        return result;
+    }
+
+    /*!
+    @brief pre-increment (++it)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator++()
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                std::advance(m_it.object_iterator, 1);
+                break;
+            }
+
+            case value_t::array:
+            {
+                std::advance(m_it.array_iterator, 1);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                ++m_it.primitive_iterator;
+                break;
+            }
+        }
+
+        return *this;
+    }
+
+    /*!
+    @brief post-decrement (it--)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator--(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        --(*this);
+        return result;
+    }
+
+    /*!
+    @brief pre-decrement (--it)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator--()
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                std::advance(m_it.object_iterator, -1);
+                break;
+            }
+
+            case value_t::array:
+            {
+                std::advance(m_it.array_iterator, -1);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                --m_it.primitive_iterator;
+                break;
+            }
+        }
+
+        return *this;
+    }
+
+    /*!
+    @brief comparison: equal
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    template < typename IterImpl, detail::enable_if_t < (std::is_same<IterImpl, iter_impl>::value || std::is_same<IterImpl, other_iter_impl>::value), std::nullptr_t > = nullptr >
+    bool operator==(const IterImpl& other) const
+    {
+        // if objects are not the same, the comparison is undefined
+        if (JSON_HEDLEY_UNLIKELY(m_object != other.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(212, "cannot compare iterators of different containers", m_object));
+        }
+
+        // value-initialized forward iterators can be compared, and must compare equal to other value-initialized iterators of the same type #4493
+        if (m_object == nullptr)
+        {
+            return true;
+        }
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                return (m_it.object_iterator == other.m_it.object_iterator);
+
+            case value_t::array:
+                return (m_it.array_iterator == other.m_it.array_iterator);
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return (m_it.primitive_iterator == other.m_it.primitive_iterator);
+        }
+    }
+
+    /*!
+    @brief comparison: not equal
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    template < typename IterImpl, detail::enable_if_t < (std::is_same<IterImpl, iter_impl>::value || std::is_same<IterImpl, other_iter_impl>::value), std::nullptr_t > = nullptr >
+    bool operator!=(const IterImpl& other) const
+    {
+        return !operator==(other);
+    }
+
+    /*!
+    @brief comparison: smaller
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    bool operator<(const iter_impl& other) const
+    {
+        // if objects are not the same, the comparison is undefined
+        if (JSON_HEDLEY_UNLIKELY(m_object != other.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(212, "cannot compare iterators of different containers", m_object));
+        }
+
+        // value-initialized forward iterators can be compared, and must compare equal to other value-initialized iterators of the same type #4493
+        if (m_object == nullptr)
+        {
+            // the iterators are both value-initialized and are to be considered equal, but this function checks for smaller, so we return false
+            return false;
+        }
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(213, "cannot compare order of object iterators", m_object));
+
+            case value_t::array:
+                return (m_it.array_iterator < other.m_it.array_iterator);
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return (m_it.primitive_iterator < other.m_it.primitive_iterator);
+        }
+    }
+
+    /*!
+    @brief comparison: less than or equal
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    bool operator<=(const iter_impl& other) const
+    {
+        return !other.operator < (*this);
+    }
+
+    /*!
+    @brief comparison: greater than
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    bool operator>(const iter_impl& other) const
+    {
+        return !operator<=(other);
+    }
+
+    /*!
+    @brief comparison: greater than or equal
+    @pre (1) The iterator is initialized; i.e. `m_object != nullptr`, or (2) both iterators are value-initialized.
+    */
+    bool operator>=(const iter_impl& other) const
+    {
+        return !operator<(other);
+    }
+
+    /*!
+    @brief add to iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator+=(difference_type i)
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(209, "cannot use offsets with object iterators", m_object));
+
+            case value_t::array:
+            {
+                std::advance(m_it.array_iterator, i);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator += i;
+                break;
+            }
+        }
+
+        return *this;
+    }
+
+    /*!
+    @brief subtract from iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator-=(difference_type i)
+    {
+        return operator+=(-i);
+    }
+
+    /*!
+    @brief add to iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator+(difference_type i) const
+    {
+        auto result = *this;
+        result += i;
+        return result;
+    }
+
+    /*!
+    @brief addition of distance and iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    friend iter_impl operator+(difference_type i, const iter_impl& it)
+    {
+        auto result = it;
+        result += i;
+        return result;
+    }
+
+    /*!
+    @brief subtract from iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator-(difference_type i) const
+    {
+        auto result = *this;
+        result -= i;
+        return result;
+    }
+
+    /*!
+    @brief return difference
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    difference_type operator-(const iter_impl& other) const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(209, "cannot use offsets with object iterators", m_object));
+
+            case value_t::array:
+                return m_it.array_iterator - other.m_it.array_iterator;
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return m_it.primitive_iterator - other.m_it.primitive_iterator;
+        }
+    }
+
+    /*!
+    @brief access to successor
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    reference operator[](difference_type n) const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(208, "cannot use operator[] for object iterators", m_object));
+
+            case value_t::array:
+                return *std::next(m_it.array_iterator, n);
+
+            case value_t::null:
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.get_value() == -n))
+                {
+                    return *m_object;
+                }
+
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+            }
+        }
+    }
+
+    /*!
+    @brief return the key of an object iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    const typename object_t::key_type& key() const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        if (JSON_HEDLEY_LIKELY(m_object->is_object()))
+        {
+            return m_it.object_iterator->first;
+        }
+
+        JSON_THROW(invalid_iterator::create(207, "cannot use key() for non-object iterators", m_object));
+    }
+
+    /*!
+    @brief return the value of an iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    reference value() const
+    {
+        return operator*();
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /// associated JSON instance
+    pointer m_object = nullptr;
+    /// the actual iterator of the associated instance
+    internal_iterator<typename std::remove_const<BasicJsonType>::type> m_it {};
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/iteration_proxy.hpp>
+
+// #include <nlohmann/detail/iterators/json_reverse_iterator.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // ptrdiff_t
+#include <iterator> // reverse_iterator
+#include <utility> // declval
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+//////////////////////
+// reverse_iterator //
+//////////////////////
+
+/*!
+@brief a template for a reverse iterator class
+
+@tparam Base the base iterator type to reverse. Valid types are @ref
+iterator (to create @ref reverse_iterator) and @ref const_iterator (to
+create @ref const_reverse_iterator).
+
+@requirement The class satisfies the following concept requirements:
+-
+[BidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator):
+  The iterator that can be moved can be moved in both directions (i.e.
+  incremented and decremented).
+- [OutputIterator](https://en.cppreference.com/w/cpp/named_req/OutputIterator):
+  It is possible to write to the pointed-to element (only if @a Base is
+  @ref iterator).
+
+@since version 1.0.0
+*/
+template<typename Base>
+class json_reverse_iterator : public std::reverse_iterator<Base>
+{
+  public:
+    using difference_type = std::ptrdiff_t;
+    /// shortcut to the reverse iterator adapter
+    using base_iterator = std::reverse_iterator<Base>;
+    /// the reference type for the pointed-to element
+    using reference = typename Base::reference;
+
+    /// create reverse iterator from iterator
+    explicit json_reverse_iterator(const typename base_iterator::iterator_type& it) noexcept
+        : base_iterator(it) {}
+
+    /// create reverse iterator from base class
+    explicit json_reverse_iterator(const base_iterator& it) noexcept : base_iterator(it) {}
+
+    /// post-increment (it++)
+    json_reverse_iterator operator++(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator++(1));
+    }
+
+    /// pre-increment (++it)
+    json_reverse_iterator& operator++()
+    {
+        return static_cast<json_reverse_iterator&>(base_iterator::operator++());
+    }
+
+    /// post-decrement (it--)
+    json_reverse_iterator operator--(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator--(1));
+    }
+
+    /// pre-decrement (--it)
+    json_reverse_iterator& operator--()
+    {
+        return static_cast<json_reverse_iterator&>(base_iterator::operator--());
+    }
+
+    /// add to iterator
+    json_reverse_iterator& operator+=(difference_type i)
+    {
+        return static_cast<json_reverse_iterator&>(base_iterator::operator+=(i));
+    }
+
+    /// add to iterator
+    json_reverse_iterator operator+(difference_type i) const
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator+(i));
+    }
+
+    /// subtract from iterator
+    json_reverse_iterator operator-(difference_type i) const
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator-(i));
+    }
+
+    /// return difference
+    difference_type operator-(const json_reverse_iterator& other) const
+    {
+        return base_iterator(*this) - base_iterator(other);
+    }
+
+    /// access to successor
+    reference operator[](difference_type n) const
+    {
+        return *(this->operator+(n));
+    }
+
+    /// return the key of an object iterator
+    auto key() const -> decltype(std::declval<Base>().key())
+    {
+        auto it = --this->base();
+        return it.key();
+    }
+
+    /// return the value of an iterator
+    reference value() const
+    {
+        auto it = --this->base();
+        return it.operator * ();
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/primitive_iterator.hpp>
+
+// #include <nlohmann/detail/json_custom_base_class.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <type_traits> // conditional, is_same
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief Default base class of the @ref basic_json class.
+
+So that the correct implementations of the copy / move ctors / assign operators
+of @ref basic_json do not require complex case distinctions
+(no base class / custom base class used as customization point),
+@ref basic_json always has a base class.
+By default, this class is used because it is empty and thus has no effect
+on the behavior of @ref basic_json.
+*/
+struct json_default_base {};
+
+template<class T>
+using json_base_class = typename std::conditional <
+                        std::is_same<T, void>::value,
+                        json_default_base,
+                        T
+                        >::type;
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/json_pointer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // all_of
+#include <cctype> // isdigit
+#include <cerrno> // errno, ERANGE
+#include <cstdlib> // strtoull
+#ifndef JSON_NO_IO
+    #include <iosfwd> // ostream
+#endif  // JSON_NO_IO
+#include <limits> // max
+#include <numeric> // accumulate
+#include <string> // string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/string_escape.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// @brief JSON Pointer defines a string syntax for identifying a specific value within a JSON document
+/// @sa https://json.nlohmann.me/api/json_pointer/
+template<typename RefStringType>
+class json_pointer
+{
+    // allow basic_json to access private members
+    NLOHMANN_BASIC_JSON_TPL_DECLARATION
+    friend class basic_json;
+
+    template<typename>
+    friend class json_pointer;
+
+    template<typename T>
+    struct string_t_helper
+    {
+        using type = T;
+    };
+
+    NLOHMANN_BASIC_JSON_TPL_DECLARATION
+    struct string_t_helper<NLOHMANN_BASIC_JSON_TPL>
+    {
+        using type = StringType;
+    };
+
+  public:
+    // for backwards compatibility accept BasicJsonType
+    using string_t = typename string_t_helper<RefStringType>::type;
+
+    /// @brief create JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/json_pointer/
+    explicit json_pointer(const string_t& s = "")
+        : reference_tokens(split(s))
+    {}
+
+    /// @brief return a string representation of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/to_string/
+    string_t to_string() const
+    {
+        return std::accumulate(reference_tokens.begin(), reference_tokens.end(),
+                               string_t{},
+                               [](const string_t& a, const string_t& b)
+        {
+            return detail::concat(a, '/', detail::escape(b));
+        });
+    }
+
+    /// @brief return a string representation of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_string/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, to_string())
+    operator string_t() const
+    {
+        return to_string();
+    }
+
+#ifndef JSON_NO_IO
+    /// @brief write string representation of the JSON pointer to stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/
+    friend std::ostream& operator<<(std::ostream& o, const json_pointer& ptr)
+    {
+        o << ptr.to_string();
+        return o;
+    }
+#endif
+
+    /// @brief append another JSON pointer at the end of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/
+    json_pointer& operator/=(const json_pointer& ptr)
+    {
+        reference_tokens.insert(reference_tokens.end(),
+                                ptr.reference_tokens.begin(),
+                                ptr.reference_tokens.end());
+        return *this;
+    }
+
+    /// @brief append an unescaped reference token at the end of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/
+    json_pointer& operator/=(string_t token)
+    {
+        push_back(std::move(token));
+        return *this;
+    }
+
+    /// @brief append an array index at the end of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/
+    json_pointer& operator/=(std::size_t array_idx)
+    {
+        return *this /= std::to_string(array_idx);
+    }
+
+    /// @brief create a new JSON pointer by appending the right JSON pointer at the end of the left JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/
+    friend json_pointer operator/(const json_pointer& lhs,
+                                  const json_pointer& rhs)
+    {
+        return json_pointer(lhs) /= rhs;
+    }
+
+    /// @brief create a new JSON pointer by appending the unescaped token at the end of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/
+    friend json_pointer operator/(const json_pointer& lhs, string_t token) // NOLINT(performance-unnecessary-value-param)
+    {
+        return json_pointer(lhs) /= std::move(token);
+    }
+
+    /// @brief create a new JSON pointer by appending the array-index-token at the end of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/
+    friend json_pointer operator/(const json_pointer& lhs, std::size_t array_idx)
+    {
+        return json_pointer(lhs) /= array_idx;
+    }
+
+    /// @brief returns the parent of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/parent_pointer/
+    json_pointer parent_pointer() const
+    {
+        if (empty())
+        {
+            return *this;
+        }
+
+        json_pointer res = *this;
+        res.pop_back();
+        return res;
+    }
+
+    /// @brief remove last reference token
+    /// @sa https://json.nlohmann.me/api/json_pointer/pop_back/
+    void pop_back()
+    {
+        if (JSON_HEDLEY_UNLIKELY(empty()))
+        {
+            JSON_THROW(detail::out_of_range::create(405, "JSON pointer has no parent", nullptr));
+        }
+
+        reference_tokens.pop_back();
+    }
+
+    /// @brief return last reference token
+    /// @sa https://json.nlohmann.me/api/json_pointer/back/
+    const string_t& back() const
+    {
+        if (JSON_HEDLEY_UNLIKELY(empty()))
+        {
+            JSON_THROW(detail::out_of_range::create(405, "JSON pointer has no parent", nullptr));
+        }
+
+        return reference_tokens.back();
+    }
+
+    /// @brief append an unescaped token at the end of the reference pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/push_back/
+    void push_back(const string_t& token)
+    {
+        reference_tokens.push_back(token);
+    }
+
+    /// @brief append an unescaped token at the end of the reference pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/push_back/
+    void push_back(string_t&& token)
+    {
+        reference_tokens.push_back(std::move(token));
+    }
+
+    /// @brief return whether pointer points to the root document
+    /// @sa https://json.nlohmann.me/api/json_pointer/empty/
+    bool empty() const noexcept
+    {
+        return reference_tokens.empty();
+    }
+
+  private:
+    /*!
+    @param[in] s  reference token to be converted into an array index
+
+    @return integer representation of @a s
+
+    @throw parse_error.106  if an array index begins with '0'
+    @throw parse_error.109  if an array index begins not with a digit
+    @throw out_of_range.404 if string @a s could not be converted to an integer
+    @throw out_of_range.410 if an array index exceeds size_type
+    */
+    template<typename BasicJsonType>
+    static typename BasicJsonType::size_type array_index(const string_t& s)
+    {
+        using size_type = typename BasicJsonType::size_type;
+
+        // error condition (cf. RFC 6901, Sect. 4)
+        if (JSON_HEDLEY_UNLIKELY(s.size() > 1 && s[0] == '0'))
+        {
+            JSON_THROW(detail::parse_error::create(106, 0, detail::concat("array index '", s, "' must not begin with '0'"), nullptr));
+        }
+
+        // error condition (cf. RFC 6901, Sect. 4)
+        if (JSON_HEDLEY_UNLIKELY(s.size() > 1 && !(s[0] >= '1' && s[0] <= '9')))
+        {
+            JSON_THROW(detail::parse_error::create(109, 0, detail::concat("array index '", s, "' is not a number"), nullptr));
+        }
+
+        const char* p = s.c_str();
+        char* p_end = nullptr; // NOLINT(misc-const-correctness)
+        errno = 0; // strtoull doesn't reset errno
+        const unsigned long long res = std::strtoull(p, &p_end, 10); // NOLINT(runtime/int)
+        if (p == p_end // invalid input or empty string
+                || errno == ERANGE // out of range
+                || JSON_HEDLEY_UNLIKELY(static_cast<std::size_t>(p_end - p) != s.size())) // incomplete read
+        {
+            JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", s, "'"), nullptr));
+        }
+
+        // only triggered on special platforms (like 32bit), see also
+        // https://github.com/nlohmann/json/pull/2203
+        if (res >= static_cast<unsigned long long>((std::numeric_limits<size_type>::max)()))  // NOLINT(runtime/int)
+        {
+            JSON_THROW(detail::out_of_range::create(410, detail::concat("array index ", s, " exceeds size_type"), nullptr));   // LCOV_EXCL_LINE
+        }
+
+        return static_cast<size_type>(res);
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    json_pointer top() const
+    {
+        if (JSON_HEDLEY_UNLIKELY(empty()))
+        {
+            JSON_THROW(detail::out_of_range::create(405, "JSON pointer has no parent", nullptr));
+        }
+
+        json_pointer result = *this;
+        result.reference_tokens = {reference_tokens[0]};
+        return result;
+    }
+
+  private:
+    /*!
+    @brief create and return a reference to the pointed to value
+
+    @complexity Linear in the number of reference tokens.
+
+    @throw parse_error.109 if array index is not a number
+    @throw type_error.313 if value cannot be unflattened
+    */
+    template<typename BasicJsonType>
+    BasicJsonType& get_and_create(BasicJsonType& j) const
+    {
+        auto* result = &j;
+
+        // in case no reference tokens exist, return a reference to the JSON value
+        // j which will be overwritten by a primitive value
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (result->type())
+            {
+                case detail::value_t::null:
+                {
+                    if (reference_token == "0")
+                    {
+                        // start a new array if reference token is 0
+                        result = &result->operator[](0);
+                    }
+                    else
+                    {
+                        // start a new object otherwise
+                        result = &result->operator[](reference_token);
+                    }
+                    break;
+                }
+
+                case detail::value_t::object:
+                {
+                    // create an entry in the object
+                    result = &result->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    // create an entry in the array
+                    result = &result->operator[](array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                /*
+                The following code is only reached if there exists a reference
+                token _and_ the current value is primitive. In this case, we have
+                an error situation, because primitive values may only occur as
+                single value; that is, with an empty list of reference tokens.
+                */
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::type_error::create(313, "invalid value to unflatten", &j));
+            }
+        }
+
+        return *result;
+    }
+
+    /*!
+    @brief return a reference to the pointed to value
+
+    @note This version does not throw if a value is not present, but tries to
+          create nested values instead. For instance, calling this function
+          with pointer `"/this/that"` on a null value is equivalent to calling
+          `operator[]("this").operator[]("that")` on that value, effectively
+          changing the null value to an object.
+
+    @param[in] ptr  a JSON value
+
+    @return reference to the JSON value pointed to by the JSON pointer
+
+    @complexity Linear in the length of the JSON pointer.
+
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    BasicJsonType& get_unchecked(BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            // convert null values to arrays or objects before continuing
+            if (ptr->is_null())
+            {
+                // check if reference token is a number
+                const bool nums =
+                    std::all_of(reference_token.begin(), reference_token.end(),
+                                [](const unsigned char x)
+                {
+                    return std::isdigit(x);
+                });
+
+                // change value to array for numbers or "-" or to object otherwise
+                *ptr = (nums || reference_token == "-")
+                       ? detail::value_t::array
+                       : detail::value_t::object;
+            }
+
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // use unchecked object access
+                    ptr = &ptr->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (reference_token == "-")
+                    {
+                        // explicitly treat "-" as index beyond the end
+                        ptr = &ptr->operator[](ptr->m_data.m_value.array->size());
+                    }
+                    else
+                    {
+                        // convert array index to number; unchecked access
+                        ptr = &ptr->operator[](array_index<BasicJsonType>(reference_token));
+                    }
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.402  if the array index '-' is used
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    BasicJsonType& get_checked(BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // note: at performs range check
+                    ptr = &ptr->at(reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" always fails the range check
+                        JSON_THROW(detail::out_of_range::create(402, detail::concat(
+                                "array index '-' (", std::to_string(ptr->m_data.m_value.array->size()),
+                                ") is out of range"), ptr));
+                    }
+
+                    // note: at performs range check
+                    ptr = &ptr->at(array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @brief return a const reference to the pointed to value
+
+    @param[in] ptr  a JSON value
+
+    @return const reference to the JSON value pointed to by the JSON
+    pointer
+
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.402  if the array index '-' is used
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    const BasicJsonType& get_unchecked(const BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // use unchecked object access
+                    ptr = &ptr->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" cannot be used for const access
+                        JSON_THROW(detail::out_of_range::create(402, detail::concat("array index '-' (", std::to_string(ptr->m_data.m_value.array->size()), ") is out of range"), ptr));
+                    }
+
+                    // use unchecked array access
+                    ptr = &ptr->operator[](array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.402  if the array index '-' is used
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    const BasicJsonType& get_checked(const BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // note: at performs range check
+                    ptr = &ptr->at(reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" always fails the range check
+                        JSON_THROW(detail::out_of_range::create(402, detail::concat(
+                                "array index '-' (", std::to_string(ptr->m_data.m_value.array->size()),
+                                ") is out of range"), ptr));
+                    }
+
+                    // note: at performs range check
+                    ptr = &ptr->at(array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    */
+    template<typename BasicJsonType>
+    bool contains(const BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    if (!ptr->contains(reference_token))
+                    {
+                        // we did not find the key in the object
+                        return false;
+                    }
+
+                    ptr = &ptr->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" always fails the range check
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(reference_token.size() == 1 && !("0" <= reference_token && reference_token <= "9")))
+                    {
+                        // invalid char
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(reference_token.size() > 1))
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!('1' <= reference_token[0] && reference_token[0] <= '9')))
+                        {
+                            // first char should be between '1' and '9'
+                            return false;
+                        }
+                        for (std::size_t i = 1; i < reference_token.size(); i++)
+                        {
+                            if (JSON_HEDLEY_UNLIKELY(!('0' <= reference_token[i] && reference_token[i] <= '9')))
+                            {
+                                // other char should be between '0' and '9'
+                                return false;
+                            }
+                        }
+                    }
+
+                    const auto idx = array_index<BasicJsonType>(reference_token);
+                    if (idx >= ptr->size())
+                    {
+                        // index out of range
+                        return false;
+                    }
+
+                    ptr = &ptr->operator[](idx);
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                {
+                    // we do not expect primitive values if there is still a
+                    // reference token to process
+                    return false;
+                }
+            }
+        }
+
+        // no reference token left means we found a primitive value
+        return true;
+    }
+
+    /*!
+    @brief split the string input to reference tokens
+
+    @note This function is only called by the json_pointer constructor.
+          All exceptions below are documented there.
+
+    @throw parse_error.107  if the pointer is not empty or begins with '/'
+    @throw parse_error.108  if character '~' is not followed by '0' or '1'
+    */
+    static std::vector<string_t> split(const string_t& reference_string)
+    {
+        std::vector<string_t> result;
+
+        // special case: empty reference string -> no reference tokens
+        if (reference_string.empty())
+        {
+            return result;
+        }
+
+        // check if nonempty reference string begins with slash
+        if (JSON_HEDLEY_UNLIKELY(reference_string[0] != '/'))
+        {
+            JSON_THROW(detail::parse_error::create(107, 1, detail::concat("JSON pointer must be empty or begin with '/' - was: '", reference_string, "'"), nullptr));
+        }
+
+        // extract the reference tokens:
+        // - slash: position of the last read slash (or end of string)
+        // - start: position after the previous slash
+        for (
+            // search for the first slash after the first character
+            std::size_t slash = reference_string.find_first_of('/', 1),
+            // set the beginning of the first reference token
+            start = 1;
+            // we can stop if start == 0 (if slash == string_t::npos)
+            start != 0;
+            // set the beginning of the next reference token
+            // (will eventually be 0 if slash == string_t::npos)
+            start = (slash == string_t::npos) ? 0 : slash + 1,
+            // find next slash
+            slash = reference_string.find_first_of('/', start))
+        {
+            // use the text between the beginning of the reference token
+            // (start) and the last slash (slash).
+            auto reference_token = reference_string.substr(start, slash - start);
+
+            // check reference tokens are properly escaped
+            for (std::size_t pos = reference_token.find_first_of('~');
+                    pos != string_t::npos;
+                    pos = reference_token.find_first_of('~', pos + 1))
+            {
+                JSON_ASSERT(reference_token[pos] == '~');
+
+                // ~ must be followed by 0 or 1
+                if (JSON_HEDLEY_UNLIKELY(pos == reference_token.size() - 1 ||
+                                         (reference_token[pos + 1] != '0' &&
+                                          reference_token[pos + 1] != '1')))
+                {
+                    JSON_THROW(detail::parse_error::create(108, 0, "escape character '~' must be followed with '0' or '1'", nullptr));
+                }
+            }
+
+            // finally, store the reference token
+            detail::unescape(reference_token);
+            result.push_back(reference_token);
+        }
+
+        return result;
+    }
+
+  private:
+    /*!
+    @param[in] reference_string  the reference string to the current value
+    @param[in] value             the value to consider
+    @param[in,out] result        the result object to insert values to
+
+    @note Empty objects or arrays are flattened to `null`.
+    */
+    template<typename BasicJsonType>
+    static void flatten(const string_t& reference_string,
+                        const BasicJsonType& value,
+                        BasicJsonType& result)
+    {
+        switch (value.type())
+        {
+            case detail::value_t::array:
+            {
+                if (value.m_data.m_value.array->empty())
+                {
+                    // flatten empty array as null
+                    result[reference_string] = nullptr;
+                }
+                else
+                {
+                    // iterate array and use index as reference string
+                    for (std::size_t i = 0; i < value.m_data.m_value.array->size(); ++i)
+                    {
+                        flatten(detail::concat<string_t>(reference_string, '/', std::to_string(i)),
+                                value.m_data.m_value.array->operator[](i), result);
+                    }
+                }
+                break;
+            }
+
+            case detail::value_t::object:
+            {
+                if (value.m_data.m_value.object->empty())
+                {
+                    // flatten empty object as null
+                    result[reference_string] = nullptr;
+                }
+                else
+                {
+                    // iterate object and use keys as reference string
+                    for (const auto& element : *value.m_data.m_value.object)
+                    {
+                        flatten(detail::concat<string_t>(reference_string, '/', detail::escape(element.first)), element.second, result);
+                    }
+                }
+                break;
+            }
+
+            case detail::value_t::null:
+            case detail::value_t::string:
+            case detail::value_t::boolean:
+            case detail::value_t::number_integer:
+            case detail::value_t::number_unsigned:
+            case detail::value_t::number_float:
+            case detail::value_t::binary:
+            case detail::value_t::discarded:
+            default:
+            {
+                // add primitive value with its reference string
+                result[reference_string] = value;
+                break;
+            }
+        }
+    }
+
+    /*!
+    @param[in] value  flattened JSON
+
+    @return unflattened JSON
+
+    @throw parse_error.109 if array index is not a number
+    @throw type_error.314  if value is not an object
+    @throw type_error.315  if object values are not primitive
+    @throw type_error.313  if value cannot be unflattened
+    */
+    template<typename BasicJsonType>
+    static BasicJsonType
+    unflatten(const BasicJsonType& value)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!value.is_object()))
+        {
+            JSON_THROW(detail::type_error::create(314, "only objects can be unflattened", &value));
+        }
+
+        BasicJsonType result;
+
+        // iterate the JSON object values
+        for (const auto& element : *value.m_data.m_value.object)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!element.second.is_primitive()))
+            {
+                JSON_THROW(detail::type_error::create(315, "values in object must be primitive", &element.second));
+            }
+
+            // assign value to reference pointed to by JSON pointer; Note that if
+            // the JSON pointer is "" (i.e., points to the whole value), function
+            // get_and_create returns a reference to result itself. An assignment
+            // will then create a primitive value.
+            json_pointer(element.first).get_and_create(result) = element.second;
+        }
+
+        return result;
+    }
+
+    // can't use conversion operator because of ambiguity
+    json_pointer<string_t> convert() const&
+    {
+        json_pointer<string_t> result;
+        result.reference_tokens = reference_tokens;
+        return result;
+    }
+
+    json_pointer<string_t> convert()&&
+    {
+        json_pointer<string_t> result;
+        result.reference_tokens = std::move(reference_tokens);
+        return result;
+    }
+
+  public:
+#if JSON_HAS_THREE_WAY_COMPARISON
+    /// @brief compares two JSON pointers for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeRhs>
+    bool operator==(const json_pointer<RefStringTypeRhs>& rhs) const noexcept
+    {
+        return reference_tokens == rhs.reference_tokens;
+    }
+
+    /// @brief compares JSON pointer and string for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer))
+    bool operator==(const string_t& rhs) const
+    {
+        return *this == json_pointer(rhs);
+    }
+
+    /// @brief 3-way compares two JSON pointers
+    template<typename RefStringTypeRhs>
+    std::strong_ordering operator<=>(const json_pointer<RefStringTypeRhs>& rhs) const noexcept // *NOPAD*
+    {
+        return  reference_tokens <=> rhs.reference_tokens; // *NOPAD*
+    }
+#else
+    /// @brief compares two JSON pointers for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs) noexcept;
+
+    /// @brief compares JSON pointer and string for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeLhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                           const StringType& rhs);
+
+    /// @brief compares string and JSON pointer for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeRhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator==(const StringType& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs);
+
+    /// @brief compares two JSON pointers for inequality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/
+    template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs) noexcept;
+
+    /// @brief compares JSON pointer and string for inequality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/
+    template<typename RefStringTypeLhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                           const StringType& rhs);
+
+    /// @brief compares string and JSON pointer for inequality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/
+    template<typename RefStringTypeRhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator!=(const StringType& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs);
+
+    /// @brief compares two JSON pointer for less-than
+    template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator<(const json_pointer<RefStringTypeLhs>& lhs,
+                          const json_pointer<RefStringTypeRhs>& rhs) noexcept;
+#endif
+
+  private:
+    /// the reference tokens
+    std::vector<string_t> reference_tokens;
+};
+
+#if !JSON_HAS_THREE_WAY_COMPARISON
+// functions cannot be defined inside class due to ODR violations
+template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+inline bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs) noexcept
+{
+    return lhs.reference_tokens == rhs.reference_tokens;
+}
+
+template<typename RefStringTypeLhs,
+         typename StringType = typename json_pointer<RefStringTypeLhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer, json_pointer))
+inline bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                       const StringType& rhs)
+{
+    return lhs == json_pointer<RefStringTypeLhs>(rhs);
+}
+
+template<typename RefStringTypeRhs,
+         typename StringType = typename json_pointer<RefStringTypeRhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer, json_pointer))
+inline bool operator==(const StringType& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs)
+{
+    return json_pointer<RefStringTypeRhs>(lhs) == rhs;
+}
+
+template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+inline bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs) noexcept
+{
+    return !(lhs == rhs);
+}
+
+template<typename RefStringTypeLhs,
+         typename StringType = typename json_pointer<RefStringTypeLhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator!=(json_pointer, json_pointer))
+inline bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                       const StringType& rhs)
+{
+    return !(lhs == rhs);
+}
+
+template<typename RefStringTypeRhs,
+         typename StringType = typename json_pointer<RefStringTypeRhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator!=(json_pointer, json_pointer))
+inline bool operator!=(const StringType& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs)
+{
+    return !(lhs == rhs);
+}
+
+template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+inline bool operator<(const json_pointer<RefStringTypeLhs>& lhs,
+                      const json_pointer<RefStringTypeRhs>& rhs) noexcept
+{
+    return lhs.reference_tokens < rhs.reference_tokens;
+}
+#endif
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/json_ref.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <initializer_list>
+#include <utility>
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename BasicJsonType>
+class json_ref
+{
+  public:
+    using value_type = BasicJsonType;
+
+    json_ref(value_type&& value)
+        : owned_value(std::move(value))
+    {}
+
+    json_ref(const value_type& value)
+        : value_ref(&value)
+    {}
+
+    json_ref(std::initializer_list<json_ref> init)
+        : owned_value(init)
+    {}
+
+    template <
+        class... Args,
+        enable_if_t<std::is_constructible<value_type, Args...>::value, int> = 0 >
+    json_ref(Args && ... args)
+        : owned_value(std::forward<Args>(args)...)
+    {}
+
+    // class should be movable only
+    json_ref(json_ref&&) noexcept = default;
+    json_ref(const json_ref&) = delete;
+    json_ref& operator=(const json_ref&) = delete;
+    json_ref& operator=(json_ref&&) = delete;
+    ~json_ref() = default;
+
+    value_type moved_or_copied() const
+    {
+        if (value_ref == nullptr)
+        {
+            return std::move(owned_value);
+        }
+        return *value_ref;
+    }
+
+    value_type const& operator*() const
+    {
+        return value_ref ? *value_ref : owned_value;
+    }
+
+    value_type const* operator->() const
+    {
+        return &** this;
+    }
+
+  private:
+    mutable value_type owned_value = nullptr;
+    value_type const* value_ref = nullptr;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/string_escape.hpp>
+
+// #include <nlohmann/detail/string_utils.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/output/binary_writer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // reverse
+#include <array> // array
+#include <map> // map
+#include <cmath> // isnan, isinf
+#include <cstdint> // uint8_t, uint16_t, uint32_t, uint64_t
+#include <cstring> // memcpy
+#include <limits> // numeric_limits
+#include <string> // string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/input/binary_reader.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/output/output_adapters.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // copy
+#include <cstddef> // size_t
+#include <iterator> // back_inserter
+#include <memory> // shared_ptr, make_shared
+#include <string> // basic_string
+#include <vector> // vector
+
+#ifndef JSON_NO_IO
+    #include <ios>      // streamsize
+    #include <ostream>  // basic_ostream
+#endif  // JSON_NO_IO
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// abstract output adapter interface
+template<typename CharType> struct output_adapter_protocol
+{
+    virtual void write_character(CharType c) = 0;
+    virtual void write_characters(const CharType* s, std::size_t length) = 0;
+    virtual ~output_adapter_protocol() = default;
+
+    output_adapter_protocol() = default;
+    output_adapter_protocol(const output_adapter_protocol&) = default;
+    output_adapter_protocol(output_adapter_protocol&&) noexcept = default;
+    output_adapter_protocol& operator=(const output_adapter_protocol&) = default;
+    output_adapter_protocol& operator=(output_adapter_protocol&&) noexcept = default;
+};
+
+/// a type to simplify interfaces
+template<typename CharType>
+using output_adapter_t = std::shared_ptr<output_adapter_protocol<CharType>>;
+
+/// output adapter for byte vectors
+template<typename CharType, typename AllocatorType = std::allocator<CharType>>
+class output_vector_adapter : public output_adapter_protocol<CharType>
+{
+  public:
+    explicit output_vector_adapter(std::vector<CharType, AllocatorType>& vec) noexcept
+        : v(vec)
+    {}
+
+    void write_character(CharType c) override
+    {
+        v.push_back(c);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    void write_characters(const CharType* s, std::size_t length) override
+    {
+        v.insert(v.end(), s, s + length);
+    }
+
+  private:
+    std::vector<CharType, AllocatorType>& v;
+};
+
+#ifndef JSON_NO_IO
+/// output adapter for output streams
+template<typename CharType>
+class output_stream_adapter : public output_adapter_protocol<CharType>
+{
+  public:
+    explicit output_stream_adapter(std::basic_ostream<CharType>& s) noexcept
+        : stream(s)
+    {}
+
+    void write_character(CharType c) override
+    {
+        stream.put(c);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    void write_characters(const CharType* s, std::size_t length) override
+    {
+        stream.write(s, static_cast<std::streamsize>(length));
+    }
+
+  private:
+    std::basic_ostream<CharType>& stream;
+};
+#endif  // JSON_NO_IO
+
+/// output adapter for basic_string
+template<typename CharType, typename StringType = std::basic_string<CharType>>
+class output_string_adapter : public output_adapter_protocol<CharType>
+{
+  public:
+    explicit output_string_adapter(StringType& s) noexcept
+        : str(s)
+    {}
+
+    void write_character(CharType c) override
+    {
+        str.push_back(c);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    void write_characters(const CharType* s, std::size_t length) override
+    {
+        str.append(s, length);
+    }
+
+  private:
+    StringType& str;
+};
+
+template<typename CharType, typename StringType = std::basic_string<CharType>>
+class output_adapter
+{
+  public:
+    template<typename AllocatorType = std::allocator<CharType>>
+    output_adapter(std::vector<CharType, AllocatorType>& vec)
+        : oa(std::make_shared<output_vector_adapter<CharType, AllocatorType>>(vec)) {}
+
+#ifndef JSON_NO_IO
+    output_adapter(std::basic_ostream<CharType>& s)
+        : oa(std::make_shared<output_stream_adapter<CharType>>(s)) {}
+#endif  // JSON_NO_IO
+
+    output_adapter(StringType& s)
+        : oa(std::make_shared<output_string_adapter<CharType, StringType>>(s)) {}
+
+    operator output_adapter_t<CharType>()
+    {
+        return oa;
+    }
+
+  private:
+    output_adapter_t<CharType> oa = nullptr;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// how to encode BJData
+enum class bjdata_version_t
+{
+    draft2,
+    draft3,
+};
+
+///////////////////
+// binary writer //
+///////////////////
+
+/*!
+@brief serialization to CBOR and MessagePack values
+*/
+template<typename BasicJsonType, typename CharType>
+class binary_writer
+{
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+
+  public:
+    /*!
+    @brief create a binary writer
+
+    @param[in] adapter  output adapter to write to
+    */
+    explicit binary_writer(output_adapter_t<CharType> adapter) : oa(std::move(adapter))
+    {
+        JSON_ASSERT(oa);
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    @pre       j.type() == value_t::object
+    */
+    void write_bson(const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::object:
+            {
+                write_bson_object(*j.m_data.m_value.object);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::array:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                JSON_THROW(type_error::create(317, concat("to serialize to BSON, top-level type must be object, but is ", j.type_name()), &j));
+            }
+        }
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    */
+    void write_cbor(const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::null:
+            {
+                oa->write_character(to_char_type(0xF6));
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                oa->write_character(j.m_data.m_value.boolean
+                                    ? to_char_type(0xF5)
+                                    : to_char_type(0xF4));
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                if (j.m_data.m_value.number_integer >= 0)
+                {
+                    // CBOR does not differentiate between positive signed
+                    // integers and unsigned integers. Therefore, we used the
+                    // code from the value_t::number_unsigned case here.
+                    if (j.m_data.m_value.number_integer <= 0x17)
+                    {
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x18));
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x19));
+                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x1A));
+                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));
+                    }
+                    else
+                    {
+                        oa->write_character(to_char_type(0x1B));
+                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));
+                    }
+                }
+                else
+                {
+                    // The conversions below encode the sign in the first
+                    // byte, and the value is converted to a positive number.
+                    const auto positive_number = -1 - j.m_data.m_value.number_integer;
+                    if (j.m_data.m_value.number_integer >= -24)
+                    {
+                        write_number(static_cast<std::uint8_t>(0x20 + positive_number));
+                    }
+                    else if (positive_number <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x38));
+                        write_number(static_cast<std::uint8_t>(positive_number));
+                    }
+                    else if (positive_number <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x39));
+                        write_number(static_cast<std::uint16_t>(positive_number));
+                    }
+                    else if (positive_number <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x3A));
+                        write_number(static_cast<std::uint32_t>(positive_number));
+                    }
+                    else
+                    {
+                        oa->write_character(to_char_type(0x3B));
+                        write_number(static_cast<std::uint64_t>(positive_number));
+                    }
+                }
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                if (j.m_data.m_value.number_unsigned <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_unsigned));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x18));
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_unsigned));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x19));
+                    write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_unsigned));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x1A));
+                    write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_unsigned));
+                }
+                else
+                {
+                    oa->write_character(to_char_type(0x1B));
+                    write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_unsigned));
+                }
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                if (std::isnan(j.m_data.m_value.number_float))
+                {
+                    // NaN is 0xf97e00 in CBOR
+                    oa->write_character(to_char_type(0xF9));
+                    oa->write_character(to_char_type(0x7E));
+                    oa->write_character(to_char_type(0x00));
+                }
+                else if (std::isinf(j.m_data.m_value.number_float))
+                {
+                    // Infinity is 0xf97c00, -Infinity is 0xf9fc00
+                    oa->write_character(to_char_type(0xf9));
+                    oa->write_character(j.m_data.m_value.number_float > 0 ? to_char_type(0x7C) : to_char_type(0xFC));
+                    oa->write_character(to_char_type(0x00));
+                }
+                else
+                {
+                    write_compact_float(j.m_data.m_value.number_float, detail::input_format_t::cbor);
+                }
+                break;
+            }
+
+            case value_t::string:
+            {
+                // step 1: write control byte and the string length
+                const auto N = j.m_data.m_value.string->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0x60 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x78));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x79));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x7A));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x7B));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write the string
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),
+                    j.m_data.m_value.string->size());
+                break;
+            }
+
+            case value_t::array:
+            {
+                // step 1: write control byte and the array size
+                const auto N = j.m_data.m_value.array->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0x80 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x98));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x99));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x9A));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x9B));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.array)
+                {
+                    write_cbor(el);
+                }
+                break;
+            }
+
+            case value_t::binary:
+            {
+                if (j.m_data.m_value.binary->has_subtype())
+                {
+                    if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xd8));
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xd9));
+                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xda));
+                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint64_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xdb));
+                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                }
+
+                // step 1: write control byte and the binary array size
+                const auto N = j.m_data.m_value.binary->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0x40 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x58));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x59));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x5A));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x5B));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write each element
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),
+                    N);
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                // step 1: write control byte and the object size
+                const auto N = j.m_data.m_value.object->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0xA0 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xB8));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xB9));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xBA));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xBB));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.object)
+                {
+                    write_cbor(el.first);
+                    write_cbor(el.second);
+                }
+                break;
+            }
+
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    */
+    void write_msgpack(const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::null: // nil
+            {
+                oa->write_character(to_char_type(0xC0));
+                break;
+            }
+
+            case value_t::boolean: // true and false
+            {
+                oa->write_character(j.m_data.m_value.boolean
+                                    ? to_char_type(0xC3)
+                                    : to_char_type(0xC2));
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                if (j.m_data.m_value.number_integer >= 0)
+                {
+                    // MessagePack does not differentiate between positive
+                    // signed integers and unsigned integers. Therefore, we used
+                    // the code from the value_t::number_unsigned case here.
+                    if (j.m_data.m_value.number_unsigned < 128)
+                    {
+                        // positive fixnum
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        // uint 8
+                        oa->write_character(to_char_type(0xCC));
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        // uint 16
+                        oa->write_character(to_char_type(0xCD));
+                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        // uint 32
+                        oa->write_character(to_char_type(0xCE));
+                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())
+                    {
+                        // uint 64
+                        oa->write_character(to_char_type(0xCF));
+                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));
+                    }
+                }
+                else
+                {
+                    if (j.m_data.m_value.number_integer >= -32)
+                    {
+                        // negative fixnum
+                        write_number(static_cast<std::int8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int8_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int8_t>::max)())
+                    {
+                        // int 8
+                        oa->write_character(to_char_type(0xD0));
+                        write_number(static_cast<std::int8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int16_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int16_t>::max)())
+                    {
+                        // int 16
+                        oa->write_character(to_char_type(0xD1));
+                        write_number(static_cast<std::int16_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int32_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int32_t>::max)())
+                    {
+                        // int 32
+                        oa->write_character(to_char_type(0xD2));
+                        write_number(static_cast<std::int32_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int64_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int64_t>::max)())
+                    {
+                        // int 64
+                        oa->write_character(to_char_type(0xD3));
+                        write_number(static_cast<std::int64_t>(j.m_data.m_value.number_integer));
+                    }
+                }
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                if (j.m_data.m_value.number_unsigned < 128)
+                {
+                    // positive fixnum
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    // uint 8
+                    oa->write_character(to_char_type(0xCC));
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // uint 16
+                    oa->write_character(to_char_type(0xCD));
+                    write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // uint 32
+                    oa->write_character(to_char_type(0xCE));
+                    write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    // uint 64
+                    oa->write_character(to_char_type(0xCF));
+                    write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));
+                }
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                write_compact_float(j.m_data.m_value.number_float, detail::input_format_t::msgpack);
+                break;
+            }
+
+            case value_t::string:
+            {
+                // step 1: write control byte and the string length
+                const auto N = j.m_data.m_value.string->size();
+                if (N <= 31)
+                {
+                    // fixstr
+                    write_number(static_cast<std::uint8_t>(0xA0 | N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    // str 8
+                    oa->write_character(to_char_type(0xD9));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // str 16
+                    oa->write_character(to_char_type(0xDA));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // str 32
+                    oa->write_character(to_char_type(0xDB));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 2: write the string
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),
+                    j.m_data.m_value.string->size());
+                break;
+            }
+
+            case value_t::array:
+            {
+                // step 1: write control byte and the array size
+                const auto N = j.m_data.m_value.array->size();
+                if (N <= 15)
+                {
+                    // fixarray
+                    write_number(static_cast<std::uint8_t>(0x90 | N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // array 16
+                    oa->write_character(to_char_type(0xDC));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // array 32
+                    oa->write_character(to_char_type(0xDD));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.array)
+                {
+                    write_msgpack(el);
+                }
+                break;
+            }
+
+            case value_t::binary:
+            {
+                // step 0: determine if the binary type has a set subtype to
+                // determine whether to use the ext or fixext types
+                const bool use_ext = j.m_data.m_value.binary->has_subtype();
+
+                // step 1: write control byte and the byte string length
+                const auto N = j.m_data.m_value.binary->size();
+                if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    std::uint8_t output_type{};
+                    bool fixed = true;
+                    if (use_ext)
+                    {
+                        switch (N)
+                        {
+                            case 1:
+                                output_type = 0xD4; // fixext 1
+                                break;
+                            case 2:
+                                output_type = 0xD5; // fixext 2
+                                break;
+                            case 4:
+                                output_type = 0xD6; // fixext 4
+                                break;
+                            case 8:
+                                output_type = 0xD7; // fixext 8
+                                break;
+                            case 16:
+                                output_type = 0xD8; // fixext 16
+                                break;
+                            default:
+                                output_type = 0xC7; // ext 8
+                                fixed = false;
+                                break;
+                        }
+
+                    }
+                    else
+                    {
+                        output_type = 0xC4; // bin 8
+                        fixed = false;
+                    }
+
+                    oa->write_character(to_char_type(output_type));
+                    if (!fixed)
+                    {
+                        write_number(static_cast<std::uint8_t>(N));
+                    }
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    const std::uint8_t output_type = use_ext
+                                                     ? 0xC8 // ext 16
+                                                     : 0xC5; // bin 16
+
+                    oa->write_character(to_char_type(output_type));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    const std::uint8_t output_type = use_ext
+                                                     ? 0xC9 // ext 32
+                                                     : 0xC6; // bin 32
+
+                    oa->write_character(to_char_type(output_type));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 1.5: if this is an ext type, write the subtype
+                if (use_ext)
+                {
+                    write_number(static_cast<std::int8_t>(j.m_data.m_value.binary->subtype()));
+                }
+
+                // step 2: write the byte string
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),
+                    N);
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                // step 1: write control byte and the object size
+                const auto N = j.m_data.m_value.object->size();
+                if (N <= 15)
+                {
+                    // fixmap
+                    write_number(static_cast<std::uint8_t>(0x80 | (N & 0xF)));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // map 16
+                    oa->write_character(to_char_type(0xDE));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // map 32
+                    oa->write_character(to_char_type(0xDF));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.object)
+                {
+                    write_msgpack(el.first);
+                    write_msgpack(el.second);
+                }
+                break;
+            }
+
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    @param[in] use_count   whether to use '#' prefixes (optimized format)
+    @param[in] use_type    whether to use '$' prefixes (optimized format)
+    @param[in] add_prefix  whether prefixes need to be used for this value
+    @param[in] use_bjdata  whether write in BJData format, default is false
+    @param[in] bjdata_version  which BJData version to use, default is draft2
+    */
+    void write_ubjson(const BasicJsonType& j, const bool use_count,
+                      const bool use_type, const bool add_prefix = true,
+                      const bool use_bjdata = false, const bjdata_version_t bjdata_version = bjdata_version_t::draft2)
+    {
+        const bool bjdata_draft3 = use_bjdata && bjdata_version == bjdata_version_t::draft3;
+
+        switch (j.type())
+        {
+            case value_t::null:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('Z'));
+                }
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(j.m_data.m_value.boolean
+                                        ? to_char_type('T')
+                                        : to_char_type('F'));
+                }
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                write_number_with_ubjson_prefix(j.m_data.m_value.number_integer, add_prefix, use_bjdata);
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                write_number_with_ubjson_prefix(j.m_data.m_value.number_unsigned, add_prefix, use_bjdata);
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                write_number_with_ubjson_prefix(j.m_data.m_value.number_float, add_prefix, use_bjdata);
+                break;
+            }
+
+            case value_t::string:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('S'));
+                }
+                write_number_with_ubjson_prefix(j.m_data.m_value.string->size(), true, use_bjdata);
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),
+                    j.m_data.m_value.string->size());
+                break;
+            }
+
+            case value_t::array:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('['));
+                }
+
+                bool prefix_required = true;
+                if (use_type && !j.m_data.m_value.array->empty())
+                {
+                    JSON_ASSERT(use_count);
+                    const CharType first_prefix = ubjson_prefix(j.front(), use_bjdata);
+                    const bool same_prefix = std::all_of(j.begin() + 1, j.end(),
+                                                         [this, first_prefix, use_bjdata](const BasicJsonType & v)
+                    {
+                        return ubjson_prefix(v, use_bjdata) == first_prefix;
+                    });
+
+                    std::vector<CharType> bjdx = {'[', '{', 'S', 'H', 'T', 'F', 'N', 'Z'}; // excluded markers in bjdata optimized type
+
+                    if (same_prefix && !(use_bjdata && std::find(bjdx.begin(), bjdx.end(), first_prefix) != bjdx.end()))
+                    {
+                        prefix_required = false;
+                        oa->write_character(to_char_type('$'));
+                        oa->write_character(first_prefix);
+                    }
+                }
+
+                if (use_count)
+                {
+                    oa->write_character(to_char_type('#'));
+                    write_number_with_ubjson_prefix(j.m_data.m_value.array->size(), true, use_bjdata);
+                }
+
+                for (const auto& el : *j.m_data.m_value.array)
+                {
+                    write_ubjson(el, use_count, use_type, prefix_required, use_bjdata, bjdata_version);
+                }
+
+                if (!use_count)
+                {
+                    oa->write_character(to_char_type(']'));
+                }
+
+                break;
+            }
+
+            case value_t::binary:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('['));
+                }
+
+                if (use_type && (bjdata_draft3 || !j.m_data.m_value.binary->empty()))
+                {
+                    JSON_ASSERT(use_count);
+                    oa->write_character(to_char_type('$'));
+                    oa->write_character(bjdata_draft3 ? 'B' : 'U');
+                }
+
+                if (use_count)
+                {
+                    oa->write_character(to_char_type('#'));
+                    write_number_with_ubjson_prefix(j.m_data.m_value.binary->size(), true, use_bjdata);
+                }
+
+                if (use_type)
+                {
+                    oa->write_characters(
+                        reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),
+                        j.m_data.m_value.binary->size());
+                }
+                else
+                {
+                    for (size_t i = 0; i < j.m_data.m_value.binary->size(); ++i)
+                    {
+                        oa->write_character(to_char_type(bjdata_draft3 ? 'B' : 'U'));
+                        oa->write_character(j.m_data.m_value.binary->data()[i]);
+                    }
+                }
+
+                if (!use_count)
+                {
+                    oa->write_character(to_char_type(']'));
+                }
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                if (use_bjdata && j.m_data.m_value.object->size() == 3 && j.m_data.m_value.object->find("_ArrayType_") != j.m_data.m_value.object->end() && j.m_data.m_value.object->find("_ArraySize_") != j.m_data.m_value.object->end() && j.m_data.m_value.object->find("_ArrayData_") != j.m_data.m_value.object->end())
+                {
+                    if (!write_bjdata_ndarray(*j.m_data.m_value.object, use_count, use_type, bjdata_version))  // decode bjdata ndarray in the JData format (https://github.com/NeuroJSON/jdata)
+                    {
+                        break;
+                    }
+                }
+
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('{'));
+                }
+
+                bool prefix_required = true;
+                if (use_type && !j.m_data.m_value.object->empty())
+                {
+                    JSON_ASSERT(use_count);
+                    const CharType first_prefix = ubjson_prefix(j.front(), use_bjdata);
+                    const bool same_prefix = std::all_of(j.begin(), j.end(),
+                                                         [this, first_prefix, use_bjdata](const BasicJsonType & v)
+                    {
+                        return ubjson_prefix(v, use_bjdata) == first_prefix;
+                    });
+
+                    std::vector<CharType> bjdx = {'[', '{', 'S', 'H', 'T', 'F', 'N', 'Z'}; // excluded markers in bjdata optimized type
+
+                    if (same_prefix && !(use_bjdata && std::find(bjdx.begin(), bjdx.end(), first_prefix) != bjdx.end()))
+                    {
+                        prefix_required = false;
+                        oa->write_character(to_char_type('$'));
+                        oa->write_character(first_prefix);
+                    }
+                }
+
+                if (use_count)
+                {
+                    oa->write_character(to_char_type('#'));
+                    write_number_with_ubjson_prefix(j.m_data.m_value.object->size(), true, use_bjdata);
+                }
+
+                for (const auto& el : *j.m_data.m_value.object)
+                {
+                    write_number_with_ubjson_prefix(el.first.size(), true, use_bjdata);
+                    oa->write_characters(
+                        reinterpret_cast<const CharType*>(el.first.c_str()),
+                        el.first.size());
+                    write_ubjson(el.second, use_count, use_type, prefix_required, use_bjdata, bjdata_version);
+                }
+
+                if (!use_count)
+                {
+                    oa->write_character(to_char_type('}'));
+                }
+
+                break;
+            }
+
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+  private:
+    //////////
+    // BSON //
+    //////////
+
+    /*!
+    @return The size of a BSON document entry header, including the id marker
+            and the entry name size (and its null-terminator).
+    */
+    static std::size_t calc_bson_entry_header_size(const string_t& name, const BasicJsonType& j)
+    {
+        const auto it = name.find(static_cast<typename string_t::value_type>(0));
+        if (JSON_HEDLEY_UNLIKELY(it != BasicJsonType::string_t::npos))
+        {
+            JSON_THROW(out_of_range::create(409, concat("BSON key cannot contain code point U+0000 (at byte ", std::to_string(it), ")"), &j));
+            static_cast<void>(j);
+        }
+
+        return /*id*/ 1ul + name.size() + /*zero-terminator*/1u;
+    }
+
+    /*!
+    @brief Writes the given @a element_type and @a name to the output adapter
+    */
+    void write_bson_entry_header(const string_t& name,
+                                 const std::uint8_t element_type)
+    {
+        oa->write_character(to_char_type(element_type)); // boolean
+        oa->write_characters(
+            reinterpret_cast<const CharType*>(name.c_str()),
+            name.size() + 1u);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and boolean value @a value
+    */
+    void write_bson_boolean(const string_t& name,
+                            const bool value)
+    {
+        write_bson_entry_header(name, 0x08);
+        oa->write_character(value ? to_char_type(0x01) : to_char_type(0x00));
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and double value @a value
+    */
+    void write_bson_double(const string_t& name,
+                           const double value)
+    {
+        write_bson_entry_header(name, 0x01);
+        write_number<double>(value, true);
+    }
+
+    /*!
+    @return The size of the BSON-encoded string in @a value
+    */
+    static std::size_t calc_bson_string_size(const string_t& value)
+    {
+        return sizeof(std::int32_t) + value.size() + 1ul;
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and string value @a value
+    */
+    void write_bson_string(const string_t& name,
+                           const string_t& value)
+    {
+        write_bson_entry_header(name, 0x02);
+
+        write_number<std::int32_t>(static_cast<std::int32_t>(value.size() + 1ul), true);
+        oa->write_characters(
+            reinterpret_cast<const CharType*>(value.c_str()),
+            value.size() + 1);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and null value
+    */
+    void write_bson_null(const string_t& name)
+    {
+        write_bson_entry_header(name, 0x0A);
+    }
+
+    /*!
+    @return The size of the BSON-encoded integer @a value
+    */
+    static std::size_t calc_bson_integer_size(const std::int64_t value)
+    {
+        return (std::numeric_limits<std::int32_t>::min)() <= value && value <= (std::numeric_limits<std::int32_t>::max)()
+               ? sizeof(std::int32_t)
+               : sizeof(std::int64_t);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and integer @a value
+    */
+    void write_bson_integer(const string_t& name,
+                            const std::int64_t value)
+    {
+        if ((std::numeric_limits<std::int32_t>::min)() <= value && value <= (std::numeric_limits<std::int32_t>::max)())
+        {
+            write_bson_entry_header(name, 0x10); // int32
+            write_number<std::int32_t>(static_cast<std::int32_t>(value), true);
+        }
+        else
+        {
+            write_bson_entry_header(name, 0x12); // int64
+            write_number<std::int64_t>(static_cast<std::int64_t>(value), true);
+        }
+    }
+
+    /*!
+    @return The size of the BSON-encoded unsigned integer in @a j
+    */
+    static constexpr std::size_t calc_bson_unsigned_size(const std::uint64_t value) noexcept
+    {
+        return (value <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+               ? sizeof(std::int32_t)
+               : sizeof(std::int64_t);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and unsigned @a value
+    */
+    void write_bson_unsigned(const string_t& name,
+                             const BasicJsonType& j)
+    {
+        if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+        {
+            write_bson_entry_header(name, 0x10 /* int32 */);
+            write_number<std::int32_t>(static_cast<std::int32_t>(j.m_data.m_value.number_unsigned), true);
+        }
+        else if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))
+        {
+            write_bson_entry_header(name, 0x12 /* int64 */);
+            write_number<std::int64_t>(static_cast<std::int64_t>(j.m_data.m_value.number_unsigned), true);
+        }
+        else
+        {
+            write_bson_entry_header(name, 0x11 /* uint64 */);
+            write_number<std::uint64_t>(static_cast<std::uint64_t>(j.m_data.m_value.number_unsigned), true);
+        }
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and object @a value
+    */
+    void write_bson_object_entry(const string_t& name,
+                                 const typename BasicJsonType::object_t& value)
+    {
+        write_bson_entry_header(name, 0x03); // object
+        write_bson_object(value);
+    }
+
+    /*!
+    @return The size of the BSON-encoded array @a value
+    */
+    static std::size_t calc_bson_array_size(const typename BasicJsonType::array_t& value)
+    {
+        std::size_t array_index = 0ul;
+
+        const std::size_t embedded_document_size = std::accumulate(std::begin(value), std::end(value), static_cast<std::size_t>(0), [&array_index](std::size_t result, const typename BasicJsonType::array_t::value_type & el)
+        {
+            return result + calc_bson_element_size(std::to_string(array_index++), el);
+        });
+
+        return sizeof(std::int32_t) + embedded_document_size + 1ul;
+    }
+
+    /*!
+    @return The size of the BSON-encoded binary array @a value
+    */
+    static std::size_t calc_bson_binary_size(const typename BasicJsonType::binary_t& value)
+    {
+        return sizeof(std::int32_t) + value.size() + 1ul;
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and array @a value
+    */
+    void write_bson_array(const string_t& name,
+                          const typename BasicJsonType::array_t& value)
+    {
+        write_bson_entry_header(name, 0x04); // array
+        write_number<std::int32_t>(static_cast<std::int32_t>(calc_bson_array_size(value)), true);
+
+        std::size_t array_index = 0ul;
+
+        for (const auto& el : value)
+        {
+            write_bson_element(std::to_string(array_index++), el);
+        }
+
+        oa->write_character(to_char_type(0x00));
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and binary value @a value
+    */
+    void write_bson_binary(const string_t& name,
+                           const binary_t& value)
+    {
+        write_bson_entry_header(name, 0x05);
+
+        write_number<std::int32_t>(static_cast<std::int32_t>(value.size()), true);
+        write_number(value.has_subtype() ? static_cast<std::uint8_t>(value.subtype()) : static_cast<std::uint8_t>(0x00));
+
+        oa->write_characters(reinterpret_cast<const CharType*>(value.data()), value.size());
+    }
+
+    /*!
+    @brief Calculates the size necessary to serialize the JSON value @a j with its @a name
+    @return The calculated size for the BSON document entry for @a j with the given @a name.
+    */
+    static std::size_t calc_bson_element_size(const string_t& name,
+            const BasicJsonType& j)
+    {
+        const auto header_size = calc_bson_entry_header_size(name, j);
+        switch (j.type())
+        {
+            case value_t::object:
+                return header_size + calc_bson_object_size(*j.m_data.m_value.object);
+
+            case value_t::array:
+                return header_size + calc_bson_array_size(*j.m_data.m_value.array);
+
+            case value_t::binary:
+                return header_size + calc_bson_binary_size(*j.m_data.m_value.binary);
+
+            case value_t::boolean:
+                return header_size + 1ul;
+
+            case value_t::number_float:
+                return header_size + 8ul;
+
+            case value_t::number_integer:
+                return header_size + calc_bson_integer_size(j.m_data.m_value.number_integer);
+
+            case value_t::number_unsigned:
+                return header_size + calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);
+
+            case value_t::string:
+                return header_size + calc_bson_string_size(*j.m_data.m_value.string);
+
+            case value_t::null:
+                return header_size + 0ul;
+
+            // LCOV_EXCL_START
+            case value_t::discarded:
+            default:
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
+                return 0ul;
+                // LCOV_EXCL_STOP
+        }
+    }
+
+    /*!
+    @brief Serializes the JSON value @a j to BSON and associates it with the
+           key @a name.
+    @param name The name to associate with the JSON entity @a j within the
+                current BSON document
+    */
+    void write_bson_element(const string_t& name,
+                            const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::object:
+                return write_bson_object_entry(name, *j.m_data.m_value.object);
+
+            case value_t::array:
+                return write_bson_array(name, *j.m_data.m_value.array);
+
+            case value_t::binary:
+                return write_bson_binary(name, *j.m_data.m_value.binary);
+
+            case value_t::boolean:
+                return write_bson_boolean(name, j.m_data.m_value.boolean);
+
+            case value_t::number_float:
+                return write_bson_double(name, j.m_data.m_value.number_float);
+
+            case value_t::number_integer:
+                return write_bson_integer(name, j.m_data.m_value.number_integer);
+
+            case value_t::number_unsigned:
+                return write_bson_unsigned(name, j);
+
+            case value_t::string:
+                return write_bson_string(name, *j.m_data.m_value.string);
+
+            case value_t::null:
+                return write_bson_null(name);
+
+            // LCOV_EXCL_START
+            case value_t::discarded:
+            default:
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
+                return;
+                // LCOV_EXCL_STOP
+        }
+    }
+
+    /*!
+    @brief Calculates the size of the BSON serialization of the given
+           JSON-object @a j.
+    @param[in] value  JSON value to serialize
+    @pre       value.type() == value_t::object
+    */
+    static std::size_t calc_bson_object_size(const typename BasicJsonType::object_t& value)
+    {
+        const std::size_t document_size = std::accumulate(value.begin(), value.end(), static_cast<std::size_t>(0),
+                                          [](size_t result, const typename BasicJsonType::object_t::value_type & el)
+        {
+            return result += calc_bson_element_size(el.first, el.second);
+        });
+
+        return sizeof(std::int32_t) + document_size + 1ul;
+    }
+
+    /*!
+    @param[in] value  JSON value to serialize
+    @pre       value.type() == value_t::object
+    */
+    void write_bson_object(const typename BasicJsonType::object_t& value)
+    {
+        write_number<std::int32_t>(static_cast<std::int32_t>(calc_bson_object_size(value)), true);
+
+        for (const auto& el : value)
+        {
+            write_bson_element(el.first, el.second);
+        }
+
+        oa->write_character(to_char_type(0x00));
+    }
+
+    //////////
+    // CBOR //
+    //////////
+
+    static constexpr CharType get_cbor_float_prefix(float /*unused*/)
+    {
+        return to_char_type(0xFA);  // Single-Precision Float
+    }
+
+    static constexpr CharType get_cbor_float_prefix(double /*unused*/)
+    {
+        return to_char_type(0xFB);  // Double-Precision Float
+    }
+
+    /////////////
+    // MsgPack //
+    /////////////
+
+    static constexpr CharType get_msgpack_float_prefix(float /*unused*/)
+    {
+        return to_char_type(0xCA);  // float 32
+    }
+
+    static constexpr CharType get_msgpack_float_prefix(double /*unused*/)
+    {
+        return to_char_type(0xCB);  // float 64
+    }
+
+    ////////////
+    // UBJSON //
+    ////////////
+
+    // UBJSON: write number (floating point)
+    template<typename NumberType, typename std::enable_if<
+                 std::is_floating_point<NumberType>::value, int>::type = 0>
+    void write_number_with_ubjson_prefix(const NumberType n,
+                                         const bool add_prefix,
+                                         const bool use_bjdata)
+    {
+        if (add_prefix)
+        {
+            oa->write_character(get_ubjson_float_prefix(n));
+        }
+        write_number(n, use_bjdata);
+    }
+
+    // UBJSON: write number (unsigned integer)
+    template<typename NumberType, typename std::enable_if<
+                 std::is_unsigned<NumberType>::value, int>::type = 0>
+    void write_number_with_ubjson_prefix(const NumberType n,
+                                         const bool add_prefix,
+                                         const bool use_bjdata)
+    {
+        if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int8_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('i'));  // int8
+            }
+            write_number(static_cast<std::uint8_t>(n), use_bjdata);
+        }
+        else if (n <= (std::numeric_limits<std::uint8_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('U'));  // uint8
+            }
+            write_number(static_cast<std::uint8_t>(n), use_bjdata);
+        }
+        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int16_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('I'));  // int16
+            }
+            write_number(static_cast<std::int16_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && n <= static_cast<uint64_t>((std::numeric_limits<uint16_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('u'));  // uint16 - bjdata only
+            }
+            write_number(static_cast<std::uint16_t>(n), use_bjdata);
+        }
+        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('l'));  // int32
+            }
+            write_number(static_cast<std::int32_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && n <= static_cast<uint64_t>((std::numeric_limits<uint32_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('m'));  // uint32 - bjdata only
+            }
+            write_number(static_cast<std::uint32_t>(n), use_bjdata);
+        }
+        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('L'));  // int64
+            }
+            write_number(static_cast<std::int64_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && n <= (std::numeric_limits<uint64_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('M'));  // uint64 - bjdata only
+            }
+            write_number(static_cast<std::uint64_t>(n), use_bjdata);
+        }
+        else
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('H'));  // high-precision number
+            }
+
+            const auto number = BasicJsonType(n).dump();
+            write_number_with_ubjson_prefix(number.size(), true, use_bjdata);
+            for (std::size_t i = 0; i < number.size(); ++i)
+            {
+                oa->write_character(to_char_type(static_cast<std::uint8_t>(number[i])));
+            }
+        }
+    }
+
+    // UBJSON: write number (signed integer)
+    template < typename NumberType, typename std::enable_if <
+                   std::is_signed<NumberType>::value&&
+                   !std::is_floating_point<NumberType>::value, int >::type = 0 >
+    void write_number_with_ubjson_prefix(const NumberType n,
+                                         const bool add_prefix,
+                                         const bool use_bjdata)
+    {
+        if ((std::numeric_limits<std::int8_t>::min)() <= n && n <= (std::numeric_limits<std::int8_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('i'));  // int8
+            }
+            write_number(static_cast<std::int8_t>(n), use_bjdata);
+        }
+        else if (static_cast<std::int64_t>((std::numeric_limits<std::uint8_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint8_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('U'));  // uint8
+            }
+            write_number(static_cast<std::uint8_t>(n), use_bjdata);
+        }
+        else if ((std::numeric_limits<std::int16_t>::min)() <= n && n <= (std::numeric_limits<std::int16_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('I'));  // int16
+            }
+            write_number(static_cast<std::int16_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && (static_cast<std::int64_t>((std::numeric_limits<std::uint16_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint16_t>::max)())))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('u'));  // uint16 - bjdata only
+            }
+            write_number(static_cast<uint16_t>(n), use_bjdata);
+        }
+        else if ((std::numeric_limits<std::int32_t>::min)() <= n && n <= (std::numeric_limits<std::int32_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('l'));  // int32
+            }
+            write_number(static_cast<std::int32_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && (static_cast<std::int64_t>((std::numeric_limits<std::uint32_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint32_t>::max)())))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('m'));  // uint32 - bjdata only
+            }
+            write_number(static_cast<uint32_t>(n), use_bjdata);
+        }
+        else if ((std::numeric_limits<std::int64_t>::min)() <= n && n <= (std::numeric_limits<std::int64_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('L'));  // int64
+            }
+            write_number(static_cast<std::int64_t>(n), use_bjdata);
+        }
+        // LCOV_EXCL_START
+        else
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('H'));  // high-precision number
+            }
+
+            const auto number = BasicJsonType(n).dump();
+            write_number_with_ubjson_prefix(number.size(), true, use_bjdata);
+            for (std::size_t i = 0; i < number.size(); ++i)
+            {
+                oa->write_character(to_char_type(static_cast<std::uint8_t>(number[i])));
+            }
+        }
+        // LCOV_EXCL_STOP
+    }
+
+    /*!
+    @brief determine the type prefix of container values
+    */
+    CharType ubjson_prefix(const BasicJsonType& j, const bool use_bjdata) const noexcept
+    {
+        switch (j.type())
+        {
+            case value_t::null:
+                return 'Z';
+
+            case value_t::boolean:
+                return j.m_data.m_value.boolean ? 'T' : 'F';
+
+            case value_t::number_integer:
+            {
+                if ((std::numeric_limits<std::int8_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int8_t>::max)())
+                {
+                    return 'i';
+                }
+                if ((std::numeric_limits<std::uint8_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    return 'U';
+                }
+                if ((std::numeric_limits<std::int16_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int16_t>::max)())
+                {
+                    return 'I';
+                }
+                if (use_bjdata && ((std::numeric_limits<std::uint16_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint16_t>::max)()))
+                {
+                    return 'u';
+                }
+                if ((std::numeric_limits<std::int32_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int32_t>::max)())
+                {
+                    return 'l';
+                }
+                if (use_bjdata && ((std::numeric_limits<std::uint32_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint32_t>::max)()))
+                {
+                    return 'm';
+                }
+                if ((std::numeric_limits<std::int64_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int64_t>::max)())
+                {
+                    return 'L';
+                }
+                // anything else is treated as high-precision number
+                return 'H'; // LCOV_EXCL_LINE
+            }
+
+            case value_t::number_unsigned:
+            {
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int8_t>::max)()))
+                {
+                    return 'i';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint8_t>::max)()))
+                {
+                    return 'U';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int16_t>::max)()))
+                {
+                    return 'I';
+                }
+                if (use_bjdata && j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint16_t>::max)()))
+                {
+                    return 'u';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+                {
+                    return 'l';
+                }
+                if (use_bjdata && j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint32_t>::max)()))
+                {
+                    return 'm';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))
+                {
+                    return 'L';
+                }
+                if (use_bjdata && j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    return 'M';
+                }
+                // anything else is treated as high-precision number
+                return 'H'; // LCOV_EXCL_LINE
+            }
+
+            case value_t::number_float:
+                return get_ubjson_float_prefix(j.m_data.m_value.number_float);
+
+            case value_t::string:
+                return 'S';
+
+            case value_t::array: // fallthrough
+            case value_t::binary:
+                return '[';
+
+            case value_t::object:
+                return '{';
+
+            case value_t::discarded:
+            default:  // discarded values
+                return 'N';
+        }
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(float /*unused*/)
+    {
+        return 'd';  // float 32
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(double /*unused*/)
+    {
+        return 'D';  // float 64
+    }
+
+    /*!
+    @return false if the object is successfully converted to a bjdata ndarray, true if the type or size is invalid
+    */
+    bool write_bjdata_ndarray(const typename BasicJsonType::object_t& value, const bool use_count, const bool use_type, const bjdata_version_t bjdata_version)
+    {
+        std::map<string_t, CharType> bjdtype = {{"uint8", 'U'},  {"int8", 'i'},  {"uint16", 'u'}, {"int16", 'I'},
+            {"uint32", 'm'}, {"int32", 'l'}, {"uint64", 'M'}, {"int64", 'L'}, {"single", 'd'}, {"double", 'D'},
+            {"char", 'C'}, {"byte", 'B'}
+        };
+
+        string_t key = "_ArrayType_";
+        auto it = bjdtype.find(static_cast<string_t>(value.at(key)));
+        if (it == bjdtype.end())
+        {
+            return true;
+        }
+        CharType dtype = it->second;
+
+        key = "_ArraySize_";
+        std::size_t len = (value.at(key).empty() ? 0 : 1);
+        for (const auto& el : value.at(key))
+        {
+            len *= static_cast<std::size_t>(el.m_data.m_value.number_unsigned);
+        }
+
+        key = "_ArrayData_";
+        if (value.at(key).size() != len)
+        {
+            return true;
+        }
+
+        oa->write_character('[');
+        oa->write_character('$');
+        oa->write_character(dtype);
+        oa->write_character('#');
+
+        key = "_ArraySize_";
+        write_ubjson(value.at(key), use_count, use_type, true,  true, bjdata_version);
+
+        key = "_ArrayData_";
+        if (dtype == 'U' || dtype == 'C' || dtype == 'B')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint8_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'i')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int8_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'u')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint16_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'I')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int16_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'm')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint32_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'l')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int32_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'M')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint64_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'L')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int64_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'd')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<float>(el.m_data.m_value.number_float), true);
+            }
+        }
+        else if (dtype == 'D')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<double>(el.m_data.m_value.number_float), true);
+            }
+        }
+        return false;
+    }
+
+    ///////////////////////
+    // Utility functions //
+    ///////////////////////
+
+    /*
+    @brief write a number to output input
+    @param[in] n number of type @a NumberType
+    @param[in] OutputIsLittleEndian Set to true if output data is
+                                 required to be little endian
+    @tparam NumberType the type of the number
+
+    @note This function needs to respect the system's endianness, because bytes
+          in CBOR, MessagePack, and UBJSON are stored in network order (big
+          endian) and therefore need reordering on little endian systems.
+          On the other hand, BSON and BJData use little endian and should reorder
+          on big endian systems.
+    */
+    template<typename NumberType>
+    void write_number(const NumberType n, const bool OutputIsLittleEndian = false)
+    {
+        // step 1: write number to array of length NumberType
+        std::array<CharType, sizeof(NumberType)> vec{};
+        std::memcpy(vec.data(), &n, sizeof(NumberType));
+
+        // step 2: write array to output (with possible reordering)
+        if (is_little_endian != OutputIsLittleEndian)
+        {
+            // reverse byte order prior to conversion if necessary
+            std::reverse(vec.begin(), vec.end());
+        }
+
+        oa->write_characters(vec.data(), sizeof(NumberType));
+    }
+
+    void write_compact_float(const number_float_t n, detail::input_format_t format)
+    {
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
+                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&
+                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(static_cast<float>(n))
+                                : get_msgpack_float_prefix(static_cast<float>(n)));
+            write_number(static_cast<float>(n));
+        }
+        else
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(n)
+                                : get_msgpack_float_prefix(n));
+            write_number(n);
+        }
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+    }
+
+  public:
+    // The following to_char_type functions are implement the conversion
+    // between uint8_t and CharType. In case CharType is not unsigned,
+    // such a conversion is required to allow values greater than 128.
+    // See <https://github.com/nlohmann/json/issues/1286> for a discussion.
+    template < typename C = CharType,
+               enable_if_t < std::is_signed<C>::value && std::is_signed<char>::value > * = nullptr >
+    static constexpr CharType to_char_type(std::uint8_t x) noexcept
+    {
+        return *reinterpret_cast<char*>(&x);
+    }
+
+    template < typename C = CharType,
+               enable_if_t < std::is_signed<C>::value && std::is_unsigned<char>::value > * = nullptr >
+    static CharType to_char_type(std::uint8_t x) noexcept
+    {
+        static_assert(sizeof(std::uint8_t) == sizeof(CharType), "size of CharType must be equal to std::uint8_t");
+        static_assert(std::is_trivial<CharType>::value, "CharType must be trivial");
+        CharType result;
+        std::memcpy(&result, &x, sizeof(x));
+        return result;
+    }
+
+    template<typename C = CharType,
+             enable_if_t<std::is_unsigned<C>::value>* = nullptr>
+    static constexpr CharType to_char_type(std::uint8_t x) noexcept
+    {
+        return x;
+    }
+
+    template < typename InputCharType, typename C = CharType,
+               enable_if_t <
+                   std::is_signed<C>::value &&
+                   std::is_signed<char>::value &&
+                   std::is_same<char, typename std::remove_cv<InputCharType>::type>::value
+                   > * = nullptr >
+    static constexpr CharType to_char_type(InputCharType x) noexcept
+    {
+        return x;
+    }
+
+  private:
+    /// whether we can assume little endianness
+    const bool is_little_endian = little_endianness();
+
+    /// the output
+    output_adapter_t<CharType> oa = nullptr;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/output/output_adapters.hpp>
+
+// #include <nlohmann/detail/output/serializer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2008 - 2009 Björn Hoehrmann <bjoern@hoehrmann.de>
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // reverse, remove, fill, find, none_of
+#include <array> // array
+#include <clocale> // localeconv, lconv
+#include <cmath> // labs, isfinite, isnan, signbit
+#include <cstddef> // size_t, ptrdiff_t
+#include <cstdint> // uint8_t
+#include <cstdio> // snprintf
+#include <limits> // numeric_limits
+#include <string> // string, char_traits
+#include <iomanip> // setfill, setw
+#include <type_traits> // is_same
+#include <utility> // move
+
+// #include <nlohmann/detail/conversions/to_chars.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2009 Florian Loitsch <https://florian.loitsch.com/>
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cmath>   // signbit, isfinite
+#include <cstdint> // intN_t, uintN_t
+#include <cstring> // memcpy, memmove
+#include <limits> // numeric_limits
+#include <type_traits> // conditional
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief implements the Grisu2 algorithm for binary to decimal floating-point
+conversion.
+
+This implementation is a slightly modified version of the reference
+implementation which may be obtained from
+http://florian.loitsch.com/publications (bench.tar.gz).
+
+The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.
+
+For a detailed description of the algorithm see:
+
+[1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with
+    Integers", Proceedings of the ACM SIGPLAN 2010 Conference on Programming
+    Language Design and Implementation, PLDI 2010
+[2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately",
+    Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language
+    Design and Implementation, PLDI 1996
+*/
+namespace dtoa_impl
+{
+
+template<typename Target, typename Source>
+Target reinterpret_bits(const Source source)
+{
+    static_assert(sizeof(Target) == sizeof(Source), "size mismatch");
+
+    Target target;
+    std::memcpy(&target, &source, sizeof(Source));
+    return target;
+}
+
+struct diyfp // f * 2^e
+{
+    static constexpr int kPrecision = 64; // = q
+
+    std::uint64_t f = 0;
+    int e = 0;
+
+    constexpr diyfp(std::uint64_t f_, int e_) noexcept : f(f_), e(e_) {}
+
+    /*!
+    @brief returns x - y
+    @pre x.e == y.e and x.f >= y.f
+    */
+    static diyfp sub(const diyfp& x, const diyfp& y) noexcept
+    {
+        JSON_ASSERT(x.e == y.e);
+        JSON_ASSERT(x.f >= y.f);
+
+        return {x.f - y.f, x.e};
+    }
+
+    /*!
+    @brief returns x * y
+    @note The result is rounded. (Only the upper q bits are returned.)
+    */
+    static diyfp mul(const diyfp& x, const diyfp& y) noexcept
+    {
+        static_assert(kPrecision == 64, "internal error");
+
+        // Computes:
+        //  f = round((x.f * y.f) / 2^q)
+        //  e = x.e + y.e + q
+
+        // Emulate the 64-bit * 64-bit multiplication:
+        //
+        // p = u * v
+        //   = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)
+        //   = (u_lo v_lo         ) + 2^32 ((u_lo v_hi         ) + (u_hi v_lo         )) + 2^64 (u_hi v_hi         )
+        //   = (p0                ) + 2^32 ((p1                ) + (p2                )) + 2^64 (p3                )
+        //   = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3                )
+        //   = (p0_lo             ) + 2^32 (p0_hi + p1_lo + p2_lo                      ) + 2^64 (p1_hi + p2_hi + p3)
+        //   = (p0_lo             ) + 2^32 (Q                                          ) + 2^64 (H                 )
+        //   = (p0_lo             ) + 2^32 (Q_lo + 2^32 Q_hi                           ) + 2^64 (H                 )
+        //
+        // (Since Q might be larger than 2^32 - 1)
+        //
+        //   = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)
+        //
+        // (Q_hi + H does not overflow a 64-bit int)
+        //
+        //   = p_lo + 2^64 p_hi
+
+        const std::uint64_t u_lo = x.f & 0xFFFFFFFFu;
+        const std::uint64_t u_hi = x.f >> 32u;
+        const std::uint64_t v_lo = y.f & 0xFFFFFFFFu;
+        const std::uint64_t v_hi = y.f >> 32u;
+
+        const std::uint64_t p0 = u_lo * v_lo;
+        const std::uint64_t p1 = u_lo * v_hi;
+        const std::uint64_t p2 = u_hi * v_lo;
+        const std::uint64_t p3 = u_hi * v_hi;
+
+        const std::uint64_t p0_hi = p0 >> 32u;
+        const std::uint64_t p1_lo = p1 & 0xFFFFFFFFu;
+        const std::uint64_t p1_hi = p1 >> 32u;
+        const std::uint64_t p2_lo = p2 & 0xFFFFFFFFu;
+        const std::uint64_t p2_hi = p2 >> 32u;
+
+        std::uint64_t Q = p0_hi + p1_lo + p2_lo;
+
+        // The full product might now be computed as
+        //
+        // p_hi = p3 + p2_hi + p1_hi + (Q >> 32)
+        // p_lo = p0_lo + (Q << 32)
+        //
+        // But in this particular case here, the full p_lo is not required.
+        // Effectively we only need to add the highest bit in p_lo to p_hi (and
+        // Q_hi + 1 does not overflow).
+
+        Q += std::uint64_t{1} << (64u - 32u - 1u); // round, ties up
+
+        const std::uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32u);
+
+        return {h, x.e + y.e + 64};
+    }
+
+    /*!
+    @brief normalize x such that the significand is >= 2^(q-1)
+    @pre x.f != 0
+    */
+    static diyfp normalize(diyfp x) noexcept
+    {
+        JSON_ASSERT(x.f != 0);
+
+        while ((x.f >> 63u) == 0)
+        {
+            x.f <<= 1u;
+            x.e--;
+        }
+
+        return x;
+    }
+
+    /*!
+    @brief normalize x such that the result has the exponent E
+    @pre e >= x.e and the upper e - x.e bits of x.f must be zero.
+    */
+    static diyfp normalize_to(const diyfp& x, const int target_exponent) noexcept
+    {
+        const int delta = x.e - target_exponent;
+
+        JSON_ASSERT(delta >= 0);
+        JSON_ASSERT(((x.f << delta) >> delta) == x.f);
+
+        return {x.f << delta, target_exponent};
+    }
+};
+
+struct boundaries
+{
+    diyfp w;
+    diyfp minus;
+    diyfp plus;
+};
+
+/*!
+Compute the (normalized) diyfp representing the input number 'value' and its
+boundaries.
+
+@pre value must be finite and positive
+*/
+template<typename FloatType>
+boundaries compute_boundaries(FloatType value)
+{
+    JSON_ASSERT(std::isfinite(value));
+    JSON_ASSERT(value > 0);
+
+    // Convert the IEEE representation into a diyfp.
+    //
+    // If v is denormal:
+    //      value = 0.F * 2^(1 - bias) = (          F) * 2^(1 - bias - (p-1))
+    // If v is normalized:
+    //      value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))
+
+    static_assert(std::numeric_limits<FloatType>::is_iec559,
+                  "internal error: dtoa_short requires an IEEE-754 floating-point implementation");
+
+    constexpr int      kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
+    constexpr int      kBias      = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
+    constexpr int      kMinExp    = 1 - kBias;
+    constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1)
+
+    using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t >::type;
+
+    const auto bits = static_cast<std::uint64_t>(reinterpret_bits<bits_type>(value));
+    const std::uint64_t E = bits >> (kPrecision - 1);
+    const std::uint64_t F = bits & (kHiddenBit - 1);
+
+    const bool is_denormal = E == 0;
+    const diyfp v = is_denormal
+                    ? diyfp(F, kMinExp)
+                    : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);
+
+    // Compute the boundaries m- and m+ of the floating-point value
+    // v = f * 2^e.
+    //
+    // Determine v- and v+, the floating-point predecessor and successor if v,
+    // respectively.
+    //
+    //      v- = v - 2^e        if f != 2^(p-1) or e == e_min                (A)
+    //         = v - 2^(e-1)    if f == 2^(p-1) and e > e_min                (B)
+    //
+    //      v+ = v + 2^e
+    //
+    // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
+    // between m- and m+ round to v, regardless of how the input rounding
+    // algorithm breaks ties.
+    //
+    //      ---+-------------+-------------+-------------+-------------+---  (A)
+    //         v-            m-            v             m+            v+
+    //
+    //      -----------------+------+------+-------------+-------------+---  (B)
+    //                       v-     m-     v             m+            v+
+
+    const bool lower_boundary_is_closer = F == 0 && E > 1;
+    const diyfp m_plus = diyfp((2 * v.f) + 1, v.e - 1);
+    const diyfp m_minus = lower_boundary_is_closer
+                          ? diyfp((4 * v.f) - 1, v.e - 2)  // (B)
+                          : diyfp((2 * v.f) - 1, v.e - 1); // (A)
+
+    // Determine the normalized w+ = m+.
+    const diyfp w_plus = diyfp::normalize(m_plus);
+
+    // Determine w- = m- such that e_(w-) = e_(w+).
+    const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);
+
+    return {diyfp::normalize(v), w_minus, w_plus};
+}
+
+// Given normalized diyfp w, Grisu needs to find a (normalized) cached
+// power-of-ten c, such that the exponent of the product c * w = f * 2^e lies
+// within a certain range [alpha, gamma] (Definition 3.2 from [1])
+//
+//      alpha <= e = e_c + e_w + q <= gamma
+//
+// or
+//
+//      f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q
+//                          <= f_c * f_w * 2^gamma
+//
+// Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies
+//
+//      2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma
+//
+// or
+//
+//      2^(q - 2 + alpha) <= c * w < 2^(q + gamma)
+//
+// The choice of (alpha,gamma) determines the size of the table and the form of
+// the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well
+// in practice:
+//
+// The idea is to cut the number c * w = f * 2^e into two parts, which can be
+// processed independently: An integral part p1, and a fractional part p2:
+//
+//      f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e
+//              = (f div 2^-e) + (f mod 2^-e) * 2^e
+//              = p1 + p2 * 2^e
+//
+// The conversion of p1 into decimal form requires a series of divisions and
+// modulos by (a power of) 10. These operations are faster for 32-bit than for
+// 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be
+// achieved by choosing
+//
+//      -e >= 32   or   e <= -32 := gamma
+//
+// In order to convert the fractional part
+//
+//      p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ...
+//
+// into decimal form, the fraction is repeatedly multiplied by 10 and the digits
+// d[-i] are extracted in order:
+//
+//      (10 * p2) div 2^-e = d[-1]
+//      (10 * p2) mod 2^-e = d[-2] / 10^1 + ...
+//
+// The multiplication by 10 must not overflow. It is sufficient to choose
+//
+//      10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64.
+//
+// Since p2 = f mod 2^-e < 2^-e,
+//
+//      -e <= 60   or   e >= -60 := alpha
+
+constexpr int kAlpha = -60;
+constexpr int kGamma = -32;
+
+struct cached_power // c = f * 2^e ~= 10^k
+{
+    std::uint64_t f;
+    int e;
+    int k;
+};
+
+/*!
+For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached
+power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c
+satisfies (Definition 3.2 from [1])
+
+     alpha <= e_c + e + q <= gamma.
+*/
+inline cached_power get_cached_power_for_binary_exponent(int e)
+{
+    // Now
+    //
+    //      alpha <= e_c + e + q <= gamma                                    (1)
+    //      ==> f_c * 2^alpha <= c * 2^e * 2^q
+    //
+    // and since the c's are normalized, 2^(q-1) <= f_c,
+    //
+    //      ==> 2^(q - 1 + alpha) <= c * 2^(e + q)
+    //      ==> 2^(alpha - e - 1) <= c
+    //
+    // If c were an exact power of ten, i.e. c = 10^k, one may determine k as
+    //
+    //      k = ceil( log_10( 2^(alpha - e - 1) ) )
+    //        = ceil( (alpha - e - 1) * log_10(2) )
+    //
+    // From the paper:
+    // "In theory the result of the procedure could be wrong since c is rounded,
+    //  and the computation itself is approximated [...]. In practice, however,
+    //  this simple function is sufficient."
+    //
+    // For IEEE double precision floating-point numbers converted into
+    // normalized diyfp's w = f * 2^e, with q = 64,
+    //
+    //      e >= -1022      (min IEEE exponent)
+    //           -52        (p - 1)
+    //           -52        (p - 1, possibly normalize denormal IEEE numbers)
+    //           -11        (normalize the diyfp)
+    //         = -1137
+    //
+    // and
+    //
+    //      e <= +1023      (max IEEE exponent)
+    //           -52        (p - 1)
+    //           -11        (normalize the diyfp)
+    //         = 960
+    //
+    // This binary exponent range [-1137,960] results in a decimal exponent
+    // range [-307,324]. One does not need to store a cached power for each
+    // k in this range. For each such k it suffices to find a cached power
+    // such that the exponent of the product lies in [alpha,gamma].
+    // This implies that the difference of the decimal exponents of adjacent
+    // table entries must be less than or equal to
+    //
+    //      floor( (gamma - alpha) * log_10(2) ) = 8.
+    //
+    // (A smaller distance gamma-alpha would require a larger table.)
+
+    // NB:
+    // Actually this function returns c, such that -60 <= e_c + e + 64 <= -34.
+
+    constexpr int kCachedPowersMinDecExp = -300;
+    constexpr int kCachedPowersDecStep = 8;
+
+    static constexpr std::array<cached_power, 79> kCachedPowers =
+    {
+        {
+            { 0xAB70FE17C79AC6CA, -1060, -300 },
+            { 0xFF77B1FCBEBCDC4F, -1034, -292 },
+            { 0xBE5691EF416BD60C, -1007, -284 },
+            { 0x8DD01FAD907FFC3C,  -980, -276 },
+            { 0xD3515C2831559A83,  -954, -268 },
+            { 0x9D71AC8FADA6C9B5,  -927, -260 },
+            { 0xEA9C227723EE8BCB,  -901, -252 },
+            { 0xAECC49914078536D,  -874, -244 },
+            { 0x823C12795DB6CE57,  -847, -236 },
+            { 0xC21094364DFB5637,  -821, -228 },
+            { 0x9096EA6F3848984F,  -794, -220 },
+            { 0xD77485CB25823AC7,  -768, -212 },
+            { 0xA086CFCD97BF97F4,  -741, -204 },
+            { 0xEF340A98172AACE5,  -715, -196 },
+            { 0xB23867FB2A35B28E,  -688, -188 },
+            { 0x84C8D4DFD2C63F3B,  -661, -180 },
+            { 0xC5DD44271AD3CDBA,  -635, -172 },
+            { 0x936B9FCEBB25C996,  -608, -164 },
+            { 0xDBAC6C247D62A584,  -582, -156 },
+            { 0xA3AB66580D5FDAF6,  -555, -148 },
+            { 0xF3E2F893DEC3F126,  -529, -140 },
+            { 0xB5B5ADA8AAFF80B8,  -502, -132 },
+            { 0x87625F056C7C4A8B,  -475, -124 },
+            { 0xC9BCFF6034C13053,  -449, -116 },
+            { 0x964E858C91BA2655,  -422, -108 },
+            { 0xDFF9772470297EBD,  -396, -100 },
+            { 0xA6DFBD9FB8E5B88F,  -369,  -92 },
+            { 0xF8A95FCF88747D94,  -343,  -84 },
+            { 0xB94470938FA89BCF,  -316,  -76 },
+            { 0x8A08F0F8BF0F156B,  -289,  -68 },
+            { 0xCDB02555653131B6,  -263,  -60 },
+            { 0x993FE2C6D07B7FAC,  -236,  -52 },
+            { 0xE45C10C42A2B3B06,  -210,  -44 },
+            { 0xAA242499697392D3,  -183,  -36 },
+            { 0xFD87B5F28300CA0E,  -157,  -28 },
+            { 0xBCE5086492111AEB,  -130,  -20 },
+            { 0x8CBCCC096F5088CC,  -103,  -12 },
+            { 0xD1B71758E219652C,   -77,   -4 },
+            { 0x9C40000000000000,   -50,    4 },
+            { 0xE8D4A51000000000,   -24,   12 },
+            { 0xAD78EBC5AC620000,     3,   20 },
+            { 0x813F3978F8940984,    30,   28 },
+            { 0xC097CE7BC90715B3,    56,   36 },
+            { 0x8F7E32CE7BEA5C70,    83,   44 },
+            { 0xD5D238A4ABE98068,   109,   52 },
+            { 0x9F4F2726179A2245,   136,   60 },
+            { 0xED63A231D4C4FB27,   162,   68 },
+            { 0xB0DE65388CC8ADA8,   189,   76 },
+            { 0x83C7088E1AAB65DB,   216,   84 },
+            { 0xC45D1DF942711D9A,   242,   92 },
+            { 0x924D692CA61BE758,   269,  100 },
+            { 0xDA01EE641A708DEA,   295,  108 },
+            { 0xA26DA3999AEF774A,   322,  116 },
+            { 0xF209787BB47D6B85,   348,  124 },
+            { 0xB454E4A179DD1877,   375,  132 },
+            { 0x865B86925B9BC5C2,   402,  140 },
+            { 0xC83553C5C8965D3D,   428,  148 },
+            { 0x952AB45CFA97A0B3,   455,  156 },
+            { 0xDE469FBD99A05FE3,   481,  164 },
+            { 0xA59BC234DB398C25,   508,  172 },
+            { 0xF6C69A72A3989F5C,   534,  180 },
+            { 0xB7DCBF5354E9BECE,   561,  188 },
+            { 0x88FCF317F22241E2,   588,  196 },
+            { 0xCC20CE9BD35C78A5,   614,  204 },
+            { 0x98165AF37B2153DF,   641,  212 },
+            { 0xE2A0B5DC971F303A,   667,  220 },
+            { 0xA8D9D1535CE3B396,   694,  228 },
+            { 0xFB9B7CD9A4A7443C,   720,  236 },
+            { 0xBB764C4CA7A44410,   747,  244 },
+            { 0x8BAB8EEFB6409C1A,   774,  252 },
+            { 0xD01FEF10A657842C,   800,  260 },
+            { 0x9B10A4E5E9913129,   827,  268 },
+            { 0xE7109BFBA19C0C9D,   853,  276 },
+            { 0xAC2820D9623BF429,   880,  284 },
+            { 0x80444B5E7AA7CF85,   907,  292 },
+            { 0xBF21E44003ACDD2D,   933,  300 },
+            { 0x8E679C2F5E44FF8F,   960,  308 },
+            { 0xD433179D9C8CB841,   986,  316 },
+            { 0x9E19DB92B4E31BA9,  1013,  324 },
+        }
+    };
+
+    // This computation gives exactly the same results for k as
+    //      k = ceil((kAlpha - e - 1) * 0.30102999566398114)
+    // for |e| <= 1500, but doesn't require floating-point operations.
+    // NB: log_10(2) ~= 78913 / 2^18
+    JSON_ASSERT(e >= -1500);
+    JSON_ASSERT(e <=  1500);
+    const int f = kAlpha - e - 1;
+    const int k = ((f * 78913) / (1 << 18)) + static_cast<int>(f > 0);
+
+    const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;
+    JSON_ASSERT(index >= 0);
+    JSON_ASSERT(static_cast<std::size_t>(index) < kCachedPowers.size());
+
+    const cached_power cached = kCachedPowers[static_cast<std::size_t>(index)];
+    JSON_ASSERT(kAlpha <= cached.e + e + 64);
+    JSON_ASSERT(kGamma >= cached.e + e + 64);
+
+    return cached;
+}
+
+/*!
+For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
+For n == 0, returns 1 and sets pow10 := 1.
+*/
+inline int find_largest_pow10(const std::uint32_t n, std::uint32_t& pow10)
+{
+    // LCOV_EXCL_START
+    if (n >= 1000000000)
+    {
+        pow10 = 1000000000;
+        return 10;
+    }
+    // LCOV_EXCL_STOP
+    if (n >= 100000000)
+    {
+        pow10 = 100000000;
+        return  9;
+    }
+    if (n >= 10000000)
+    {
+        pow10 = 10000000;
+        return  8;
+    }
+    if (n >= 1000000)
+    {
+        pow10 = 1000000;
+        return  7;
+    }
+    if (n >= 100000)
+    {
+        pow10 = 100000;
+        return  6;
+    }
+    if (n >= 10000)
+    {
+        pow10 = 10000;
+        return  5;
+    }
+    if (n >= 1000)
+    {
+        pow10 = 1000;
+        return  4;
+    }
+    if (n >= 100)
+    {
+        pow10 = 100;
+        return  3;
+    }
+    if (n >= 10)
+    {
+        pow10 = 10;
+        return  2;
+    }
+
+    pow10 = 1;
+    return 1;
+}
+
+inline void grisu2_round(char* buf, int len, std::uint64_t dist, std::uint64_t delta,
+                         std::uint64_t rest, std::uint64_t ten_k)
+{
+    JSON_ASSERT(len >= 1);
+    JSON_ASSERT(dist <= delta);
+    JSON_ASSERT(rest <= delta);
+    JSON_ASSERT(ten_k > 0);
+
+    //               <--------------------------- delta ---->
+    //                                  <---- dist --------->
+    // --------------[------------------+-------------------]--------------
+    //               M-                 w                   M+
+    //
+    //                                  ten_k
+    //                                <------>
+    //                                       <---- rest ---->
+    // --------------[------------------+----+--------------]--------------
+    //                                  w    V
+    //                                       = buf * 10^k
+    //
+    // ten_k represents a unit-in-the-last-place in the decimal representation
+    // stored in buf.
+    // Decrement buf by ten_k while this takes buf closer to w.
+
+    // The tests are written in this order to avoid overflow in unsigned
+    // integer arithmetic.
+
+    while (rest < dist
+            && delta - rest >= ten_k
+            && (rest + ten_k < dist || dist - rest > rest + ten_k - dist))
+    {
+        JSON_ASSERT(buf[len - 1] != '0');
+        buf[len - 1]--;
+        rest += ten_k;
+    }
+}
+
+/*!
+Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.
+M- and M+ must be normalized and share the same exponent -60 <= e <= -32.
+*/
+inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent,
+                             diyfp M_minus, diyfp w, diyfp M_plus)
+{
+    static_assert(kAlpha >= -60, "internal error");
+    static_assert(kGamma <= -32, "internal error");
+
+    // Generates the digits (and the exponent) of a decimal floating-point
+    // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
+    // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
+    //
+    //               <--------------------------- delta ---->
+    //                                  <---- dist --------->
+    // --------------[------------------+-------------------]--------------
+    //               M-                 w                   M+
+    //
+    // Grisu2 generates the digits of M+ from left to right and stops as soon as
+    // V is in [M-,M+].
+
+    JSON_ASSERT(M_plus.e >= kAlpha);
+    JSON_ASSERT(M_plus.e <= kGamma);
+
+    std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
+    std::uint64_t dist  = diyfp::sub(M_plus, w      ).f; // (significand of (M+ - w ), implicit exponent is e)
+
+    // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
+    //
+    //      M+ = f * 2^e
+    //         = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
+    //         = ((p1        ) * 2^-e + (p2        )) * 2^e
+    //         = p1 + p2 * 2^e
+
+    const diyfp one(std::uint64_t{1} << -M_plus.e, M_plus.e);
+
+    auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
+    std::uint64_t p2 = M_plus.f & (one.f - 1);                    // p2 = f mod 2^-e
+
+    // 1)
+    //
+    // Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]
+
+    JSON_ASSERT(p1 > 0);
+
+    std::uint32_t pow10{};
+    const int k = find_largest_pow10(p1, pow10);
+
+    //      10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)
+    //
+    //      p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))
+    //         = (d[k-1]         ) * 10^(k-1) + (p1 mod 10^(k-1))
+    //
+    //      M+ = p1                                             + p2 * 2^e
+    //         = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1))          + p2 * 2^e
+    //         = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e
+    //         = d[k-1] * 10^(k-1) + (                         rest) * 2^e
+    //
+    // Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)
+    //
+    //      p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]
+    //
+    // but stop as soon as
+    //
+    //      rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e
+
+    int n = k;
+    while (n > 0)
+    {
+        // Invariants:
+        //      M+ = buffer * 10^n + (p1 + p2 * 2^e)    (buffer = 0 for n = k)
+        //      pow10 = 10^(n-1) <= p1 < 10^n
+        //
+        const std::uint32_t d = p1 / pow10;  // d = p1 div 10^(n-1)
+        const std::uint32_t r = p1 % pow10;  // r = p1 mod 10^(n-1)
+        //
+        //      M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e
+        //         = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e)
+        //
+        JSON_ASSERT(d <= 9);
+        buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
+        //
+        //      M+ = buffer * 10^(n-1) + (r + p2 * 2^e)
+        //
+        p1 = r;
+        n--;
+        //
+        //      M+ = buffer * 10^n + (p1 + p2 * 2^e)
+        //      pow10 = 10^n
+        //
+
+        // Now check if enough digits have been generated.
+        // Compute
+        //
+        //      p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e
+        //
+        // Note:
+        // Since rest and delta share the same exponent e, it suffices to
+        // compare the significands.
+        const std::uint64_t rest = (std::uint64_t{p1} << -one.e) + p2;
+        if (rest <= delta)
+        {
+            // V = buffer * 10^n, with M- <= V <= M+.
+
+            decimal_exponent += n;
+
+            // We may now just stop. But instead look if the buffer could be
+            // decremented to bring V closer to w.
+            //
+            // pow10 = 10^n is now 1 ulp in the decimal representation V.
+            // The rounding procedure works with diyfp's with an implicit
+            // exponent of e.
+            //
+            //      10^n = (10^n * 2^-e) * 2^e = ulp * 2^e
+            //
+            const std::uint64_t ten_n = std::uint64_t{pow10} << -one.e;
+            grisu2_round(buffer, length, dist, delta, rest, ten_n);
+
+            return;
+        }
+
+        pow10 /= 10;
+        //
+        //      pow10 = 10^(n-1) <= p1 < 10^n
+        // Invariants restored.
+    }
+
+    // 2)
+    //
+    // The digits of the integral part have been generated:
+    //
+    //      M+ = d[k-1]...d[1]d[0] + p2 * 2^e
+    //         = buffer            + p2 * 2^e
+    //
+    // Now generate the digits of the fractional part p2 * 2^e.
+    //
+    // Note:
+    // No decimal point is generated: the exponent is adjusted instead.
+    //
+    // p2 actually represents the fraction
+    //
+    //      p2 * 2^e
+    //          = p2 / 2^-e
+    //          = d[-1] / 10^1 + d[-2] / 10^2 + ...
+    //
+    // Now generate the digits d[-m] of p1 from left to right (m = 1,2,...)
+    //
+    //      p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m
+    //                      + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...)
+    //
+    // using
+    //
+    //      10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e)
+    //                = (                   d) * 2^-e + (                   r)
+    //
+    // or
+    //      10^m * p2 * 2^e = d + r * 2^e
+    //
+    // i.e.
+    //
+    //      M+ = buffer + p2 * 2^e
+    //         = buffer + 10^-m * (d + r * 2^e)
+    //         = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e
+    //
+    // and stop as soon as 10^-m * r * 2^e <= delta * 2^e
+
+    JSON_ASSERT(p2 > delta);
+
+    int m = 0;
+    for (;;)
+    {
+        // Invariant:
+        //      M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e
+        //         = buffer * 10^-m + 10^-m * (p2                                 ) * 2^e
+        //         = buffer * 10^-m + 10^-m * (1/10 * (10 * p2)                   ) * 2^e
+        //         = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e
+        //
+        JSON_ASSERT(p2 <= (std::numeric_limits<std::uint64_t>::max)() / 10);
+        p2 *= 10;
+        const std::uint64_t d = p2 >> -one.e;     // d = (10 * p2) div 2^-e
+        const std::uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e
+        //
+        //      M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e
+        //         = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e))
+        //         = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e
+        //
+        JSON_ASSERT(d <= 9);
+        buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
+        //
+        //      M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e
+        //
+        p2 = r;
+        m++;
+        //
+        //      M+ = buffer * 10^-m + 10^-m * p2 * 2^e
+        // Invariant restored.
+
+        // Check if enough digits have been generated.
+        //
+        //      10^-m * p2 * 2^e <= delta * 2^e
+        //              p2 * 2^e <= 10^m * delta * 2^e
+        //                    p2 <= 10^m * delta
+        delta *= 10;
+        dist  *= 10;
+        if (p2 <= delta)
+        {
+            break;
+        }
+    }
+
+    // V = buffer * 10^-m, with M- <= V <= M+.
+
+    decimal_exponent -= m;
+
+    // 1 ulp in the decimal representation is now 10^-m.
+    // Since delta and dist are now scaled by 10^m, we need to do the
+    // same with ulp in order to keep the units in sync.
+    //
+    //      10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e
+    //
+    const std::uint64_t ten_m = one.f;
+    grisu2_round(buffer, length, dist, delta, p2, ten_m);
+
+    // By construction this algorithm generates the shortest possible decimal
+    // number (Loitsch, Theorem 6.2) which rounds back to w.
+    // For an input number of precision p, at least
+    //
+    //      N = 1 + ceil(p * log_10(2))
+    //
+    // decimal digits are sufficient to identify all binary floating-point
+    // numbers (Matula, "In-and-Out conversions").
+    // This implies that the algorithm does not produce more than N decimal
+    // digits.
+    //
+    //      N = 17 for p = 53 (IEEE double precision)
+    //      N = 9  for p = 24 (IEEE single precision)
+}
+
+/*!
+v = buf * 10^decimal_exponent
+len is the length of the buffer (number of decimal digits)
+The buffer must be large enough, i.e. >= max_digits10.
+*/
+JSON_HEDLEY_NON_NULL(1)
+inline void grisu2(char* buf, int& len, int& decimal_exponent,
+                   diyfp m_minus, diyfp v, diyfp m_plus)
+{
+    JSON_ASSERT(m_plus.e == m_minus.e);
+    JSON_ASSERT(m_plus.e == v.e);
+
+    //  --------(-----------------------+-----------------------)--------    (A)
+    //          m-                      v                       m+
+    //
+    //  --------------------(-----------+-----------------------)--------    (B)
+    //                      m-          v                       m+
+    //
+    // First scale v (and m- and m+) such that the exponent is in the range
+    // [alpha, gamma].
+
+    const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);
+
+    const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k
+
+    // The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]
+    const diyfp w       = diyfp::mul(v,       c_minus_k);
+    const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);
+    const diyfp w_plus  = diyfp::mul(m_plus,  c_minus_k);
+
+    //  ----(---+---)---------------(---+---)---------------(---+---)----
+    //          w-                      w                       w+
+    //          = c*m-                  = c*v                   = c*m+
+    //
+    // diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and
+    // w+ are now off by a small amount.
+    // In fact:
+    //
+    //      w - v * 10^k < 1 ulp
+    //
+    // To account for this inaccuracy, add resp. subtract 1 ulp.
+    //
+    //  --------+---[---------------(---+---)---------------]---+--------
+    //          w-  M-                  w                   M+  w+
+    //
+    // Now any number in [M-, M+] (bounds included) will round to w when input,
+    // regardless of how the input rounding algorithm breaks ties.
+    //
+    // And digit_gen generates the shortest possible such number in [M-, M+].
+    // Note that this does not mean that Grisu2 always generates the shortest
+    // possible number in the interval (m-, m+).
+    const diyfp M_minus(w_minus.f + 1, w_minus.e);
+    const diyfp M_plus (w_plus.f  - 1, w_plus.e );
+
+    decimal_exponent = -cached.k; // = -(-k) = k
+
+    grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);
+}
+
+/*!
+v = buf * 10^decimal_exponent
+len is the length of the buffer (number of decimal digits)
+The buffer must be large enough, i.e. >= max_digits10.
+*/
+template<typename FloatType>
+JSON_HEDLEY_NON_NULL(1)
+void grisu2(char* buf, int& len, int& decimal_exponent, FloatType value)
+{
+    static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3,
+                  "internal error: not enough precision");
+
+    JSON_ASSERT(std::isfinite(value));
+    JSON_ASSERT(value > 0);
+
+    // If the neighbors (and boundaries) of 'value' are always computed for double-precision
+    // numbers, all float's can be recovered using strtod (and strtof). However, the resulting
+    // decimal representations are not exactly "short".
+    //
+    // The documentation for 'std::to_chars' (https://en.cppreference.com/w/cpp/utility/to_chars)
+    // says "value is converted to a string as if by std::sprintf in the default ("C") locale"
+    // and since sprintf promotes floats to doubles, I think this is exactly what 'std::to_chars'
+    // does.
+    // On the other hand, the documentation for 'std::to_chars' requires that "parsing the
+    // representation using the corresponding std::from_chars function recovers value exactly". That
+    // indicates that single precision floating-point numbers should be recovered using
+    // 'std::strtof'.
+    //
+    // NB: If the neighbors are computed for single-precision numbers, there is a single float
+    //     (7.0385307e-26f) which can't be recovered using strtod. The resulting double precision
+    //     value is off by 1 ulp.
+#if 0 // NOLINT(readability-avoid-unconditional-preprocessor-if)
+    const boundaries w = compute_boundaries(static_cast<double>(value));
+#else
+    const boundaries w = compute_boundaries(value);
+#endif
+
+    grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus);
+}
+
+/*!
+@brief appends a decimal representation of e to buf
+@return a pointer to the element following the exponent.
+@pre -1000 < e < 1000
+*/
+JSON_HEDLEY_NON_NULL(1)
+JSON_HEDLEY_RETURNS_NON_NULL
+inline char* append_exponent(char* buf, int e)
+{
+    JSON_ASSERT(e > -1000);
+    JSON_ASSERT(e <  1000);
+
+    if (e < 0)
+    {
+        e = -e;
+        *buf++ = '-';
+    }
+    else
+    {
+        *buf++ = '+';
+    }
+
+    auto k = static_cast<std::uint32_t>(e);
+    if (k < 10)
+    {
+        // Always print at least two digits in the exponent.
+        // This is for compatibility with printf("%g").
+        *buf++ = '0';
+        *buf++ = static_cast<char>('0' + k);
+    }
+    else if (k < 100)
+    {
+        *buf++ = static_cast<char>('0' + (k / 10));
+        k %= 10;
+        *buf++ = static_cast<char>('0' + k);
+    }
+    else
+    {
+        *buf++ = static_cast<char>('0' + (k / 100));
+        k %= 100;
+        *buf++ = static_cast<char>('0' + (k / 10));
+        k %= 10;
+        *buf++ = static_cast<char>('0' + k);
+    }
+
+    return buf;
+}
+
+/*!
+@brief prettify v = buf * 10^decimal_exponent
+
+If v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point
+notation. Otherwise it will be printed in exponential notation.
+
+@pre min_exp < 0
+@pre max_exp > 0
+*/
+JSON_HEDLEY_NON_NULL(1)
+JSON_HEDLEY_RETURNS_NON_NULL
+inline char* format_buffer(char* buf, int len, int decimal_exponent,
+                           int min_exp, int max_exp)
+{
+    JSON_ASSERT(min_exp < 0);
+    JSON_ASSERT(max_exp > 0);
+
+    const int k = len;
+    const int n = len + decimal_exponent;
+
+    // v = buf * 10^(n-k)
+    // k is the length of the buffer (number of decimal digits)
+    // n is the position of the decimal point relative to the start of the buffer.
+
+    if (k <= n && n <= max_exp)
+    {
+        // digits[000]
+        // len <= max_exp + 2
+
+        std::memset(buf + k, '0', static_cast<size_t>(n) - static_cast<size_t>(k));
+        // Make it look like a floating-point number (#362, #378)
+        buf[n + 0] = '.';
+        buf[n + 1] = '0';
+        return buf + (static_cast<size_t>(n) + 2);
+    }
+
+    if (0 < n && n <= max_exp)
+    {
+        // dig.its
+        // len <= max_digits10 + 1
+
+        JSON_ASSERT(k > n);
+
+        std::memmove(buf + (static_cast<size_t>(n) + 1), buf + n, static_cast<size_t>(k) - static_cast<size_t>(n));
+        buf[n] = '.';
+        return buf + (static_cast<size_t>(k) + 1U);
+    }
+
+    if (min_exp < n && n <= 0)
+    {
+        // 0.[000]digits
+        // len <= 2 + (-min_exp - 1) + max_digits10
+
+        std::memmove(buf + (2 + static_cast<size_t>(-n)), buf, static_cast<size_t>(k));
+        buf[0] = '0';
+        buf[1] = '.';
+        std::memset(buf + 2, '0', static_cast<size_t>(-n));
+        return buf + (2U + static_cast<size_t>(-n) + static_cast<size_t>(k));
+    }
+
+    if (k == 1)
+    {
+        // dE+123
+        // len <= 1 + 5
+
+        buf += 1;
+    }
+    else
+    {
+        // d.igitsE+123
+        // len <= max_digits10 + 1 + 5
+
+        std::memmove(buf + 2, buf + 1, static_cast<size_t>(k) - 1);
+        buf[1] = '.';
+        buf += 1 + static_cast<size_t>(k);
+    }
+
+    *buf++ = 'e';
+    return append_exponent(buf, n - 1);
+}
+
+}  // namespace dtoa_impl
+
+/*!
+@brief generates a decimal representation of the floating-point number value in [first, last).
+
+The format of the resulting decimal representation is similar to printf's %g
+format. Returns an iterator pointing past-the-end of the decimal representation.
+
+@note The input number must be finite, i.e. NaN's and Inf's are not supported.
+@note The buffer must be large enough.
+@note The result is NOT null-terminated.
+*/
+template<typename FloatType>
+JSON_HEDLEY_NON_NULL(1, 2)
+JSON_HEDLEY_RETURNS_NON_NULL
+char* to_chars(char* first, const char* last, FloatType value)
+{
+    static_cast<void>(last); // maybe unused - fix warning
+    JSON_ASSERT(std::isfinite(value));
+
+    // Use signbit(value) instead of (value < 0) since signbit works for -0.
+    if (std::signbit(value))
+    {
+        value = -value;
+        *first++ = '-';
+    }
+
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+    if (value == 0) // +-0
+    {
+        *first++ = '0';
+        // Make it look like a floating-point number (#362, #378)
+        *first++ = '.';
+        *first++ = '0';
+        return first;
+    }
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+
+    JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10);
+
+    // Compute v = buffer * 10^decimal_exponent.
+    // The decimal digits are stored in the buffer, which needs to be interpreted
+    // as an unsigned decimal integer.
+    // len is the length of the buffer, i.e. the number of decimal digits.
+    int len = 0;
+    int decimal_exponent = 0;
+    dtoa_impl::grisu2(first, len, decimal_exponent, value);
+
+    JSON_ASSERT(len <= std::numeric_limits<FloatType>::max_digits10);
+
+    // Format the buffer like printf("%.*g", prec, value)
+    constexpr int kMinExp = -4;
+    // Use digits10 here to increase compatibility with version 2.
+    constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10;
+
+    JSON_ASSERT(last - first >= kMaxExp + 2);
+    JSON_ASSERT(last - first >= 2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10);
+    JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10 + 6);
+
+    return dtoa_impl::format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp);
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/output/binary_writer.hpp>
+
+// #include <nlohmann/detail/output/output_adapters.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+///////////////////
+// serialization //
+///////////////////
+
+/// how to treat decoding errors
+enum class error_handler_t
+{
+    strict,  ///< throw a type_error exception in case of invalid UTF-8
+    replace, ///< replace invalid UTF-8 sequences with U+FFFD
+    ignore   ///< ignore invalid UTF-8 sequences
+};
+
+template<typename BasicJsonType>
+class serializer
+{
+    using string_t = typename BasicJsonType::string_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using binary_char_t = typename BasicJsonType::binary_t::value_type;
+    static constexpr std::uint8_t UTF8_ACCEPT = 0;
+    static constexpr std::uint8_t UTF8_REJECT = 1;
+
+  public:
+    /*!
+    @param[in] s  output stream to serialize to
+    @param[in] ichar  indentation character to use
+    @param[in] error_handler_  how to react on decoding errors
+    */
+    serializer(output_adapter_t<char> s, const char ichar,
+               error_handler_t error_handler_ = error_handler_t::strict)
+        : o(std::move(s))
+        , loc(std::localeconv())
+        , thousands_sep(loc->thousands_sep == nullptr ? '\0' : std::char_traits<char>::to_char_type(* (loc->thousands_sep)))
+        , decimal_point(loc->decimal_point == nullptr ? '\0' : std::char_traits<char>::to_char_type(* (loc->decimal_point)))
+        , indent_char(ichar)
+        , indent_string(512, indent_char)
+        , error_handler(error_handler_)
+    {}
+
+    // delete because of pointer members
+    serializer(const serializer&) = delete;
+    serializer& operator=(const serializer&) = delete;
+    serializer(serializer&&) = delete;
+    serializer& operator=(serializer&&) = delete;
+    ~serializer() = default;
+
+    /*!
+    @brief internal implementation of the serialization function
+
+    This function is called by the public member function dump and organizes
+    the serialization internally. The indentation level is propagated as
+    additional parameter. In case of arrays and objects, the function is
+    called recursively.
+
+    - strings and object keys are escaped using `escape_string()`
+    - integer numbers are converted implicitly via `operator<<`
+    - floating-point numbers are converted to a string using `"%g"` format
+    - binary values are serialized as objects containing the subtype and the
+      byte array
+
+    @param[in] val               value to serialize
+    @param[in] pretty_print      whether the output shall be pretty-printed
+    @param[in] ensure_ascii If @a ensure_ascii is true, all non-ASCII characters
+    in the output are escaped with `\uXXXX` sequences, and the result consists
+    of ASCII characters only.
+    @param[in] indent_step       the indent level
+    @param[in] current_indent    the current indent level (only used internally)
+    */
+    void dump(const BasicJsonType& val,
+              const bool pretty_print,
+              const bool ensure_ascii,
+              const unsigned int indent_step,
+              const unsigned int current_indent = 0)
+    {
+        switch (val.m_data.m_type)
+        {
+            case value_t::object:
+            {
+                if (val.m_data.m_value.object->empty())
+                {
+                    o->write_characters("{}", 2);
+                    return;
+                }
+
+                if (pretty_print)
+                {
+                    o->write_characters("{\n", 2);
+
+                    // variable to hold indentation for recursive calls
+                    const auto new_indent = current_indent + indent_step;
+                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))
+                    {
+                        indent_string.resize(indent_string.size() * 2, ' ');
+                    }
+
+                    // first n-1 elements
+                    auto i = val.m_data.m_value.object->cbegin();
+                    for (std::size_t cnt = 0; cnt < val.m_data.m_value.object->size() - 1; ++cnt, ++i)
+                    {
+                        o->write_characters(indent_string.c_str(), new_indent);
+                        o->write_character('\"');
+                        dump_escaped(i->first, ensure_ascii);
+                        o->write_characters("\": ", 3);
+                        dump(i->second, true, ensure_ascii, indent_step, new_indent);
+                        o->write_characters(",\n", 2);
+                    }
+
+                    // last element
+                    JSON_ASSERT(i != val.m_data.m_value.object->cend());
+                    JSON_ASSERT(std::next(i) == val.m_data.m_value.object->cend());
+                    o->write_characters(indent_string.c_str(), new_indent);
+                    o->write_character('\"');
+                    dump_escaped(i->first, ensure_ascii);
+                    o->write_characters("\": ", 3);
+                    dump(i->second, true, ensure_ascii, indent_step, new_indent);
+
+                    o->write_character('\n');
+                    o->write_characters(indent_string.c_str(), current_indent);
+                    o->write_character('}');
+                }
+                else
+                {
+                    o->write_character('{');
+
+                    // first n-1 elements
+                    auto i = val.m_data.m_value.object->cbegin();
+                    for (std::size_t cnt = 0; cnt < val.m_data.m_value.object->size() - 1; ++cnt, ++i)
+                    {
+                        o->write_character('\"');
+                        dump_escaped(i->first, ensure_ascii);
+                        o->write_characters("\":", 2);
+                        dump(i->second, false, ensure_ascii, indent_step, current_indent);
+                        o->write_character(',');
+                    }
+
+                    // last element
+                    JSON_ASSERT(i != val.m_data.m_value.object->cend());
+                    JSON_ASSERT(std::next(i) == val.m_data.m_value.object->cend());
+                    o->write_character('\"');
+                    dump_escaped(i->first, ensure_ascii);
+                    o->write_characters("\":", 2);
+                    dump(i->second, false, ensure_ascii, indent_step, current_indent);
+
+                    o->write_character('}');
+                }
+
+                return;
+            }
+
+            case value_t::array:
+            {
+                if (val.m_data.m_value.array->empty())
+                {
+                    o->write_characters("[]", 2);
+                    return;
+                }
+
+                if (pretty_print)
+                {
+                    o->write_characters("[\n", 2);
+
+                    // variable to hold indentation for recursive calls
+                    const auto new_indent = current_indent + indent_step;
+                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))
+                    {
+                        indent_string.resize(indent_string.size() * 2, ' ');
+                    }
+
+                    // first n-1 elements
+                    for (auto i = val.m_data.m_value.array->cbegin();
+                            i != val.m_data.m_value.array->cend() - 1; ++i)
+                    {
+                        o->write_characters(indent_string.c_str(), new_indent);
+                        dump(*i, true, ensure_ascii, indent_step, new_indent);
+                        o->write_characters(",\n", 2);
+                    }
+
+                    // last element
+                    JSON_ASSERT(!val.m_data.m_value.array->empty());
+                    o->write_characters(indent_string.c_str(), new_indent);
+                    dump(val.m_data.m_value.array->back(), true, ensure_ascii, indent_step, new_indent);
+
+                    o->write_character('\n');
+                    o->write_characters(indent_string.c_str(), current_indent);
+                    o->write_character(']');
+                }
+                else
+                {
+                    o->write_character('[');
+
+                    // first n-1 elements
+                    for (auto i = val.m_data.m_value.array->cbegin();
+                            i != val.m_data.m_value.array->cend() - 1; ++i)
+                    {
+                        dump(*i, false, ensure_ascii, indent_step, current_indent);
+                        o->write_character(',');
+                    }
+
+                    // last element
+                    JSON_ASSERT(!val.m_data.m_value.array->empty());
+                    dump(val.m_data.m_value.array->back(), false, ensure_ascii, indent_step, current_indent);
+
+                    o->write_character(']');
+                }
+
+                return;
+            }
+
+            case value_t::string:
+            {
+                o->write_character('\"');
+                dump_escaped(*val.m_data.m_value.string, ensure_ascii);
+                o->write_character('\"');
+                return;
+            }
+
+            case value_t::binary:
+            {
+                if (pretty_print)
+                {
+                    o->write_characters("{\n", 2);
+
+                    // variable to hold indentation for recursive calls
+                    const auto new_indent = current_indent + indent_step;
+                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))
+                    {
+                        indent_string.resize(indent_string.size() * 2, ' ');
+                    }
+
+                    o->write_characters(indent_string.c_str(), new_indent);
+
+                    o->write_characters("\"bytes\": [", 10);
+
+                    if (!val.m_data.m_value.binary->empty())
+                    {
+                        for (auto i = val.m_data.m_value.binary->cbegin();
+                                i != val.m_data.m_value.binary->cend() - 1; ++i)
+                        {
+                            dump_integer(*i);
+                            o->write_characters(", ", 2);
+                        }
+                        dump_integer(val.m_data.m_value.binary->back());
+                    }
+
+                    o->write_characters("],\n", 3);
+                    o->write_characters(indent_string.c_str(), new_indent);
+
+                    o->write_characters("\"subtype\": ", 11);
+                    if (val.m_data.m_value.binary->has_subtype())
+                    {
+                        dump_integer(val.m_data.m_value.binary->subtype());
+                    }
+                    else
+                    {
+                        o->write_characters("null", 4);
+                    }
+                    o->write_character('\n');
+                    o->write_characters(indent_string.c_str(), current_indent);
+                    o->write_character('}');
+                }
+                else
+                {
+                    o->write_characters("{\"bytes\":[", 10);
+
+                    if (!val.m_data.m_value.binary->empty())
+                    {
+                        for (auto i = val.m_data.m_value.binary->cbegin();
+                                i != val.m_data.m_value.binary->cend() - 1; ++i)
+                        {
+                            dump_integer(*i);
+                            o->write_character(',');
+                        }
+                        dump_integer(val.m_data.m_value.binary->back());
+                    }
+
+                    o->write_characters("],\"subtype\":", 12);
+                    if (val.m_data.m_value.binary->has_subtype())
+                    {
+                        dump_integer(val.m_data.m_value.binary->subtype());
+                        o->write_character('}');
+                    }
+                    else
+                    {
+                        o->write_characters("null}", 5);
+                    }
+                }
+                return;
+            }
+
+            case value_t::boolean:
+            {
+                if (val.m_data.m_value.boolean)
+                {
+                    o->write_characters("true", 4);
+                }
+                else
+                {
+                    o->write_characters("false", 5);
+                }
+                return;
+            }
+
+            case value_t::number_integer:
+            {
+                dump_integer(val.m_data.m_value.number_integer);
+                return;
+            }
+
+            case value_t::number_unsigned:
+            {
+                dump_integer(val.m_data.m_value.number_unsigned);
+                return;
+            }
+
+            case value_t::number_float:
+            {
+                dump_float(val.m_data.m_value.number_float);
+                return;
+            }
+
+            case value_t::discarded:
+            {
+                o->write_characters("<discarded>", 11);
+                return;
+            }
+
+            case value_t::null:
+            {
+                o->write_characters("null", 4);
+                return;
+            }
+
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /*!
+    @brief dump escaped string
+
+    Escape a string by replacing certain special characters by a sequence of an
+    escape character (backslash) and another character and other control
+    characters by a sequence of "\u" followed by a four-digit hex
+    representation. The escaped string is written to output stream @a o.
+
+    @param[in] s  the string to escape
+    @param[in] ensure_ascii  whether to escape non-ASCII characters with
+                             \uXXXX sequences
+
+    @complexity Linear in the length of string @a s.
+    */
+    void dump_escaped(const string_t& s, const bool ensure_ascii)
+    {
+        std::uint32_t codepoint{};
+        std::uint8_t state = UTF8_ACCEPT;
+        std::size_t bytes = 0;  // number of bytes written to string_buffer
+
+        // number of bytes written at the point of the last valid byte
+        std::size_t bytes_after_last_accept = 0;
+        std::size_t undumped_chars = 0;
+
+        for (std::size_t i = 0; i < s.size(); ++i)
+        {
+            const auto byte = static_cast<std::uint8_t>(s[i]);
+
+            switch (decode(state, codepoint, byte))
+            {
+                case UTF8_ACCEPT:  // decode found a new code point
+                {
+                    switch (codepoint)
+                    {
+                        case 0x08: // backspace
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'b';
+                            break;
+                        }
+
+                        case 0x09: // horizontal tab
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 't';
+                            break;
+                        }
+
+                        case 0x0A: // newline
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'n';
+                            break;
+                        }
+
+                        case 0x0C: // formfeed
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'f';
+                            break;
+                        }
+
+                        case 0x0D: // carriage return
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'r';
+                            break;
+                        }
+
+                        case 0x22: // quotation mark
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = '\"';
+                            break;
+                        }
+
+                        case 0x5C: // reverse solidus
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = '\\';
+                            break;
+                        }
+
+                        default:
+                        {
+                            // escape control characters (0x00..0x1F) or, if
+                            // ensure_ascii parameter is used, non-ASCII characters
+                            if ((codepoint <= 0x1F) || (ensure_ascii && (codepoint >= 0x7F)))
+                            {
+                                if (codepoint <= 0xFFFF)
+                                {
+                                    // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                                    static_cast<void>((std::snprintf)(string_buffer.data() + bytes, 7, "\\u%04x",
+                                                                      static_cast<std::uint16_t>(codepoint)));
+                                    bytes += 6;
+                                }
+                                else
+                                {
+                                    // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                                    static_cast<void>((std::snprintf)(string_buffer.data() + bytes, 13, "\\u%04x\\u%04x",
+                                                                      static_cast<std::uint16_t>(0xD7C0u + (codepoint >> 10u)),
+                                                                      static_cast<std::uint16_t>(0xDC00u + (codepoint & 0x3FFu))));
+                                    bytes += 12;
+                                }
+                            }
+                            else
+                            {
+                                // copy byte to buffer (all previous bytes
+                                // been copied have in default case above)
+                                string_buffer[bytes++] = s[i];
+                            }
+                            break;
+                        }
+                    }
+
+                    // write buffer and reset index; there must be 13 bytes
+                    // left, as this is the maximal number of bytes to be
+                    // written ("\uxxxx\uxxxx\0") for one code point
+                    if (string_buffer.size() - bytes < 13)
+                    {
+                        o->write_characters(string_buffer.data(), bytes);
+                        bytes = 0;
+                    }
+
+                    // remember the byte position of this accept
+                    bytes_after_last_accept = bytes;
+                    undumped_chars = 0;
+                    break;
+                }
+
+                case UTF8_REJECT:  // decode found invalid UTF-8 byte
+                {
+                    switch (error_handler)
+                    {
+                        case error_handler_t::strict:
+                        {
+                            JSON_THROW(type_error::create(316, concat("invalid UTF-8 byte at index ", std::to_string(i), ": 0x", hex_bytes(byte | 0)), nullptr));
+                        }
+
+                        case error_handler_t::ignore:
+                        case error_handler_t::replace:
+                        {
+                            // in case we saw this character the first time, we
+                            // would like to read it again, because the byte
+                            // may be OK for itself, but just not OK for the
+                            // previous sequence
+                            if (undumped_chars > 0)
+                            {
+                                --i;
+                            }
+
+                            // reset length buffer to the last accepted index;
+                            // thus removing/ignoring the invalid characters
+                            bytes = bytes_after_last_accept;
+
+                            if (error_handler == error_handler_t::replace)
+                            {
+                                // add a replacement character
+                                if (ensure_ascii)
+                                {
+                                    string_buffer[bytes++] = '\\';
+                                    string_buffer[bytes++] = 'u';
+                                    string_buffer[bytes++] = 'f';
+                                    string_buffer[bytes++] = 'f';
+                                    string_buffer[bytes++] = 'f';
+                                    string_buffer[bytes++] = 'd';
+                                }
+                                else
+                                {
+                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\xEF');
+                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\xBF');
+                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\xBD');
+                                }
+
+                                // write buffer and reset index; there must be 13 bytes
+                                // left, as this is the maximal number of bytes to be
+                                // written ("\uxxxx\uxxxx\0") for one code point
+                                if (string_buffer.size() - bytes < 13)
+                                {
+                                    o->write_characters(string_buffer.data(), bytes);
+                                    bytes = 0;
+                                }
+
+                                bytes_after_last_accept = bytes;
+                            }
+
+                            undumped_chars = 0;
+
+                            // continue processing the string
+                            state = UTF8_ACCEPT;
+                            break;
+                        }
+
+                        default:            // LCOV_EXCL_LINE
+                            JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+                    }
+                    break;
+                }
+
+                default:  // decode found yet incomplete multi-byte code point
+                {
+                    if (!ensure_ascii)
+                    {
+                        // code point will not be escaped - copy byte to buffer
+                        string_buffer[bytes++] = s[i];
+                    }
+                    ++undumped_chars;
+                    break;
+                }
+            }
+        }
+
+        // we finished processing the string
+        if (JSON_HEDLEY_LIKELY(state == UTF8_ACCEPT))
+        {
+            // write buffer
+            if (bytes > 0)
+            {
+                o->write_characters(string_buffer.data(), bytes);
+            }
+        }
+        else
+        {
+            // we finish reading, but do not accept: string was incomplete
+            switch (error_handler)
+            {
+                case error_handler_t::strict:
+                {
+                    JSON_THROW(type_error::create(316, concat("incomplete UTF-8 string; last byte: 0x", hex_bytes(static_cast<std::uint8_t>(s.back() | 0))), nullptr));
+                }
+
+                case error_handler_t::ignore:
+                {
+                    // write all accepted bytes
+                    o->write_characters(string_buffer.data(), bytes_after_last_accept);
+                    break;
+                }
+
+                case error_handler_t::replace:
+                {
+                    // write all accepted bytes
+                    o->write_characters(string_buffer.data(), bytes_after_last_accept);
+                    // add a replacement character
+                    if (ensure_ascii)
+                    {
+                        o->write_characters("\\ufffd", 6);
+                    }
+                    else
+                    {
+                        o->write_characters("\xEF\xBF\xBD", 3);
+                    }
+                    break;
+                }
+
+                default:            // LCOV_EXCL_LINE
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+            }
+        }
+    }
+
+  private:
+    /*!
+    @brief count digits
+
+    Count the number of decimal (base 10) digits for an input unsigned integer.
+
+    @param[in] x  unsigned integer number to count its digits
+    @return    number of decimal digits
+    */
+    unsigned int count_digits(number_unsigned_t x) noexcept
+    {
+        unsigned int n_digits = 1;
+        for (;;)
+        {
+            if (x < 10)
+            {
+                return n_digits;
+            }
+            if (x < 100)
+            {
+                return n_digits + 1;
+            }
+            if (x < 1000)
+            {
+                return n_digits + 2;
+            }
+            if (x < 10000)
+            {
+                return n_digits + 3;
+            }
+            x = x / 10000u;
+            n_digits += 4;
+        }
+    }
+
+    /*!
+     * @brief convert a byte to a uppercase hex representation
+     * @param[in] byte byte to represent
+     * @return representation ("00".."FF")
+     */
+    static std::string hex_bytes(std::uint8_t byte)
+    {
+        std::string result = "FF";
+        constexpr const char* nibble_to_hex = "0123456789ABCDEF";
+        result[0] = nibble_to_hex[byte / 16];
+        result[1] = nibble_to_hex[byte % 16];
+        return result;
+    }
+
+    // templates to avoid warnings about useless casts
+    template <typename NumberType, enable_if_t<std::is_signed<NumberType>::value, int> = 0>
+    bool is_negative_number(NumberType x)
+    {
+        return x < 0;
+    }
+
+    template < typename NumberType, enable_if_t <std::is_unsigned<NumberType>::value, int > = 0 >
+    bool is_negative_number(NumberType /*unused*/)
+    {
+        return false;
+    }
+
+    /*!
+    @brief dump an integer
+
+    Dump a given integer to output stream @a o. Works internally with
+    @a number_buffer.
+
+    @param[in] x  integer number (signed or unsigned) to dump
+    @tparam NumberType either @a number_integer_t or @a number_unsigned_t
+    */
+    template < typename NumberType, detail::enable_if_t <
+                   std::is_integral<NumberType>::value ||
+                   std::is_same<NumberType, number_unsigned_t>::value ||
+                   std::is_same<NumberType, number_integer_t>::value ||
+                   std::is_same<NumberType, binary_char_t>::value,
+                   int > = 0 >
+    void dump_integer(NumberType x)
+    {
+        static constexpr std::array<std::array<char, 2>, 100> digits_to_99
+        {
+            {
+                {{'0', '0'}}, {{'0', '1'}}, {{'0', '2'}}, {{'0', '3'}}, {{'0', '4'}}, {{'0', '5'}}, {{'0', '6'}}, {{'0', '7'}}, {{'0', '8'}}, {{'0', '9'}},
+                {{'1', '0'}}, {{'1', '1'}}, {{'1', '2'}}, {{'1', '3'}}, {{'1', '4'}}, {{'1', '5'}}, {{'1', '6'}}, {{'1', '7'}}, {{'1', '8'}}, {{'1', '9'}},
+                {{'2', '0'}}, {{'2', '1'}}, {{'2', '2'}}, {{'2', '3'}}, {{'2', '4'}}, {{'2', '5'}}, {{'2', '6'}}, {{'2', '7'}}, {{'2', '8'}}, {{'2', '9'}},
+                {{'3', '0'}}, {{'3', '1'}}, {{'3', '2'}}, {{'3', '3'}}, {{'3', '4'}}, {{'3', '5'}}, {{'3', '6'}}, {{'3', '7'}}, {{'3', '8'}}, {{'3', '9'}},
+                {{'4', '0'}}, {{'4', '1'}}, {{'4', '2'}}, {{'4', '3'}}, {{'4', '4'}}, {{'4', '5'}}, {{'4', '6'}}, {{'4', '7'}}, {{'4', '8'}}, {{'4', '9'}},
+                {{'5', '0'}}, {{'5', '1'}}, {{'5', '2'}}, {{'5', '3'}}, {{'5', '4'}}, {{'5', '5'}}, {{'5', '6'}}, {{'5', '7'}}, {{'5', '8'}}, {{'5', '9'}},
+                {{'6', '0'}}, {{'6', '1'}}, {{'6', '2'}}, {{'6', '3'}}, {{'6', '4'}}, {{'6', '5'}}, {{'6', '6'}}, {{'6', '7'}}, {{'6', '8'}}, {{'6', '9'}},
+                {{'7', '0'}}, {{'7', '1'}}, {{'7', '2'}}, {{'7', '3'}}, {{'7', '4'}}, {{'7', '5'}}, {{'7', '6'}}, {{'7', '7'}}, {{'7', '8'}}, {{'7', '9'}},
+                {{'8', '0'}}, {{'8', '1'}}, {{'8', '2'}}, {{'8', '3'}}, {{'8', '4'}}, {{'8', '5'}}, {{'8', '6'}}, {{'8', '7'}}, {{'8', '8'}}, {{'8', '9'}},
+                {{'9', '0'}}, {{'9', '1'}}, {{'9', '2'}}, {{'9', '3'}}, {{'9', '4'}}, {{'9', '5'}}, {{'9', '6'}}, {{'9', '7'}}, {{'9', '8'}}, {{'9', '9'}},
+            }
+        };
+
+        // special case for "0"
+        if (x == 0)
+        {
+            o->write_character('0');
+            return;
+        }
+
+        // use a pointer to fill the buffer
+        auto buffer_ptr = number_buffer.begin(); // NOLINT(llvm-qualified-auto,readability-qualified-auto,cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+
+        number_unsigned_t abs_value;
+
+        unsigned int n_chars{};
+
+        if (is_negative_number(x))
+        {
+            *buffer_ptr = '-';
+            abs_value = remove_sign(static_cast<number_integer_t>(x));
+
+            // account one more byte for the minus sign
+            n_chars = 1 + count_digits(abs_value);
+        }
+        else
+        {
+            abs_value = static_cast<number_unsigned_t>(x);
+            n_chars = count_digits(abs_value);
+        }
+
+        // spare 1 byte for '\0'
+        JSON_ASSERT(n_chars < number_buffer.size() - 1);
+
+        // jump to the end to generate the string from backward,
+        // so we later avoid reversing the result
+        buffer_ptr += n_chars;
+
+        // Fast int2ascii implementation inspired by "Fastware" talk by Andrei Alexandrescu
+        // See: https://www.youtube.com/watch?v=o4-CwDo2zpg
+        while (abs_value >= 100)
+        {
+            const auto digits_index = static_cast<unsigned>((abs_value % 100));
+            abs_value /= 100;
+            *(--buffer_ptr) = digits_to_99[digits_index][1];
+            *(--buffer_ptr) = digits_to_99[digits_index][0];
+        }
+
+        if (abs_value >= 10)
+        {
+            const auto digits_index = static_cast<unsigned>(abs_value);
+            *(--buffer_ptr) = digits_to_99[digits_index][1];
+            *(--buffer_ptr) = digits_to_99[digits_index][0];
+        }
+        else
+        {
+            *(--buffer_ptr) = static_cast<char>('0' + abs_value);
+        }
+
+        o->write_characters(number_buffer.data(), n_chars);
+    }
+
+    /*!
+    @brief dump a floating-point number
+
+    Dump a given floating-point number to output stream @a o. Works internally
+    with @a number_buffer.
+
+    @param[in] x  floating-point number to dump
+    */
+    void dump_float(number_float_t x)
+    {
+        // NaN / inf
+        if (!std::isfinite(x))
+        {
+            o->write_characters("null", 4);
+            return;
+        }
+
+        // If number_float_t is an IEEE-754 single or double precision number,
+        // use the Grisu2 algorithm to produce short numbers which are
+        // guaranteed to round-trip, using strtof and strtod, resp.
+        //
+        // NB: The test below works if <long double> == <double>.
+        static constexpr bool is_ieee_single_or_double
+            = (std::numeric_limits<number_float_t>::is_iec559 && std::numeric_limits<number_float_t>::digits == 24 && std::numeric_limits<number_float_t>::max_exponent == 128) ||
+              (std::numeric_limits<number_float_t>::is_iec559 && std::numeric_limits<number_float_t>::digits == 53 && std::numeric_limits<number_float_t>::max_exponent == 1024);
+
+        dump_float(x, std::integral_constant<bool, is_ieee_single_or_double>());
+    }
+
+    void dump_float(number_float_t x, std::true_type /*is_ieee_single_or_double*/)
+    {
+        auto* begin = number_buffer.data();
+        auto* end = ::nlohmann::detail::to_chars(begin, begin + number_buffer.size(), x);
+
+        o->write_characters(begin, static_cast<size_t>(end - begin));
+    }
+
+    void dump_float(number_float_t x, std::false_type /*is_ieee_single_or_double*/)
+    {
+        // get number of digits for a float -> text -> float round-trip
+        static constexpr auto d = std::numeric_limits<number_float_t>::max_digits10;
+
+        // the actual conversion
+        // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+        std::ptrdiff_t len = (std::snprintf)(number_buffer.data(), number_buffer.size(), "%.*g", d, x);
+
+        // negative value indicates an error
+        JSON_ASSERT(len > 0);
+        // check if buffer was large enough
+        JSON_ASSERT(static_cast<std::size_t>(len) < number_buffer.size());
+
+        // erase thousands separator
+        if (thousands_sep != '\0')
+        {
+            // NOLINTNEXTLINE(readability-qualified-auto,llvm-qualified-auto): std::remove returns an iterator, see https://github.com/nlohmann/json/issues/3081
+            const auto end = std::remove(number_buffer.begin(), number_buffer.begin() + len, thousands_sep);
+            std::fill(end, number_buffer.end(), '\0');
+            JSON_ASSERT((end - number_buffer.begin()) <= len);
+            len = (end - number_buffer.begin());
+        }
+
+        // convert decimal point to '.'
+        if (decimal_point != '\0' && decimal_point != '.')
+        {
+            // NOLINTNEXTLINE(readability-qualified-auto,llvm-qualified-auto): std::find returns an iterator, see https://github.com/nlohmann/json/issues/3081
+            const auto dec_pos = std::find(number_buffer.begin(), number_buffer.end(), decimal_point);
+            if (dec_pos != number_buffer.end())
+            {
+                *dec_pos = '.';
+            }
+        }
+
+        o->write_characters(number_buffer.data(), static_cast<std::size_t>(len));
+
+        // determine if we need to append ".0"
+        const bool value_is_int_like =
+            std::none_of(number_buffer.begin(), number_buffer.begin() + len + 1,
+                         [](char c)
+        {
+            return c == '.' || c == 'e';
+        });
+
+        if (value_is_int_like)
+        {
+            o->write_characters(".0", 2);
+        }
+    }
+
+    /*!
+    @brief check whether a string is UTF-8 encoded
+
+    The function checks each byte of a string whether it is UTF-8 encoded. The
+    result of the check is stored in the @a state parameter. The function must
+    be called initially with state 0 (accept). State 1 means the string must
+    be rejected, because the current byte is not allowed. If the string is
+    completely processed, but the state is non-zero, the string ended
+    prematurely; that is, the last byte indicated more bytes should have
+    followed.
+
+    @param[in,out] state  the state of the decoding
+    @param[in,out] codep  codepoint (valid only if resulting state is UTF8_ACCEPT)
+    @param[in] byte       next byte to decode
+    @return               new state
+
+    @note The function has been edited: a std::array is used.
+
+    @copyright Copyright (c) 2008-2009 Bjoern Hoehrmann <bjoern@hoehrmann.de>
+    @sa http://bjoern.hoehrmann.de/utf-8/decoder/dfa/
+    */
+    static std::uint8_t decode(std::uint8_t& state, std::uint32_t& codep, const std::uint8_t byte) noexcept
+    {
+        static const std::array<std::uint8_t, 400> utf8d =
+        {
+            {
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 00..1F
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 20..3F
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 40..5F
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 60..7F
+                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, // 80..9F
+                7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, // A0..BF
+                8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // C0..DF
+                0xA, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x4, 0x3, 0x3, // E0..EF
+                0xB, 0x6, 0x6, 0x6, 0x5, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, // F0..FF
+                0x0, 0x1, 0x2, 0x3, 0x5, 0x8, 0x7, 0x1, 0x1, 0x1, 0x4, 0x6, 0x1, 0x1, 0x1, 0x1, // s0..s0
+                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, // s1..s2
+                1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, // s3..s4
+                1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, // s5..s6
+                1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 // s7..s8
+            }
+        };
+
+        JSON_ASSERT(byte < utf8d.size());
+        const std::uint8_t type = utf8d[byte];
+
+        codep = (state != UTF8_ACCEPT)
+                ? (byte & 0x3fu) | (codep << 6u)
+                : (0xFFu >> type) & (byte);
+
+        const std::size_t index = 256u + (static_cast<size_t>(state) * 16u) + static_cast<size_t>(type);
+        JSON_ASSERT(index < utf8d.size());
+        state = utf8d[index];
+        return state;
+    }
+
+    /*
+     * Overload to make the compiler happy while it is instantiating
+     * dump_integer for number_unsigned_t.
+     * Must never be called.
+     */
+    number_unsigned_t remove_sign(number_unsigned_t x)
+    {
+        JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        return x; // LCOV_EXCL_LINE
+    }
+
+    /*
+     * Helper function for dump_integer
+     *
+     * This function takes a negative signed integer and returns its absolute
+     * value as unsigned integer. The plus/minus shuffling is necessary as we can
+     * not directly remove the sign of an arbitrary signed integer as the
+     * absolute values of INT_MIN and INT_MAX are usually not the same. See
+     * #1708 for details.
+     */
+    number_unsigned_t remove_sign(number_integer_t x) noexcept
+    {
+        JSON_ASSERT(x < 0 && x < (std::numeric_limits<number_integer_t>::max)()); // NOLINT(misc-redundant-expression)
+        return static_cast<number_unsigned_t>(-(x + 1)) + 1;
+    }
+
+  private:
+    /// the output of the serializer
+    output_adapter_t<char> o = nullptr;
+
+    /// a (hopefully) large enough character buffer
+    std::array<char, 64> number_buffer{{}};
+
+    /// the locale
+    const std::lconv* loc = nullptr;
+    /// the locale's thousand separator character
+    const char thousands_sep = '\0';
+    /// the locale's decimal point character
+    const char decimal_point = '\0';
+
+    /// string buffer
+    std::array<char, 512> string_buffer{{}};
+
+    /// the indentation character
+    const char indent_char;
+    /// the indentation string
+    string_t indent_string;
+
+    /// error_handler how to react on decoding errors
+    const error_handler_t error_handler;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/value_t.hpp>
+
+// #include <nlohmann/json_fwd.hpp>
+
+// #include <nlohmann/ordered_map.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <functional> // equal_to, less
+#include <initializer_list> // initializer_list
+#include <iterator> // input_iterator_tag, iterator_traits
+#include <memory> // allocator
+#include <stdexcept> // for out_of_range
+#include <type_traits> // enable_if, is_convertible
+#include <utility> // pair
+#include <vector> // vector
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// ordered_map: a minimal map-like container that preserves insertion order
+/// for use within nlohmann::basic_json<ordered_map>
+template <class Key, class T, class IgnoredLess = std::less<Key>,
+          class Allocator = std::allocator<std::pair<const Key, T>>>
+              struct ordered_map : std::vector<std::pair<const Key, T>, Allocator>
+{
+    using key_type = Key;
+    using mapped_type = T;
+    using Container = std::vector<std::pair<const Key, T>, Allocator>;
+    using iterator = typename Container::iterator;
+    using const_iterator = typename Container::const_iterator;
+    using size_type = typename Container::size_type;
+    using value_type = typename Container::value_type;
+#ifdef JSON_HAS_CPP_14
+    using key_compare = std::equal_to<>;
+#else
+    using key_compare = std::equal_to<Key>;
+#endif
+
+    // Explicit constructors instead of `using Container::Container`
+    // otherwise older compilers choke on it (GCC <= 5.5, xcode <= 9.4)
+    ordered_map() noexcept(noexcept(Container())) : Container{} {}
+    explicit ordered_map(const Allocator& alloc) noexcept(noexcept(Container(alloc))) : Container{alloc} {}
+    template <class It>
+    ordered_map(It first, It last, const Allocator& alloc = Allocator())
+        : Container{first, last, alloc} {}
+    ordered_map(std::initializer_list<value_type> init, const Allocator& alloc = Allocator() )
+        : Container{init, alloc} {}
+
+    std::pair<iterator, bool> emplace(const key_type& key, T&& t)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return {it, false};
+            }
+        }
+        Container::emplace_back(key, std::forward<T>(t));
+        return {std::prev(this->end()), true};
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    std::pair<iterator, bool> emplace(KeyType && key, T && t)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return {it, false};
+            }
+        }
+        Container::emplace_back(std::forward<KeyType>(key), std::forward<T>(t));
+        return {std::prev(this->end()), true};
+    }
+
+    T& operator[](const key_type& key)
+    {
+        return emplace(key, T{}).first->second;
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    T & operator[](KeyType && key)
+    {
+        return emplace(std::forward<KeyType>(key), T{}).first->second;
+    }
+
+    const T& operator[](const key_type& key) const
+    {
+        return at(key);
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    const T & operator[](KeyType && key) const
+    {
+        return at(std::forward<KeyType>(key));
+    }
+
+    T& at(const key_type& key)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    T & at(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    const T& at(const key_type& key) const
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    const T & at(KeyType && key) const // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    size_type erase(const key_type& key)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                // Since we cannot move const Keys, re-construct them in place
+                for (auto next = it; ++next != this->end(); ++it)
+                {
+                    it->~value_type(); // Destroy but keep allocation
+                    new (&*it) value_type{std::move(*next)};
+                }
+                Container::pop_back();
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    size_type erase(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                // Since we cannot move const Keys, re-construct them in place
+                for (auto next = it; ++next != this->end(); ++it)
+                {
+                    it->~value_type(); // Destroy but keep allocation
+                    new (&*it) value_type{std::move(*next)};
+                }
+                Container::pop_back();
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    iterator erase(iterator pos)
+    {
+        return erase(pos, std::next(pos));
+    }
+
+    iterator erase(iterator first, iterator last)
+    {
+        if (first == last)
+        {
+            return first;
+        }
+
+        const auto elements_affected = std::distance(first, last);
+        const auto offset = std::distance(Container::begin(), first);
+
+        // This is the start situation. We need to delete elements_affected
+        // elements (3 in this example: e, f, g), and need to return an
+        // iterator past the last deleted element (h in this example).
+        // Note that offset is the distance from the start of the vector
+        // to first. We will need this later.
+
+        // [ a, b, c, d, e, f, g, h, i, j ]
+        //               ^        ^
+        //             first    last
+
+        // Since we cannot move const Keys, we re-construct them in place.
+        // We start at first and re-construct (viz. copy) the elements from
+        // the back of the vector. Example for first iteration:
+
+        //               ,--------.
+        //               v        |   destroy e and re-construct with h
+        // [ a, b, c, d, e, f, g, h, i, j ]
+        //               ^        ^
+        //               it       it + elements_affected
+
+        for (auto it = first; std::next(it, elements_affected) != Container::end(); ++it)
+        {
+            it->~value_type(); // destroy but keep allocation
+            new (&*it) value_type{std::move(*std::next(it, elements_affected))}; // "move" next element to it
+        }
+
+        // [ a, b, c, d, h, i, j, h, i, j ]
+        //               ^        ^
+        //             first    last
+
+        // remove the unneeded elements at the end of the vector
+        Container::resize(this->size() - static_cast<size_type>(elements_affected));
+
+        // [ a, b, c, d, h, i, j ]
+        //               ^        ^
+        //             first    last
+
+        // first is now pointing past the last deleted element, but we cannot
+        // use this iterator, because it may have been invalidated by the
+        // resize call. Instead, we can return begin() + offset.
+        return Container::begin() + offset;
+    }
+
+    size_type count(const key_type& key) const
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    size_type count(KeyType && key) const // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    iterator find(const key_type& key)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it;
+            }
+        }
+        return Container::end();
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    iterator find(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it;
+            }
+        }
+        return Container::end();
+    }
+
+    const_iterator find(const key_type& key) const
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it;
+            }
+        }
+        return Container::end();
+    }
+
+    std::pair<iterator, bool> insert( value_type&& value )
+    {
+        return emplace(value.first, std::move(value.second));
+    }
+
+    std::pair<iterator, bool> insert( const value_type& value )
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, value.first))
+            {
+                return {it, false};
+            }
+        }
+        Container::push_back(value);
+        return {--this->end(), true};
+    }
+
+    template<typename InputIt>
+    using require_input_iter = typename std::enable_if<std::is_convertible<typename std::iterator_traits<InputIt>::iterator_category,
+        std::input_iterator_tag>::value>::type;
+
+    template<typename InputIt, typename = require_input_iter<InputIt>>
+    void insert(InputIt first, InputIt last)
+    {
+        for (auto it = first; it != last; ++it)
+        {
+            insert(*it);
+        }
+    }
+
+private:
+    JSON_NO_UNIQUE_ADDRESS key_compare m_compare = key_compare();
+};
+
+NLOHMANN_JSON_NAMESPACE_END
+
+
+#if defined(JSON_HAS_CPP_17)
+    #if JSON_HAS_STATIC_RTTI
+        #include <any>
+    #endif
+    #include <string_view>
+#endif
+
+/*!
+@brief namespace for Niels Lohmann
+@see https://github.com/nlohmann
+@since version 1.0.0
+*/
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/*!
+@brief a class to store JSON values
+
+@internal
+@invariant The member variables @a m_value and @a m_type have the following
+relationship:
+- If `m_type == value_t::object`, then `m_value.object != nullptr`.
+- If `m_type == value_t::array`, then `m_value.array != nullptr`.
+- If `m_type == value_t::string`, then `m_value.string != nullptr`.
+The invariants are checked by member function assert_invariant().
+
+@note ObjectType trick from https://stackoverflow.com/a/9860911
+@endinternal
+
+@since version 1.0.0
+
+@nosubgrouping
+*/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+class basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-special-member-functions)
+    : public ::nlohmann::detail::json_base_class<CustomBaseClass>
+{
+  private:
+    template<detail::value_t> friend struct detail::external_constructor;
+
+    template<typename>
+    friend class ::nlohmann::json_pointer;
+    // can be restored when json_pointer backwards compatibility is removed
+    // friend ::nlohmann::json_pointer<StringType>;
+
+    template<typename BasicJsonType, typename InputType>
+    friend class ::nlohmann::detail::parser;
+    friend ::nlohmann::detail::serializer<basic_json>;
+    template<typename BasicJsonType>
+    friend class ::nlohmann::detail::iter_impl;
+    template<typename BasicJsonType, typename CharType>
+    friend class ::nlohmann::detail::binary_writer;
+    template<typename BasicJsonType, typename InputType, typename SAX>
+    friend class ::nlohmann::detail::binary_reader;
+    template<typename BasicJsonType, typename InputAdapterType>
+    friend class ::nlohmann::detail::json_sax_dom_parser;
+    template<typename BasicJsonType, typename InputAdapterType>
+    friend class ::nlohmann::detail::json_sax_dom_callback_parser;
+    friend class ::nlohmann::detail::exception;
+
+    /// workaround type for MSVC
+    using basic_json_t = NLOHMANN_BASIC_JSON_TPL;
+    using json_base_class_t = ::nlohmann::detail::json_base_class<CustomBaseClass>;
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    // convenience aliases for types residing in namespace detail;
+    using lexer = ::nlohmann::detail::lexer_base<basic_json>;
+
+    template<typename InputAdapterType>
+    static ::nlohmann::detail::parser<basic_json, InputAdapterType> parser(
+        InputAdapterType adapter,
+        detail::parser_callback_t<basic_json>cb = nullptr,
+        const bool allow_exceptions = true,
+        const bool ignore_comments = false
+                                 )
+    {
+        return ::nlohmann::detail::parser<basic_json, InputAdapterType>(std::move(adapter),
+            std::move(cb), allow_exceptions, ignore_comments);
+    }
+
+  private:
+    using primitive_iterator_t = ::nlohmann::detail::primitive_iterator_t;
+    template<typename BasicJsonType>
+    using internal_iterator = ::nlohmann::detail::internal_iterator<BasicJsonType>;
+    template<typename BasicJsonType>
+    using iter_impl = ::nlohmann::detail::iter_impl<BasicJsonType>;
+    template<typename Iterator>
+    using iteration_proxy = ::nlohmann::detail::iteration_proxy<Iterator>;
+    template<typename Base> using json_reverse_iterator = ::nlohmann::detail::json_reverse_iterator<Base>;
+
+    template<typename CharType>
+    using output_adapter_t = ::nlohmann::detail::output_adapter_t<CharType>;
+
+    template<typename InputType>
+    using binary_reader = ::nlohmann::detail::binary_reader<basic_json, InputType>;
+    template<typename CharType> using binary_writer = ::nlohmann::detail::binary_writer<basic_json, CharType>;
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    using serializer = ::nlohmann::detail::serializer<basic_json>;
+
+  public:
+    using value_t = detail::value_t;
+    /// JSON Pointer, see @ref nlohmann::json_pointer
+    using json_pointer = ::nlohmann::json_pointer<StringType>;
+    template<typename T, typename SFINAE>
+    using json_serializer = JSONSerializer<T, SFINAE>;
+    /// how to treat decoding errors
+    using error_handler_t = detail::error_handler_t;
+    /// how to treat CBOR tags
+    using cbor_tag_handler_t = detail::cbor_tag_handler_t;
+    /// how to encode BJData
+    using bjdata_version_t = detail::bjdata_version_t;
+    /// helper type for initializer lists of basic_json values
+    using initializer_list_t = std::initializer_list<detail::json_ref<basic_json>>;
+
+    using input_format_t = detail::input_format_t;
+    /// SAX interface type, see @ref nlohmann::json_sax
+    using json_sax_t = json_sax<basic_json>;
+
+    ////////////////
+    // exceptions //
+    ////////////////
+
+    /// @name exceptions
+    /// Classes to implement user-defined exceptions.
+    /// @{
+
+    using exception = detail::exception;
+    using parse_error = detail::parse_error;
+    using invalid_iterator = detail::invalid_iterator;
+    using type_error = detail::type_error;
+    using out_of_range = detail::out_of_range;
+    using other_error = detail::other_error;
+
+    /// @}
+
+    /////////////////////
+    // container types //
+    /////////////////////
+
+    /// @name container types
+    /// The canonic container types to use @ref basic_json like any other STL
+    /// container.
+    /// @{
+
+    /// the type of elements in a basic_json container
+    using value_type = basic_json;
+
+    /// the type of an element reference
+    using reference = value_type&;
+    /// the type of an element const reference
+    using const_reference = const value_type&;
+
+    /// a type to represent differences between iterators
+    using difference_type = std::ptrdiff_t;
+    /// a type to represent container sizes
+    using size_type = std::size_t;
+
+    /// the allocator type
+    using allocator_type = AllocatorType<basic_json>;
+
+    /// the type of an element pointer
+    using pointer = typename std::allocator_traits<allocator_type>::pointer;
+    /// the type of an element const pointer
+    using const_pointer = typename std::allocator_traits<allocator_type>::const_pointer;
+
+    /// an iterator for a basic_json container
+    using iterator = iter_impl<basic_json>;
+    /// a const iterator for a basic_json container
+    using const_iterator = iter_impl<const basic_json>;
+    /// a reverse iterator for a basic_json container
+    using reverse_iterator = json_reverse_iterator<typename basic_json::iterator>;
+    /// a const reverse iterator for a basic_json container
+    using const_reverse_iterator = json_reverse_iterator<typename basic_json::const_iterator>;
+
+    /// @}
+
+    /// @brief returns the allocator associated with the container
+    /// @sa https://json.nlohmann.me/api/basic_json/get_allocator/
+    static allocator_type get_allocator()
+    {
+        return allocator_type();
+    }
+
+    /// @brief returns version information on the library
+    /// @sa https://json.nlohmann.me/api/basic_json/meta/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json meta()
+    {
+        basic_json result;
+
+        result["copyright"] = "(C) 2013-2025 Niels Lohmann";
+        result["name"] = "JSON for Modern C++";
+        result["url"] = "https://github.com/nlohmann/json";
+        result["version"]["string"] =
+            detail::concat(std::to_string(NLOHMANN_JSON_VERSION_MAJOR), '.',
+                           std::to_string(NLOHMANN_JSON_VERSION_MINOR), '.',
+                           std::to_string(NLOHMANN_JSON_VERSION_PATCH));
+        result["version"]["major"] = NLOHMANN_JSON_VERSION_MAJOR;
+        result["version"]["minor"] = NLOHMANN_JSON_VERSION_MINOR;
+        result["version"]["patch"] = NLOHMANN_JSON_VERSION_PATCH;
+
+#ifdef _WIN32
+        result["platform"] = "win32";
+#elif defined __linux__
+        result["platform"] = "linux";
+#elif defined __APPLE__
+        result["platform"] = "apple";
+#elif defined __unix__
+        result["platform"] = "unix";
+#else
+        result["platform"] = "unknown";
+#endif
+
+#if defined(__ICC) || defined(__INTEL_COMPILER)
+        result["compiler"] = {{"family", "icc"}, {"version", __INTEL_COMPILER}};
+#elif defined(__clang__)
+        result["compiler"] = {{"family", "clang"}, {"version", __clang_version__}};
+#elif defined(__GNUC__) || defined(__GNUG__)
+        result["compiler"] = {{"family", "gcc"}, {"version", detail::concat(
+                    std::to_string(__GNUC__), '.',
+                    std::to_string(__GNUC_MINOR__), '.',
+                    std::to_string(__GNUC_PATCHLEVEL__))
+            }
+        };
+#elif defined(__HP_cc) || defined(__HP_aCC)
+        result["compiler"] = "hp"
+#elif defined(__IBMCPP__)
+        result["compiler"] = {{"family", "ilecpp"}, {"version", __IBMCPP__}};
+#elif defined(_MSC_VER)
+        result["compiler"] = {{"family", "msvc"}, {"version", _MSC_VER}};
+#elif defined(__PGI)
+        result["compiler"] = {{"family", "pgcpp"}, {"version", __PGI}};
+#elif defined(__SUNPRO_CC)
+        result["compiler"] = {{"family", "sunpro"}, {"version", __SUNPRO_CC}};
+#else
+        result["compiler"] = {{"family", "unknown"}, {"version", "unknown"}};
+#endif
+
+#if defined(_MSVC_LANG)
+        result["compiler"]["c++"] = std::to_string(_MSVC_LANG);
+#elif defined(__cplusplus)
+        result["compiler"]["c++"] = std::to_string(__cplusplus);
+#else
+        result["compiler"]["c++"] = "unknown";
+#endif
+        return result;
+    }
+
+    ///////////////////////////
+    // JSON value data types //
+    ///////////////////////////
+
+    /// @name JSON value data types
+    /// The data types to store a JSON value. These types are derived from
+    /// the template arguments passed to class @ref basic_json.
+    /// @{
+
+    /// @brief default object key comparator type
+    /// The actual object key comparator type (@ref object_comparator_t) may be
+    /// different.
+    /// @sa https://json.nlohmann.me/api/basic_json/default_object_comparator_t/
+#if defined(JSON_HAS_CPP_14)
+    // use of transparent comparator avoids unnecessary repeated construction of temporaries
+    // in functions involving lookup by key with types other than object_t::key_type (aka. StringType)
+    using default_object_comparator_t = std::less<>;
+#else
+    using default_object_comparator_t = std::less<StringType>;
+#endif
+
+    /// @brief a type for an object
+    /// @sa https://json.nlohmann.me/api/basic_json/object_t/
+    using object_t = ObjectType<StringType,
+          basic_json,
+          default_object_comparator_t,
+          AllocatorType<std::pair<const StringType,
+          basic_json>>>;
+
+    /// @brief a type for an array
+    /// @sa https://json.nlohmann.me/api/basic_json/array_t/
+    using array_t = ArrayType<basic_json, AllocatorType<basic_json>>;
+
+    /// @brief a type for a string
+    /// @sa https://json.nlohmann.me/api/basic_json/string_t/
+    using string_t = StringType;
+
+    /// @brief a type for a boolean
+    /// @sa https://json.nlohmann.me/api/basic_json/boolean_t/
+    using boolean_t = BooleanType;
+
+    /// @brief a type for a number (integer)
+    /// @sa https://json.nlohmann.me/api/basic_json/number_integer_t/
+    using number_integer_t = NumberIntegerType;
+
+    /// @brief a type for a number (unsigned)
+    /// @sa https://json.nlohmann.me/api/basic_json/number_unsigned_t/
+    using number_unsigned_t = NumberUnsignedType;
+
+    /// @brief a type for a number (floating-point)
+    /// @sa https://json.nlohmann.me/api/basic_json/number_float_t/
+    using number_float_t = NumberFloatType;
+
+    /// @brief a type for a packed binary type
+    /// @sa https://json.nlohmann.me/api/basic_json/binary_t/
+    using binary_t = nlohmann::byte_container_with_subtype<BinaryType>;
+
+    /// @brief object key comparator type
+    /// @sa https://json.nlohmann.me/api/basic_json/object_comparator_t/
+    using object_comparator_t = detail::actual_object_comparator_t<basic_json>;
+
+    /// @}
+
+  private:
+
+    /// helper for exception-safe object creation
+    template<typename T, typename... Args>
+    JSON_HEDLEY_RETURNS_NON_NULL
+    static T* create(Args&& ... args)
+    {
+        AllocatorType<T> alloc;
+        using AllocatorTraits = std::allocator_traits<AllocatorType<T>>;
+
+        auto deleter = [&](T * obj)
+        {
+            AllocatorTraits::deallocate(alloc, obj, 1);
+        };
+        std::unique_ptr<T, decltype(deleter)> obj(AllocatorTraits::allocate(alloc, 1), deleter);
+        AllocatorTraits::construct(alloc, obj.get(), std::forward<Args>(args)...);
+        JSON_ASSERT(obj != nullptr);
+        return obj.release();
+    }
+
+    ////////////////////////
+    // JSON value storage //
+    ////////////////////////
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /*!
+    @brief a JSON value
+
+    The actual storage for a JSON value of the @ref basic_json class. This
+    union combines the different storage types for the JSON value types
+    defined in @ref value_t.
+
+    JSON type | value_t type    | used type
+    --------- | --------------- | ------------------------
+    object    | object          | pointer to @ref object_t
+    array     | array           | pointer to @ref array_t
+    string    | string          | pointer to @ref string_t
+    boolean   | boolean         | @ref boolean_t
+    number    | number_integer  | @ref number_integer_t
+    number    | number_unsigned | @ref number_unsigned_t
+    number    | number_float    | @ref number_float_t
+    binary    | binary          | pointer to @ref binary_t
+    null      | null            | *no value is stored*
+
+    @note Variable-length types (objects, arrays, and strings) are stored as
+    pointers. The size of the union should not exceed 64 bits if the default
+    value types are used.
+
+    @since version 1.0.0
+    */
+    union json_value
+    {
+        /// object (stored with pointer to save storage)
+        object_t* object;
+        /// array (stored with pointer to save storage)
+        array_t* array;
+        /// string (stored with pointer to save storage)
+        string_t* string;
+        /// binary (stored with pointer to save storage)
+        binary_t* binary;
+        /// boolean
+        boolean_t boolean;
+        /// number (integer)
+        number_integer_t number_integer;
+        /// number (unsigned integer)
+        number_unsigned_t number_unsigned;
+        /// number (floating-point)
+        number_float_t number_float;
+
+        /// default constructor (for null values)
+        json_value() = default;
+        /// constructor for booleans
+        json_value(boolean_t v) noexcept : boolean(v) {}
+        /// constructor for numbers (integer)
+        json_value(number_integer_t v) noexcept : number_integer(v) {}
+        /// constructor for numbers (unsigned)
+        json_value(number_unsigned_t v) noexcept : number_unsigned(v) {}
+        /// constructor for numbers (floating-point)
+        json_value(number_float_t v) noexcept : number_float(v) {}
+        /// constructor for empty values of a given type
+        json_value(value_t t)
+        {
+            switch (t)
+            {
+                case value_t::object:
+                {
+                    object = create<object_t>();
+                    break;
+                }
+
+                case value_t::array:
+                {
+                    array = create<array_t>();
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    string = create<string_t>("");
+                    break;
+                }
+
+                case value_t::binary:
+                {
+                    binary = create<binary_t>();
+                    break;
+                }
+
+                case value_t::boolean:
+                {
+                    boolean = static_cast<boolean_t>(false);
+                    break;
+                }
+
+                case value_t::number_integer:
+                {
+                    number_integer = static_cast<number_integer_t>(0);
+                    break;
+                }
+
+                case value_t::number_unsigned:
+                {
+                    number_unsigned = static_cast<number_unsigned_t>(0);
+                    break;
+                }
+
+                case value_t::number_float:
+                {
+                    number_float = static_cast<number_float_t>(0.0);
+                    break;
+                }
+
+                case value_t::null:
+                {
+                    object = nullptr;  // silence warning, see #821
+                    break;
+                }
+
+                case value_t::discarded:
+                default:
+                {
+                    object = nullptr;  // silence warning, see #821
+                    if (JSON_HEDLEY_UNLIKELY(t == value_t::null))
+                    {
+                        JSON_THROW(other_error::create(500, "961c151d2e87f2686a955a9be24d316f1362bf21 3.12.0", nullptr)); // LCOV_EXCL_LINE
+                    }
+                    break;
+                }
+            }
+        }
+
+        /// constructor for strings
+        json_value(const string_t& value) : string(create<string_t>(value)) {}
+
+        /// constructor for rvalue strings
+        json_value(string_t&& value) : string(create<string_t>(std::move(value))) {}
+
+        /// constructor for objects
+        json_value(const object_t& value) : object(create<object_t>(value)) {}
+
+        /// constructor for rvalue objects
+        json_value(object_t&& value) : object(create<object_t>(std::move(value))) {}
+
+        /// constructor for arrays
+        json_value(const array_t& value) : array(create<array_t>(value)) {}
+
+        /// constructor for rvalue arrays
+        json_value(array_t&& value) : array(create<array_t>(std::move(value))) {}
+
+        /// constructor for binary arrays
+        json_value(const typename binary_t::container_type& value) : binary(create<binary_t>(value)) {}
+
+        /// constructor for rvalue binary arrays
+        json_value(typename binary_t::container_type&& value) : binary(create<binary_t>(std::move(value))) {}
+
+        /// constructor for binary arrays (internal type)
+        json_value(const binary_t& value) : binary(create<binary_t>(value)) {}
+
+        /// constructor for rvalue binary arrays (internal type)
+        json_value(binary_t&& value) : binary(create<binary_t>(std::move(value))) {}
+
+        void destroy(value_t t)
+        {
+            if (
+                (t == value_t::object && object == nullptr) ||
+                (t == value_t::array && array == nullptr) ||
+                (t == value_t::string && string == nullptr) ||
+                (t == value_t::binary && binary == nullptr)
+            )
+            {
+                //not initialized (e.g. due to exception in the ctor)
+                return;
+            }
+            if (t == value_t::array || t == value_t::object)
+            {
+                // flatten the current json_value to a heap-allocated stack
+                std::vector<basic_json> stack;
+
+                // move the top-level items to stack
+                if (t == value_t::array)
+                {
+                    stack.reserve(array->size());
+                    std::move(array->begin(), array->end(), std::back_inserter(stack));
+                }
+                else
+                {
+                    stack.reserve(object->size());
+                    for (auto&& it : *object)
+                    {
+                        stack.push_back(std::move(it.second));
+                    }
+                }
+
+                while (!stack.empty())
+                {
+                    // move the last item to local variable to be processed
+                    basic_json current_item(std::move(stack.back()));
+                    stack.pop_back();
+
+                    // if current_item is array/object, move
+                    // its children to the stack to be processed later
+                    if (current_item.is_array())
+                    {
+                        std::move(current_item.m_data.m_value.array->begin(), current_item.m_data.m_value.array->end(), std::back_inserter(stack));
+
+                        current_item.m_data.m_value.array->clear();
+                    }
+                    else if (current_item.is_object())
+                    {
+                        for (auto&& it : *current_item.m_data.m_value.object)
+                        {
+                            stack.push_back(std::move(it.second));
+                        }
+
+                        current_item.m_data.m_value.object->clear();
+                    }
+
+                    // it's now safe that current_item get destructed
+                    // since it doesn't have any children
+                }
+            }
+
+            switch (t)
+            {
+                case value_t::object:
+                {
+                    AllocatorType<object_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, object);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, object, 1);
+                    break;
+                }
+
+                case value_t::array:
+                {
+                    AllocatorType<array_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, array);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, array, 1);
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    AllocatorType<string_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, string);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, string, 1);
+                    break;
+                }
+
+                case value_t::binary:
+                {
+                    AllocatorType<binary_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, binary);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, binary, 1);
+                    break;
+                }
+
+                case value_t::null:
+                case value_t::boolean:
+                case value_t::number_integer:
+                case value_t::number_unsigned:
+                case value_t::number_float:
+                case value_t::discarded:
+                default:
+                {
+                    break;
+                }
+            }
+        }
+    };
+
+  private:
+    /*!
+    @brief checks the class invariants
+
+    This function asserts the class invariants. It needs to be called at the
+    end of every constructor to make sure that created objects respect the
+    invariant. Furthermore, it has to be called each time the type of a JSON
+    value is changed, because the invariant expresses a relationship between
+    @a m_type and @a m_value.
+
+    Furthermore, the parent relation is checked for arrays and objects: If
+    @a check_parents true and the value is an array or object, then the
+    container's elements must have the current value as parent.
+
+    @param[in] check_parents  whether the parent relation should be checked.
+               The value is true by default and should only be set to false
+               during destruction of objects when the invariant does not
+               need to hold.
+    */
+    void assert_invariant(bool check_parents = true) const noexcept
+    {
+        JSON_ASSERT(m_data.m_type != value_t::object || m_data.m_value.object != nullptr);
+        JSON_ASSERT(m_data.m_type != value_t::array || m_data.m_value.array != nullptr);
+        JSON_ASSERT(m_data.m_type != value_t::string || m_data.m_value.string != nullptr);
+        JSON_ASSERT(m_data.m_type != value_t::binary || m_data.m_value.binary != nullptr);
+
+#if JSON_DIAGNOSTICS
+        JSON_TRY
+        {
+            // cppcheck-suppress assertWithSideEffect
+            JSON_ASSERT(!check_parents || !is_structured() || std::all_of(begin(), end(), [this](const basic_json & j)
+            {
+                return j.m_parent == this;
+            }));
+        }
+        JSON_CATCH(...) {} // LCOV_EXCL_LINE
+#endif
+        static_cast<void>(check_parents);
+    }
+
+    void set_parents()
+    {
+#if JSON_DIAGNOSTICS
+        switch (m_data.m_type)
+        {
+            case value_t::array:
+            {
+                for (auto& element : *m_data.m_value.array)
+                {
+                    element.m_parent = this;
+                }
+                break;
+            }
+
+            case value_t::object:
+            {
+                for (auto& element : *m_data.m_value.object)
+                {
+                    element.second.m_parent = this;
+                }
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                break;
+        }
+#endif
+    }
+
+    iterator set_parents(iterator it, typename iterator::difference_type count_set_parents)
+    {
+#if JSON_DIAGNOSTICS
+        for (typename iterator::difference_type i = 0; i < count_set_parents; ++i)
+        {
+            (it + i)->m_parent = this;
+        }
+#else
+        static_cast<void>(count_set_parents);
+#endif
+        return it;
+    }
+
+    reference set_parent(reference j, std::size_t old_capacity = detail::unknown_size())
+    {
+#if JSON_DIAGNOSTICS
+        if (old_capacity != detail::unknown_size())
+        {
+            // see https://github.com/nlohmann/json/issues/2838
+            JSON_ASSERT(type() == value_t::array);
+            if (JSON_HEDLEY_UNLIKELY(m_data.m_value.array->capacity() != old_capacity))
+            {
+                // capacity has changed: update all parents
+                set_parents();
+                return j;
+            }
+        }
+
+        // ordered_json uses a vector internally, so pointers could have
+        // been invalidated; see https://github.com/nlohmann/json/issues/2962
+#ifdef JSON_HEDLEY_MSVC_VERSION
+#pragma warning(push )
+#pragma warning(disable : 4127) // ignore warning to replace if with if constexpr
+#endif
+        if (detail::is_ordered_map<object_t>::value)
+        {
+            set_parents();
+            return j;
+        }
+#ifdef JSON_HEDLEY_MSVC_VERSION
+#pragma warning( pop )
+#endif
+
+        j.m_parent = this;
+#else
+        static_cast<void>(j);
+        static_cast<void>(old_capacity);
+#endif
+        return j;
+    }
+
+  public:
+    //////////////////////////
+    // JSON parser callback //
+    //////////////////////////
+
+    /// @brief parser event types
+    /// @sa https://json.nlohmann.me/api/basic_json/parse_event_t/
+    using parse_event_t = detail::parse_event_t;
+
+    /// @brief per-element parser callback type
+    /// @sa https://json.nlohmann.me/api/basic_json/parser_callback_t/
+    using parser_callback_t = detail::parser_callback_t<basic_json>;
+
+    //////////////////
+    // constructors //
+    //////////////////
+
+    /// @name constructors and destructors
+    /// Constructors of class @ref basic_json, copy/move constructor, copy
+    /// assignment, static functions creating objects, and the destructor.
+    /// @{
+
+    /// @brief create an empty value with a given type
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(const value_t v)
+        : m_data(v)
+    {
+        assert_invariant();
+    }
+
+    /// @brief create a null object
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(std::nullptr_t = nullptr) noexcept // NOLINT(bugprone-exception-escape)
+        : basic_json(value_t::null)
+    {
+        assert_invariant();
+    }
+
+    /// @brief create a JSON value from compatible types
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    template < typename CompatibleType,
+               typename U = detail::uncvref_t<CompatibleType>,
+               detail::enable_if_t <
+                   !detail::is_basic_json<U>::value && detail::is_compatible_type<basic_json_t, U>::value, int > = 0 >
+    basic_json(CompatibleType && val) noexcept(noexcept( // NOLINT(bugprone-forwarding-reference-overload,bugprone-exception-escape)
+            JSONSerializer<U>::to_json(std::declval<basic_json_t&>(),
+                                       std::forward<CompatibleType>(val))))
+    {
+        JSONSerializer<U>::to_json(*this, std::forward<CompatibleType>(val));
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief create a JSON value from an existing one
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    template < typename BasicJsonType,
+               detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value&& !std::is_same<basic_json, BasicJsonType>::value, int > = 0 >
+    basic_json(const BasicJsonType& val)
+#if JSON_DIAGNOSTIC_POSITIONS
+        : start_position(val.start_pos()),
+          end_position(val.end_pos())
+#endif
+    {
+        using other_boolean_t = typename BasicJsonType::boolean_t;
+        using other_number_float_t = typename BasicJsonType::number_float_t;
+        using other_number_integer_t = typename BasicJsonType::number_integer_t;
+        using other_number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+        using other_string_t = typename BasicJsonType::string_t;
+        using other_object_t = typename BasicJsonType::object_t;
+        using other_array_t = typename BasicJsonType::array_t;
+        using other_binary_t = typename BasicJsonType::binary_t;
+
+        switch (val.type())
+        {
+            case value_t::boolean:
+                JSONSerializer<other_boolean_t>::to_json(*this, val.template get<other_boolean_t>());
+                break;
+            case value_t::number_float:
+                JSONSerializer<other_number_float_t>::to_json(*this, val.template get<other_number_float_t>());
+                break;
+            case value_t::number_integer:
+                JSONSerializer<other_number_integer_t>::to_json(*this, val.template get<other_number_integer_t>());
+                break;
+            case value_t::number_unsigned:
+                JSONSerializer<other_number_unsigned_t>::to_json(*this, val.template get<other_number_unsigned_t>());
+                break;
+            case value_t::string:
+                JSONSerializer<other_string_t>::to_json(*this, val.template get_ref<const other_string_t&>());
+                break;
+            case value_t::object:
+                JSONSerializer<other_object_t>::to_json(*this, val.template get_ref<const other_object_t&>());
+                break;
+            case value_t::array:
+                JSONSerializer<other_array_t>::to_json(*this, val.template get_ref<const other_array_t&>());
+                break;
+            case value_t::binary:
+                JSONSerializer<other_binary_t>::to_json(*this, val.template get_ref<const other_binary_t&>());
+                break;
+            case value_t::null:
+                *this = nullptr;
+                break;
+            case value_t::discarded:
+                m_data.m_type = value_t::discarded;
+                break;
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+        JSON_ASSERT(m_data.m_type == val.type());
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief create a container (array or object) from an initializer list
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(initializer_list_t init,
+               bool type_deduction = true,
+               value_t manual_type = value_t::array)
+    {
+        // check if each element is an array with two elements whose first
+        // element is a string
+        bool is_an_object = std::all_of(init.begin(), init.end(),
+                                        [](const detail::json_ref<basic_json>& element_ref)
+        {
+            // The cast is to ensure op[size_type] is called, bearing in mind size_type may not be int;
+            // (many string types can be constructed from 0 via its null-pointer guise, so we get a
+            // broken call to op[key_type], the wrong semantics and a 4804 warning on Windows)
+            return element_ref->is_array() && element_ref->size() == 2 && (*element_ref)[static_cast<size_type>(0)].is_string();
+        });
+
+        // adjust type if type deduction is not wanted
+        if (!type_deduction)
+        {
+            // if array is wanted, do not create an object though possible
+            if (manual_type == value_t::array)
+            {
+                is_an_object = false;
+            }
+
+            // if object is wanted but impossible, throw an exception
+            if (JSON_HEDLEY_UNLIKELY(manual_type == value_t::object && !is_an_object))
+            {
+                JSON_THROW(type_error::create(301, "cannot create object from initializer list", nullptr));
+            }
+        }
+
+        if (is_an_object)
+        {
+            // the initializer list is a list of pairs -> create object
+            m_data.m_type = value_t::object;
+            m_data.m_value = value_t::object;
+
+            for (auto& element_ref : init)
+            {
+                auto element = element_ref.moved_or_copied();
+                m_data.m_value.object->emplace(
+                    std::move(*((*element.m_data.m_value.array)[0].m_data.m_value.string)),
+                    std::move((*element.m_data.m_value.array)[1]));
+            }
+        }
+        else
+        {
+            // the initializer list describes an array -> create array
+            m_data.m_type = value_t::array;
+            m_data.m_value.array = create<array_t>(init.begin(), init.end());
+        }
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief explicitly create a binary array (without subtype)
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(const typename binary_t::container_type& init)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = init;
+        return res;
+    }
+
+    /// @brief explicitly create a binary array (with subtype)
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(const typename binary_t::container_type& init, typename binary_t::subtype_type subtype)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = binary_t(init, subtype);
+        return res;
+    }
+
+    /// @brief explicitly create a binary array
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(typename binary_t::container_type&& init)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = std::move(init);
+        return res;
+    }
+
+    /// @brief explicitly create a binary array (with subtype)
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(typename binary_t::container_type&& init, typename binary_t::subtype_type subtype)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = binary_t(std::move(init), subtype);
+        return res;
+    }
+
+    /// @brief explicitly create an array from an initializer list
+    /// @sa https://json.nlohmann.me/api/basic_json/array/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json array(initializer_list_t init = {})
+    {
+        return basic_json(init, false, value_t::array);
+    }
+
+    /// @brief explicitly create an object from an initializer list
+    /// @sa https://json.nlohmann.me/api/basic_json/object/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json object(initializer_list_t init = {})
+    {
+        return basic_json(init, false, value_t::object);
+    }
+
+    /// @brief construct an array with count copies of given value
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(size_type cnt, const basic_json& val):
+        m_data{cnt, val}
+    {
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief construct a JSON container given an iterator range
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    template < class InputIT, typename std::enable_if <
+                   std::is_same<InputIT, typename basic_json_t::iterator>::value ||
+                   std::is_same<InputIT, typename basic_json_t::const_iterator>::value, int >::type = 0 >
+    basic_json(InputIT first, InputIT last) // NOLINT(performance-unnecessary-value-param)
+    {
+        JSON_ASSERT(first.m_object != nullptr);
+        JSON_ASSERT(last.m_object != nullptr);
+
+        // make sure iterator fits the current value
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(201, "iterators are not compatible", nullptr));
+        }
+
+        // copy type from first iterator
+        m_data.m_type = first.m_object->m_data.m_type;
+
+        // check if iterator range is complete for primitive values
+        switch (m_data.m_type)
+        {
+            case value_t::boolean:
+            case value_t::number_float:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::string:
+            {
+                if (JSON_HEDLEY_UNLIKELY(!first.m_it.primitive_iterator.is_begin()
+                                         || !last.m_it.primitive_iterator.is_end()))
+                {
+                    JSON_THROW(invalid_iterator::create(204, "iterators out of range", first.m_object));
+                }
+                break;
+            }
+
+            case value_t::null:
+            case value_t::object:
+            case value_t::array:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                break;
+        }
+
+        switch (m_data.m_type)
+        {
+            case value_t::number_integer:
+            {
+                m_data.m_value.number_integer = first.m_object->m_data.m_value.number_integer;
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                m_data.m_value.number_unsigned = first.m_object->m_data.m_value.number_unsigned;
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                m_data.m_value.number_float = first.m_object->m_data.m_value.number_float;
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                m_data.m_value.boolean = first.m_object->m_data.m_value.boolean;
+                break;
+            }
+
+            case value_t::string:
+            {
+                m_data.m_value = *first.m_object->m_data.m_value.string;
+                break;
+            }
+
+            case value_t::object:
+            {
+                m_data.m_value.object = create<object_t>(first.m_it.object_iterator,
+                                        last.m_it.object_iterator);
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_data.m_value.array = create<array_t>(first.m_it.array_iterator,
+                                                       last.m_it.array_iterator);
+                break;
+            }
+
+            case value_t::binary:
+            {
+                m_data.m_value = *first.m_object->m_data.m_value.binary;
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                JSON_THROW(invalid_iterator::create(206, detail::concat("cannot construct with iterators from ", first.m_object->type_name()), first.m_object));
+        }
+
+        set_parents();
+        assert_invariant();
+    }
+
+    ///////////////////////////////////////
+    // other constructors and destructor //
+    ///////////////////////////////////////
+
+    template<typename JsonRef,
+             detail::enable_if_t<detail::conjunction<detail::is_json_ref<JsonRef>,
+                                 std::is_same<typename JsonRef::value_type, basic_json>>::value, int> = 0 >
+    basic_json(const JsonRef& ref) : basic_json(ref.moved_or_copied()) {}
+
+    /// @brief copy constructor
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(const basic_json& other)
+        : json_base_class_t(other)
+#if JSON_DIAGNOSTIC_POSITIONS
+        , start_position(other.start_position)
+        , end_position(other.end_position)
+#endif
+    {
+        m_data.m_type = other.m_data.m_type;
+        // check of passed value is valid
+        other.assert_invariant();
+
+        switch (m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_data.m_value = *other.m_data.m_value.object;
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_data.m_value = *other.m_data.m_value.array;
+                break;
+            }
+
+            case value_t::string:
+            {
+                m_data.m_value = *other.m_data.m_value.string;
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                m_data.m_value = other.m_data.m_value.boolean;
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                m_data.m_value = other.m_data.m_value.number_integer;
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                m_data.m_value = other.m_data.m_value.number_unsigned;
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                m_data.m_value = other.m_data.m_value.number_float;
+                break;
+            }
+
+            case value_t::binary:
+            {
+                m_data.m_value = *other.m_data.m_value.binary;
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                break;
+        }
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief move constructor
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(basic_json&& other) noexcept
+        : json_base_class_t(std::forward<json_base_class_t>(other)),
+          m_data(std::move(other.m_data)) // cppcheck-suppress[accessForwarded] TODO check
+#if JSON_DIAGNOSTIC_POSITIONS
+        , start_position(other.start_position) // cppcheck-suppress[accessForwarded] TODO check
+        , end_position(other.end_position) // cppcheck-suppress[accessForwarded] TODO check
+#endif
+    {
+        // check that passed value is valid
+        other.assert_invariant(false); // cppcheck-suppress[accessForwarded]
+
+        // invalidate payload
+        other.m_data.m_type = value_t::null;
+        other.m_data.m_value = {};
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        other.start_position = std::string::npos;
+        other.end_position = std::string::npos;
+#endif
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief copy assignment
+    /// @sa https://json.nlohmann.me/api/basic_json/operator=/
+    basic_json& operator=(basic_json other) noexcept (
+        std::is_nothrow_move_constructible<value_t>::value&&
+        std::is_nothrow_move_assignable<value_t>::value&&
+        std::is_nothrow_move_constructible<json_value>::value&&
+        std::is_nothrow_move_assignable<json_value>::value&&
+        std::is_nothrow_move_assignable<json_base_class_t>::value
+    )
+    {
+        // check that passed value is valid
+        other.assert_invariant();
+
+        using std::swap;
+        swap(m_data.m_type, other.m_data.m_type);
+        swap(m_data.m_value, other.m_data.m_value);
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        swap(start_position, other.start_position);
+        swap(end_position, other.end_position);
+#endif
+
+        json_base_class_t::operator=(std::move(other));
+
+        set_parents();
+        assert_invariant();
+        return *this;
+    }
+
+    /// @brief destructor
+    /// @sa https://json.nlohmann.me/api/basic_json/~basic_json/
+    ~basic_json() noexcept
+    {
+        assert_invariant(false);
+    }
+
+    /// @}
+
+  public:
+    ///////////////////////
+    // object inspection //
+    ///////////////////////
+
+    /// @name object inspection
+    /// Functions to inspect the type of a JSON value.
+    /// @{
+
+    /// @brief serialization
+    /// @sa https://json.nlohmann.me/api/basic_json/dump/
+    string_t dump(const int indent = -1,
+                  const char indent_char = ' ',
+                  const bool ensure_ascii = false,
+                  const error_handler_t error_handler = error_handler_t::strict) const
+    {
+        string_t result;
+        serializer s(detail::output_adapter<char, string_t>(result), indent_char, error_handler);
+
+        if (indent >= 0)
+        {
+            s.dump(*this, true, ensure_ascii, static_cast<unsigned int>(indent));
+        }
+        else
+        {
+            s.dump(*this, false, ensure_ascii, 0);
+        }
+
+        return result;
+    }
+
+    /// @brief return the type of the JSON value (explicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/type/
+    constexpr value_t type() const noexcept
+    {
+        return m_data.m_type;
+    }
+
+    /// @brief return whether type is primitive
+    /// @sa https://json.nlohmann.me/api/basic_json/is_primitive/
+    constexpr bool is_primitive() const noexcept
+    {
+        return is_null() || is_string() || is_boolean() || is_number() || is_binary();
+    }
+
+    /// @brief return whether type is structured
+    /// @sa https://json.nlohmann.me/api/basic_json/is_structured/
+    constexpr bool is_structured() const noexcept
+    {
+        return is_array() || is_object();
+    }
+
+    /// @brief return whether value is null
+    /// @sa https://json.nlohmann.me/api/basic_json/is_null/
+    constexpr bool is_null() const noexcept
+    {
+        return m_data.m_type == value_t::null;
+    }
+
+    /// @brief return whether value is a boolean
+    /// @sa https://json.nlohmann.me/api/basic_json/is_boolean/
+    constexpr bool is_boolean() const noexcept
+    {
+        return m_data.m_type == value_t::boolean;
+    }
+
+    /// @brief return whether value is a number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number/
+    constexpr bool is_number() const noexcept
+    {
+        return is_number_integer() || is_number_float();
+    }
+
+    /// @brief return whether value is an integer number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number_integer/
+    constexpr bool is_number_integer() const noexcept
+    {
+        return m_data.m_type == value_t::number_integer || m_data.m_type == value_t::number_unsigned;
+    }
+
+    /// @brief return whether value is an unsigned integer number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number_unsigned/
+    constexpr bool is_number_unsigned() const noexcept
+    {
+        return m_data.m_type == value_t::number_unsigned;
+    }
+
+    /// @brief return whether value is a floating-point number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number_float/
+    constexpr bool is_number_float() const noexcept
+    {
+        return m_data.m_type == value_t::number_float;
+    }
+
+    /// @brief return whether value is an object
+    /// @sa https://json.nlohmann.me/api/basic_json/is_object/
+    constexpr bool is_object() const noexcept
+    {
+        return m_data.m_type == value_t::object;
+    }
+
+    /// @brief return whether value is an array
+    /// @sa https://json.nlohmann.me/api/basic_json/is_array/
+    constexpr bool is_array() const noexcept
+    {
+        return m_data.m_type == value_t::array;
+    }
+
+    /// @brief return whether value is a string
+    /// @sa https://json.nlohmann.me/api/basic_json/is_string/
+    constexpr bool is_string() const noexcept
+    {
+        return m_data.m_type == value_t::string;
+    }
+
+    /// @brief return whether value is a binary array
+    /// @sa https://json.nlohmann.me/api/basic_json/is_binary/
+    constexpr bool is_binary() const noexcept
+    {
+        return m_data.m_type == value_t::binary;
+    }
+
+    /// @brief return whether value is discarded
+    /// @sa https://json.nlohmann.me/api/basic_json/is_discarded/
+    constexpr bool is_discarded() const noexcept
+    {
+        return m_data.m_type == value_t::discarded;
+    }
+
+    /// @brief return the type of the JSON value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_value_t/
+    constexpr operator value_t() const noexcept
+    {
+        return m_data.m_type;
+    }
+
+    /// @}
+
+  private:
+    //////////////////
+    // value access //
+    //////////////////
+
+    /// get a boolean (explicit)
+    boolean_t get_impl(boolean_t* /*unused*/) const
+    {
+        if (JSON_HEDLEY_LIKELY(is_boolean()))
+        {
+            return m_data.m_value.boolean;
+        }
+
+        JSON_THROW(type_error::create(302, detail::concat("type must be boolean, but is ", type_name()), this));
+    }
+
+    /// get a pointer to the value (object)
+    object_t* get_impl_ptr(object_t* /*unused*/) noexcept
+    {
+        return is_object() ? m_data.m_value.object : nullptr;
+    }
+
+    /// get a pointer to the value (object)
+    constexpr const object_t* get_impl_ptr(const object_t* /*unused*/) const noexcept
+    {
+        return is_object() ? m_data.m_value.object : nullptr;
+    }
+
+    /// get a pointer to the value (array)
+    array_t* get_impl_ptr(array_t* /*unused*/) noexcept
+    {
+        return is_array() ? m_data.m_value.array : nullptr;
+    }
+
+    /// get a pointer to the value (array)
+    constexpr const array_t* get_impl_ptr(const array_t* /*unused*/) const noexcept
+    {
+        return is_array() ? m_data.m_value.array : nullptr;
+    }
+
+    /// get a pointer to the value (string)
+    string_t* get_impl_ptr(string_t* /*unused*/) noexcept
+    {
+        return is_string() ? m_data.m_value.string : nullptr;
+    }
+
+    /// get a pointer to the value (string)
+    constexpr const string_t* get_impl_ptr(const string_t* /*unused*/) const noexcept
+    {
+        return is_string() ? m_data.m_value.string : nullptr;
+    }
+
+    /// get a pointer to the value (boolean)
+    boolean_t* get_impl_ptr(boolean_t* /*unused*/) noexcept
+    {
+        return is_boolean() ? &m_data.m_value.boolean : nullptr;
+    }
+
+    /// get a pointer to the value (boolean)
+    constexpr const boolean_t* get_impl_ptr(const boolean_t* /*unused*/) const noexcept
+    {
+        return is_boolean() ? &m_data.m_value.boolean : nullptr;
+    }
+
+    /// get a pointer to the value (integer number)
+    number_integer_t* get_impl_ptr(number_integer_t* /*unused*/) noexcept
+    {
+        return m_data.m_type == value_t::number_integer ? &m_data.m_value.number_integer : nullptr;
+    }
+
+    /// get a pointer to the value (integer number)
+    constexpr const number_integer_t* get_impl_ptr(const number_integer_t* /*unused*/) const noexcept
+    {
+        return m_data.m_type == value_t::number_integer ? &m_data.m_value.number_integer : nullptr;
+    }
+
+    /// get a pointer to the value (unsigned number)
+    number_unsigned_t* get_impl_ptr(number_unsigned_t* /*unused*/) noexcept
+    {
+        return is_number_unsigned() ? &m_data.m_value.number_unsigned : nullptr;
+    }
+
+    /// get a pointer to the value (unsigned number)
+    constexpr const number_unsigned_t* get_impl_ptr(const number_unsigned_t* /*unused*/) const noexcept
+    {
+        return is_number_unsigned() ? &m_data.m_value.number_unsigned : nullptr;
+    }
+
+    /// get a pointer to the value (floating-point number)
+    number_float_t* get_impl_ptr(number_float_t* /*unused*/) noexcept
+    {
+        return is_number_float() ? &m_data.m_value.number_float : nullptr;
+    }
+
+    /// get a pointer to the value (floating-point number)
+    constexpr const number_float_t* get_impl_ptr(const number_float_t* /*unused*/) const noexcept
+    {
+        return is_number_float() ? &m_data.m_value.number_float : nullptr;
+    }
+
+    /// get a pointer to the value (binary)
+    binary_t* get_impl_ptr(binary_t* /*unused*/) noexcept
+    {
+        return is_binary() ? m_data.m_value.binary : nullptr;
+    }
+
+    /// get a pointer to the value (binary)
+    constexpr const binary_t* get_impl_ptr(const binary_t* /*unused*/) const noexcept
+    {
+        return is_binary() ? m_data.m_value.binary : nullptr;
+    }
+
+    /*!
+    @brief helper function to implement get_ref()
+
+    This function helps to implement get_ref() without code duplication for
+    const and non-const overloads
+
+    @tparam ThisType will be deduced as `basic_json` or `const basic_json`
+
+    @throw type_error.303 if ReferenceType does not match underlying value
+    type of the current JSON
+    */
+    template<typename ReferenceType, typename ThisType>
+    static ReferenceType get_ref_impl(ThisType& obj)
+    {
+        // delegate the call to get_ptr<>()
+        auto* ptr = obj.template get_ptr<typename std::add_pointer<ReferenceType>::type>();
+
+        if (JSON_HEDLEY_LIKELY(ptr != nullptr))
+        {
+            return *ptr;
+        }
+
+        JSON_THROW(type_error::create(303, detail::concat("incompatible ReferenceType for get_ref, actual type is ", obj.type_name()), &obj));
+    }
+
+  public:
+    /// @name value access
+    /// Direct access to the stored value of a JSON value.
+    /// @{
+
+    /// @brief get a pointer value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ptr/
+    template<typename PointerType, typename std::enable_if<
+                 std::is_pointer<PointerType>::value, int>::type = 0>
+    auto get_ptr() noexcept -> decltype(std::declval<basic_json_t&>().get_impl_ptr(std::declval<PointerType>()))
+    {
+        // delegate the call to get_impl_ptr<>()
+        return get_impl_ptr(static_cast<PointerType>(nullptr));
+    }
+
+    /// @brief get a pointer value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ptr/
+    template < typename PointerType, typename std::enable_if <
+                   std::is_pointer<PointerType>::value&&
+                   std::is_const<typename std::remove_pointer<PointerType>::type>::value, int >::type = 0 >
+    constexpr auto get_ptr() const noexcept -> decltype(std::declval<const basic_json_t&>().get_impl_ptr(std::declval<PointerType>()))
+    {
+        // delegate the call to get_impl_ptr<>() const
+        return get_impl_ptr(static_cast<PointerType>(nullptr));
+    }
+
+  private:
+    /*!
+    @brief get a value (explicit)
+
+    Explicit type conversion between the JSON value and a compatible value
+    which is [CopyConstructible](https://en.cppreference.com/w/cpp/named_req/CopyConstructible)
+    and [DefaultConstructible](https://en.cppreference.com/w/cpp/named_req/DefaultConstructible).
+    The value is converted by calling the @ref json_serializer<ValueType>
+    `from_json()` method.
+
+    The function is equivalent to executing
+    @code {.cpp}
+    ValueType ret;
+    JSONSerializer<ValueType>::from_json(*this, ret);
+    return ret;
+    @endcode
+
+    This overloads is chosen if:
+    - @a ValueType is not @ref basic_json,
+    - @ref json_serializer<ValueType> has a `from_json()` method of the form
+      `void from_json(const basic_json&, ValueType&)`, and
+    - @ref json_serializer<ValueType> does not have a `from_json()` method of
+      the form `ValueType from_json(const basic_json&)`
+
+    @tparam ValueType the returned value type
+
+    @return copy of the JSON value, converted to @a ValueType
+
+    @throw what @ref json_serializer<ValueType> `from_json()` method throws
+
+    @liveexample{The example below shows several conversions from JSON values
+    to other types. There a few things to note: (1) Floating-point numbers can
+    be converted to integers\, (2) A JSON array can be converted to a standard
+    `std::vector<short>`\, (3) A JSON object can be converted to C++
+    associative containers such as `std::unordered_map<std::string\,
+    json>`.,get__ValueType_const}
+
+    @since version 2.1.0
+    */
+    template < typename ValueType,
+               detail::enable_if_t <
+                   detail::is_default_constructible<ValueType>::value&&
+                   detail::has_from_json<basic_json_t, ValueType>::value,
+                   int > = 0 >
+    ValueType get_impl(detail::priority_tag<0> /*unused*/) const noexcept(noexcept(
+            JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>(), std::declval<ValueType&>())))
+    {
+        auto ret = ValueType();
+        JSONSerializer<ValueType>::from_json(*this, ret);
+        return ret;
+    }
+
+    /*!
+    @brief get a value (explicit); special case
+
+    Explicit type conversion between the JSON value and a compatible value
+    which is **not** [CopyConstructible](https://en.cppreference.com/w/cpp/named_req/CopyConstructible)
+    and **not** [DefaultConstructible](https://en.cppreference.com/w/cpp/named_req/DefaultConstructible).
+    The value is converted by calling the @ref json_serializer<ValueType>
+    `from_json()` method.
+
+    The function is equivalent to executing
+    @code {.cpp}
+    return JSONSerializer<ValueType>::from_json(*this);
+    @endcode
+
+    This overloads is chosen if:
+    - @a ValueType is not @ref basic_json and
+    - @ref json_serializer<ValueType> has a `from_json()` method of the form
+      `ValueType from_json(const basic_json&)`
+
+    @note If @ref json_serializer<ValueType> has both overloads of
+    `from_json()`, this one is chosen.
+
+    @tparam ValueType the returned value type
+
+    @return copy of the JSON value, converted to @a ValueType
+
+    @throw what @ref json_serializer<ValueType> `from_json()` method throws
+
+    @since version 2.1.0
+    */
+    template < typename ValueType,
+               detail::enable_if_t <
+                   detail::has_non_default_from_json<basic_json_t, ValueType>::value,
+                   int > = 0 >
+    ValueType get_impl(detail::priority_tag<1> /*unused*/) const noexcept(noexcept(
+            JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>())))
+    {
+        return JSONSerializer<ValueType>::from_json(*this);
+    }
+
+    /*!
+    @brief get special-case overload
+
+    This overloads converts the current @ref basic_json in a different
+    @ref basic_json type
+
+    @tparam BasicJsonType == @ref basic_json
+
+    @return a copy of *this, converted into @a BasicJsonType
+
+    @complexity Depending on the implementation of the called `from_json()`
+                method.
+
+    @since version 3.2.0
+    */
+    template < typename BasicJsonType,
+               detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value,
+                   int > = 0 >
+    BasicJsonType get_impl(detail::priority_tag<2> /*unused*/) const
+    {
+        return *this;
+    }
+
+    /*!
+    @brief get special-case overload
+
+    This overloads avoids a lot of template boilerplate, it can be seen as the
+    identity method
+
+    @tparam BasicJsonType == @ref basic_json
+
+    @return a copy of *this
+
+    @complexity Constant.
+
+    @since version 2.1.0
+    */
+    template<typename BasicJsonType,
+             detail::enable_if_t<
+                 std::is_same<BasicJsonType, basic_json_t>::value,
+                 int> = 0>
+    basic_json get_impl(detail::priority_tag<3> /*unused*/) const
+    {
+        return *this;
+    }
+
+    /*!
+    @brief get a pointer value (explicit)
+    @copydoc get()
+    */
+    template<typename PointerType,
+             detail::enable_if_t<
+                 std::is_pointer<PointerType>::value,
+                 int> = 0>
+    constexpr auto get_impl(detail::priority_tag<4> /*unused*/) const noexcept
+    -> decltype(std::declval<const basic_json_t&>().template get_ptr<PointerType>())
+    {
+        // delegate the call to get_ptr
+        return get_ptr<PointerType>();
+    }
+
+  public:
+    /*!
+    @brief get a (pointer) value (explicit)
+
+    Performs explicit type conversion between the JSON value and a compatible value if required.
+
+    - If the requested type is a pointer to the internally stored JSON value that pointer is returned.
+    No copies are made.
+
+    - If the requested type is the current @ref basic_json, or a different @ref basic_json convertible
+    from the current @ref basic_json.
+
+    - Otherwise the value is converted by calling the @ref json_serializer<ValueType> `from_json()`
+    method.
+
+    @tparam ValueTypeCV the provided value type
+    @tparam ValueType the returned value type
+
+    @return copy of the JSON value, converted to @tparam ValueType if necessary
+
+    @throw what @ref json_serializer<ValueType> `from_json()` method throws if conversion is required
+
+    @since version 2.1.0
+    */
+    template < typename ValueTypeCV, typename ValueType = detail::uncvref_t<ValueTypeCV>>
+#if defined(JSON_HAS_CPP_14)
+    constexpr
+#endif
+    auto get() const noexcept(
+    noexcept(std::declval<const basic_json_t&>().template get_impl<ValueType>(detail::priority_tag<4> {})))
+    -> decltype(std::declval<const basic_json_t&>().template get_impl<ValueType>(detail::priority_tag<4> {}))
+    {
+        // we cannot static_assert on ValueTypeCV being non-const, because
+        // there is support for get<const basic_json_t>(), which is why we
+        // still need the uncvref
+        static_assert(!std::is_reference<ValueTypeCV>::value,
+                      "get() cannot be used with reference types, you might want to use get_ref()");
+        return get_impl<ValueType>(detail::priority_tag<4> {});
+    }
+
+    /*!
+    @brief get a pointer value (explicit)
+
+    Explicit pointer access to the internally stored JSON value. No copies are
+    made.
+
+    @warning The pointer becomes invalid if the underlying JSON object
+    changes.
+
+    @tparam PointerType pointer type; must be a pointer to @ref array_t, @ref
+    object_t, @ref string_t, @ref boolean_t, @ref number_integer_t,
+    @ref number_unsigned_t, or @ref number_float_t.
+
+    @return pointer to the internally stored JSON value if the requested
+    pointer type @a PointerType fits to the JSON value; `nullptr` otherwise
+
+    @complexity Constant.
+
+    @liveexample{The example below shows how pointers to internal values of a
+    JSON value can be requested. Note that no type conversions are made and a
+    `nullptr` is returned if the value and the requested pointer type does not
+    match.,get__PointerType}
+
+    @sa see @ref get_ptr() for explicit pointer-member access
+
+    @since version 1.0.0
+    */
+    template<typename PointerType, typename std::enable_if<
+                 std::is_pointer<PointerType>::value, int>::type = 0>
+    auto get() noexcept -> decltype(std::declval<basic_json_t&>().template get_ptr<PointerType>())
+    {
+        // delegate the call to get_ptr
+        return get_ptr<PointerType>();
+    }
+
+    /// @brief get a value (explicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_to/
+    template < typename ValueType,
+               detail::enable_if_t <
+                   !detail::is_basic_json<ValueType>::value&&
+                   detail::has_from_json<basic_json_t, ValueType>::value,
+                   int > = 0 >
+    ValueType & get_to(ValueType& v) const noexcept(noexcept(
+            JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>(), v)))
+    {
+        JSONSerializer<ValueType>::from_json(*this, v);
+        return v;
+    }
+
+    // specialization to allow calling get_to with a basic_json value
+    // see https://github.com/nlohmann/json/issues/2175
+    template<typename ValueType,
+             detail::enable_if_t <
+                 detail::is_basic_json<ValueType>::value,
+                 int> = 0>
+    ValueType & get_to(ValueType& v) const
+    {
+        v = *this;
+        return v;
+    }
+
+    template <
+        typename T, std::size_t N,
+        typename Array = T (&)[N], // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+        detail::enable_if_t <
+            detail::has_from_json<basic_json_t, Array>::value, int > = 0 >
+    Array get_to(T (&v)[N]) const // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+    noexcept(noexcept(JSONSerializer<Array>::from_json(
+                          std::declval<const basic_json_t&>(), v)))
+    {
+        JSONSerializer<Array>::from_json(*this, v);
+        return v;
+    }
+
+    /// @brief get a reference value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ref/
+    template<typename ReferenceType, typename std::enable_if<
+                 std::is_reference<ReferenceType>::value, int>::type = 0>
+    ReferenceType get_ref()
+    {
+        // delegate call to get_ref_impl
+        return get_ref_impl<ReferenceType>(*this);
+    }
+
+    /// @brief get a reference value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ref/
+    template < typename ReferenceType, typename std::enable_if <
+                   std::is_reference<ReferenceType>::value&&
+                   std::is_const<typename std::remove_reference<ReferenceType>::type>::value, int >::type = 0 >
+    ReferenceType get_ref() const
+    {
+        // delegate call to get_ref_impl
+        return get_ref_impl<ReferenceType>(*this);
+    }
+
+    /*!
+    @brief get a value (implicit)
+
+    Implicit type conversion between the JSON value and a compatible value.
+    The call is realized by calling @ref get() const.
+
+    @tparam ValueType non-pointer type compatible to the JSON value, for
+    instance `int` for JSON integer numbers, `bool` for JSON booleans, or
+    `std::vector` types for JSON arrays. The character type of @ref string_t
+    as well as an initializer list of this type is excluded to avoid
+    ambiguities as these types implicitly convert to `std::string`.
+
+    @return copy of the JSON value, converted to type @a ValueType
+
+    @throw type_error.302 in case passed type @a ValueType is incompatible
+    to the JSON value type (e.g., the JSON value is of type boolean, but a
+    string is requested); see example below
+
+    @complexity Linear in the size of the JSON value.
+
+    @liveexample{The example below shows several conversions from JSON values
+    to other types. There a few things to note: (1) Floating-point numbers can
+    be converted to integers\, (2) A JSON array can be converted to a standard
+    `std::vector<short>`\, (3) A JSON object can be converted to C++
+    associative containers such as `std::unordered_map<std::string\,
+    json>`.,operator__ValueType}
+
+    @since version 1.0.0
+    */
+    template < typename ValueType, typename std::enable_if <
+                   detail::conjunction <
+                       detail::negation<std::is_pointer<ValueType>>,
+                       detail::negation<std::is_same<ValueType, std::nullptr_t>>,
+                       detail::negation<std::is_same<ValueType, detail::json_ref<basic_json>>>,
+                                        detail::negation<std::is_same<ValueType, typename string_t::value_type>>,
+                                        detail::negation<detail::is_basic_json<ValueType>>,
+                                        detail::negation<std::is_same<ValueType, std::initializer_list<typename string_t::value_type>>>,
+#if defined(JSON_HAS_CPP_17) && (defined(__GNUC__) || (defined(_MSC_VER) && _MSC_VER >= 1910 && _MSC_VER <= 1914))
+                                                detail::negation<std::is_same<ValueType, std::string_view>>,
+#endif
+#if defined(JSON_HAS_CPP_17) && JSON_HAS_STATIC_RTTI
+                                                detail::negation<std::is_same<ValueType, std::any>>,
+#endif
+                                                detail::is_detected_lazy<detail::get_template_function, const basic_json_t&, ValueType>
+                                                >::value, int >::type = 0 >
+                                        JSON_EXPLICIT operator ValueType() const
+    {
+        // delegate the call to get<>() const
+        return get<ValueType>();
+    }
+
+    /// @brief get a binary value
+    /// @sa https://json.nlohmann.me/api/basic_json/get_binary/
+    binary_t& get_binary()
+    {
+        if (!is_binary())
+        {
+            JSON_THROW(type_error::create(302, detail::concat("type must be binary, but is ", type_name()), this));
+        }
+
+        return *get_ptr<binary_t*>();
+    }
+
+    /// @brief get a binary value
+    /// @sa https://json.nlohmann.me/api/basic_json/get_binary/
+    const binary_t& get_binary() const
+    {
+        if (!is_binary())
+        {
+            JSON_THROW(type_error::create(302, detail::concat("type must be binary, but is ", type_name()), this));
+        }
+
+        return *get_ptr<const binary_t*>();
+    }
+
+    /// @}
+
+    ////////////////////
+    // element access //
+    ////////////////////
+
+    /// @name element access
+    /// Access to the JSON value.
+    /// @{
+
+    /// @brief access specified array element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    reference at(size_type idx)
+    {
+        // at only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            JSON_TRY
+            {
+                return set_parent(m_data.m_value.array->at(idx));
+            }
+            JSON_CATCH (std::out_of_range&)
+            {
+                // create better exception explanation
+                JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), this));
+            } // cppcheck-suppress[missingReturn]
+        }
+        else
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+    }
+
+    /// @brief access specified array element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    const_reference at(size_type idx) const
+    {
+        // at only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            JSON_TRY
+            {
+                return m_data.m_value.array->at(idx);
+            }
+            JSON_CATCH (std::out_of_range&)
+            {
+                // create better exception explanation
+                JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), this));
+            } // cppcheck-suppress[missingReturn]
+        }
+        else
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    reference at(const typename object_t::key_type& key)
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(key);
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", key, "' not found"), this));
+        }
+        return set_parent(it->second);
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    reference at(KeyType && key)
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", string_t(std::forward<KeyType>(key)), "' not found"), this));
+        }
+        return set_parent(it->second);
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    const_reference at(const typename object_t::key_type& key) const
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(key);
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", key, "' not found"), this));
+        }
+        return it->second;
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    const_reference at(KeyType && key) const
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", string_t(std::forward<KeyType>(key)), "' not found"), this));
+        }
+        return it->second;
+    }
+
+    /// @brief access specified array element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    reference operator[](size_type idx)
+    {
+        // implicitly convert null value to an empty array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value.array = create<array_t>();
+            assert_invariant();
+        }
+
+        // operator[] only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            // fill up array with null values if given idx is outside range
+            if (idx >= m_data.m_value.array->size())
+            {
+#if JSON_DIAGNOSTICS
+                // remember array size & capacity before resizing
+                const auto old_size = m_data.m_value.array->size();
+                const auto old_capacity = m_data.m_value.array->capacity();
+#endif
+                m_data.m_value.array->resize(idx + 1);
+
+#if JSON_DIAGNOSTICS
+                if (JSON_HEDLEY_UNLIKELY(m_data.m_value.array->capacity() != old_capacity))
+                {
+                    // capacity has changed: update all parents
+                    set_parents();
+                }
+                else
+                {
+                    // set parent for values added above
+                    set_parents(begin() + static_cast<typename iterator::difference_type>(old_size), static_cast<typename iterator::difference_type>(idx + 1 - old_size));
+                }
+#endif
+                assert_invariant();
+            }
+
+            return m_data.m_value.array->operator[](idx);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a numeric argument with ", type_name()), this));
+    }
+
+    /// @brief access specified array element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    const_reference operator[](size_type idx) const
+    {
+        // const operator[] only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            return m_data.m_value.array->operator[](idx);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a numeric argument with ", type_name()), this));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    reference operator[](typename object_t::key_type key) // NOLINT(performance-unnecessary-value-param)
+    {
+        // implicitly convert null value to an empty object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value.object = create<object_t>();
+            assert_invariant();
+        }
+
+        // operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto result = m_data.m_value.object->emplace(std::move(key), nullptr);
+            return set_parent(result.first->second);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    const_reference operator[](const typename object_t::key_type& key) const
+    {
+        // const operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto it = m_data.m_value.object->find(key);
+            JSON_ASSERT(it != m_data.m_value.object->end());
+            return it->second;
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+    // these two functions resolve a (const) char * ambiguity affecting Clang and MSVC
+    // (they seemingly cannot be constrained to resolve the ambiguity)
+    template<typename T>
+    reference operator[](T* key)
+    {
+        return operator[](typename object_t::key_type(key));
+    }
+
+    template<typename T>
+    const_reference operator[](T* key) const
+    {
+        return operator[](typename object_t::key_type(key));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    reference operator[](KeyType && key)
+    {
+        // implicitly convert null value to an empty object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value.object = create<object_t>();
+            assert_invariant();
+        }
+
+        // operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto result = m_data.m_value.object->emplace(std::forward<KeyType>(key), nullptr);
+            return set_parent(result.first->second);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    const_reference operator[](KeyType && key) const
+    {
+        // const operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+            JSON_ASSERT(it != m_data.m_value.object->end());
+            return it->second;
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+  private:
+    template<typename KeyType>
+    using is_comparable_with_object_key = detail::is_comparable <
+        object_comparator_t, const typename object_t::key_type&, KeyType >;
+
+    template<typename ValueType>
+    using value_return_type = std::conditional <
+        detail::is_c_string_uncvref<ValueType>::value,
+        string_t, typename std::decay<ValueType>::type >;
+
+  public:
+    /// @brief access specified object element with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, detail::enable_if_t <
+                   !detail::is_transparent<object_comparator_t>::value
+                   && detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ValueType value(const typename object_t::key_type& key, const ValueType& default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(key);
+            if (it != end())
+            {
+                return it->template get<ValueType>();
+            }
+
+            return default_value;
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   !detail::is_transparent<object_comparator_t>::value
+                   && detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ReturnType value(const typename object_t::key_type& key, ValueType && default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(key);
+            if (it != end())
+            {
+                return it->template get<ReturnType>();
+            }
+
+            return std::forward<ValueType>(default_value);
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class KeyType, detail::enable_if_t <
+                   detail::is_transparent<object_comparator_t>::value
+                   && !detail::is_json_pointer<KeyType>::value
+                   && is_comparable_with_object_key<KeyType>::value
+                   && detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ValueType value(KeyType && key, const ValueType& default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(std::forward<KeyType>(key));
+            if (it != end())
+            {
+                return it->template get<ValueType>();
+            }
+
+            return default_value;
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element via JSON Pointer with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class KeyType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   detail::is_transparent<object_comparator_t>::value
+                   && !detail::is_json_pointer<KeyType>::value
+                   && is_comparable_with_object_key<KeyType>::value
+                   && detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ReturnType value(KeyType && key, ValueType && default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(std::forward<KeyType>(key));
+            if (it != end())
+            {
+                return it->template get<ReturnType>();
+            }
+
+            return std::forward<ValueType>(default_value);
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element via JSON Pointer with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, detail::enable_if_t <
+                   detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ValueType value(const json_pointer& ptr, const ValueType& default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if pointer resolves a value, return it or use default value
+            JSON_TRY
+            {
+                return ptr.get_checked(this).template get<ValueType>();
+            }
+            JSON_INTERNAL_CATCH (out_of_range&)
+            {
+                return default_value;
+            }
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element via JSON Pointer with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ReturnType value(const json_pointer& ptr, ValueType && default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if pointer resolves a value, return it or use default value
+            JSON_TRY
+            {
+                return ptr.get_checked(this).template get<ReturnType>();
+            }
+            JSON_INTERNAL_CATCH (out_of_range&)
+            {
+                return std::forward<ValueType>(default_value);
+            }
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    template < class ValueType, class BasicJsonType, detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value
+                   && detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    ValueType value(const ::nlohmann::json_pointer<BasicJsonType>& ptr, const ValueType& default_value) const
+    {
+        return value(ptr.convert(), default_value);
+    }
+
+    template < class ValueType, class BasicJsonType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value
+                   && detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    ReturnType value(const ::nlohmann::json_pointer<BasicJsonType>& ptr, ValueType && default_value) const
+    {
+        return value(ptr.convert(), std::forward<ValueType>(default_value));
+    }
+
+    /// @brief access the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/front/
+    reference front()
+    {
+        return *begin();
+    }
+
+    /// @brief access the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/front/
+    const_reference front() const
+    {
+        return *cbegin();
+    }
+
+    /// @brief access the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/back/
+    reference back()
+    {
+        auto tmp = end();
+        --tmp;
+        return *tmp;
+    }
+
+    /// @brief access the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/back/
+    const_reference back() const
+    {
+        auto tmp = cend();
+        --tmp;
+        return *tmp;
+    }
+
+    /// @brief remove element given an iterator
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    template < class IteratorType, detail::enable_if_t <
+                   std::is_same<IteratorType, typename basic_json_t::iterator>::value ||
+                   std::is_same<IteratorType, typename basic_json_t::const_iterator>::value, int > = 0 >
+    IteratorType erase(IteratorType pos) // NOLINT(performance-unnecessary-value-param)
+    {
+        // make sure iterator fits the current value
+        if (JSON_HEDLEY_UNLIKELY(this != pos.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+        }
+
+        IteratorType result = end();
+
+        switch (m_data.m_type)
+        {
+            case value_t::boolean:
+            case value_t::number_float:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::string:
+            case value_t::binary:
+            {
+                if (JSON_HEDLEY_UNLIKELY(!pos.m_it.primitive_iterator.is_begin()))
+                {
+                    JSON_THROW(invalid_iterator::create(205, "iterator out of range", this));
+                }
+
+                if (is_string())
+                {
+                    AllocatorType<string_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.string);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.string, 1);
+                    m_data.m_value.string = nullptr;
+                }
+                else if (is_binary())
+                {
+                    AllocatorType<binary_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.binary);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.binary, 1);
+                    m_data.m_value.binary = nullptr;
+                }
+
+                m_data.m_type = value_t::null;
+                assert_invariant();
+                break;
+            }
+
+            case value_t::object:
+            {
+                result.m_it.object_iterator = m_data.m_value.object->erase(pos.m_it.object_iterator);
+                break;
+            }
+
+            case value_t::array:
+            {
+                result.m_it.array_iterator = m_data.m_value.array->erase(pos.m_it.array_iterator);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        return result;
+    }
+
+    /// @brief remove elements given an iterator range
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    template < class IteratorType, detail::enable_if_t <
+                   std::is_same<IteratorType, typename basic_json_t::iterator>::value ||
+                   std::is_same<IteratorType, typename basic_json_t::const_iterator>::value, int > = 0 >
+    IteratorType erase(IteratorType first, IteratorType last) // NOLINT(performance-unnecessary-value-param)
+    {
+        // make sure iterator fits the current value
+        if (JSON_HEDLEY_UNLIKELY(this != first.m_object || this != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(203, "iterators do not fit current value", this));
+        }
+
+        IteratorType result = end();
+
+        switch (m_data.m_type)
+        {
+            case value_t::boolean:
+            case value_t::number_float:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::string:
+            case value_t::binary:
+            {
+                if (JSON_HEDLEY_LIKELY(!first.m_it.primitive_iterator.is_begin()
+                                       || !last.m_it.primitive_iterator.is_end()))
+                {
+                    JSON_THROW(invalid_iterator::create(204, "iterators out of range", this));
+                }
+
+                if (is_string())
+                {
+                    AllocatorType<string_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.string);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.string, 1);
+                    m_data.m_value.string = nullptr;
+                }
+                else if (is_binary())
+                {
+                    AllocatorType<binary_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.binary);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.binary, 1);
+                    m_data.m_value.binary = nullptr;
+                }
+
+                m_data.m_type = value_t::null;
+                assert_invariant();
+                break;
+            }
+
+            case value_t::object:
+            {
+                result.m_it.object_iterator = m_data.m_value.object->erase(first.m_it.object_iterator,
+                                              last.m_it.object_iterator);
+                break;
+            }
+
+            case value_t::array:
+            {
+                result.m_it.array_iterator = m_data.m_value.array->erase(first.m_it.array_iterator,
+                                             last.m_it.array_iterator);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        return result;
+    }
+
+  private:
+    template < typename KeyType, detail::enable_if_t <
+                   detail::has_erase_with_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    size_type erase_internal(KeyType && key)
+    {
+        // this erase only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        return m_data.m_value.object->erase(std::forward<KeyType>(key));
+    }
+
+    template < typename KeyType, detail::enable_if_t <
+                   !detail::has_erase_with_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    size_type erase_internal(KeyType && key)
+    {
+        // this erase only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        const auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+        if (it != m_data.m_value.object->end())
+        {
+            m_data.m_value.object->erase(it);
+            return 1;
+        }
+        return 0;
+    }
+
+  public:
+
+    /// @brief remove element from a JSON object given a key
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    size_type erase(const typename object_t::key_type& key)
+    {
+        // the indirection via erase_internal() is added to avoid making this
+        // function a template and thus de-rank it during overload resolution
+        return erase_internal(key);
+    }
+
+    /// @brief remove element from a JSON object given a key
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    size_type erase(KeyType && key)
+    {
+        return erase_internal(std::forward<KeyType>(key));
+    }
+
+    /// @brief remove element from a JSON array given an index
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    void erase(const size_type idx)
+    {
+        // this erase only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            if (JSON_HEDLEY_UNLIKELY(idx >= size()))
+            {
+                JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), this));
+            }
+
+            m_data.m_value.array->erase(m_data.m_value.array->begin() + static_cast<difference_type>(idx));
+        }
+        else
+        {
+            JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+    }
+
+    /// @}
+
+    ////////////
+    // lookup //
+    ////////////
+
+    /// @name lookup
+    /// @{
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    iterator find(const typename object_t::key_type& key)
+    {
+        auto result = end();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(key);
+        }
+
+        return result;
+    }
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    const_iterator find(const typename object_t::key_type& key) const
+    {
+        auto result = cend();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(key);
+        }
+
+        return result;
+    }
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    iterator find(KeyType && key)
+    {
+        auto result = end();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(std::forward<KeyType>(key));
+        }
+
+        return result;
+    }
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    const_iterator find(KeyType && key) const
+    {
+        auto result = cend();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(std::forward<KeyType>(key));
+        }
+
+        return result;
+    }
+
+    /// @brief returns the number of occurrences of a key in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/count/
+    size_type count(const typename object_t::key_type& key) const
+    {
+        // return 0 for all nonobject types
+        return is_object() ? m_data.m_value.object->count(key) : 0;
+    }
+
+    /// @brief returns the number of occurrences of a key in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/count/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    size_type count(KeyType && key) const
+    {
+        // return 0 for all nonobject types
+        return is_object() ? m_data.m_value.object->count(std::forward<KeyType>(key)) : 0;
+    }
+
+    /// @brief check the existence of an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/contains/
+    bool contains(const typename object_t::key_type& key) const
+    {
+        return is_object() && m_data.m_value.object->find(key) != m_data.m_value.object->end();
+    }
+
+    /// @brief check the existence of an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/contains/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    bool contains(KeyType && key) const
+    {
+        return is_object() && m_data.m_value.object->find(std::forward<KeyType>(key)) != m_data.m_value.object->end();
+    }
+
+    /// @brief check the existence of an element in a JSON object given a JSON pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/contains/
+    bool contains(const json_pointer& ptr) const
+    {
+        return ptr.contains(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    bool contains(const typename ::nlohmann::json_pointer<BasicJsonType>& ptr) const
+    {
+        return ptr.contains(this);
+    }
+
+    /// @}
+
+    ///////////////
+    // iterators //
+    ///////////////
+
+    /// @name iterators
+    /// @{
+
+    /// @brief returns an iterator to the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/begin/
+    iterator begin() noexcept
+    {
+        iterator result(this);
+        result.set_begin();
+        return result;
+    }
+
+    /// @brief returns an iterator to the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/begin/
+    const_iterator begin() const noexcept
+    {
+        return cbegin();
+    }
+
+    /// @brief returns a const iterator to the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/cbegin/
+    const_iterator cbegin() const noexcept
+    {
+        const_iterator result(this);
+        result.set_begin();
+        return result;
+    }
+
+    /// @brief returns an iterator to one past the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/end/
+    iterator end() noexcept
+    {
+        iterator result(this);
+        result.set_end();
+        return result;
+    }
+
+    /// @brief returns an iterator to one past the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/end/
+    const_iterator end() const noexcept
+    {
+        return cend();
+    }
+
+    /// @brief returns an iterator to one past the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/cend/
+    const_iterator cend() const noexcept
+    {
+        const_iterator result(this);
+        result.set_end();
+        return result;
+    }
+
+    /// @brief returns an iterator to the reverse-beginning
+    /// @sa https://json.nlohmann.me/api/basic_json/rbegin/
+    reverse_iterator rbegin() noexcept
+    {
+        return reverse_iterator(end());
+    }
+
+    /// @brief returns an iterator to the reverse-beginning
+    /// @sa https://json.nlohmann.me/api/basic_json/rbegin/
+    const_reverse_iterator rbegin() const noexcept
+    {
+        return crbegin();
+    }
+
+    /// @brief returns an iterator to the reverse-end
+    /// @sa https://json.nlohmann.me/api/basic_json/rend/
+    reverse_iterator rend() noexcept
+    {
+        return reverse_iterator(begin());
+    }
+
+    /// @brief returns an iterator to the reverse-end
+    /// @sa https://json.nlohmann.me/api/basic_json/rend/
+    const_reverse_iterator rend() const noexcept
+    {
+        return crend();
+    }
+
+    /// @brief returns a const reverse iterator to the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/crbegin/
+    const_reverse_iterator crbegin() const noexcept
+    {
+        return const_reverse_iterator(cend());
+    }
+
+    /// @brief returns a const reverse iterator to one before the first
+    /// @sa https://json.nlohmann.me/api/basic_json/crend/
+    const_reverse_iterator crend() const noexcept
+    {
+        return const_reverse_iterator(cbegin());
+    }
+
+  public:
+    /// @brief wrapper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    /// @deprecated This function is deprecated since 3.1.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use @ref items() instead;
+    ///             that is, replace `json::iterator_wrapper(j)` with `j.items()`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.1.0, items())
+    static iteration_proxy<iterator> iterator_wrapper(reference ref) noexcept
+    {
+        return ref.items();
+    }
+
+    /// @brief wrapper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    /// @deprecated This function is deprecated since 3.1.0 and will be removed in
+    ///         version 4.0.0 of the library. Please use @ref items() instead;
+    ///         that is, replace `json::iterator_wrapper(j)` with `j.items()`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.1.0, items())
+    static iteration_proxy<const_iterator> iterator_wrapper(const_reference ref) noexcept
+    {
+        return ref.items();
+    }
+
+    /// @brief helper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    iteration_proxy<iterator> items() noexcept
+    {
+        return iteration_proxy<iterator>(*this);
+    }
+
+    /// @brief helper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    iteration_proxy<const_iterator> items() const noexcept
+    {
+        return iteration_proxy<const_iterator>(*this);
+    }
+
+    /// @}
+
+    //////////////
+    // capacity //
+    //////////////
+
+    /// @name capacity
+    /// @{
+
+    /// @brief checks whether the container is empty.
+    /// @sa https://json.nlohmann.me/api/basic_json/empty/
+    bool empty() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::null:
+            {
+                // null values are empty
+                return true;
+            }
+
+            case value_t::array:
+            {
+                // delegate call to array_t::empty()
+                return m_data.m_value.array->empty();
+            }
+
+            case value_t::object:
+            {
+                // delegate call to object_t::empty()
+                return m_data.m_value.object->empty();
+            }
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // all other types are nonempty
+                return false;
+            }
+        }
+    }
+
+    /// @brief returns the number of elements
+    /// @sa https://json.nlohmann.me/api/basic_json/size/
+    size_type size() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::null:
+            {
+                // null values are empty
+                return 0;
+            }
+
+            case value_t::array:
+            {
+                // delegate call to array_t::size()
+                return m_data.m_value.array->size();
+            }
+
+            case value_t::object:
+            {
+                // delegate call to object_t::size()
+                return m_data.m_value.object->size();
+            }
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // all other types have size 1
+                return 1;
+            }
+        }
+    }
+
+    /// @brief returns the maximum possible number of elements
+    /// @sa https://json.nlohmann.me/api/basic_json/max_size/
+    size_type max_size() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::array:
+            {
+                // delegate call to array_t::max_size()
+                return m_data.m_value.array->max_size();
+            }
+
+            case value_t::object:
+            {
+                // delegate call to object_t::max_size()
+                return m_data.m_value.object->max_size();
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // all other types have max_size() == size()
+                return size();
+            }
+        }
+    }
+
+    /// @}
+
+    ///////////////
+    // modifiers //
+    ///////////////
+
+    /// @name modifiers
+    /// @{
+
+    /// @brief clears the contents
+    /// @sa https://json.nlohmann.me/api/basic_json/clear/
+    void clear() noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::number_integer:
+            {
+                m_data.m_value.number_integer = 0;
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                m_data.m_value.number_unsigned = 0;
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                m_data.m_value.number_float = 0.0;
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                m_data.m_value.boolean = false;
+                break;
+            }
+
+            case value_t::string:
+            {
+                m_data.m_value.string->clear();
+                break;
+            }
+
+            case value_t::binary:
+            {
+                m_data.m_value.binary->clear();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_data.m_value.array->clear();
+                break;
+            }
+
+            case value_t::object:
+            {
+                m_data.m_value.object->clear();
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(basic_json&& val)
+    {
+        // push_back only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))
+        {
+            JSON_THROW(type_error::create(308, detail::concat("cannot use push_back() with ", type_name()), this));
+        }
+
+        // transform null object into an array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value = value_t::array;
+            assert_invariant();
+        }
+
+        // add element to array (move semantics)
+        const auto old_capacity = m_data.m_value.array->capacity();
+        m_data.m_value.array->push_back(std::move(val));
+        set_parent(m_data.m_value.array->back(), old_capacity);
+        // if val is moved from, basic_json move constructor marks it null, so we do not call the destructor
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(basic_json&& val)
+    {
+        push_back(std::move(val));
+        return *this;
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(const basic_json& val)
+    {
+        // push_back only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))
+        {
+            JSON_THROW(type_error::create(308, detail::concat("cannot use push_back() with ", type_name()), this));
+        }
+
+        // transform null object into an array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value = value_t::array;
+            assert_invariant();
+        }
+
+        // add element to array
+        const auto old_capacity = m_data.m_value.array->capacity();
+        m_data.m_value.array->push_back(val);
+        set_parent(m_data.m_value.array->back(), old_capacity);
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(const basic_json& val)
+    {
+        push_back(val);
+        return *this;
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(const typename object_t::value_type& val)
+    {
+        // push_back only works for null objects or objects
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_object())))
+        {
+            JSON_THROW(type_error::create(308, detail::concat("cannot use push_back() with ", type_name()), this));
+        }
+
+        // transform null object into an object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value = value_t::object;
+            assert_invariant();
+        }
+
+        // add element to object
+        auto res = m_data.m_value.object->insert(val);
+        set_parent(res.first->second);
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(const typename object_t::value_type& val)
+    {
+        push_back(val);
+        return *this;
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(initializer_list_t init)
+    {
+        if (is_object() && init.size() == 2 && (*init.begin())->is_string())
+        {
+            basic_json&& key = init.begin()->moved_or_copied();
+            push_back(typename object_t::value_type(
+                          std::move(key.get_ref<string_t&>()), (init.begin() + 1)->moved_or_copied()));
+        }
+        else
+        {
+            push_back(basic_json(init));
+        }
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(initializer_list_t init)
+    {
+        push_back(init);
+        return *this;
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/emplace_back/
+    template<class... Args>
+    reference emplace_back(Args&& ... args)
+    {
+        // emplace_back only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))
+        {
+            JSON_THROW(type_error::create(311, detail::concat("cannot use emplace_back() with ", type_name()), this));
+        }
+
+        // transform null object into an array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value = value_t::array;
+            assert_invariant();
+        }
+
+        // add element to array (perfect forwarding)
+        const auto old_capacity = m_data.m_value.array->capacity();
+        m_data.m_value.array->emplace_back(std::forward<Args>(args)...);
+        return set_parent(m_data.m_value.array->back(), old_capacity);
+    }
+
+    /// @brief add an object to an object if key does not exist
+    /// @sa https://json.nlohmann.me/api/basic_json/emplace/
+    template<class... Args>
+    std::pair<iterator, bool> emplace(Args&& ... args)
+    {
+        // emplace only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_object())))
+        {
+            JSON_THROW(type_error::create(311, detail::concat("cannot use emplace() with ", type_name()), this));
+        }
+
+        // transform null object into an object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value = value_t::object;
+            assert_invariant();
+        }
+
+        // add element to array (perfect forwarding)
+        auto res = m_data.m_value.object->emplace(std::forward<Args>(args)...);
+        set_parent(res.first->second);
+
+        // create result iterator and set iterator to the result of emplace
+        auto it = begin();
+        it.m_it.object_iterator = res.first;
+
+        // return pair of iterator and boolean
+        return {it, res.second};
+    }
+
+    /// Helper for insertion of an iterator
+    /// @note: This uses std::distance to support GCC 4.8,
+    ///        see https://github.com/nlohmann/json/pull/1257
+    template<typename... Args>
+    iterator insert_iterator(const_iterator pos, Args&& ... args) // NOLINT(performance-unnecessary-value-param)
+    {
+        iterator result(this);
+        JSON_ASSERT(m_data.m_value.array != nullptr);
+
+        auto insert_pos = std::distance(m_data.m_value.array->begin(), pos.m_it.array_iterator);
+        m_data.m_value.array->insert(pos.m_it.array_iterator, std::forward<Args>(args)...);
+        result.m_it.array_iterator = m_data.m_value.array->begin() + insert_pos;
+
+        // This could have been written as:
+        // result.m_it.array_iterator = m_data.m_value.array->insert(pos.m_it.array_iterator, cnt, val);
+        // but the return value of insert is missing in GCC 4.8, so it is written this way instead.
+
+        set_parents();
+        return result;
+    }
+
+    /// @brief inserts element into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, const basic_json& val) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            // check if iterator pos fits to this JSON value
+            if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+            {
+                JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+            }
+
+            // insert to array and return iterator
+            return insert_iterator(pos, val);
+        }
+
+        JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+    }
+
+    /// @brief inserts element into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, basic_json&& val) // NOLINT(performance-unnecessary-value-param)
+    {
+        return insert(pos, val);
+    }
+
+    /// @brief inserts copies of element into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, size_type cnt, const basic_json& val) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            // check if iterator pos fits to this JSON value
+            if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+            {
+                JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+            }
+
+            // insert to array and return iterator
+            return insert_iterator(pos, cnt, val);
+        }
+
+        JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+    }
+
+    /// @brief inserts range of elements into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, const_iterator first, const_iterator last) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_UNLIKELY(!is_array()))
+        {
+            JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+        }
+
+        // check if iterator pos fits to this JSON value
+        if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+        }
+
+        // check if range iterators belong to the same JSON object
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(210, "iterators do not fit", this));
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(first.m_object == this))
+        {
+            JSON_THROW(invalid_iterator::create(211, "passed iterators may not belong to container", this));
+        }
+
+        // insert to array and return iterator
+        return insert_iterator(pos, first.m_it.array_iterator, last.m_it.array_iterator);
+    }
+
+    /// @brief inserts elements from initializer list into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, initializer_list_t ilist) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_UNLIKELY(!is_array()))
+        {
+            JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+        }
+
+        // check if iterator pos fits to this JSON value
+        if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+        }
+
+        // insert to array and return iterator
+        return insert_iterator(pos, ilist.begin(), ilist.end());
+    }
+
+    /// @brief inserts range of elements into object
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    void insert(const_iterator first, const_iterator last) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+        }
+
+        // check if range iterators belong to the same JSON object
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(210, "iterators do not fit", this));
+        }
+
+        // passed iterators must belong to objects
+        if (JSON_HEDLEY_UNLIKELY(!first.m_object->is_object()))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterators first and last must point to objects", this));
+        }
+
+        m_data.m_value.object->insert(first.m_it.object_iterator, last.m_it.object_iterator);
+        set_parents();
+    }
+
+    /// @brief updates a JSON object from another object, overwriting existing keys
+    /// @sa https://json.nlohmann.me/api/basic_json/update/
+    void update(const_reference j, bool merge_objects = false)
+    {
+        update(j.begin(), j.end(), merge_objects);
+    }
+
+    /// @brief updates a JSON object from another object, overwriting existing keys
+    /// @sa https://json.nlohmann.me/api/basic_json/update/
+    void update(const_iterator first, const_iterator last, bool merge_objects = false) // NOLINT(performance-unnecessary-value-param)
+    {
+        // implicitly convert null value to an empty object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value.object = create<object_t>();
+            assert_invariant();
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(312, detail::concat("cannot use update() with ", type_name()), this));
+        }
+
+        // check if range iterators belong to the same JSON object
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(210, "iterators do not fit", this));
+        }
+
+        // passed iterators must belong to objects
+        if (JSON_HEDLEY_UNLIKELY(!first.m_object->is_object()))
+        {
+            JSON_THROW(type_error::create(312, detail::concat("cannot use update() with ", first.m_object->type_name()), first.m_object));
+        }
+
+        for (auto it = first; it != last; ++it)
+        {
+            if (merge_objects && it.value().is_object())
+            {
+                auto it2 = m_data.m_value.object->find(it.key());
+                if (it2 != m_data.m_value.object->end())
+                {
+                    it2->second.update(it.value(), true);
+                    continue;
+                }
+            }
+            m_data.m_value.object->operator[](it.key()) = it.value();
+#if JSON_DIAGNOSTICS
+            m_data.m_value.object->operator[](it.key()).m_parent = this;
+#endif
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(reference other) noexcept (
+        std::is_nothrow_move_constructible<value_t>::value&&
+        std::is_nothrow_move_assignable<value_t>::value&&
+        std::is_nothrow_move_constructible<json_value>::value&& // NOLINT(cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+        std::is_nothrow_move_assignable<json_value>::value
+    )
+    {
+        std::swap(m_data.m_type, other.m_data.m_type);
+        std::swap(m_data.m_value, other.m_data.m_value);
+
+        set_parents();
+        other.set_parents();
+        assert_invariant();
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    friend void swap(reference left, reference right) noexcept (
+        std::is_nothrow_move_constructible<value_t>::value&&
+        std::is_nothrow_move_assignable<value_t>::value&&
+        std::is_nothrow_move_constructible<json_value>::value&& // NOLINT(cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+        std::is_nothrow_move_assignable<json_value>::value
+    )
+    {
+        left.swap(right);
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(array_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.array), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(array_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(object_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.object), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(object_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(string_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for strings
+        if (JSON_HEDLEY_LIKELY(is_string()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.string), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(string_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(binary_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for strings
+        if (JSON_HEDLEY_LIKELY(is_binary()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.binary), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(binary_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(typename binary_t::container_type& other) // NOLINT(bugprone-exception-escape)
+    {
+        // swap only works for strings
+        if (JSON_HEDLEY_LIKELY(is_binary()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.binary), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(binary_t::container_type&) with ", type_name()), this));
+        }
+    }
+
+    /// @}
+
+    //////////////////////////////////////////
+    // lexicographical comparison operators //
+    //////////////////////////////////////////
+
+    /// @name lexicographical comparison operators
+    /// @{
+
+    // note parentheses around operands are necessary; see
+    // https://github.com/nlohmann/json/issues/1530
+#define JSON_IMPLEMENT_OPERATOR(op, null_result, unordered_result, default_result)                       \
+    const auto lhs_type = lhs.type();                                                                    \
+    const auto rhs_type = rhs.type();                                                                    \
+    \
+    if (lhs_type == rhs_type) /* NOLINT(readability/braces) */                                           \
+    {                                                                                                    \
+        switch (lhs_type)                                                                                \
+        {                                                                                                \
+            case value_t::array:                                                                         \
+                return (*lhs.m_data.m_value.array) op (*rhs.m_data.m_value.array);                                     \
+                \
+            case value_t::object:                                                                        \
+                return (*lhs.m_data.m_value.object) op (*rhs.m_data.m_value.object);                                   \
+                \
+            case value_t::null:                                                                          \
+                return (null_result);                                                                    \
+                \
+            case value_t::string:                                                                        \
+                return (*lhs.m_data.m_value.string) op (*rhs.m_data.m_value.string);                                   \
+                \
+            case value_t::boolean:                                                                       \
+                return (lhs.m_data.m_value.boolean) op (rhs.m_data.m_value.boolean);                                   \
+                \
+            case value_t::number_integer:                                                                \
+                return (lhs.m_data.m_value.number_integer) op (rhs.m_data.m_value.number_integer);                     \
+                \
+            case value_t::number_unsigned:                                                               \
+                return (lhs.m_data.m_value.number_unsigned) op (rhs.m_data.m_value.number_unsigned);                   \
+                \
+            case value_t::number_float:                                                                  \
+                return (lhs.m_data.m_value.number_float) op (rhs.m_data.m_value.number_float);                         \
+                \
+            case value_t::binary:                                                                        \
+                return (*lhs.m_data.m_value.binary) op (*rhs.m_data.m_value.binary);                                   \
+                \
+            case value_t::discarded:                                                                     \
+            default:                                                                                     \
+                return (unordered_result);                                                               \
+        }                                                                                                \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_integer && rhs_type == value_t::number_float)                   \
+    {                                                                                                    \
+        return static_cast<number_float_t>(lhs.m_data.m_value.number_integer) op rhs.m_data.m_value.number_float;      \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_float && rhs_type == value_t::number_integer)                   \
+    {                                                                                                    \
+        return lhs.m_data.m_value.number_float op static_cast<number_float_t>(rhs.m_data.m_value.number_integer);      \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_unsigned && rhs_type == value_t::number_float)                  \
+    {                                                                                                    \
+        return static_cast<number_float_t>(lhs.m_data.m_value.number_unsigned) op rhs.m_data.m_value.number_float;     \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_float && rhs_type == value_t::number_unsigned)                  \
+    {                                                                                                    \
+        return lhs.m_data.m_value.number_float op static_cast<number_float_t>(rhs.m_data.m_value.number_unsigned);     \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_unsigned && rhs_type == value_t::number_integer)                \
+    {                                                                                                    \
+        return static_cast<number_integer_t>(lhs.m_data.m_value.number_unsigned) op rhs.m_data.m_value.number_integer; \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_integer && rhs_type == value_t::number_unsigned)                \
+    {                                                                                                    \
+        return lhs.m_data.m_value.number_integer op static_cast<number_integer_t>(rhs.m_data.m_value.number_unsigned); \
+    }                                                                                                    \
+    else if(compares_unordered(lhs, rhs))\
+    {\
+        return (unordered_result);\
+    }\
+    \
+    return (default_result);
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    // returns true if:
+    // - any operand is NaN and the other operand is of number type
+    // - any operand is discarded
+    // in legacy mode, discarded values are considered ordered if
+    // an operation is computed as an odd number of inverses of others
+    static bool compares_unordered(const_reference lhs, const_reference rhs, bool inverse = false) noexcept
+    {
+        if ((lhs.is_number_float() && std::isnan(lhs.m_data.m_value.number_float) && rhs.is_number())
+                || (rhs.is_number_float() && std::isnan(rhs.m_data.m_value.number_float) && lhs.is_number()))
+        {
+            return true;
+        }
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+        return (lhs.is_discarded() || rhs.is_discarded()) && !inverse;
+#else
+        static_cast<void>(inverse);
+        return lhs.is_discarded() || rhs.is_discarded();
+#endif
+    }
+
+  private:
+    bool compares_unordered(const_reference rhs, bool inverse = false) const noexcept
+    {
+        return compares_unordered(*this, rhs, inverse);
+    }
+
+  public:
+#if JSON_HAS_THREE_WAY_COMPARISON
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    bool operator==(const_reference rhs) const noexcept
+    {
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+        const_reference lhs = *this;
+        JSON_IMPLEMENT_OPERATOR( ==, true, false, false)
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+    }
+
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    bool operator==(ScalarType rhs) const noexcept
+    {
+        return *this == basic_json(rhs);
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    bool operator!=(const_reference rhs) const noexcept
+    {
+        if (compares_unordered(rhs, true))
+        {
+            return false;
+        }
+        return !operator==(rhs);
+    }
+
+    /// @brief comparison: 3-way
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_spaceship/
+    std::partial_ordering operator<=>(const_reference rhs) const noexcept // *NOPAD*
+    {
+        const_reference lhs = *this;
+        // default_result is used if we cannot compare values. In that case,
+        // we compare types.
+        JSON_IMPLEMENT_OPERATOR(<=>, // *NOPAD*
+                                std::partial_ordering::equivalent,
+                                std::partial_ordering::unordered,
+                                lhs_type <=> rhs_type) // *NOPAD*
+    }
+
+    /// @brief comparison: 3-way
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_spaceship/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    std::partial_ordering operator<=>(ScalarType rhs) const noexcept // *NOPAD*
+    {
+        return *this <=> basic_json(rhs); // *NOPAD*
+    }
+
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+    // all operators that are computed as an odd number of inverses of others
+    // need to be overloaded to emulate the legacy comparison behavior
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON)
+    bool operator<=(const_reference rhs) const noexcept
+    {
+        if (compares_unordered(rhs, true))
+        {
+            return false;
+        }
+        return !(rhs < *this);
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    bool operator<=(ScalarType rhs) const noexcept
+    {
+        return *this <= basic_json(rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON)
+    bool operator>=(const_reference rhs) const noexcept
+    {
+        if (compares_unordered(rhs, true))
+        {
+            return false;
+        }
+        return !(*this < rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    bool operator>=(ScalarType rhs) const noexcept
+    {
+        return *this >= basic_json(rhs);
+    }
+#endif
+#else
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    friend bool operator==(const_reference lhs, const_reference rhs) noexcept
+    {
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+        JSON_IMPLEMENT_OPERATOR( ==, true, false, false)
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+    }
+
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator==(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs == basic_json(rhs);
+    }
+
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator==(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) == rhs;
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    friend bool operator!=(const_reference lhs, const_reference rhs) noexcept
+    {
+        if (compares_unordered(lhs, rhs, true))
+        {
+            return false;
+        }
+        return !(lhs == rhs);
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator!=(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs != basic_json(rhs);
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator!=(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) != rhs;
+    }
+
+    /// @brief comparison: less than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/
+    friend bool operator<(const_reference lhs, const_reference rhs) noexcept
+    {
+        // default_result is used if we cannot compare values. In that case,
+        // we compare types. Note we have to call the operator explicitly,
+        // because MSVC has problems otherwise.
+        JSON_IMPLEMENT_OPERATOR( <, false, false, operator<(lhs_type, rhs_type))
+    }
+
+    /// @brief comparison: less than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs < basic_json(rhs);
+    }
+
+    /// @brief comparison: less than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) < rhs;
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    friend bool operator<=(const_reference lhs, const_reference rhs) noexcept
+    {
+        if (compares_unordered(lhs, rhs, true))
+        {
+            return false;
+        }
+        return !(rhs < lhs);
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<=(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs <= basic_json(rhs);
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<=(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) <= rhs;
+    }
+
+    /// @brief comparison: greater than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/
+    friend bool operator>(const_reference lhs, const_reference rhs) noexcept
+    {
+        // double inverse
+        if (compares_unordered(lhs, rhs))
+        {
+            return false;
+        }
+        return !(lhs <= rhs);
+    }
+
+    /// @brief comparison: greater than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs > basic_json(rhs);
+    }
+
+    /// @brief comparison: greater than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) > rhs;
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    friend bool operator>=(const_reference lhs, const_reference rhs) noexcept
+    {
+        if (compares_unordered(lhs, rhs, true))
+        {
+            return false;
+        }
+        return !(lhs < rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>=(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs >= basic_json(rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>=(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) >= rhs;
+    }
+#endif
+
+#undef JSON_IMPLEMENT_OPERATOR
+
+    /// @}
+
+    ///////////////////
+    // serialization //
+    ///////////////////
+
+    /// @name serialization
+    /// @{
+#ifndef JSON_NO_IO
+    /// @brief serialize to stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/
+    friend std::ostream& operator<<(std::ostream& o, const basic_json& j)
+    {
+        // read width member and use it as indentation parameter if nonzero
+        const bool pretty_print = o.width() > 0;
+        const auto indentation = pretty_print ? o.width() : 0;
+
+        // reset width to 0 for subsequent calls to this stream
+        o.width(0);
+
+        // do the actual serialization
+        serializer s(detail::output_adapter<char>(o), o.fill());
+        s.dump(j, pretty_print, false, static_cast<unsigned int>(indentation));
+        return o;
+    }
+
+    /// @brief serialize to stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/
+    /// @deprecated This function is deprecated since 3.0.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use
+    ///             operator<<(std::ostream&, const basic_json&) instead; that is,
+    ///             replace calls like `j >> o;` with `o << j;`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.0.0, operator<<(std::ostream&, const basic_json&))
+    friend std::ostream& operator>>(const basic_json& j, std::ostream& o)
+    {
+        return o << j;
+    }
+#endif  // JSON_NO_IO
+    /// @}
+
+    /////////////////////
+    // deserialization //
+    /////////////////////
+
+    /// @name deserialization
+    /// @{
+
+    /// @brief deserialize from a compatible input
+    /// @sa https://json.nlohmann.me/api/basic_json/parse/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json parse(InputType&& i,
+                            parser_callback_t cb = nullptr,
+                            const bool allow_exceptions = true,
+                            const bool ignore_comments = false)
+    {
+        basic_json result;
+        parser(detail::input_adapter(std::forward<InputType>(i)), std::move(cb), allow_exceptions, ignore_comments).parse(true, result); // cppcheck-suppress[accessMoved,accessForwarded]
+        return result;
+    }
+
+    /// @brief deserialize from a pair of character iterators
+    /// @sa https://json.nlohmann.me/api/basic_json/parse/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json parse(IteratorType first,
+                            IteratorType last,
+                            parser_callback_t cb = nullptr,
+                            const bool allow_exceptions = true,
+                            const bool ignore_comments = false)
+    {
+        basic_json result;
+        parser(detail::input_adapter(std::move(first), std::move(last)), std::move(cb), allow_exceptions, ignore_comments).parse(true, result); // cppcheck-suppress[accessMoved]
+        return result;
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, parse(ptr, ptr + len))
+    static basic_json parse(detail::span_input_adapter&& i,
+                            parser_callback_t cb = nullptr,
+                            const bool allow_exceptions = true,
+                            const bool ignore_comments = false)
+    {
+        basic_json result;
+        parser(i.get(), std::move(cb), allow_exceptions, ignore_comments).parse(true, result); // cppcheck-suppress[accessMoved]
+        return result;
+    }
+
+    /// @brief check if the input is valid JSON
+    /// @sa https://json.nlohmann.me/api/basic_json/accept/
+    template<typename InputType>
+    static bool accept(InputType&& i,
+                       const bool ignore_comments = false)
+    {
+        return parser(detail::input_adapter(std::forward<InputType>(i)), nullptr, false, ignore_comments).accept(true);
+    }
+
+    /// @brief check if the input is valid JSON
+    /// @sa https://json.nlohmann.me/api/basic_json/accept/
+    template<typename IteratorType>
+    static bool accept(IteratorType first, IteratorType last,
+                       const bool ignore_comments = false)
+    {
+        return parser(detail::input_adapter(std::move(first), std::move(last)), nullptr, false, ignore_comments).accept(true);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, accept(ptr, ptr + len))
+    static bool accept(detail::span_input_adapter&& i,
+                       const bool ignore_comments = false)
+    {
+        return parser(i.get(), nullptr, false, ignore_comments).accept(true);
+    }
+
+    /// @brief generate SAX events
+    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/
+    template <typename InputType, typename SAX>
+    JSON_HEDLEY_NON_NULL(2)
+    static bool sax_parse(InputType&& i, SAX* sax,
+                          input_format_t format = input_format_t::json,
+                          const bool strict = true,
+                          const bool ignore_comments = false)
+    {
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        return format == input_format_t::json
+               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)
+               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);
+    }
+
+    /// @brief generate SAX events
+    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/
+    template<class IteratorType, class SAX>
+    JSON_HEDLEY_NON_NULL(3)
+    static bool sax_parse(IteratorType first, IteratorType last, SAX* sax,
+                          input_format_t format = input_format_t::json,
+                          const bool strict = true,
+                          const bool ignore_comments = false)
+    {
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        return format == input_format_t::json
+               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)
+               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);
+    }
+
+    /// @brief generate SAX events
+    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/
+    /// @deprecated This function is deprecated since 3.8.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use
+    ///             sax_parse(ptr, ptr + len) instead.
+    template <typename SAX>
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, sax_parse(ptr, ptr + len, ...))
+    JSON_HEDLEY_NON_NULL(2)
+    static bool sax_parse(detail::span_input_adapter&& i, SAX* sax,
+                          input_format_t format = input_format_t::json,
+                          const bool strict = true,
+                          const bool ignore_comments = false)
+    {
+        auto ia = i.get();
+        return format == input_format_t::json
+               // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)
+               // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);
+    }
+#ifndef JSON_NO_IO
+    /// @brief deserialize from stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gtgt/
+    /// @deprecated This stream operator is deprecated since 3.0.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use
+    ///             operator>>(std::istream&, basic_json&) instead; that is,
+    ///             replace calls like `j << i;` with `i >> j;`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.0.0, operator>>(std::istream&, basic_json&))
+    friend std::istream& operator<<(basic_json& j, std::istream& i)
+    {
+        return operator>>(i, j);
+    }
+
+    /// @brief deserialize from stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gtgt/
+    friend std::istream& operator>>(std::istream& i, basic_json& j)
+    {
+        parser(detail::input_adapter(i)).parse(false, j);
+        return i;
+    }
+#endif  // JSON_NO_IO
+    /// @}
+
+    ///////////////////////////
+    // convenience functions //
+    ///////////////////////////
+
+    /// @brief return the type as string
+    /// @sa https://json.nlohmann.me/api/basic_json/type_name/
+    JSON_HEDLEY_RETURNS_NON_NULL
+    const char* type_name() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::null:
+                return "null";
+            case value_t::object:
+                return "object";
+            case value_t::array:
+                return "array";
+            case value_t::string:
+                return "string";
+            case value_t::boolean:
+                return "boolean";
+            case value_t::binary:
+                return "binary";
+            case value_t::discarded:
+                return "discarded";
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            default:
+                return "number";
+        }
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    //////////////////////
+    // member variables //
+    //////////////////////
+
+    struct data
+    {
+        /// the type of the current element
+        value_t m_type = value_t::null;
+
+        /// the value of the current element
+        json_value m_value = {};
+
+        data(const value_t v)
+            : m_type(v), m_value(v)
+        {
+        }
+
+        data(size_type cnt, const basic_json& val)
+            : m_type(value_t::array)
+        {
+            m_value.array = create<array_t>(cnt, val);
+        }
+
+        data() noexcept = default;
+        data(data&&) noexcept = default;
+        data(const data&) noexcept = delete;
+        data& operator=(data&&) noexcept = delete;
+        data& operator=(const data&) noexcept = delete;
+
+        ~data() noexcept
+        {
+            m_value.destroy(m_type);
+        }
+    };
+
+    data m_data = {};
+
+#if JSON_DIAGNOSTICS
+    /// a pointer to a parent value (for debugging purposes)
+    basic_json* m_parent = nullptr;
+#endif
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    /// the start position of the value
+    std::size_t start_position = std::string::npos;
+    /// the end position of the value
+    std::size_t end_position = std::string::npos;
+  public:
+    constexpr std::size_t start_pos() const noexcept
+    {
+        return start_position;
+    }
+
+    constexpr std::size_t end_pos() const noexcept
+    {
+        return end_position;
+    }
+#endif
+
+    //////////////////////////////////////////
+    // binary serialization/deserialization //
+    //////////////////////////////////////////
+
+    /// @name binary serialization/deserialization support
+    /// @{
+
+  public:
+    /// @brief create a CBOR serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/
+    static std::vector<std::uint8_t> to_cbor(const basic_json& j)
+    {
+        std::vector<std::uint8_t> result;
+        to_cbor(j, result);
+        return result;
+    }
+
+    /// @brief create a CBOR serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/
+    static void to_cbor(const basic_json& j, detail::output_adapter<std::uint8_t> o)
+    {
+        binary_writer<std::uint8_t>(o).write_cbor(j);
+    }
+
+    /// @brief create a CBOR serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/
+    static void to_cbor(const basic_json& j, detail::output_adapter<char> o)
+    {
+        binary_writer<char>(o).write_cbor(j);
+    }
+
+    /// @brief create a MessagePack serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/
+    static std::vector<std::uint8_t> to_msgpack(const basic_json& j)
+    {
+        std::vector<std::uint8_t> result;
+        to_msgpack(j, result);
+        return result;
+    }
+
+    /// @brief create a MessagePack serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/
+    static void to_msgpack(const basic_json& j, detail::output_adapter<std::uint8_t> o)
+    {
+        binary_writer<std::uint8_t>(o).write_msgpack(j);
+    }
+
+    /// @brief create a MessagePack serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/
+    static void to_msgpack(const basic_json& j, detail::output_adapter<char> o)
+    {
+        binary_writer<char>(o).write_msgpack(j);
+    }
+
+    /// @brief create a UBJSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/
+    static std::vector<std::uint8_t> to_ubjson(const basic_json& j,
+            const bool use_size = false,
+            const bool use_type = false)
+    {
+        std::vector<std::uint8_t> result;
+        to_ubjson(j, result, use_size, use_type);
+        return result;
+    }
+
+    /// @brief create a UBJSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/
+    static void to_ubjson(const basic_json& j, detail::output_adapter<std::uint8_t> o,
+                          const bool use_size = false, const bool use_type = false)
+    {
+        binary_writer<std::uint8_t>(o).write_ubjson(j, use_size, use_type);
+    }
+
+    /// @brief create a UBJSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/
+    static void to_ubjson(const basic_json& j, detail::output_adapter<char> o,
+                          const bool use_size = false, const bool use_type = false)
+    {
+        binary_writer<char>(o).write_ubjson(j, use_size, use_type);
+    }
+
+    /// @brief create a BJData serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/
+    static std::vector<std::uint8_t> to_bjdata(const basic_json& j,
+            const bool use_size = false,
+            const bool use_type = false,
+            const bjdata_version_t version = bjdata_version_t::draft2)
+    {
+        std::vector<std::uint8_t> result;
+        to_bjdata(j, result, use_size, use_type, version);
+        return result;
+    }
+
+    /// @brief create a BJData serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/
+    static void to_bjdata(const basic_json& j, detail::output_adapter<std::uint8_t> o,
+                          const bool use_size = false, const bool use_type = false,
+                          const bjdata_version_t version = bjdata_version_t::draft2)
+    {
+        binary_writer<std::uint8_t>(o).write_ubjson(j, use_size, use_type, true, true, version);
+    }
+
+    /// @brief create a BJData serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/
+    static void to_bjdata(const basic_json& j, detail::output_adapter<char> o,
+                          const bool use_size = false, const bool use_type = false,
+                          const bjdata_version_t version = bjdata_version_t::draft2)
+    {
+        binary_writer<char>(o).write_ubjson(j, use_size, use_type, true, true, version);
+    }
+
+    /// @brief create a BSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/
+    static std::vector<std::uint8_t> to_bson(const basic_json& j)
+    {
+        std::vector<std::uint8_t> result;
+        to_bson(j, result);
+        return result;
+    }
+
+    /// @brief create a BSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/
+    static void to_bson(const basic_json& j, detail::output_adapter<std::uint8_t> o)
+    {
+        binary_writer<std::uint8_t>(o).write_bson(j);
+    }
+
+    /// @brief create a BSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/
+    static void to_bson(const basic_json& j, detail::output_adapter<char> o)
+    {
+        binary_writer<char>(o).write_bson(j);
+    }
+
+    /// @brief create a JSON value from an input in CBOR format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_cbor/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_cbor(InputType&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in CBOR format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_cbor/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_cbor(IteratorType first, IteratorType last,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_cbor(ptr, ptr + len))
+    static basic_json from_cbor(const T* ptr, std::size_t len,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        return from_cbor(ptr, ptr + len, strict, allow_exceptions, tag_handler);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_cbor(ptr, ptr + len))
+    static basic_json from_cbor(detail::span_input_adapter&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in MessagePack format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_msgpack/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_msgpack(InputType&& i,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in MessagePack format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_msgpack/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_msgpack(IteratorType first, IteratorType last,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_msgpack(ptr, ptr + len))
+    static basic_json from_msgpack(const T* ptr, std::size_t len,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        return from_msgpack(ptr, ptr + len, strict, allow_exceptions);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_msgpack(ptr, ptr + len))
+    static basic_json from_msgpack(detail::span_input_adapter&& i,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in UBJSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_ubjson/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_ubjson(InputType&& i,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in UBJSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_ubjson/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_ubjson(IteratorType first, IteratorType last,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_ubjson(ptr, ptr + len))
+    static basic_json from_ubjson(const T* ptr, std::size_t len,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        return from_ubjson(ptr, ptr + len, strict, allow_exceptions);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_ubjson(ptr, ptr + len))
+    static basic_json from_ubjson(detail::span_input_adapter&& i,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BJData format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bjdata/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bjdata(InputType&& i,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bjdata).sax_parse(input_format_t::bjdata, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BJData format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bjdata/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bjdata(IteratorType first, IteratorType last,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bjdata).sax_parse(input_format_t::bjdata, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bson/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bson(InputType&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bson/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bson(IteratorType first, IteratorType last,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_bson(ptr, ptr + len))
+    static basic_json from_bson(const T* ptr, std::size_t len,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        return from_bson(ptr, ptr + len, strict, allow_exceptions);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_bson(ptr, ptr + len))
+    static basic_json from_bson(detail::span_input_adapter&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+    /// @}
+
+    //////////////////////////
+    // JSON Pointer support //
+    //////////////////////////
+
+    /// @name JSON Pointer functions
+    /// @{
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    reference operator[](const json_pointer& ptr)
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    reference operator[](const ::nlohmann::json_pointer<BasicJsonType>& ptr)
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    const_reference operator[](const json_pointer& ptr) const
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    const_reference operator[](const ::nlohmann::json_pointer<BasicJsonType>& ptr) const
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    reference at(const json_pointer& ptr)
+    {
+        return ptr.get_checked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    reference at(const ::nlohmann::json_pointer<BasicJsonType>& ptr)
+    {
+        return ptr.get_checked(this);
+    }
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    const_reference at(const json_pointer& ptr) const
+    {
+        return ptr.get_checked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    const_reference at(const ::nlohmann::json_pointer<BasicJsonType>& ptr) const
+    {
+        return ptr.get_checked(this);
+    }
+
+    /// @brief return flattened JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/flatten/
+    basic_json flatten() const
+    {
+        basic_json result(value_t::object);
+        json_pointer::flatten("", *this, result);
+        return result;
+    }
+
+    /// @brief unflatten a previously flattened JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/unflatten/
+    basic_json unflatten() const
+    {
+        return json_pointer::unflatten(*this);
+    }
+
+    /// @}
+
+    //////////////////////////
+    // JSON Patch functions //
+    //////////////////////////
+
+    /// @name JSON Patch functions
+    /// @{
+
+    /// @brief applies a JSON patch in-place without copying the object
+    /// @sa https://json.nlohmann.me/api/basic_json/patch/
+    void patch_inplace(const basic_json& json_patch)
+    {
+        basic_json& result = *this;
+        // the valid JSON Patch operations
+        enum class patch_operations {add, remove, replace, move, copy, test, invalid};
+
+        const auto get_op = [](const string_t& op)
+        {
+            if (op == "add")
+            {
+                return patch_operations::add;
+            }
+            if (op == "remove")
+            {
+                return patch_operations::remove;
+            }
+            if (op == "replace")
+            {
+                return patch_operations::replace;
+            }
+            if (op == "move")
+            {
+                return patch_operations::move;
+            }
+            if (op == "copy")
+            {
+                return patch_operations::copy;
+            }
+            if (op == "test")
+            {
+                return patch_operations::test;
+            }
+
+            return patch_operations::invalid;
+        };
+
+        // wrapper for "add" operation; add value at ptr
+        const auto operation_add = [&result](json_pointer & ptr, const basic_json & val)
+        {
+            // adding to the root of the target document means replacing it
+            if (ptr.empty())
+            {
+                result = val;
+                return;
+            }
+
+            // make sure the top element of the pointer exists
+            json_pointer const top_pointer = ptr.top();
+            if (top_pointer != ptr)
+            {
+                result.at(top_pointer);
+            }
+
+            // get reference to parent of JSON pointer ptr
+            const auto last_path = ptr.back();
+            ptr.pop_back();
+            // parent must exist when performing patch add per RFC6902 specs
+            basic_json& parent = result.at(ptr);
+
+            switch (parent.m_data.m_type)
+            {
+                case value_t::null:
+                case value_t::object:
+                {
+                    // use operator[] to add value
+                    parent[last_path] = val;
+                    break;
+                }
+
+                case value_t::array:
+                {
+                    if (last_path == "-")
+                    {
+                        // special case: append to back
+                        parent.push_back(val);
+                    }
+                    else
+                    {
+                        const auto idx = json_pointer::template array_index<basic_json_t>(last_path);
+                        if (JSON_HEDLEY_UNLIKELY(idx > parent.size()))
+                        {
+                            // avoid undefined behavior
+                            JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), &parent));
+                        }
+
+                        // default case: insert add offset
+                        parent.insert(parent.begin() + static_cast<difference_type>(idx), val);
+                    }
+                    break;
+                }
+
+                // if there exists a parent it cannot be primitive
+                case value_t::string: // LCOV_EXCL_LINE
+                case value_t::boolean: // LCOV_EXCL_LINE
+                case value_t::number_integer: // LCOV_EXCL_LINE
+                case value_t::number_unsigned: // LCOV_EXCL_LINE
+                case value_t::number_float: // LCOV_EXCL_LINE
+                case value_t::binary: // LCOV_EXCL_LINE
+                case value_t::discarded: // LCOV_EXCL_LINE
+                default:            // LCOV_EXCL_LINE
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+            }
+        };
+
+        // wrapper for "remove" operation; remove value at ptr
+        const auto operation_remove = [this, & result](json_pointer & ptr)
+        {
+            // get reference to parent of JSON pointer ptr
+            const auto last_path = ptr.back();
+            ptr.pop_back();
+            basic_json& parent = result.at(ptr);
+
+            // remove child
+            if (parent.is_object())
+            {
+                // perform range check
+                auto it = parent.find(last_path);
+                if (JSON_HEDLEY_LIKELY(it != parent.end()))
+                {
+                    parent.erase(it);
+                }
+                else
+                {
+                    JSON_THROW(out_of_range::create(403, detail::concat("key '", last_path, "' not found"), this));
+                }
+            }
+            else if (parent.is_array())
+            {
+                // note erase performs range check
+                parent.erase(json_pointer::template array_index<basic_json_t>(last_path));
+            }
+        };
+
+        // type check: top level value must be an array
+        if (JSON_HEDLEY_UNLIKELY(!json_patch.is_array()))
+        {
+            JSON_THROW(parse_error::create(104, 0, "JSON patch must be an array of objects", &json_patch));
+        }
+
+        // iterate and apply the operations
+        for (const auto& val : json_patch)
+        {
+            // wrapper to get a value for an operation
+            const auto get_value = [&val](const string_t& op,
+                                          const string_t& member,
+                                          bool string_type) -> basic_json &
+            {
+                // find value
+                auto it = val.m_data.m_value.object->find(member);
+
+                // context-sensitive error message
+                const auto error_msg = (op == "op") ? "operation" : detail::concat("operation '", op, '\''); // NOLINT(bugprone-unused-local-non-trivial-variable)
+
+                // check if desired value is present
+                if (JSON_HEDLEY_UNLIKELY(it == val.m_data.m_value.object->end()))
+                {
+                    // NOLINTNEXTLINE(performance-inefficient-string-concatenation)
+                    JSON_THROW(parse_error::create(105, 0, detail::concat(error_msg, " must have member '", member, "'"), &val));
+                }
+
+                // check if result is of type string
+                if (JSON_HEDLEY_UNLIKELY(string_type && !it->second.is_string()))
+                {
+                    // NOLINTNEXTLINE(performance-inefficient-string-concatenation)
+                    JSON_THROW(parse_error::create(105, 0, detail::concat(error_msg, " must have string member '", member, "'"), &val));
+                }
+
+                // no error: return value
+                return it->second;
+            };
+
+            // type check: every element of the array must be an object
+            if (JSON_HEDLEY_UNLIKELY(!val.is_object()))
+            {
+                JSON_THROW(parse_error::create(104, 0, "JSON patch must be an array of objects", &val));
+            }
+
+            // collect mandatory members
+            const auto op = get_value("op", "op", true).template get<string_t>();
+            const auto path = get_value(op, "path", true).template get<string_t>();
+            json_pointer ptr(path);
+
+            switch (get_op(op))
+            {
+                case patch_operations::add:
+                {
+                    operation_add(ptr, get_value("add", "value", false));
+                    break;
+                }
+
+                case patch_operations::remove:
+                {
+                    operation_remove(ptr);
+                    break;
+                }
+
+                case patch_operations::replace:
+                {
+                    // the "path" location must exist - use at()
+                    result.at(ptr) = get_value("replace", "value", false);
+                    break;
+                }
+
+                case patch_operations::move:
+                {
+                    const auto from_path = get_value("move", "from", true).template get<string_t>();
+                    json_pointer from_ptr(from_path);
+
+                    // the "from" location must exist - use at()
+                    basic_json const v = result.at(from_ptr);
+
+                    // The move operation is functionally identical to a
+                    // "remove" operation on the "from" location, followed
+                    // immediately by an "add" operation at the target
+                    // location with the value that was just removed.
+                    operation_remove(from_ptr);
+                    operation_add(ptr, v);
+                    break;
+                }
+
+                case patch_operations::copy:
+                {
+                    const auto from_path = get_value("copy", "from", true).template get<string_t>();
+                    const json_pointer from_ptr(from_path);
+
+                    // the "from" location must exist - use at()
+                    basic_json const v = result.at(from_ptr);
+
+                    // The copy is functionally identical to an "add"
+                    // operation at the target location using the value
+                    // specified in the "from" member.
+                    operation_add(ptr, v);
+                    break;
+                }
+
+                case patch_operations::test:
+                {
+                    bool success = false;
+                    JSON_TRY
+                    {
+                        // check if "value" matches the one at "path"
+                        // the "path" location must exist - use at()
+                        success = (result.at(ptr) == get_value("test", "value", false));
+                    }
+                    JSON_INTERNAL_CATCH (out_of_range&)
+                    {
+                        // ignore out of range errors: success remains false
+                    }
+
+                    // throw an exception if test fails
+                    if (JSON_HEDLEY_UNLIKELY(!success))
+                    {
+                        JSON_THROW(other_error::create(501, detail::concat("unsuccessful: ", val.dump()), &val));
+                    }
+
+                    break;
+                }
+
+                case patch_operations::invalid:
+                default:
+                {
+                    // op must be "add", "remove", "replace", "move", "copy", or
+                    // "test"
+                    JSON_THROW(parse_error::create(105, 0, detail::concat("operation value '", op, "' is invalid"), &val));
+                }
+            }
+        }
+    }
+
+    /// @brief applies a JSON patch to a copy of the current object
+    /// @sa https://json.nlohmann.me/api/basic_json/patch/
+    basic_json patch(const basic_json& json_patch) const
+    {
+        basic_json result = *this;
+        result.patch_inplace(json_patch);
+        return result;
+    }
+
+    /// @brief creates a diff as a JSON patch
+    /// @sa https://json.nlohmann.me/api/basic_json/diff/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json diff(const basic_json& source, const basic_json& target,
+                           const string_t& path = "")
+    {
+        // the patch
+        basic_json result(value_t::array);
+
+        // if the values are the same, return empty patch
+        if (source == target)
+        {
+            return result;
+        }
+
+        if (source.type() != target.type())
+        {
+            // different types: replace value
+            result.push_back(
+            {
+                {"op", "replace"}, {"path", path}, {"value", target}
+            });
+            return result;
+        }
+
+        switch (source.type())
+        {
+            case value_t::array:
+            {
+                // first pass: traverse common elements
+                std::size_t i = 0;
+                while (i < source.size() && i < target.size())
+                {
+                    // recursive call to compare array values at index i
+                    auto temp_diff = diff(source[i], target[i], detail::concat<string_t>(path, '/', detail::to_string<string_t>(i)));
+                    result.insert(result.end(), temp_diff.begin(), temp_diff.end());
+                    ++i;
+                }
+
+                // We now reached the end of at least one array
+                // in a second pass, traverse the remaining elements
+
+                // remove my remaining elements
+                const auto end_index = static_cast<difference_type>(result.size());
+                while (i < source.size())
+                {
+                    // add operations in reverse order to avoid invalid
+                    // indices
+                    result.insert(result.begin() + end_index, object(
+                    {
+                        {"op", "remove"},
+                        {"path", detail::concat<string_t>(path, '/', detail::to_string<string_t>(i))}
+                    }));
+                    ++i;
+                }
+
+                // add other remaining elements
+                while (i < target.size())
+                {
+                    result.push_back(
+                    {
+                        {"op", "add"},
+                        {"path", detail::concat<string_t>(path, "/-")},
+                        {"value", target[i]}
+                    });
+                    ++i;
+                }
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                // first pass: traverse this object's elements
+                for (auto it = source.cbegin(); it != source.cend(); ++it)
+                {
+                    // escape the key name to be used in a JSON patch
+                    const auto path_key = detail::concat<string_t>(path, '/', detail::escape(it.key()));
+
+                    if (target.find(it.key()) != target.end())
+                    {
+                        // recursive call to compare object values at key it
+                        auto temp_diff = diff(it.value(), target[it.key()], path_key);
+                        result.insert(result.end(), temp_diff.begin(), temp_diff.end());
+                    }
+                    else
+                    {
+                        // found a key that is not in o -> remove it
+                        result.push_back(object(
+                        {
+                            {"op", "remove"}, {"path", path_key}
+                        }));
+                    }
+                }
+
+                // second pass: traverse other object's elements
+                for (auto it = target.cbegin(); it != target.cend(); ++it)
+                {
+                    if (source.find(it.key()) == source.end())
+                    {
+                        // found a key that is not in this -> add it
+                        const auto path_key = detail::concat<string_t>(path, '/', detail::escape(it.key()));
+                        result.push_back(
+                        {
+                            {"op", "add"}, {"path", path_key},
+                            {"value", it.value()}
+                        });
+                    }
+                }
+
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // both primitive type: replace value
+                result.push_back(
+                {
+                    {"op", "replace"}, {"path", path}, {"value", target}
+                });
+                break;
+            }
+        }
+
+        return result;
+    }
+    /// @}
+
+    ////////////////////////////////
+    // JSON Merge Patch functions //
+    ////////////////////////////////
+
+    /// @name JSON Merge Patch functions
+    /// @{
+
+    /// @brief applies a JSON Merge Patch
+    /// @sa https://json.nlohmann.me/api/basic_json/merge_patch/
+    void merge_patch(const basic_json& apply_patch)
+    {
+        if (apply_patch.is_object())
+        {
+            if (!is_object())
+            {
+                *this = object();
+            }
+            for (auto it = apply_patch.begin(); it != apply_patch.end(); ++it)
+            {
+                if (it.value().is_null())
+                {
+                    erase(it.key());
+                }
+                else
+                {
+                    operator[](it.key()).merge_patch(it.value());
+                }
+            }
+        }
+        else
+        {
+            *this = apply_patch;
+        }
+    }
+
+    /// @}
+};
+
+/// @brief user-defined to_string function for JSON values
+/// @sa https://json.nlohmann.me/api/basic_json/to_string/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+std::string to_string(const NLOHMANN_BASIC_JSON_TPL& j)
+{
+    return j.dump();
+}
+
+inline namespace literals
+{
+inline namespace json_literals
+{
+
+/// @brief user-defined string literal for JSON values
+/// @sa https://json.nlohmann.me/api/basic_json/operator_literal_json/
+JSON_HEDLEY_NON_NULL(1)
+#if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)
+    inline nlohmann::json operator ""_json(const char* s, std::size_t n)
+#else
+    inline nlohmann::json operator "" _json(const char* s, std::size_t n)
+#endif
+{
+    return nlohmann::json::parse(s, s + n);
+}
+
+/// @brief user-defined string literal for JSON pointer
+/// @sa https://json.nlohmann.me/api/basic_json/operator_literal_json_pointer/
+JSON_HEDLEY_NON_NULL(1)
+#if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)
+    inline nlohmann::json::json_pointer operator ""_json_pointer(const char* s, std::size_t n)
+#else
+    inline nlohmann::json::json_pointer operator "" _json_pointer(const char* s, std::size_t n)
+#endif
+{
+    return nlohmann::json::json_pointer(std::string(s, n));
+}
+
+}  // namespace json_literals
+}  // namespace literals
+NLOHMANN_JSON_NAMESPACE_END
+
+///////////////////////
+// nonmember support //
+///////////////////////
+
+namespace std // NOLINT(cert-dcl58-cpp)
+{
+
+/// @brief hash value for JSON objects
+/// @sa https://json.nlohmann.me/api/basic_json/std_hash/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+struct hash<nlohmann::NLOHMANN_BASIC_JSON_TPL> // NOLINT(cert-dcl58-cpp)
+{
+    std::size_t operator()(const nlohmann::NLOHMANN_BASIC_JSON_TPL& j) const
+    {
+        return nlohmann::detail::hash(j);
+    }
+};
+
+// specialization for std::less<value_t>
+template<>
+struct less< ::nlohmann::detail::value_t> // do not remove the space after '<', see https://github.com/nlohmann/json/pull/679
+{
+    /*!
+    @brief compare two value_t enum values
+    @since version 3.0.0
+    */
+    bool operator()(::nlohmann::detail::value_t lhs,
+                    ::nlohmann::detail::value_t rhs) const noexcept
+    {
+#if JSON_HAS_THREE_WAY_COMPARISON
+        return std::is_lt(lhs <=> rhs); // *NOPAD*
+#else
+        return ::nlohmann::detail::operator<(lhs, rhs);
+#endif
+    }
+};
+
+// C++20 prohibit function specialization in the std namespace.
+#ifndef JSON_HAS_CPP_20
+
+/// @brief exchanges the values of two JSON objects
+/// @sa https://json.nlohmann.me/api/basic_json/std_swap/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+inline void swap(nlohmann::NLOHMANN_BASIC_JSON_TPL& j1, nlohmann::NLOHMANN_BASIC_JSON_TPL& j2) noexcept(  // NOLINT(readability-inconsistent-declaration-parameter-name, cert-dcl58-cpp)
+    is_nothrow_move_constructible<nlohmann::NLOHMANN_BASIC_JSON_TPL>::value&&                          // NOLINT(misc-redundant-expression,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    is_nothrow_move_assignable<nlohmann::NLOHMANN_BASIC_JSON_TPL>::value)
+{
+    j1.swap(j2);
+}
+
+#endif
+
+}  // namespace std
+
+#if JSON_USE_GLOBAL_UDLS
+    #if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)
+        using nlohmann::literals::json_literals::operator ""_json; // NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+        using nlohmann::literals::json_literals::operator ""_json_pointer; //NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+    #else
+        using nlohmann::literals::json_literals::operator "" _json; // NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+        using nlohmann::literals::json_literals::operator "" _json_pointer; //NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+    #endif
+#endif
+
+// #include <nlohmann/detail/macro_unscope.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// restore clang diagnostic settings
+#if defined(__clang__)
+    #pragma clang diagnostic pop
+#endif
+
+// clean up
+#undef JSON_ASSERT
+#undef JSON_INTERNAL_CATCH
+#undef JSON_THROW
+#undef JSON_PRIVATE_UNLESS_TESTED
+#undef NLOHMANN_BASIC_JSON_TPL_DECLARATION
+#undef NLOHMANN_BASIC_JSON_TPL
+#undef JSON_EXPLICIT
+#undef NLOHMANN_CAN_CALL_STD_FUNC_IMPL
+#undef JSON_INLINE_VARIABLE
+#undef JSON_NO_UNIQUE_ADDRESS
+#undef JSON_DISABLE_ENUM_SERIALIZATION
+#undef JSON_USE_GLOBAL_UDLS
+
+#ifndef JSON_TEST_KEEP_MACROS
+    #undef JSON_CATCH
+    #undef JSON_TRY
+    #undef JSON_HAS_CPP_11
+    #undef JSON_HAS_CPP_14
+    #undef JSON_HAS_CPP_17
+    #undef JSON_HAS_CPP_20
+    #undef JSON_HAS_CPP_23
+    #undef JSON_HAS_FILESYSTEM
+    #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+    #undef JSON_HAS_THREE_WAY_COMPARISON
+    #undef JSON_HAS_RANGES
+    #undef JSON_HAS_STATIC_RTTI
+    #undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+#endif
+
+// #include <nlohmann/thirdparty/hedley/hedley_undef.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#undef JSON_HEDLEY_ALWAYS_INLINE
+#undef JSON_HEDLEY_ARM_VERSION
+#undef JSON_HEDLEY_ARM_VERSION_CHECK
+#undef JSON_HEDLEY_ARRAY_PARAM
+#undef JSON_HEDLEY_ASSUME
+#undef JSON_HEDLEY_BEGIN_C_DECLS
+#undef JSON_HEDLEY_CLANG_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_CLANG_HAS_BUILTIN
+#undef JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_CLANG_HAS_EXTENSION
+#undef JSON_HEDLEY_CLANG_HAS_FEATURE
+#undef JSON_HEDLEY_CLANG_HAS_WARNING
+#undef JSON_HEDLEY_COMPCERT_VERSION
+#undef JSON_HEDLEY_COMPCERT_VERSION_CHECK
+#undef JSON_HEDLEY_CONCAT
+#undef JSON_HEDLEY_CONCAT3
+#undef JSON_HEDLEY_CONCAT3_EX
+#undef JSON_HEDLEY_CONCAT_EX
+#undef JSON_HEDLEY_CONST
+#undef JSON_HEDLEY_CONSTEXPR
+#undef JSON_HEDLEY_CONST_CAST
+#undef JSON_HEDLEY_CPP_CAST
+#undef JSON_HEDLEY_CRAY_VERSION
+#undef JSON_HEDLEY_CRAY_VERSION_CHECK
+#undef JSON_HEDLEY_C_DECL
+#undef JSON_HEDLEY_DEPRECATED
+#undef JSON_HEDLEY_DEPRECATED_FOR
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION
+#undef JSON_HEDLEY_DIAGNOSTIC_POP
+#undef JSON_HEDLEY_DIAGNOSTIC_PUSH
+#undef JSON_HEDLEY_DMC_VERSION
+#undef JSON_HEDLEY_DMC_VERSION_CHECK
+#undef JSON_HEDLEY_EMPTY_BASES
+#undef JSON_HEDLEY_EMSCRIPTEN_VERSION
+#undef JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK
+#undef JSON_HEDLEY_END_C_DECLS
+#undef JSON_HEDLEY_FLAGS
+#undef JSON_HEDLEY_FLAGS_CAST
+#undef JSON_HEDLEY_GCC_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_GCC_HAS_BUILTIN
+#undef JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_GCC_HAS_EXTENSION
+#undef JSON_HEDLEY_GCC_HAS_FEATURE
+#undef JSON_HEDLEY_GCC_HAS_WARNING
+#undef JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK
+#undef JSON_HEDLEY_GCC_VERSION
+#undef JSON_HEDLEY_GCC_VERSION_CHECK
+#undef JSON_HEDLEY_GNUC_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_GNUC_HAS_BUILTIN
+#undef JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_GNUC_HAS_EXTENSION
+#undef JSON_HEDLEY_GNUC_HAS_FEATURE
+#undef JSON_HEDLEY_GNUC_HAS_WARNING
+#undef JSON_HEDLEY_GNUC_VERSION
+#undef JSON_HEDLEY_GNUC_VERSION_CHECK
+#undef JSON_HEDLEY_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_HAS_BUILTIN
+#undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS
+#undef JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_HAS_EXTENSION
+#undef JSON_HEDLEY_HAS_FEATURE
+#undef JSON_HEDLEY_HAS_WARNING
+#undef JSON_HEDLEY_IAR_VERSION
+#undef JSON_HEDLEY_IAR_VERSION_CHECK
+#undef JSON_HEDLEY_IBM_VERSION
+#undef JSON_HEDLEY_IBM_VERSION_CHECK
+#undef JSON_HEDLEY_IMPORT
+#undef JSON_HEDLEY_INLINE
+#undef JSON_HEDLEY_INTEL_CL_VERSION
+#undef JSON_HEDLEY_INTEL_CL_VERSION_CHECK
+#undef JSON_HEDLEY_INTEL_VERSION
+#undef JSON_HEDLEY_INTEL_VERSION_CHECK
+#undef JSON_HEDLEY_IS_CONSTANT
+#undef JSON_HEDLEY_IS_CONSTEXPR_
+#undef JSON_HEDLEY_LIKELY
+#undef JSON_HEDLEY_MALLOC
+#undef JSON_HEDLEY_MCST_LCC_VERSION
+#undef JSON_HEDLEY_MCST_LCC_VERSION_CHECK
+#undef JSON_HEDLEY_MESSAGE
+#undef JSON_HEDLEY_MSVC_VERSION
+#undef JSON_HEDLEY_MSVC_VERSION_CHECK
+#undef JSON_HEDLEY_NEVER_INLINE
+#undef JSON_HEDLEY_NON_NULL
+#undef JSON_HEDLEY_NO_ESCAPE
+#undef JSON_HEDLEY_NO_RETURN
+#undef JSON_HEDLEY_NO_THROW
+#undef JSON_HEDLEY_NULL
+#undef JSON_HEDLEY_PELLES_VERSION
+#undef JSON_HEDLEY_PELLES_VERSION_CHECK
+#undef JSON_HEDLEY_PGI_VERSION
+#undef JSON_HEDLEY_PGI_VERSION_CHECK
+#undef JSON_HEDLEY_PREDICT
+#undef JSON_HEDLEY_PRINTF_FORMAT
+#undef JSON_HEDLEY_PRIVATE
+#undef JSON_HEDLEY_PUBLIC
+#undef JSON_HEDLEY_PURE
+#undef JSON_HEDLEY_REINTERPRET_CAST
+#undef JSON_HEDLEY_REQUIRE
+#undef JSON_HEDLEY_REQUIRE_CONSTEXPR
+#undef JSON_HEDLEY_REQUIRE_MSG
+#undef JSON_HEDLEY_RESTRICT
+#undef JSON_HEDLEY_RETURNS_NON_NULL
+#undef JSON_HEDLEY_SENTINEL
+#undef JSON_HEDLEY_STATIC_ASSERT
+#undef JSON_HEDLEY_STATIC_CAST
+#undef JSON_HEDLEY_STRINGIFY
+#undef JSON_HEDLEY_STRINGIFY_EX
+#undef JSON_HEDLEY_SUNPRO_VERSION
+#undef JSON_HEDLEY_SUNPRO_VERSION_CHECK
+#undef JSON_HEDLEY_TINYC_VERSION
+#undef JSON_HEDLEY_TINYC_VERSION_CHECK
+#undef JSON_HEDLEY_TI_ARMCL_VERSION
+#undef JSON_HEDLEY_TI_ARMCL_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL2000_VERSION
+#undef JSON_HEDLEY_TI_CL2000_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL430_VERSION
+#undef JSON_HEDLEY_TI_CL430_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL6X_VERSION
+#undef JSON_HEDLEY_TI_CL6X_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL7X_VERSION
+#undef JSON_HEDLEY_TI_CL7X_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CLPRU_VERSION
+#undef JSON_HEDLEY_TI_CLPRU_VERSION_CHECK
+#undef JSON_HEDLEY_TI_VERSION
+#undef JSON_HEDLEY_TI_VERSION_CHECK
+#undef JSON_HEDLEY_UNAVAILABLE
+#undef JSON_HEDLEY_UNLIKELY
+#undef JSON_HEDLEY_UNPREDICTABLE
+#undef JSON_HEDLEY_UNREACHABLE
+#undef JSON_HEDLEY_UNREACHABLE_RETURN
+#undef JSON_HEDLEY_VERSION
+#undef JSON_HEDLEY_VERSION_DECODE_MAJOR
+#undef JSON_HEDLEY_VERSION_DECODE_MINOR
+#undef JSON_HEDLEY_VERSION_DECODE_REVISION
+#undef JSON_HEDLEY_VERSION_ENCODE
+#undef JSON_HEDLEY_WARNING
+#undef JSON_HEDLEY_WARN_UNUSED_RESULT
+#undef JSON_HEDLEY_WARN_UNUSED_RESULT_MSG
+#undef JSON_HEDLEY_FALL_THROUGH
+
+
+
+#endif  // INCLUDE_NLOHMANN_JSON_HPP_
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/BANK-PROOF.md b/research/gen4-retiming-entrances-target/vendor/pr276/BANK-PROOF.md
new file mode 100644
index 0000000000..62560a4fb9
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/BANK-PROOF.md
@@ -0,0 +1,37 @@
+# Five-stage stage-private completed banks
+
+This is a finite bank-allocation extension of the PR197/PR200 completed-bank construction to PR234's five-stage bit geometry, retained from eumemic's source527 package and applied here to the gen4 independent helper census. It does not claim a new all-size compiler theorem or replace the scalar admission.
+
+For one complete local invocation, the source-bound physical telescope has no data/helper cross blocks. On an independent helper with genuine entrance projector sigma its endpoint is the exact partial swap D_(I24-sigma), supported in the active local window. This holds on arbitrary correlated dirty contents. The complemented inverse invocation has the same residual: its reversed endpoints are 0 and I24-sigma. Source-owned gauges are visible-data paths and are excluded from the independent helper census.
+
+In stage i, PR234 routes the helper at local class d to physical class g=d*tau_i. Relative to g, the residual is P_i=tau_i*diag(I24-sigma,0,...,0)*tau_i, supported only in H_i. We give each stage a disjoint collection of banks. Every bank is filled by disjoint coordinate blocks of total dimension120. For the actual gauge chart B whose columns are residual columns followed by gauge columns, set
+
+    N_b=(b+1)*Pi_b*embed_i(B^-1).
+
+For an ungauged role B=I24. Pi_b is the explicit coordinate permutation sending the first residual coordinates in H_i to the assigned bank interval. Thus N_b*P_i*N_b^-1 is exactly that coordinate projector. The scalar leaves conjugation unchanged. The checker reconstructs every actual chart, checks both inverse identities, the G-orthogonality of its two summands, its residual action and its elementary factorization. Therefore this is a projector identity for the actual bases, not a rank substitution.
+
+The bank route is g -> g*N_b^-1, hence d*tau_i*N_b^-1 in the original local invocation. If the bank class is h, its residual is h*N_b*P_i*N_b^-1*h^-1. Every occurrence visits every bank class once because right multiplication is a bijection on the complete GL cover. If two roles in one local invocation are assigned the same bank family, their distinct N_b give distinct bank classes. Distinctness is literal: choose a coordinate j outside H_i. The embedded inverse fixes e_j; N_b*e_j=(b+1)e_(Pi_b(j)). The resulting columns differ for all b, at every eligible prime q>2^80 and every local ring Z/q^w. All scalars are between 1 and 40 and remain distinct units. The proof uses the full GL cover, not a projective quotient.
+
+Complete the entire cover sweep for each stage and replica in fixed order before its boundary phase. The complete local source endpoint separates every bank from the data and other banks, so each subsequent invocation may receive arbitrary dirty bank contents. For each bank, its block projectors are disjoint and sum to I120. The literal partial swaps therefore compose to D_I120 on every address column. The common inherited ancestor chart is the same for each block and cancels between blocks. The checker verifies all240 address columns, the reverse schedule, and failures from omitting or repeating a block. No new independence assumption on dirt is used.
+
+The five bank collections remain separate, and each is touched only in its own stage. This gives every physical bank its full required endpoint once. The data stage routes, bridge maps, idle children and final exchanges remain PR234's. Consequently there are no independent exterior rank5a children. Their removal follows from the completed bank endpoint; no internal, data, compensation or copied-center child is removed.
+
+For gen4 the actual residual families are 3:266 (rank-21 entrances), 4:2200 (rank-20 entrances) and 24:13944 (ungauged roles). Sixty physical replicas fill each stage with these exact 120-dimensional patterns:
+
+| Blocks | Banks per stage |
+| --- | ---: |
+| 40 of dimension 3 | 399 |
+| 30 of dimension 4 | 4400 |
+| 5 of dimension 24 | 167328 |
+
+There are 172127 banks per stage, 860635 total banks and 422400 data families. Literal stock is 1283035. Its per-replica normalized value is 256607/12. The checker enumerates each of 4923000 actual role/replica/stage assignments exactly once, verifies the actual role's chart rank, and hashes the complete allocation.
+
+Every actual chart (370 distinct entrance bases) uses at most 186 factors. At most 119 coordinate transpositions and 120 scalar-coordinate factors give 425 normalizer factors. A conservative added out-and-back selector bill, in addition to all retained PR234 route and scalar bills, is
+
+    2*5*60*((1283035-1)+16410*120*425)=502915820400 < 2^40.
+
+The literal stock, not the rational per-replica stock, must be used for physical role routing and finite storage. All60 scalar replicas execute, and all recursive child counts are multiplied by60 in a literal realization. Any smaller integer normalization used only in the moment arithmetic must be distinguished from the literal replica count. Serial execution may share an external copied-center work stream only after erasure. The fixed bank selector bill is explicitly charged before the inherited positive ordinary-leaf gap absorbs it. After completion removal the maximum child is50 of120, so a single level halves; the histogram remains a one-level profile.
+
+This witness leaves the full scalar/integer/sign audits, frame ledgers, exact global lowering, prime guard, complete fallback profile and 47 outer inequalities to the integrator (verify.py). Its input charts/census are the independently admitted gen4 helper. Existing compiler, common weighted chart, restored selectors, complete-stream routing and all-size analytic hypotheses remain conditional as in the cited sources.
+
+Prepared with OpenAI Codex assistance (source527 package, eumemic); gen4 numbers rebound with Claude assistance. Apache-2.0; inherited source attribution remains unchanged.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/LICENSE b/research/gen4-retiming-entrances-target/vendor/pr276/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/MANIFEST.json b/research/gen4-retiming-entrances-target/vendor/pr276/MANIFEST.json
new file mode 100644
index 0000000000..f248218f71
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/MANIFEST.json
@@ -0,0 +1,115 @@
+{
+  "files": {
+    "BANK-PROOF.md": "bbc328e05848a211c981288514380a4ba12fddaed16c9d23328b5764502be411",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "fa439daf29eb87d38cfdcf60c7ff43af7854fdc7e71570ae79b76dd524427f90",
+    "PR-STATEMENT.md": "1741f2d9e3c8d61c2ab2a27298b33c3ea8579fc09c00fcbb979186be7b6e6dbd",
+    "PROOF.md": "c4adbffdc7181b67ba61db134ca40e6b731e836ca07607d7ce6a76fb7434df9e",
+    "README.md": "1741f2d9e3c8d61c2ab2a27298b33c3ea8579fc09c00fcbb979186be7b6e6dbd",
+    "UPSTREAM-PR234-NOTICE.md": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+    "UPSTREAM-PR234-PROOF.md": "c9722b07256758cd3b307dd46689f99984c66e16c3dd934f9c34e551620bfc0f",
+    "bank_check.py": "fb25305ddd97e8341bef591e04c6fcd9e8cc06ef9207a340eb883045d43a40ff",
+    "bank_template.py": "ca97c34524b409621336c0d4046f26e8da156f4b657c9d94463d8025ddfdbb4a",
+    "base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "code/complex_basis.py": "52d68781eaf6d9decf02446a532a7336fcf15924a9f6781ba0833d038decb9f8",
+    "code/complex_labels.py": "ff5d5e914ef1be0f0cc30283a1ee39089b77e4b572f09543e7313d126bd26256",
+    "code/complex_scalars.py": "fa035447c1f3a5e878dfc18a900942aa180d8bfde03cdce2d21d9bf8b8409429",
+    "code/complex_splice.py": "ed8f7f55530bab64e25b98ee614e1152ded8a6259c48d32b3ae26bab4b93848c",
+    "code/geometry527.py": "733a0f4bc946be5662c73e62ca287ef9ca9bc000e5de090947776c40a8ffc83f",
+    "code/global_lowering.py": "12e89150ef633d027d842378caa113a8240225d3dfdaac5177448c061e126206",
+    "code/physical527.py": "e5a1730f498ad355002f26de8881a02ad2fac119657ebdaa85017047e0cccdb1",
+    "finite_check.py": "693a93308edcb44bc649b33a6ece1de4d93daefcead2eac36215d7c18730edbd",
+    "gen4bit/NOTICE-PR200": "9e82089424092c1dabc2341a09ead255633d78c90dbdc199c4336ca1c0f3bdf4",
+    "gen4bit/README.md": "7e037532a7469053c590164e9b347e90c9d21968d82920c8bacd73eaad1a6af0",
+    "gen4bit/bit/base_word.py": "9fe3a81b7561d2b09c086f63fac4626e88a32369ef8bc5579c94878de1218a89",
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+    "math_check.py": "706d9e0a2e2092393914809109be39012c0182edf4eb1bb76bf05f9e51fde713",
+    "moment.py": "9d465c716c6b910ff66e1453e3bf0057608a787b5f5361be93781f42cb3370f7",
+    "notices/PR210-coordinated-crossover-NOTICE": "9fc5561c0995892dbdde777c713899486920c32d3562392f5f72377a4953bf98",
+    "notices/PR230-NOTICE": "7dfbad087ee49b74fd5075d517eaa263c5dd3d4fbd4c69bfba34ee1cb55e837f",
+    "notices/PR230-PROVENANCE.json": "19957e28a8ad26281bfe8bfaf8ae16191be53e729a8870a6154671b3384959d4",
+    "notices/README.md": "a4c288228cf8360d8d04c62b0f51177de5682d1f5d3bae341e6b850af766c26e",
+    "notices/base-bit-PR200-PR202-NOTICE": "c9850418622aea8d1382a230306c940947b5da818f4854b4b272ed60cf239f6c",
+    "notices/source527-loader-NOTICE.md": "ee632728cc4d89565292d288f8289f483ac794b5d02cc6e42c2b2c43c43ff1d8",
+    "outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "parity_transform.py": "9ed3ff2767c046d11aa1be248eaba93755740131745f673ad9d26a3e77e7b02a",
+    "portable_bit.py": "c8d18bdc5a123f14be330e94d96509be8b5eec71ccc68e0fabc649ac1ee6f218",
+    "portable_complex.py": "797e144c0040d78a4731a6eaa61c0edb9803a08462f885ed014cbca9d9991d82",
+    "prepare.py": "00b13cb18e2d1dd26f207a20a7183b9e357a92a9b2906371e6fae9cb8cc197b3",
+    "prime_check.py": "d1682e044773ca8e8b131b82e58186c8d97e597f0d8a7d74aaeee06cf5204973",
+    "prime_witnesses.py": "98cd03bc9582e7bd0ab194c191ea8eea940539e510051443ab9fd3e572a364ab",
+    "proof/FINITE_BIT_ACCOUNTING.md": "602923520af184670170bf159fde7b4c72e79a72570eddd7746b7c97bc51fc5b",
+    "proof/INTEGRATED_PROOF.md": "cff22391e71a50bad27a1e832d5c0a2c8b2446df55adb1297c8b1485b3761257",
+    "proof/PARITY-CONTRACT.md": "a9246be656e31f1a21d5ec714e002f51be0aa07c36e1528066a25b2c7a02db91",
+    "proof/README.md": "5f40cb6dda3992f98ffc43159af1be080bd6c18411bc7d02464f230993f3074f",
+    "proof/copied-centers-lemma.tex": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe",
+    "proof/primary/03-motifs.tex": "ed76761194988a01af77ead0ea6469cb5dcd29690ab985a0b5a4006b0f2b69bb",
+    "proof/primary/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "proof/primary/PROVENANCE.md": "dd9054c58aa92c44b0ef5f691ad4dc52b8ead2f20a9843d4399d6c300d616023",
+    "proof/primary/UPSTREAM-README.md": "8d1ceff898a4e0e681679f91c4def485820be9e99f04e4861f2ce601a364723e",
+    "proof/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "proof/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "raw_ledger.py": "e9701ab9d4f30c6bac6fa69853a2069624ad237666b85cfe6d31a8a7c806e28b",
+    "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
+    "scalar/word.py": "e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42",
+    "scalar_check.py": "bbc25d3df09bf0ce2cb92f623f46579b504b37a9447a144a6cd1cb8e63701b7f",
+    "verify.py": "996789f2c0e1ee17ccd6b9e634ce67384578595846cd5bac7f2c3901df2da307",
+    "virtual_check.py": "155144478a5c45d630c1b0d43cadbeb53b96306270fa4e0ad8c4d403d9045971"
+  },
+  "schema": "gen4-parity-fused-five-stage-banks-inputs/1"
+}
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/NOTICE.md b/research/gen4-retiming-entrances-target/vendor/pr276/NOTICE.md
new file mode 100644
index 0000000000..37e2779a2e
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/NOTICE.md
@@ -0,0 +1,52 @@
+# Attribution and licence
+
+Apache-2.0 applies. Original headers, licences, notices and AI-assistance disclosures are preserved. The
+credits below do not imply review or endorsement.
+
+## Inherited, unchanged or with rebound constants
+
+- **Five-stage architecture and finite interface package:** Henry Grant (hcg890), PR234, and Jacob
+  Sussman's five-stage construction and gcert/1 export. The complete inherited five-stage credits are in
+  `UPSTREAM-PR234-NOTICE.md`.
+- **Package machinery:** eumemic's source527 package, prepared with substantial OpenAI Codex assistance,
+  with its lineage: Dugongue's PR207/PR216 finite and bank admissions, Rohan Arun's PR211 and sennemmi's
+  PR230 frame work, and eumemic's PR210. Their notices are retained verbatim in `notices/`.
+  This covers the scalar program `scalar/word.py` (byte-identical), the physical event emitter, the parity
+  fusion, the raw-ledger census, the stage-private bank template and checker, the moment, prime and
+  finite-bill checks, and `verify.py`. In this package they are rebound to the gen4 helper's constants;
+  the logic is unchanged.
+- **Banks:** Evan McKinney's PR197 completed-bank method. Rohan Arun's PR237 published the width-120
+  application first.
+- **Complex supplier:** Avi Eisenberg (ikeboy)'s PR193 helper, inside Sussman's five-stage certificate.
+  The original disclosures are in `inputs/complex`.
+- **Physical-word classes:** Chafik Boukhalfa (chafreaky)'s PR200 `bit/word.py` and `bit/base_word.py`,
+  vendored unchanged in `gen4bit/bit`. `gen4bit/NOTICE-PR200` is PR200's own notice.
+- **Checker:** eumemic's PR168-v4 `check_paired_cube_bit.py`, vendored unchanged.
+- **Paired-cube framework and its developments:**
+  - icekylinx's PR144: paired-coordinate/shared-core framework and configurable local channels.
+  - PR161/PR168 (eumemic): annealed modules, nested schedules and the generator.
+  - James Chang's PR166 and PR162's carrier rule.
+
+## New in this package
+
+**The gen4 bit word.** This covers:
+
+- the arc-aware per-cube local design (`local_design()` recipe trees and `data/local_design_p12.json`);
+- the re-annealed all-but-one module (`data/qmod_p12.json`);
+- the centre-sharing pair module (`data/pair_module_p12.json` and the patch in `finish()`);
+- the frozen arcs (`data/arcs_p12.json`).
+
+**Its physical-layer producers.** `gen4bit/producer/make_physical.py` and `descent.py` are new
+implementations of PR200's stated rules.
+
+**Package integration.** This covers:
+
+- `prepare.py` and `virtual_check.py`;
+- the rewritten `scalar_check.py` controls;
+- the rank-21 geometry check;
+- the gen4 bank patterns and documentation.
+
+All of this was prepared by DreamingOfClouds with Anthropic Claude assistance. The circuit and module
+search was run by Claude agents (simulated annealing, CP-SAT and exact one-instance compiles), and every
+reported number was re-run with the exact generator. No exclusive priority is claimed for any inherited
+design or theorem interface.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/PR-STATEMENT.md b/research/gen4-retiming-entrances-target/vendor/pr276/PR-STATEMENT.md
new file mode 100644
index 0000000000..645ae4de4f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/PR-STATEMENT.md
@@ -0,0 +1,57 @@
+κ = 7.22869827347495e-4
+
+# gen4 bit word in the five-stage completed banks
+
+A conditional finite construction with **κ = 144573965469499/(2·10¹⁷) ≈ 7.22869827347495 × 10⁻⁴**.
+
+The package keeps PR234's five-stage layout, the completed width-120 entrance banks and the whole
+verification chain of eumemic's source527 package. Only the bit helper changes. It is a new paired-cube
+bit word, **gen4**, with three changes to PR168's generator:
+
+- a different per-cube local circuit;
+- a pair module whose extra root is the copied centre;
+- a re-annealed all-but-one module.
+
+Its virtual word needs 17,904 auxiliary roles, against 18,908 for PR200's word. After 1,494
+compensated reuse pairs and descended operation frames, the physical helper has **16,410** independent
+dirty registers, against source527's 16,587, which needed 527 source loans and 34 terminal sinks. The bit
+supplier still binds.
+
+| one invocation, m = 120 | source527 (current package) | gen4 (this package) |
+| --- | ---: | ---: |
+| virtual auxiliary roles | 18,908 (PR200 word) | 17,904 |
+| compensated reuse pairs | 1,760 | 1,494 |
+| source loans / terminal sinks | 527 / 34 | 0 / 0 |
+| independent dirty registers R | 16,587 | 16,410 |
+| independent entrances (ranks) | 2,279 (12, 13, 18, 20) | 2,466 (20, 21) |
+| literal stock, 60 replicas | 1,304,935 | 1,283,035 |
+| normalized stock / deficit | 260,987 / 52,800 | 256,607 / 52,800 |
+| bit coarse saving | 7.10573897320284e-4 | 7.23392746398452e-4 |
+| κ | 7.10069340338651e-4 | **7.22869827347495e-4** |
+
+Run with Python 3.11+ and assertions enabled:
+
+```sh
+python3 -m pip install -r requirements.txt
+python3 -B verify.py --output /tmp/gen4-five-stage-verification
+```
+
+The output directory must be new and outside this immutable package. Verification takes about five
+minutes, uses no network and runs no producer. It performs these checks:
+
+- the PR168-v4 checker on the virtual word, with its five mutation controls;
+- PR200's physical-word proof, exactly as PR200 ran it: frames, handoffs, the physical row and all-column replays, with 4 adverse controls;
+- the retained source527 scalar program on all 19,930 formal F₂ columns, both integer decoder signs and 11 corruptions;
+- the physical event emitter, parity fusion and five-stage global lowering, with exact h=24/m=120 geometry;
+- exact determinants for 26,249 bases;
+- 370 bank charts and all 4,923,000 bank assignments;
+- the retained complex supplier, both rational moment engines, the 47 outer inequalities and the finite bill.
+
+`gen4bit/producer/regenerate.py` rebuilds the five pinned bit-word files from the generator and the two
+physical-layer producers, and checks them byte for byte. This is provenance only, not part of the proof.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows,
+selectors, tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic
+reduction. The included finite checks do not replace those hypotheses. See `PROOF.md` for the
+verification chain, `BANK-PROOF.md` for the banks, `gen4bit/README.md` for the bit word and `NOTICE.md`
+for attribution.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/PROOF.md b/research/gen4-retiming-entrances-target/vendor/pr276/PROOF.md
new file mode 100644
index 0000000000..6145c8e686
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/PROOF.md
@@ -0,0 +1,150 @@
+κ = 7.22869827347495e-4
+
+# Source-bound finite verification
+
+The bit helper is the gen4 paired-cube bit word, a reversible local word in which all inputs and dirty
+registers are formal variables. Every later stage is the source527 package's (eumemic). This file states
+what each stage checks for gen4 and what changed relative to source527.
+
+## The bit word
+
+`gen4bit/selected/bit` pins five files: the signed graph, the virtual profile, the physical word, the exact
+frames and the partner-pair chronology.
+
+**Virtual word.** `virtual_check.py` runs eumemic's PR168-v4 package checker, unmodified and vendored in
+`gen4bit/references/pr168-v4`. It checks:
+
+- exact frames (A·Bᵀ = 0, complementary ranks) and the mod-2 decoder with stars and side parts;
+- geometry: source lines, side-root common caps, operand nesting and centre star spans;
+- role and target chains on node frames, and the partner chronology;
+- G-nondegeneracy of every used frame;
+- a literal F₂ dirty-scratch replay and the independent ledger recount.
+
+All five mutation controls are rejected. The profile is R = 17,904, W = 21,424, m = 72, deficit 1,936,
+the same deficit as every PR168-derived word.
+
+**Physical layer.** The same `virtual` stage then runs Chafik Boukhalfa's PR200 classes
+(`gen4bit/bit/word.py` and `base_word.py`), also unmodified, exactly as PR200's `bit/prove.py` runs them on
+its own word. `prepare.py` builds the verifier context from the same classes. They check:
+
+- every changed operation frame (1,802) is nondegenerate and contains its node's value span;
+- the execution order preserves each role chronology;
+- gauges are untouched in phase one, every gauge read precedes its role's first use, and gauge targets equal response supports;
+- the 1,494 handoffs are one-to-one between ungauged non-root donors and gauged recipients;
+- each donor is dead before its recipient's read, and its last frame lies in the recipient's gauge frame;
+- all gate ports are distinct.
+
+The stage also recomputes the physical row:
+
+- phase one is exactly the centre closure;
+- every addition's actual operands are checked;
+- every physical role chain and the actual target chronology are nested;
+- the deficit telescopes, at 1,936.
+
+It executes the physical word on all 19,930 formal columns over F₂ and on the defining integer decoder.
+Four adverse controls are rejected: an omitted compensation, a missing partner delivery, a stale recipient
+read, and a zero operation frame. `prepare.py` also recomputes the literal adjoint and asserts it equals
+PR200's.
+
+The handoffs follow PR200's rule. A recipient is read immediately before its first operation. The only
+recipients used are rank-21 gauges with no strictly larger gauge later on any of their targets, so every
+target chain stays nested. The actual chronology is rechecked by the scalar program.
+
+## Unchanged scalar program and empty selections
+
+`scalar/word.py` is the source527 scalar program, byte-identical (sha256 e675d4eb…). Its source527
+selections are all empty for gen4:
+
+- source loans, early and gauge mixes, retimed prefixes;
+- aggregation, rank and echelon groups;
+- fresh and paired source reads, terminal sinks.
+
+The program then executes exactly the PR200 physical word:
+
+1. dirty compensation at D0;
+2. V injection and the phase-one gates;
+3. the 24 copied-centre scatters;
+4. gauge reads at their read times, interleaved with the remaining gates;
+5. side roots, then partner mixes and deliveries;
+6. cleanup, the inverse gates, and V removal.
+
+`scalar_check.py` runs it on all 19,930 formal F₂ columns (1,760 sources, 1,760 targets and 16,410 dirty
+registers) and in both defining-integer directions with 24-bit packing.
+
+The 25 source527 mutations exercise selections that gen4 does not have. They are replaced by 11
+corruptions of the actual gen4 context, each of which must make the unchanged program fail:
+
+- a dropped gauge, dirty or recipient compensation;
+- a misrouted gauge response;
+- a flipped compensation sign, checked over Z;
+- a recipient read before its donor's last write;
+- a gauge read after its first use;
+- an omitted gate, centre scatter, partner delivery or source injection.
+
+## Physical events, parity fusion and global lowering
+
+`code/physical527.py` observes the scalar program and emits the physical frame tags. The emitter is
+source527's, unchanged except the register count. The local scalar projection must equal the independent
+observer, and every MOVE is checked as an exact frame inclusion.
+
+`parity_transform.py` deletes the 1,510,656 even-coefficient payload ADDs, which are identities over F₂.
+It merges no MOVE chains for gen4, so the paid local histogram is unchanged. The independent
+required-use census rebuilds every path from the surviving operations and mathematical endpoints, checks
+both reflected inclusions, and matches the instruction histogram. The 626,360 surviving payload additions
+and their literal inverse are replayed on every F₂ column, with cancellation-free signed prefix bounds
+21,725 (forward) and 1,850,360 (inverse). The proof/PARITY-CONTRACT.md argument applies unchanged.
+
+`code/global_lowering.py` is PR234's lowering with the register count and the entrance census rebound. It
+expands all five stages, the idle and bridge phases, the 2,466 completions and the terminal exchange. It
+checks every operand namespace and the paid five-stage histogram:
+
+- 487,546 calls;
+- rank mass 2,809,600;
+- deficit 4,400 = 4v − 5ℓ.
+
+`code/geometry527.py` checks the exact rational h=24/m=120 routes, the eight idle boundary pairs for two
+actual ports, and the completion projectors and five disjoint windows. It does so for two actual rank-20
+entrance bases and, newly, one actual rank-21 basis.
+
+## Primes, banks, moments and finite bill
+
+**Primes.** `prime_check.py` recomputes the cleared-Gram determinant of every consumed basis: 26,249
+distinct bases, at most 118 bits. Only 2, 3 and 5 are stripped, every residual is below 2⁸⁰, and the
+retained prime range q > 2⁸⁰ is unchanged.
+
+**Banks.** The independent entrances are 2,200 of rank 20 and 266 of rank 21, with 370 distinct bases.
+Their residual families have widths 4 and 3. `BANK-PROOF.md` gives the stage-private banks:
+
+- (3⁴⁰) × 399 banks;
+- (4³⁰) × 4,400 banks;
+- (24⁵) × 167,328 banks.
+
+`bank_check.py` rebuilds the 370 charts (at most 186 factors) and enumerates all 4,923,000
+role/replica/stage assignments, checking the callable route map and both endpoint directions. It removes
+exactly the 2,466 rank-5a exterior completions.
+
+**Moments.** Literal stock is 1,283,035. The normalized profile has m = 120, W = 256,607, rank mass
+30,740,040, deficit 52,800 and largest child 50. Two independent rational moment engines, including the
+complete 10⁻¹⁶ bad-class fallback, give the bit coarse saving 180848186599613/(2.5·10¹⁷). The adjacent
+10⁻¹⁸ grid point is rejected.
+
+**Assembly.** The retained complex supplier (PR234/PR193 at m = 110, coarse 747454944651775/10¹⁸) is
+rerun. The bit supplier binds. Three completed ordinary-leaf levels feed the unchanged balanced outer
+assembly: all 47 strict inequalities and seven margins are positive, and the adjacent final grid point
+fails.
+
+**Finite bill.** `finite_check.py` pays every PR234 primitive and router allowance on the literal 60
+replicas and stock, and adds all 502,915,820,400 bank selector calls.
+
+## Scope
+
+The proof boundary is unchanged and conditional. The following are inherited interfaces:
+
+- the all-size weighted compiler and common ancestor charts;
+- restored rows and completed ordinary leaves;
+- selectors, exact-tape routing and prime supply;
+- precision/recovery and retained complex symbolic correctness;
+- analytic transfer.
+
+These checks establish the stated finite construction under those interfaces. They do not rebuild Lean or
+execute a multiplier at all input sizes.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/README.md b/research/gen4-retiming-entrances-target/vendor/pr276/README.md
new file mode 100644
index 0000000000..645ae4de4f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/README.md
@@ -0,0 +1,57 @@
+κ = 7.22869827347495e-4
+
+# gen4 bit word in the five-stage completed banks
+
+A conditional finite construction with **κ = 144573965469499/(2·10¹⁷) ≈ 7.22869827347495 × 10⁻⁴**.
+
+The package keeps PR234's five-stage layout, the completed width-120 entrance banks and the whole
+verification chain of eumemic's source527 package. Only the bit helper changes. It is a new paired-cube
+bit word, **gen4**, with three changes to PR168's generator:
+
+- a different per-cube local circuit;
+- a pair module whose extra root is the copied centre;
+- a re-annealed all-but-one module.
+
+Its virtual word needs 17,904 auxiliary roles, against 18,908 for PR200's word. After 1,494
+compensated reuse pairs and descended operation frames, the physical helper has **16,410** independent
+dirty registers, against source527's 16,587, which needed 527 source loans and 34 terminal sinks. The bit
+supplier still binds.
+
+| one invocation, m = 120 | source527 (current package) | gen4 (this package) |
+| --- | ---: | ---: |
+| virtual auxiliary roles | 18,908 (PR200 word) | 17,904 |
+| compensated reuse pairs | 1,760 | 1,494 |
+| source loans / terminal sinks | 527 / 34 | 0 / 0 |
+| independent dirty registers R | 16,587 | 16,410 |
+| independent entrances (ranks) | 2,279 (12, 13, 18, 20) | 2,466 (20, 21) |
+| literal stock, 60 replicas | 1,304,935 | 1,283,035 |
+| normalized stock / deficit | 260,987 / 52,800 | 256,607 / 52,800 |
+| bit coarse saving | 7.10573897320284e-4 | 7.23392746398452e-4 |
+| κ | 7.10069340338651e-4 | **7.22869827347495e-4** |
+
+Run with Python 3.11+ and assertions enabled:
+
+```sh
+python3 -m pip install -r requirements.txt
+python3 -B verify.py --output /tmp/gen4-five-stage-verification
+```
+
+The output directory must be new and outside this immutable package. Verification takes about five
+minutes, uses no network and runs no producer. It performs these checks:
+
+- the PR168-v4 checker on the virtual word, with its five mutation controls;
+- PR200's physical-word proof, exactly as PR200 ran it: frames, handoffs, the physical row and all-column replays, with 4 adverse controls;
+- the retained source527 scalar program on all 19,930 formal F₂ columns, both integer decoder signs and 11 corruptions;
+- the physical event emitter, parity fusion and five-stage global lowering, with exact h=24/m=120 geometry;
+- exact determinants for 26,249 bases;
+- 370 bank charts and all 4,923,000 bank assignments;
+- the retained complex supplier, both rational moment engines, the 47 outer inequalities and the finite bill.
+
+`gen4bit/producer/regenerate.py` rebuilds the five pinned bit-word files from the generator and the two
+physical-layer producers, and checks them byte for byte. This is provenance only, not part of the proof.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows,
+selectors, tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic
+reduction. The included finite checks do not replace those hypotheses. See `PROOF.md` for the
+verification chain, `BANK-PROOF.md` for the banks, `gen4bit/README.md` for the bit word and `NOTICE.md`
+for attribution.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/UPSTREAM-PR234-NOTICE.md b/research/gen4-retiming-entrances-target/vendor/pr276/UPSTREAM-PR234-NOTICE.md
new file mode 100644
index 0000000000..5f8fbb25c1
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/UPSTREAM-PR234-NOTICE.md
@@ -0,0 +1,13 @@
+# Attribution and licence
+
+This contribution uses Apache-2.0. Original source headers, licences and notices are preserved. These credits do not imply review or endorsement by the named contributors or OpenAI.
+
+- Jacob Sussman: five-stage complex geometry and published gcert/1 export in wht-power-saving-lean at f010392c923279e3dd59ef3aa5fedad23affc5fd. Original Claude assistance disclosure retained in inputs/complex/NOTICE.
+- Avi Eisenberg / ikeboy: retained PR193 source-assisted complex helper and donor selection at 187e1010ac8b259af8e9b5166f68b64bc27b4b47.
+- eumemic: current PR210 frames, gauges, source borrowing and retimed bit helper at df95878d11190518e45ef9717c9ee05011f88ace.
+- Chafik Boukhalfa / chafreaky: PR200 physical bit construction carried by PR202 at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, Douglas Colkitt, OpenAI and earlier contributors retain the attribution and original assistance disclosures in the supplied source notices. The exact outer assembly also credits Zhihao Chen and the RaD / hipotures balanced reduction in its original header.
+
+The paired-cube helper design predates Sussman’s certificate export. The new contribution here is the explicit source-bound five-stage composition, adapters, paid accounting and reproducible finite verification. No exclusive priority is claimed for the inherited designs or theorem interfaces.
+
+Assisted with ChatGPT.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/UPSTREAM-PR234-PROOF.md b/research/gen4-retiming-entrances-target/vendor/pr276/UPSTREAM-PR234-PROOF.md
new file mode 100644
index 0000000000..dbd8806967
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/UPSTREAM-PR234-PROOF.md
@@ -0,0 +1,29 @@
+# Five-stage finite composition and retained hypotheses
+
+The expected conditional saving is κ = 703701743496697 / 10^18. The fresh verifier establishes the finite construction and exact arithmetic under the inherited source and all-size interfaces below.
+
+## Bit construction
+
+The pinned source471 helper is checked on all 20,163 independent F2 source, target and dirty columns. Its physical realization is the exact input/output frame telescope, with all source loans, donor/recipient identifications, compensated reads, terminal substitutions and cleanup retained. Copied centers are complete temporary streams; their reverse implementation copies the original anew, transforms and scatters that copy, then erases it. It does not reverse an erasure.
+
+The five phase-major invocations use the explicitly routed source owners X1, Y1, X1, Y2 and X2. Each helper's five separated residuals occupy disjoint windows. One split rank-5a exterior correction completes each genuine independent entrance of rank a. All 2,279 corrections remain paid, and source-owned gauges stay within the visible-data paths. Actual rational matrix checks establish bridge equality, nested idle changes and terminal exchanges. Cover expansion has a barrier after each phase, across every class.
+
+The fresh program has m=120, W=23,683, 495,304 children, rank mass 2,837,560 and deficit 4,400. All 120 rank-22 copied-center calls are included. Exact cleared-Gram determinants and factor witnesses are recomputed for every consumed basis. Fivefold direct sums introduce no new excluded primes. The retained weighted q-local compiler, unit-pivot fallback, prime-supply and complete-stream tape proofs remain hypotheses.
+
+The proper child ratio 5/6 requires halving degree four. The one-level weighted recurrence is retained; its histogram is not multiplied by four. The finite accounting rederives route factors, scalar work, internal row stock, strict moment/linear gaps and explicit finite cutoff expressions. Unknown constants of inherited primitive implementations remain quantified constants, not invented measured costs. See proof/FINITE_BIT_ACCOUNTING.md and the included original bit/row/copied-center source texts.
+
+## Complex construction
+
+The published gcert/1 baseline is pinned to Sussman's f010392 revision and the PR193 paired-cube helper. Its live-label walk, scalar programs, copied-center lifetimes, final climbs before cleanup, exact symbolic splice and finite guard are regenerated. Exact complex frame identities retain their phase representatives. Physical work stock 24,127 is separately charged; the live recursion denominator remains 14,692.
+
+The pinned scalar identities hAi, hBi, hx, hy and hid, the Lab.inv dirty-lifting theorem and five-window geometry/NetCert theorems are inherited source proofs. The command does not rebuild their Lean proof chain or claim a fresh all-column complex scalar proof. General Clifford synthesis, charged complete-stream movement, common-grid precision and restored-row proofs remain stated analytic dependencies. Their consumed declarations and sources are hash-pinned under inputs/complex/.
+
+## Arithmetic and outer reduction
+
+Both rational moments are freshly enclosed. Three finite ordinary-leaf levels start from the retained completed ordinary saving 384599/10^10; the unattained coarse limiting saving is not used as an ordinary leaf. Exact outer assembly checks all 47 strict inequalities and seven margins and rejects the next 10^-18 κ grid point. Precision/recovery, prime supply, completed ordinary leaves and the fixed-tape all-size reduction remain hypotheses.
+
+proof/INTEGRATED_PROOF.md preserves the detailed original composition argument. Its development filenames identify the original evidence; V8's executable dependency closure is exclusively MANIFEST.json and the fresh calls in verify.py. Development receipts and their historical source trees are not runtime inputs.
+
+No claim is made of unconditional all-size formalization, global optimality or measured multiplier performance. Original lineage and assistance disclosures are preserved in NOTICE.md and the supplied source notices.
+
+Assisted with ChatGPT.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/bank_check.py b/research/gen4-retiming-entrances-target/vendor/pr276/bank_check.py
new file mode 100644
index 0000000000..ad7bed1610
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/bank_check.py
@@ -0,0 +1,254 @@
+"""Fresh context-bound stage-private120-coordinate completed bank admission.
+
+No saved chart, receipt, physical census or old source tree is consumed.
+The fraction-free inverse routine derives from the retained PR197/PR200 bank
+checker. Inherited attribution/notices apply. Apache-2.0.
+Prepared with substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from math import gcd
+from pathlib import Path
+import hashlib,json,struct,time
+from bank_template import BankPlan
+
+assert __debug__, 'Do not run bank admission under -O.'
+HERE=Path(__file__).resolve().parent
+
+def inverse_integer(a):
+    """Fraction-free Gauss-Jordan, returning C,d with aC=Ca=dI."""
+    n=len(a);m=[list(row)+[int(i==j)for j in range(n)]for i,row in enumerate(a)]
+    previous=1;factors=[]
+    for k in range(n):
+        pivot=next((i for i in range(k,n)if m[i][k]),None)
+        assert pivot is not None,'singular actual bank chart'
+        m[k],m[pivot]=m[pivot],m[k]
+        if pivot!=k:factors.append(('swap',k,pivot,1,1))
+        p=m[k][k]
+        if p!=previous:
+            ratio=Q(previous,p);factors.append(('scale',k,k,ratio.numerator,ratio.denominator))
+        for i in range(n):
+            if i==k:continue
+            u=m[i][k]
+            if u:
+                ratio=Q(-u,previous);factors.append(('add',i,k,ratio.numerator,ratio.denominator))
+            for j in range(2*n):
+                if j==k:continue
+                value=p*m[i][j]-u*m[k][j];assert value%previous==0;m[i][j]=value//previous
+            m[i][k]=0
+        previous=p
+    d=m[0][0];assert d and all(m[i][j]==d*int(i==j)for i in range(n)for j in range(n))
+    c=[row[n:]for row in m];common=abs(d)
+    for row in c:
+        for x in row:common=gcd(common,x)
+    d//=common;c=[[x//common for x in row]for row in c]
+    if d<0:d=-d;c=[[-x for x in row]for row in c]
+    return c,d,factors
+
+def census(context):
+    W,C,roles=context['W'],context['C'],context['regs']
+    assert len(roles)==len(set(roles))==16410 and roles==sorted(roles)
+    assert set(roles)==set(W.phys.values())-set(context['borrow'])-context['removed']
+    assert not(set(roles)&set(context['borrow']))
+    gauge_frames={role:W.gauge[role]['frame']for role in roles if role in W.gauge}
+    assert Counter(C.dimf[f]for f in gauge_frames.values())=={20:2200,21:266}
+    families={}
+    for role in roles:
+        rank=24-C.dimf[gauge_frames[role]]if role in gauge_frames else 24
+        families.setdefault(rank,[]).append(role)
+    assert {r:len(xs)for r,xs in families.items()}=={3:266,4:2200,24:13944}
+    return families,gauge_frames
+
+class BankLowerer:
+    """Final full-address lowering of the already checked logical IR.
+
+    Scalar/projection/geometry fields are retained byte-for-byte; only stream
+    operands change to the proven bank namespaces. Completion discharge is
+    checked separately by run(), and no completion opcode is emitted.
+    """
+    def __init__(self,context,lower):
+        families,gauges=census(context)
+        self.plan=BankPlan(families,gauges,context['regs']);self.lower=lower
+    def iter_stage(self,stage,replica):
+        for row in self.lower.iter_stage(stage):yield self.plan.map_stage_row(stage,replica,row)
+    def iter_idle(self,which,replica):
+        for row in self.lower.iter_idle(which):yield self.plan.map_boundary_row(replica,row)
+    def iter_bridges(self,which,replica):
+        for row in self.lower.iter_bridges(which):yield self.plan.map_boundary_row(replica,row)
+    def iter_exchanges(self,replica):
+        for row in self.lower.iter_exchanges():yield self.plan.map_boundary_row(replica,row)
+    def phases(self):
+        """Each iterator is expanded over all cover classes before next phase."""
+        for stage in range(5):
+            for replica in range(60):
+                yield('helper',stage,replica,lambda s=stage,r=replica:self.iter_stage(s,r))
+            if stage in(1,2,4):
+                which={1:0,2:1,4:2}[stage]
+                for replica in range(60):
+                    yield('idle',which,replica,lambda i=which,r=replica:self.iter_idle(i,r))
+                    yield('bridge',which,replica,lambda i=which,r=replica:self.iter_bridges(i,r))
+        for replica in range(60):yield('terminal_exchange',0,replica,lambda r=replica:self.iter_exchanges(r))
+
+def bind(context,lower):return BankLowerer(context,lower)
+
+def run(context,global_result,lower,progress=lambda text:None):
+    begun=time.monotonic();W,C=context['W'],context['C']
+    api_pin=hashlib.sha256((HERE/'bank_template.py').read_bytes()).hexdigest()
+    families,gauge_frames=census(context);bound=bind(context,lower);plan=bound.plan
+    assert lower.W is W and lower.C is C
+    # Derive all actual chart bases and exact inverse/factor programs afresh.
+    charts=[];maxops=maxnum=maxden=0
+    for frame,count in sorted(Counter(gauge_frames.values()).items()):
+        residual=[]
+        for a in C.A[frame]:
+            row=[15*x-sum(a)for x in a];d=gcd(*row);assert d;residual.append([x//d for x in row])
+        source=C.B[frame];rank=len(residual)
+        assert rank+len(source)==24 and len(source)==C.dimf[frame]
+        assert all(9*sum(x*y for x,y in zip(a,b))-sum(a)*sum(b)==0 for a in residual for b in source)
+        B=list(map(list,zip(*(residual+list(source)))));A,d,ops=inverse_integer(B)
+        for L,R in((A,B),(B,A)):
+            assert all(sum(x*y for x,y in zip(row,col))==d*int(i==j)for i,row in enumerate(L)for j,col in enumerate(zip(*R)))
+        P=[[sum(B[i][k]*A[k][j]for k in range(rank))for j in range(24)]for i in range(24)]
+        assert sum(P[i][i]for i in range(24))==d*rank
+        assert all(sum(P[i][k]*B[k][j]for k in range(24))==(d*B[i][j]if j<rank else 0)for i in range(24)for j in range(24))
+        replay=[list(map(Q,row))for row in B]
+        for op,i,j,a,b in ops:
+            if op=='swap':replay[i],replay[j]=replay[j],replay[i]
+            elif op=='scale':replay[i]=[Q(a,b)*x for x in replay[i]]
+            else:
+                assert op=='add';replay[i]=[x+Q(a,b)*y for x,y in zip(replay[i],replay[j])]
+        assert all(x==int(i==j)for i,row in enumerate(replay)for j,x in enumerate(row))
+        maxops=max(maxops,len(ops));maxnum=max(maxnum,max(abs(op[3])for op in ops));maxden=max(maxden,d,max(op[4]for op in ops))
+        charts.append(dict(frame=frame,count=count,residual_rank=rank,basis=B,inverse_numerator=A,inverse_denominator=d,factors=ops))
+    assert len(charts)==370 and max(maxnum,maxden)<2**80 and maxops==186
+    progress('Rebuilt370 exact actual gauge charts')
+    # Match each consumed completion to one actual independent entrance.
+    expected=[]
+    for j,role in enumerate(context['regs']):
+        f=gauge_frames.get(role,lower.ZERO)
+        assert lower.initial[2*W.v+j]==f
+        if role in gauge_frames:expected.append((4*W.v+j,f,C.dimf[f]))
+    assert list(lower.entrances)==expected and len(expected)==2466
+    completions=list(lower.iter_completions())
+    assert completions==[(6,family,-1,0,5*a,f,-1,0)for family,f,a in expected]
+    removed=Counter(row[4]for row in completions)
+    assert removed=={100:2200,105:266}
+    H=Counter({int(r):n for r,n in global_result['paid_histogram'].items()})
+    assert sum(H.values())==global_result['paid_calls']
+    for r,n in removed.items():assert H[r]==n;del H[r]
+    assert max(H)==50 and sum(H.values())==485080 and sum(r*n for r,n in H.items())==2561670
+    literal=Counter({r:60*n for r,n in H.items()})
+    assert 120*plan.live_families-sum(r*n for r,n in literal.items())==60*4400
+    # Independently enumerate each physical role/replica/stage slot.
+    incidence=hashlib.sha256();assignments=0;normalizers_checked=set();endpoint_controls=[]
+    for stage in range(5):
+        used=Counter();bank=0;assigned=set()
+        outside=next(j for j in range(120)if not 24*stage<=j<24*(stage+1))
+        for pattern,(widths,count)in enumerate(plan.patterns):
+            offset=0;witnesses=[]
+            for block,rank in enumerate(widths):
+                original=list(range(24*stage,24*stage+rank));target=list(range(offset,offset+rank))
+                src=original+[j for j in range(120)if j not in original];dst=target+[j for j in range(120)if j not in target];pi=dict(zip(src,dst))
+                witnesses.append((pi[outside],block+1));offset+=rank
+            assert len(set(witnesses))==len(widths)
+            if stage==0:
+                offsets=[sum(widths[:b])for b in range(len(widths))]
+                def endpoint(blocks):
+                    state=list(range(240))
+                    for b in blocks:
+                        for j in range(offsets[b],offsets[b]+widths[b]):state[j],state[120+j]=state[120+j],state[j]
+                    return state
+                blocks=list(range(len(widths)));full=list(range(120,240))+list(range(120))
+                assert endpoint(blocks)==full and endpoint(blocks+blocks[::-1])==list(range(240))
+                assert endpoint(blocks[:-1])!=full and endpoint(blocks+[0])!=full
+                endpoint_controls.append(dict(pattern=pattern,forward_columns=240,inverse_columns=240,omitted_rejected=True,repeated_rejected=True))
+            for b in range(bank,bank+count):
+                offset=0
+                for block,rank in enumerate(widths):
+                    q=used[rank];role=families[rank][q//60];replica=q%60;used[rank]+=1
+                    assert(role,replica)not in assigned;assigned.add((role,replica))
+                    a=plan.assignment(stage,replica,role);frame=gauge_frames.get(role)
+                    assert a==dict(family=plan.data_families+stage*plan.banks_per_stage+b,stage_bank=b,pattern=pattern,block=block,offset=offset,rank=rank,frame=frame,scalar=block+1)
+                    key=stage,pattern,block,frame
+                    if key not in normalizers_checked:
+                        N=plan.normalizer(stage,replica,role)
+                        assert N['unit_column_witness']==witnesses[block]and N['inverse_chart_frame']==frame and N['chart_window']==stage
+                        assert N['permutation'][24*stage:24*stage+rank]==tuple(range(offset,offset+rank))
+                        normalizers_checked.add(key)
+                    incidence.update(f'{stage},{pattern},{role},{replica},{b},{block},{offset},{rank}\n'.encode())
+                    assignments+=1;offset+=rank
+                assert offset==120
+            bank+=count
+        assert bank==plan.banks_per_stage and len(assigned)==60*len(context['regs'])and used=={r:60*len(xs)for r,xs in families.items()}
+    assert assignments==4923000
+    progress('Matched all4923000 literal bank assignments')
+    namespace=hashlib.sha256();collisions=0
+    for stage in range(5):
+        for replica in range(60):
+            addresses=[plan.local_address(stage,replica,i)for i in range(plan.local_work+1)]
+            assert len(set(addresses))==len(addresses)and addresses[-1]==(plan.work_family,('external_work',0))
+            assert all(f<plan.live_families for f,route in addresses[:-1])
+            collisions+=len(addresses)-len({f for f,route in addresses})
+            for f,route in addresses:namespace.update(f'{stage},{replica},{f},{route}\n'.encode())
+    assert collisions==0
+    # Bind every actual logical operand and mathematical field to the callable
+    # address substitution once per stage. The300 injective namespace maps
+    # above then instantiate all sixty replicas without replaying scalar algebra.
+    stream=struct.Struct('<8i');stage_checks=[];actual_helper_uses=set();paid=Counter()
+    for stage in range(5):
+        digest=hashlib.sha256();rows=0;stage_paid=Counter();kinds=Counter()
+        # Full addresses indexed by the original logical family; wrappers use
+        # exactly this tested local inverse and namespace construction.
+        addresses={}
+        for local in range(plan.local_work+1):
+            family=4*W.v+len(context['regs'])if local==plan.local_work else plan.active[stage][0]*W.v+local if local<W.v else plan.active[stage][1]*W.v+local-W.v if local<2*W.v else 4*W.v+local-2*W.v
+            assert plan.local_from_logical_family(stage,family)==local
+            addresses[family]=plan.local_address(stage,0,local)
+        for row in lower.iter_stage(stage):
+            op,a,b,c,f,z,s,rev=row;assert s==stage and rev==int(stage in(1,3))
+            mapped=plan.map_stage_row(stage,0,row)
+            assert mapped==(op,addresses[a],addresses[b]if op in(1,2)else b,c,f,z,s,rev)
+            for family in([a,b]if op in(1,2)else[a]):
+                if 4*W.v<=family<4*W.v+len(context['regs']):actual_helper_uses.add(family-4*W.v)
+            if op==0 and f:stage_paid[f]+=1
+            digest.update(stream.pack(*row));rows+=1;kinds[op]+=1
+        assert stage_paid==Counter({int(r):n for r,n in lower.ns['result']['paid_histogram'].items()})
+        paid.update(stage_paid)
+        stage_checks.append(dict(stage=stage,records=rows,logical_operand_binding_sha256=digest.hexdigest(),opcode_counts=dict(kinds),all_actual_operands_mapped=True))
+    assert actual_helper_uses==set(range(len(context['regs'])))
+    for which in range(3):
+        for row in lower.iter_idle(which):
+            mapped=plan.map_boundary_row(0,row);assert mapped[0]==4;paid[row[4]]+=1
+        for row in lower.iter_bridges(which):assert plan.map_boundary_row(0,row)[0]==5
+    exchanges=sum(1 for row in lower.iter_exchanges()if plan.map_boundary_row(0,row)[0]==7)
+    assert exchanges==2*W.v and paid==H
+    phases=[(kind,stage,replica)for kind,stage,replica,fn in bound.phases()]
+    assert len(phases)==720 and sum(kind=='helper'for kind,s,r in phases)==300
+    assert all(phases.index(('idle',which,r))<phases.index(('bridge',which,r))for which in range(3)for r in range(60))
+    controls=[]
+    try:plan.map_boundary_row(0,completions[0])
+    except AssertionError:controls.append('silent completion discharge')
+    else:raise AssertionError('completion passed address mapper')
+    assert hashlib.sha256((HERE/'bank_template.py').read_bytes()).hexdigest()==api_pin
+    factors=maxops+119+120;K=2*5*60*((plan.live_families-1)+len(context['regs'])*120*factors)
+    assert factors==425 and K==502915820400<2**40
+    result=dict(status='PASS_FRESH_CONTEXT_BOUND_COMPLETE_BANKS_AND_CALLABLE_LOWERING',
+        all_assignments_match=True,all_logical_helpers_bound=True,independent_completions_removed=len(completions),
+        removed_completion_histogram=dict(removed),literal_paid_histogram=dict(sorted(literal.items())),literal_stock=plan.live_families,
+        normalized_stock=str(Q(plan.live_families,60)),physical_replicas=60,bank_families=5*plan.banks_per_stage,data_families=plan.data_families,
+        assignments=assignments,incidence_sha256=incidence.hexdigest(),charts=len(charts),
+        chart_sha256=hashlib.sha256(json.dumps(charts,sort_keys=True,separators=(',',':')).encode()).hexdigest(),
+        max_chart_factors=maxops,max_factor_numerator=maxnum,max_denominator=maxden,normalizer_factor_bound=factors,
+        conservative_extra_selector_calls=K,distinct_actual_normalizers=len(normalizers_checked),
+        full_namespaces_checked=300,namespace_sha256=namespace.hexdigest(),intentional_family_collisions=collisions,
+        local_instruction_bindings=stage_checks,endpoint_checks=endpoint_controls,phase_schedule=phases,
+        completions_discharged_by='Each stage-private bank partitions all120 coordinates; all240 arbitrary-dirty address columns and inverse checked.',
+        inherited_geometry='Helper originalclass d*tau_i maps to bank d*tau_i*N^-1. N conjugates its actual residual in H_i into the assigned coordinate block. Data routes and boundary projectors remain PR234s.',
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),api_sha256=api_pin,
+        rejected_controls=controls,seconds=time.monotonic()-begun)
+    bank_keys=('literal_stock','normalized_stock','physical_replicas','bank_families','data_families','assignments',
+        'incidence_sha256','charts','chart_sha256','max_chart_factors','max_factor_numerator','max_denominator',
+        'normalizer_factor_bound','conservative_extra_selector_calls','distinct_actual_normalizers','endpoint_checks')
+    banks={k:result[k]for k in bank_keys};banks['status']='PASS_FRESH_ACTUAL_CHARTS_AND_COMPLETE_BANKS'
+    banks.update(gen4_roles=len(context['regs']),banks_total=5*plan.banks_per_stage)
+    return dict(banks=banks,banked_result=result)
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/bank_template.py b/research/gen4-retiming-entrances-target/vendor/pr276/bank_template.py
new file mode 100644
index 0000000000..d2bd3c0165
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/bank_template.py
@@ -0,0 +1,181 @@
+"""Callable stage-private120-coordinate bank address template.
+
+The caller supplies the freshly admitted actual helper role families and gauge
+chart IDs. This module owns no paths, global frame registry or source loading.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from collections import Counter
+
+
+class BankPlan:
+    m, h, stages, replicas, v = 120, 24, 5, 60, 1760
+    patterns = ((tuple([3]*40),399),
+                (tuple([4]*30),4400),
+                (tuple([24]*5),167328))
+
+    active = ((0,1),(1,0),(0,1),(3,2),(2,3))
+
+    def __init__(self, families, gauge_frames, helper_roles=None):
+        self.families = {r:tuple(rows) for r,rows in families.items() if rows}
+        assert {r:len(rows) for r,rows in self.families.items()} == {3:266,4:2200,24:13944}
+        self.role_index = {}
+        for rank,rows in self.families.items():
+            assert tuple(sorted(rows)) == rows and len(set(rows)) == len(rows)
+            for i,role in enumerate(rows):
+                assert role not in self.role_index
+                self.role_index[role]=(rank,i)
+        self.gauge_frames = dict(gauge_frames)
+        assert set(self.gauge_frames) == {role for r,rows in self.families.items() if r<self.h for role in rows}
+        self.helper_roles=tuple(sorted(self.role_index) if helper_roles is None else helper_roles)
+        assert len(self.helper_roles)==len(self.role_index) and set(self.helper_roles)==set(self.role_index)
+        self.local_work=2*self.v+len(self.helper_roles)
+        self.banks_per_stage=sum(count for widths,count in self.patterns)
+        self.data_families=self.replicas*4*self.v
+        self.live_families=self.data_families+self.stages*self.banks_per_stage
+        self.work_family=self.live_families
+        assert (self.banks_per_stage,self.data_families,self.live_families)==(172127,422400,1283035)
+        self.segments={}
+        used=Counter();bank_start=0
+        for pattern,(widths,count) in enumerate(self.patterns):
+            assert sum(widths)==self.m
+            for rank in set(widths):
+                blocks=tuple(b for b,r in enumerate(widths) if r==rank)
+                n=len(blocks)*count
+                self.segments.setdefault(rank,[]).append((used[rank],used[rank]+n,pattern,bank_start,blocks))
+                used[rank]+=n
+            bank_start+=count
+        assert used=={r:self.replicas*len(rows) for r,rows in self.families.items()}
+
+    def assignment(self, stage, replica, role):
+        """Exact bank family/block for one actual independent helper occurrence."""
+        assert 0<=stage<self.stages and 0<=replica<self.replicas
+        rank,role_index=self.role_index[role]
+        q=role_index*self.replicas+replica
+        for lo,hi,pattern,bank_start,blocks in self.segments[rank]:
+            if lo<=q<hi:
+                bank_offset,within=divmod(q-lo,len(blocks))
+                bank=bank_start+bank_offset;block=blocks[within]
+                widths=self.patterns[pattern][0]
+                return dict(family=self.data_families+stage*self.banks_per_stage+bank,
+                            stage_bank=bank,pattern=pattern,block=block,
+                            offset=sum(widths[:block]),rank=rank,
+                            frame=self.gauge_frames.get(role),scalar=block+1)
+        raise AssertionError('unallocated actual helper occurrence')
+
+    def data_family(self, replica, bank, port):
+        assert 0<=replica<self.replicas and 0<=bank<4 and 0<=port<self.v
+        return (4*replica+bank)*self.v+port
+
+    def normalizer(self, stage, replica, role):
+        """Finite exact data for N=scalar Pi embed_stage(B^-1).
+
+        frame=None denotes identity B=I24. The caller resolves other IDs in
+        its freshly admitted frame registry/charts. inverse_chart remains an
+        exact rational factor program; no floating matrix is consumed.
+        """
+        a=self.assignment(stage,replica,role)
+        original=tuple(range(self.h*stage,self.h*stage+a['rank']))
+        target=tuple(range(a['offset'],a['offset']+a['rank']))
+        src=original+tuple(j for j in range(self.m) if j not in original)
+        dst=target+tuple(j for j in range(self.m) if j not in target)
+        pi=dict(zip(src,dst))
+        assert set(pi)==set(pi.values())==set(range(self.m))
+        permutation=tuple(pi[j] for j in range(self.m))
+        outside=next(j for j in range(self.m) if not self.h*stage<=j<self.h*(stage+1))
+        return dict(scalar=a['scalar'],permutation=permutation,
+                    inverse_chart_frame=a['frame'],chart_window=stage,
+                    outside_column=outside,unit_column_witness=(pi[outside],a['scalar']))
+
+    def address(self, stage, replica, role, cover='d'):
+        """Original class d*tau_i routed to the actual bank by N^-1.
+
+        Multiplication order is literal. A consumer must lower the factor
+        list right-to-left for inverse N, keeping chart/scalar denominators.
+        """
+        a=self.assignment(stage,replica,role)
+        N=('normalizer',stage,a['pattern'],a['block'],a['frame'])
+        return a['family'],('right',cover,('tau',stage),('inverse',N))
+
+    def local_family(self, stage, replica, local):
+        """Live family for the admitted local physical register index.
+
+        Family equality does not imply address equality for banked helpers.
+        Consumers must use local_address for ADD nonalias/namespace checks.
+        """
+        assert 0<=stage<self.stages and 0<=replica<self.replicas
+        assert 0<=local<=self.local_work
+        if local==self.local_work:return self.work_family
+        if local<self.v:return self.data_family(replica,self.active[stage][0],local)
+        if local<2*self.v:return self.data_family(replica,self.active[stage][1],local-self.v)
+        return self.assignment(stage,replica,self.helper_roles[local-2*self.v])['family']
+
+    def local_address(self, stage, replica, local, cover='d'):
+        family=self.local_family(stage,replica,local)
+        if local==self.local_work:return family,('external_work',0)
+        if local<2*self.v:
+            route=('class',cover) if stage==0 else ('right',cover,('rho',stage,local%self.v))
+            return family,route
+        return self.address(stage,replica,self.helper_roles[local-2*self.v],cover)
+
+    def local_from_logical_family(self, stage, family):
+        """Invert PR234's logical five-stage family map for one active stage."""
+        logical_work=4*self.v+len(self.helper_roles)
+        assert 0<=family<=logical_work
+        if family==logical_work:return self.local_work
+        if family>=4*self.v:return 2*self.v+family-4*self.v
+        bank,port=divmod(family,self.v)
+        if bank==self.active[stage][0]:return port
+        assert bank==self.active[stage][1], 'stage references an inactive data bank'
+        return self.v+port
+
+    def map_stage_row(self, stage, replica, row, cover='d'):
+        """Lower an unchanged logical8-field MOVE/ADD/COPY/ERASE record.
+
+        All mathematical fields remain unchanged. The two operand slots now
+        contain exact (family,route) keys when they denote streams; frame IDs
+        in MOVE's old/new slots are not mistaken for stream operands.
+        """
+        op,a,b,c,f,z,s,rev=row
+        assert op in(0,1,2,3) and s==stage and rev==int(stage in(1,3))
+        def address(family):
+            return self.local_address(stage,replica,self.local_from_logical_family(stage,family),cover)
+        physical_a=address(a)
+        physical_b=address(b) if op in(1,2) else b
+        if op in(1,2):assert physical_a!=physical_b
+        return (op,physical_a,physical_b,c,f,z,s,rev)
+
+    def map_boundary_row(self, replica, row, cover='d'):
+        """Lower an IDLE/BRIDGE/EXCHANGE with its existing exact projector.
+
+        Boundary projectors already include the checked data-route conjugacy;
+        their physical class is d. Independent completion rows must be
+        discharged explicitly by the bank endpoint verifier, never skipped
+        implicitly by this address mapper.
+        """
+        op,a,b,c,f,z,s,rev=row
+        assert op in(4,5,7), 'only proved bank completion may discharge opcode6'
+        def address(family):
+            assert 0<=family<4*self.v
+            bank,port=divmod(family,self.v)
+            return self.data_family(replica,bank,port),('class',cover)
+        physical_a=address(a)
+        physical_b=address(b) if op in(5,7) else b
+        if op in(5,7):assert physical_a!=physical_b
+        return (op,physical_a,physical_b,c,f,z,s,rev)
+
+    def phase_schedule(self):
+        """Phase-major schedule; every cover class is completed per replica.
+
+        Each emitted stage phase means: for the indicated replica, iterate
+        every cover class and execute the entire local scalar telescope.
+        Boundary phases occur after all60 replicas of that stage finish.
+        """
+        for stage in range(self.stages):
+            for replica in range(self.replicas):
+                yield ('stage',stage,replica,'all_cover_classes')
+            if stage in (1,2,4):
+                for replica in range(self.replicas):
+                    yield ('idle',stage,replica,'all_cover_classes')
+                    yield ('bridge',stage,replica,'all_cover_classes')
+        for replica in range(self.replicas):
+            yield ('terminal_exchange',replica,'all_cover_classes')
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/base_two_moment.py b/research/gen4-retiming-entrances-target/vendor/pr276/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_basis.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_basis.py
new file mode 100644
index 0000000000..8c400798a5
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_basis.py
@@ -0,0 +1,35 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+def need(b, why):
+    if not b: raise ValueError(why)
+
+def gl_count_test():
+    # Exhaustively test a literal binary Gaussian-elimination implementation
+    # through m=4. Row swaps cost three selected-bit additions.
+    out=[]
+    for m in range(1,5):
+        good=mx=0
+        for word in range(1<<(m*m)):
+            rows=[(word>>(m*i))&((1<<m)-1) for i in range(m)]
+            ops=0
+            for k in range(m):
+                p=next((i for i in range(k,m) if rows[i]>>k&1),None)
+                if p is None: break
+                if p!=k: rows[p],rows[k]=rows[k],rows[p];ops+=3
+                for i in range(m):
+                    if i!=k and rows[i]>>k&1: rows[i]^=rows[k];ops+=1
+            else:
+                need(rows==[1<<i for i in range(m)],'basis reduction endpoint')
+                need(ops<=m*(m-1)+3*m,'row-addition count')
+                good+=1;mx=max(mx,ops)
+        need(good==prod((1<<m)-(1<<i) for i in range(m)),'GL coverage')
+        out.append(dict(m=m,invertible_matrices=good,maximum_selected_bit_additions=mx))
+    return out
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_labels.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_labels.py
new file mode 100644
index 0000000000..1f27d6de34
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_labels.py
@@ -0,0 +1,176 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+BASE = dict(h=22, v=1320, R=9412, cst=440, N=262944)
+EXPECTED_H = {1:29178,2:12398,3:9923,4:4209,5:1950,6:1605,7:706,8:1531,
+              9:429,10:930,11:354,12:1197,13:127,14:742,15:1879,16:88,
+              17:81,18:2653,19:167,20:22}
+class Reject(ValueError):
+    pass
+
+def need(ok, msg):
+    if not ok:
+        raise Reject(msg)
+
+def digest(obj):
+    return sha256(json.dumps(obj, separators=(",",":"), sort_keys=True).encode()).hexdigest()
+
+def hist(counter):
+    return {str(k):v for k,v in sorted(counter.items()) if v}
+
+def role(r,v):
+    return "x" if r < v else "y" if r < 2*v else "s"
+
+def reduce_binary(x, frame):
+    for b in frame:
+        if x & (1 << (b.bit_length()-1)):
+            x ^= b
+    return x
+
+def coeff(a,b, where):
+    need(type(a) is int and type(b) is int and b>0, f"{where}: coefficient shape")
+    q=Fraction(a,b)
+    odd=q.denominator
+    while odd%2==0:
+        odd//=2
+    need(odd in (1,3), f"{where}: literal coefficient outside dyadic/divisor-three grid")
+    return q
+
+def replay_label_counts(c):
+    """Full finite LABEL walk only. Never multiplies the 12,052-square scalar map."""
+    need(c.get("format")=="gcert/1", "format")
+    need(all(c.get(k)==v for k,v in BASE.items()), "baseline parameter/count mismatch")
+    h,v,R=c["h"],c["v"],c["R"]; n=2*v+R
+    need(c.get("ext")==[], "baseline has no exterior-gauged helper inputs")
+    frames=c["frames"]; dim=list(map(len,frames))
+    need(len(frames)==18248, "baseline frame-table count")
+    need(frames[0]==[] and frames[1]==[1<<i for i in range(h-1,-1,-1)], "zero/full frames")
+    need(len({tuple(f) for f in frames})==len(frames), "duplicate frames")
+    for f in frames:
+        need(all(type(b) is int and 0<b<1<<h for b in f), "frame bit range")
+        piv=[b.bit_length()-1 for b in f]
+        need(all(piv[i]>piv[i+1] for i in range(len(piv)-1)), "frame pivot order")
+        need(all(not(b>>p&1) for i,b in enumerate(f) for j,p in enumerate(piv) if i!=j),
+             "frame is not reduced echelon")
+    ports=c["ports"]
+    need(len(ports)==v==len(set(ports)), "port count/uniqueness")
+    need(all(type(p) is int and 0<p<(1<<h)-1 and p.bit_count()%2 for p in ports), "unit port/gap")
+    start=c["start"]; final=c["final"]
+    need(len(start)==len(final)==n, "live invocation role count")
+    need(all(type(f) is int and 0<=f<len(frames) for f in start+final), "endpoint frame ID")
+    for t,p in enumerate(ports):
+        need(frames[start[t]]==[p] and final[t]==1, "X endpoint")
+        need(start[v+t]==0 and dim[final[v+t]]==h-1 and
+             all((p&u).bit_count()%2==0 for u in frames[final[v+t]]), "Y endpoint")
+    need(all(f==0 for f in start[2*v:]) and all(f==1 for f in final[2*v:]), "helper endpoints")
+    need(c["ret"] and len(c["ret"])==22, "temporary-center count")
+    need([x[0] for x in c["ret"]]==list(range(22)), "center numbering")
+    need(len({x[1] for x in c["ret"]})==22, "center retained slots repeat")
+    need(c["scat"]=={"inside":[1,3],"outside":[-1,6]}, "baseline scatter rule")
+    need(len(c["A"])==12158 and len(c["B"])==30878, "phase gate count")
+    cur=start.copy(); pairs=set()
+    by_role={r:Counter() for r in "xysc"}
+    by_phase={p:Counter() for p in ("A","copy","B","final")}
+    literal=Counter(); kind=Counter(); ybracket=Counter(); ypiv=set(); ytarget=set()
+    totals={p:dict(gates=0,scalar_additions=0,register_visits=0,spectator_visits=0)
+            for p in ("A","B")}
+    transitions=0
+    def climb(reg,new,phase):
+        nonlocal transitions
+        old=cur[reg]
+        if old==new:
+            return
+        need(dim[old]<dim[new], f"{phase}: frame does not strictly climb")
+        pair=(old,new)
+        if pair not in pairs:
+            need(all(reduce_binary(b,frames[new])==0 for b in frames[old]), f"{phase}: nonnested frames")
+            pairs.add(pair)
+        rank=dim[new]-dim[old]
+        by_role[role(reg,v)][rank]+=1; by_phase[phase][rank]+=1
+        cur[reg]=new;transitions+=1
+    for phase in ("A","B"):
+        for i,g in enumerate(c[phase]):
+            where=f"{phase}[{i}]"
+            need(isinstance(g,list) and len(g)>=4 and g[0] in ("out","in"), where+": gate shape")
+            tag,f,pivot,terms=g[:4]
+            need(len(g)==(5 if tag=="out" else 4), where+": gate arity")
+            need(type(f) is int and 0<=f<len(frames), where+": frame ID")
+            need(all(isinstance(x,list) and len(x)==3 for x in terms), where+": terms")
+            spectators=g[4] if tag=="out" else []
+            regs=[pivot]+[x[0] for x in terms]+spectators
+            need(all(type(r) is int and 0<=r<n for r in regs) and len(set(regs))==len(regs),
+                 where+": duplicate/out-of-range register")
+            need(phase!="A" or all(not(v<=r<2*v) for r in regs), where+": Y role before scatter")
+            totals[phase]["gates"]+=1
+            totals[phase]["register_visits"]+=len(regs)
+            totals[phase]["spectator_visits"]+=len(spectators)
+            for reg,a,b in terms:
+                target,source=(reg,pivot) if tag=="out" else (pivot,reg)
+                sr,tr=role(source,v),role(target,v)
+                need((sr,tr) in {("x","s"),("s","s"),("s","y"),("x","y"),("x","x"),("y","y")},
+                     where+": forbidden role direction")
+                need(phase!="A" or (sr,tr) in {("x","s"),("s","s")}, where+": phase A role direction")
+                q=coeff(a,b,where)
+                need(q!=0,where+": zero scalar addition")
+                literal[str(q)]+=1;kind[f"{phase}:{sr}->{tr}"]+=1
+                totals[phase]["scalar_additions"]+=1
+                if sr==tr=="y":
+                    ybracket[(source,target)]+=q;ypiv.add(source);ytarget.add(target)
+            for r in regs:
+                climb(r,f,phase)
+        if phase=="A":
+            cut=cur.copy()
+            need(all(cur[v+t]==0 for t in range(v)), "scatter: Y role moved too early")
+            for k,r,f in c["ret"]:
+                need(type(r) is int and 2*v<=r<n, "scatter: center source is not a helper role")
+                need(type(f) is int and 0<=f<len(frames) and cur[r]==f and dim[f]==20,
+                     "scatter: center label/rank mismatch")
+                by_role["c"][20]+=1;by_phase["copy"][20]+=1
+    need(not ypiv.intersection(ytarget) and all(q==0 for q in ybracket.values()), "Y bracket cancellation")
+    before_final=cur.copy()
+    for r,f in enumerate(final):
+        climb(r,f,"final")
+    need(cur==final,"final label state")
+    measured={r:hist(cn) for r,cn in by_role.items()}
+    need(measured==c["blocks"], "role histogram/count mismatch")
+    combined=sum(by_role.values(),Counter())
+    need(dict(combined)==EXPECTED_H, "baseline invocation histogram mismatch")
+    mass=sum(r*k for r,k in combined.items())
+    need(mass==c["N"]==R*h+2*v*(h-1)+c["cst"], "rank mass")
+    need(sum(r*k for r,k in by_role["c"].items())==c["cst"],"temporary-center rank mass")
+    scatter=Counter(str(coeff(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]),"scatter"))
+                    for p in ports for k in range(22))
+    return {
+        "frame_count":len(frames),"tested_distinct_nested_pairs":len(pairs),
+        "live_registers_per_invocation":n,"temporary_centers":22,
+        "ranked_live_transitions":transitions,
+        "phase_stats":totals,"role_histograms":measured,
+        "phase_histograms":{p:hist(x) for p,x in by_phase.items()},
+        "invocation_histogram":hist(combined),"invocation_calls":sum(combined.values()),
+        "invocation_rank_mass":mass,"retained_centers":c["ret"],
+        "phase_state_sha256":{"start":digest(start),"after_A":digest(cut),
+                              "after_B":digest(before_final),"final":digest(final)},
+        "literal_gate_coefficients":dict(sorted(literal.items())),
+        "scalar_role_directions":dict(sorted(kind.items())),
+        "scatter_coefficients":dict(sorted(scatter.items())),
+        "scatter_additions":sum(scatter.values()),"Cc_copy_additions":22,
+        "two_hosts_metadata_count":len(c["two_hosts"]),
+        "two_hosts_note":"Metadata only; not an independent allocator or host-use proof.",
+        "Y_bracket_pairs":len(ybracket),
+        "literal_inverse":"Each nonself additive shear inverts by negating its coefficient; inverse phase reverses order; inverse transpose keeps chronological order and swaps source/target with negation.",
+        "limits":["No scalar all-column replay","No old-response or cleanup matrix formed",
+                  "No generated Lean data comparison or kernel build","No physical stream compiler"]
+    }
+
+def scalar_word(ops):
+    matrix=[[int(i==j) for j in range(4)] for i in range(4)]
+    for target,source,q in ops:
+        matrix[target]=[a+q*b for a,b in zip(matrix[target],matrix[source])]
+    return matrix
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_scalars.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_scalars.py
new file mode 100644
index 0000000000..771057b567
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_scalars.py
@@ -0,0 +1,216 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+V,R,H=1320,9412,22
+def need(x,msg):
+    if not x:raise ValueError(msg)
+
+def kind(r):return "X" if r<V else "Y" if r<2*V else "S"
+
+def live(r):return ("L",r)
+
+def tmp(r):return ("T",r-2*V)
+
+def center(k):return ("C",k)
+
+def add(t,s,q):return ("add",t,s,q.numerator,q.denominator)
+
+def clear(t):return ("clear",t)
+
+def copy(t,s):return ("copy",t,s)
+
+def flat(gs):
+    out=[]
+    for g in gs:
+        need(g[0] in ["in","out"],"literal additive gate")
+        for r,a,b in g[3]:
+            t,s=(r,g[2]) if g[0]=="out" else (g[2],r)
+            need(t!=s and kind(s)!="Y" and not(kind(s)=="S" and kind(t)=="X"),
+                 "projection requires Y never read and no helper-to-X gate")
+            out.append((t,s,Q(a,b)))
+    return out
+
+def old_positive(A,B,c):
+    """Circuit with inputs temp S and live Y; X fixed at zero.
+    tempS output is irrelevant. Y output is Y_in + K tempS_in."""
+    def part(gs):
+        for t,s,q in gs:
+            if kind(s)=="X":continue
+            need(kind(s)=="S" and kind(t) in ["S","Y"],"old-response shape")
+            yield add(tmp(t) if kind(t)=="S" else live(t),tmp(s),q)
+    yield from part(A)
+    for t,p in enumerate(c["ports"]):
+        for k,r,_ in c["ret"]:
+            q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+            yield add(live(V+t),tmp(r),q)
+    yield from part(B)
+
+def old_word(orientation,K):
+    if orientation=="forward":
+        yield from (copy(("T",q),live(2*V+q)) for q in range(R))
+        for e in K:
+            op,t,s,a,b=e
+            yield add(t,s,Q(-a if t[0]=="L" else a,b))
+    else:
+        yield from (clear(("T",q)) for q in range(R))
+        for op,t,s,a,b in reversed(K):
+            yield add(s,t,Q(a,b))
+        yield from (add(live(2*V+q),("T",q),Q(1)) for q in range(R))
+    yield from (clear(("T",q)) for q in range(R))
+
+def cleanup(orientation,AB):
+    for t,s,q in reversed(AB):
+        if kind(t)=="Y":continue
+        if orientation=="forward":yield add(live(t),live(s),-q)
+        else:yield add(live(s),live(t),q)
+
+def main_scalar(orientation,A,B,c):
+    def phase(gs):
+        for t,s,q in gs:
+            if orientation=="forward":yield add(live(t),live(s),q)
+            else:yield add(live(s),live(t),-q)
+    yield from phase(A)
+    # Every center is a complete temporary stream and one rank20 child,
+    # initialized/read/discarded before the next center uses the work stock.
+    for k,r,_ in c["ret"]:
+        yield clear(center(k))
+        if orientation=="forward":yield add(center(k),live(r),Q(1))
+        for t,p in enumerate(c["ports"]):
+            q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+            if orientation=="backward":yield add(center(k),live(V+t),q)
+        yield ("recursive_center",k,20)
+        if orientation=="forward":
+            for t,p in enumerate(c["ports"]):
+                q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+                yield add(live(V+t),center(k),q)
+        else:yield add(live(r),center(k),Q(-1))
+        yield clear(center(k))
+    yield from phase(B)
+
+def inv_schedule(orientation,A,B,c):
+    K=list(old_positive(A,B,c))
+    yield from ((p,e) for p,es in [
+       ("old_response",old_word(orientation,K)),
+       ("main",main_scalar(orientation,A,B,c)),
+       ("cleanup",cleanup(orientation,A+B))] for e in es)
+
+def coeff_steps(q):
+    """Non-destructive coefficient expansion using one complete work stream.
+    Copy source, double/halve/divide by3 as needed, add/subtract, clear.
+    Counts Gaussian operations; multiply by2 for real/imag component primitives."""
+    a,b=abs(q.numerator),q.denominator
+    need(a in (1,2) and b in (1,2,3,6),"unsupported new coefficient")
+    return 3+int(a==2)+int(b%2==0)+int(b%3==0)
+
+def bill(schedule):
+    phases={p:Counter() for p in ("old_response","main","cleanup")}
+    coeffs={p:Counter() for p in phases}
+    tape=sha256()
+    for p,e in schedule:
+        tape.update((json.dumps((p,e),separators=(",",":"))+"\n").encode())
+        phases[p]["all_macros"]+=1
+        if e[0]=="recursive_center":
+            phases[p]["recursive_centers"]+=1
+            phases[p]["recursive_rank_mass"]+=e[2]
+            continue
+        phases[p]["scalar_macros"]+=1
+        phases[p][e[0]]+=1
+        if e[0]=="add":
+            q=Q(e[3],e[4]);coeffs[p][str(q)]+=1
+            phases[p]["Gaussian_primitive_steps"]+=coeff_steps(q)
+            phases[p]["scalar_log2_magnitude_charge"]+=1+int(abs(q)==2)
+            phases[p]["halving_exposure"]+=int(q.denominator%2==0)
+            phases[p]["divisor3_exposure"]+=int(q.denominator%3==0)
+        else:phases[p]["Gaussian_primitive_steps"]+=1
+    for p in phases:phases[p]["real_component_primitive_steps"]=2*phases[p]["Gaussian_primitive_steps"]
+    total=sum((Counter({k:v for k,v in x.items() if k not in ["recursive_rank_mass"]}) for x in phases.values()),Counter())
+    return {"phases":{p:dict(x) for p,x in phases.items()},"coefficient_histograms":{p:dict(x) for p,x in coeffs.items()},
+            "totals":dict(total),"schedule_sha256":tape.hexdigest(),
+            "other_main_recursive_calls":"70147 existing live-label transitions, unchanged; not scalar macros"}
+
+def mm(A,B):return [[sum((x*y for x,y in zip(row,col)),Q(0)) for col in zip(*B)] for row in A]
+
+def lifecycle(schedule):
+    """Verify that new scalar-only work stock never survives into a child."""
+    initialized=set();dirty=set();active_centers=set();seen_main=False;children=0
+    for phase,e in schedule:
+        if phase=="main" and not seen_main:
+            need(not dirty,"old-response tableau survives into recursive main phase")
+            seen_main=True
+        need(e[0] in ("add","copy","clear","recursive_center"),"unknown or unpaid recursive operation")
+        if e[0]=="recursive_center":
+            k=e[1]
+            need(type(k) is int and 0<=k<22 and e[2]==20,"new temporary entered uncharged child")
+            need(phase=="main" and not dirty,"old-response temporary used during child")
+            need(active_centers<=set([k]),"other center was not discarded before next child")
+            children+=1
+            continue
+        target=e[1]
+        source=e[2] if e[0] in ("add","copy") else None
+        if source and source[0]=="T":need(source[1] in initialized,"uninitialized temporary read")
+        if target[0]=="T":
+            need(phase=="old_response","scalar-only tableau touched after recursive phase begins")
+            initialized.add(target[1])
+            if e[0]=="clear":dirty.discard(target[1])
+            else:dirty.add(target[1])
+        if target[0]=="C":
+            if e[0]=="clear":active_centers.discard(target[1])
+            else:active_centers.add(target[1])
+        if e[0]=="add":
+            # Coefficient expansion is deliberately local: copy into W,
+            # optionally double/halve/divide3, accumulate, and clear W.
+            expanded=["copy_work"]+["scale"]*(coeff_steps(Q(e[3],e[4]))-3)+["accumulate","clear_work"]
+            need(expanded[-1]=="clear_work","coefficient work survived scalar macro")
+    need(not dirty and not active_centers,"temporary stock not erased at invocation end")
+    need(children==22,"center child count changed")
+    return {"tableau_cleared_before_entire_main_phase":True,"tableau_absent_from_all_children":True,
+            "coefficient_work_cleared_per_add":True,"center_children":children,
+            "new_recursive_children":0,"moment_live_width":14692,
+            "new_work_stock_only":9413,"complete_stream_fraction":"1/(14692*|Orth(110,2)|)"}
+
+def ident(n):return [[Q(int(i==j)) for j in range(n)] for i in range(n)]
+
+def matrix(n,gs):
+    a=ident(n)
+    for t,s,q in gs:a[t]=[x+q*y for x,y in zip(a[t],a[s])]
+    return a
+
+def toy_checks():
+    # 2 X, 3 S, 2 Y. Explicit nontrivial X mixing is undone; helper map
+    # and K are otherwise arbitrary. Exact Fraction checks cover every column
+    # of THIS TINY TEMPLATE, not of the published 12052-register source.
+    n=7;X={0,1};S={2,3,4};Y={5,6}
+    gs=[(2,0,Q(1)),(3,2,Q(2)),(5,3,Q(-1,6)),(0,1,Q(1,2)),
+        (4,0,Q(2)),(2,4,Q(1,2)),(6,2,Q(1,3)),(0,1,Q(-1,2)),
+        (3,1,Q(-1)),(5,4,Q(1)),(6,0,Q(1))]
+    M=matrix(n,gs)
+    need(all(M[i]==ident(n)[i] for i in X),"toy source rows not restored")
+    Ugs=[e for e in gs if e[0] not in Y]
+    U=matrix(n,Ugs)
+    Uinv=matrix(n,[(t,s,-q) for t,s,q in reversed(Ugs)])
+    need(mm(Uinv,U)==ident(n),"restricted inverse identity")
+    Mi=matrix(n,[(t,s,-q) for t,s,q in reversed(gs)])
+    g8=[Mi[i] if i in S else ident(n)[i] for i in range(n)]
+    h8=[M[i] if i in S else ident(n)[i] for i in range(n)]
+    need(g8==Uinv and h8==U,"cleanup projection identities")
+    Ut=matrix(n,[(s,t,q) for t,s,q in reversed(Ugs)])
+    need(Ut==[list(x) for x in zip(*U)],"backward cleanup transpose")
+    Kgs=[e for e in gs if e[1] not in X]
+    Kmat=matrix(n,Kgs)
+    need(all(Kmat[i][j]==M[i][j] for i in Y for j in S),"zero-source old response")
+    Kt=matrix(n,[(s,t,q) for t,s,q in reversed(Kgs)])
+    need(all(Kt[i][j]==M[j][i] for i in S for j in Y),"old response adjoint")
+    bad=matrix(n,[(t,s,q) for t,s,q in reversed(Ugs)])
+    need(bad!=g8,"wrong inverse sign must fail")
+    bad_order=matrix(n,[(s,t,q) for t,s,q in Ugs])
+    need(bad_order!=Ut,"unreversed transpose must fail")
+    return {"tiny_exact_template_columns_checked":7,"checks_passed":7,
+            "wrong_inverse_sign_rejected":True,"unreversed_transpose_rejected":True,
+            "published_full_scalar_replay":False}
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_splice.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_splice.py
new file mode 100644
index 0000000000..11373d1d57
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/complex_splice.py
@@ -0,0 +1,277 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+V,R,H,N,W=1320,9412,22,12052,14692
+PHASES=["old_response","ad0","A","centers","B","final","adF","cleanup","done"]
+def need(x,s):
+    if not x:raise ValueError(s)
+
+def blobhash(p):return sha256(p.read_bytes()).hexdigest()
+
+def digest(x):return sha256(json.dumps(x,separators=(',',':'),sort_keys=True).encode()).hexdigest()
+
+def role(r):return 'X' if r<V else 'Y' if r<2*V else 'S'
+
+def add(t,s,q):return ('add',t,s,q.numerator,q.denominator)
+
+def L(r):return ('L',r)
+
+def T(r):return ('T',r-2*V)
+
+def C(k):return ('C',k)
+
+def clear(t):return ('clear',t)
+
+def copy(t,s):return ('copy',t,s)
+
+def flat(gs):
+    for g in gs:
+        for r,a,b in g[3]:
+            t,s=(r,g[2]) if g[0]=='out' else (g[2],r)
+            need(t!=s and role(s)!='Y' and (role(s),role(t))!=('S','X'),'scalar projection shape')
+            yield t,s,Q(a,b)
+
+def scal(phase,e,frame):return ('scalar',phase,e,frame)
+
+def lower_scalar(e):
+    # The coefficient work stream is disjoint from every live and center role.
+    if e[0] in ['copy','clear']:return [e]
+    _,t,s,a,b=e;work=('W',0)
+    out=[copy(work,s)]
+    if abs(a)==2:out.append(('double',work))
+    if b%2==0:out.append(('halve',work))
+    if b%3==0:out.append(('divide3',work))
+    return out+[('accumulate',t,work,1 if a>0 else -1),clear(work)]
+
+def emit(c,ori):
+    """Construct the complete local parametric invocation, before cover routing.
+    One role stream is its full complete address rectangle. Frame labels denote
+    exact canonical representatives, never just rank or binary matrices.
+    """
+    A=list(flat(c['A']));B=list(flat(c['B']));cur=c['start'].copy()
+    K=[]
+    for part in (A,None,B):
+        if part is None:
+            for t,p in enumerate(c['ports']):
+                for k,r,f in c['ret']:
+                    K.append(add(L(V+t),T(r),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))))
+        else:
+            for t,s,q in part:
+                if role(s)=='X':continue
+                K.append(add(T(t) if role(t)=='S' else L(t),T(s),q))
+    yield ('phase','old_response')
+    if ori=='forward':
+        for q in range(R):yield scal('old_response',copy(('T',q),L(2*V+q)),'old0')
+        for _,t,s,a,b in K:yield scal('old_response',add(t,s,Q(-a if t[0]=='L' else a,b)),'old0')
+    else:
+        for q in range(R):yield scal('old_response',clear(('T',q)),'old0')
+        for _,t,s,a,b in reversed(K):yield scal('old_response',add(s,t,Q(a,b)),'old0')
+        for q in range(R):yield scal('old_response',add(L(2*V+q),('T',q),Q(1)),'old0')
+    for q in range(R):yield scal('old_response',clear(('T',q)),'old0')
+    yield ('phase','ad0')
+    for r,f in enumerate(c['start']):yield ('adapter','old_to_new',r,f)
+    for part in ['A','centers','B','final']:
+        yield ('phase',part)
+        if part in ['A','B']:
+            for g in c[part]:
+                regs=[g[2]]+[x[0] for x in g[3]]+(g[4] if g[0]=='out' else [])
+                for r in regs:
+                    if cur[r]!=g[1]:
+                        old=cur[r];cur[r]=g[1]
+                        yield ('climb',part,r,old,g[1],len(c['frames'][g[1]])-len(c['frames'][old]))
+                for t,s,q in flat([g]):
+                    e=add(L(t),L(s),q) if ori=='forward' else add(L(s),L(t),-q)
+                    yield scal('main',e,g[1])
+        elif part=='centers':
+            for k,r,f in c['ret']:
+                yield scal('main',clear(C(k)),f if ori=='forward' else 0)
+                if ori=='forward':yield scal('main',add(C(k),L(r),Q(1)),f)
+                else:
+                    for t,p in enumerate(c['ports']):
+                        yield scal('main',add(C(k),L(V+t),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0)
+                yield ('center',k,f if ori=='forward' else 0,0 if ori=='forward' else f,20)
+                if ori=='forward':
+                    for t,p in enumerate(c['ports']):
+                        yield scal('main',add(L(V+t),C(k),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0)
+                else:yield scal('main',add(L(r),C(k),Q(-1)),f)
+                yield scal('main',clear(C(k)),0 if ori=='forward' else f)
+        else:
+            for r,f in enumerate(c['final']):
+                if cur[r]!=f:
+                    old=cur[r];cur[r]=f
+                    yield ('climb','final',r,old,f,len(c['frames'][f])-len(c['frames'][old]))
+    yield ('phase','adF')
+    for r,f in enumerate(c['final']):yield ('adapter','new_to_old',r,f)
+    yield ('phase','cleanup')
+    for t,s,q in reversed(A+B):
+        if role(t)=='Y':continue
+        e=add(L(t),L(s),-q) if ori=='forward' else add(L(s),L(t),q)
+        yield scal('cleanup',e,'old1')
+    yield ('phase','done')
+
+def contains(U,V):
+    for u in U:
+        for v in V:
+            if u>>(v.bit_length()-1)&1:u^=v
+        if u:return False
+    return True
+
+def validate(events,c,ori,manifest,bill):
+    phase=None;seen=[];cur=c['start'].copy();cent={};dirty=set();initialized=set()
+    climbed=Counter();hist=Counter();projection=sha256();whole=sha256();counts=Counter();ad0=[];adF=[]
+    pairs=set();states={};all_frame_incidence=0;primitive=sha256();primitive_count=0
+    for ev in events:
+        whole.update((json.dumps(ev,separators=(',',':'))+'\n').encode())
+        tag=ev[0];counts[tag]+=1
+        if tag=='phase':
+            if phase=='A':states['after_A']=digest(cur)
+            if phase=='B':states['after_B']=digest(cur)
+            if phase=='final':states['final']=digest(cur)
+            phase=ev[1];seen.append(phase)
+            need(seen==PHASES[:len(seen)],'strict old/A/copy/B/final/adapter/cleanup chronology')
+            if phase=='ad0':need(not dirty,'old-response tableau survived before label recursion')
+            if phase=='A':need(ad0==list(enumerate(c['start'])),'missing or reordered exact entry adapter')
+            if phase=='adF':need(cur==c['final'],'final climbs omitted before cleanup')
+            if phase=='cleanup':need(adF==list(enumerate(c['final'])),'missing or reordered exact final adapter')
+            continue
+        if tag=='adapter':
+            _,which,r,f=ev
+            if which=='old_to_new':need(phase=='ad0','entry adapter position');ad0.append((r,f))
+            else:need(which=='new_to_old' and phase=='adF','final adapter position');adF.append((r,f))
+        elif tag=='climb':
+            _,p,r,old,new,d=ev
+            need(phase==p and p in ['A','B','final'],'live child outside source label walk')
+            need(not dirty and not cent,'new work stock or center active during live child')
+            need(cur[r]==old and d==len(c['frames'][new])-len(c['frames'][old]) and d>0,'wrong exact child endpoints/rank')
+            pair=(old,new)
+            if pair not in pairs:need(contains(c['frames'][old],c['frames'][new]),'nonnested child');pairs.add(pair)
+            cur[r]=new;climbed[p]+=1;hist[d]+=1
+        elif tag=='center':
+            _,k,old,new,d=ev
+            need(phase=='centers' and not dirty and set(cent)=={k},'center child ownership')
+            need(cent[k]==old and (k,c['ret'][k][1],c['ret'][k][2])==tuple(c['ret'][k]),'center input frame')
+            f=c['ret'][k][2]
+            need((old,new,d)==((f,0,20) if ori=='forward' else (0,f,20)),'center child direction/rank')
+            cent[k]=new;hist[d]+=1
+            projection.update((json.dumps(('main',('recursive_center',k,d)),separators=(',',':'))+'\n').encode())
+        elif tag=='scalar':
+            _,p,e,f=ev
+            need(p==('main' if phase in ['A','centers','B'] else phase),'scalar phase binding')
+            need(e[0] in ['add','copy','clear'],'unpaid scalar operation')
+            target=e[1];source=e[2] if e[0] in ['add','copy'] else None
+            for x in [target]+([source] if source else []):
+                bank,r=x
+                if bank=='T':need(phase=='old_response' and 0<=r<R,'tableau outside old response')
+                elif bank=='C':need(phase=='centers' and 0<=r<H,'center outside copied block')
+                elif bank=='L':
+                    need(0<=r<N,'live register range')
+                    if phase=='old_response':need(role(r) in ['S','Y'] and f=='old0','old response not at common old0')
+                    elif phase=='cleanup':need(role(r) in ['X','S'] and f=='old1' and cur[r]==1,'cleanup not at common old1')
+                    else:need(cur[r]==f,'scalar incidence uses wrong exact label');all_frame_incidence+=1
+                else:raise ValueError('unknown stream namespace')
+            if source and source[0]=='T':need(source[1] in initialized,'read before tableau initialization')
+            if source and source[0]=='C':need(cent.get(source[1])==f,'center source frame')
+            if target[0]=='T':
+                if e[0]=='add':need(target[1] in initialized,'tableau accumulation before initialization')
+                initialized.add(target[1])
+                if e[0]=='clear':dirty.discard(target[1])
+                else:dirty.add(target[1])
+            if target[0]=='C':
+                if e[0]=='clear':
+                    if target[1] in cent:del cent[target[1]]
+                else:
+                    need(not cent or set(cent)=={target[1]},'overlapping center lifetimes')
+                    need(cent.get(target[1],f)==f,'center target frame');cent[target[1]]=f
+            if e[0]=='add':need(e[4] in [1,2,3,6] and abs(e[3]) in [1,2],'unrecorded coefficient')
+            projection.update((json.dumps((p,e),separators=(',',':'))+'\n').encode())
+            lowered=lower_scalar(e)
+            if e[0]=='add':need(lowered[-1]==('clear',('W',0)),'coefficient work survives scalar macro')
+            for op in lowered:
+                primitive.update((json.dumps((p,op),separators=(',',':'))+'\n').encode())
+                primitive_count+=1
+        else:raise ValueError('unknown physical event')
+    need(seen==PHASES and not dirty and not cent,'incomplete invocation or dirty temporary')
+    need(dict(climbed)=={'A':13798,'B':46937,'final':9412},'live transition count/partition')
+    need(counts['center']==22 and counts['climb']==70147,'paid children omitted or doubled')
+    need({str(k):v for k,v in sorted(hist.items())}==manifest['checks']['invocation_histogram'],'paid source histogram changed')
+    need(states=={k:v for k,v in manifest['checks']['phase_state_sha256'].items() if k!='start'},'exact label states differ')
+    need(projection.hexdigest()==bill[ori]['schedule_sha256'],'complete scalar program differs from checked bill')
+    need(2*primitive_count==bill[ori]['totals']['real_component_primitive_steps'],'independent primitive expansion bill')
+    return dict(events=sum(counts.values()),event_counts=dict(counts),program_sha256=whole.hexdigest(),
+        scalar_projection_sha256=projection.hexdigest(),live_transition_partition=dict(climbed),
+        paid_children=counts['climb']+counts['center'],final_climbs_before_cleanup=True,
+        exact_common_label_live_incidences=all_frame_incidence,distinct_nested_pairs=len(pairs),
+        exact_label_state_sha256=states,old_response_erased_before_all_children=True,
+        entry_and_exit_old_new_adapters=2*N,Gaussian_primitives=primitive_count,
+        real_component_primitives=2*primitive_count,scalar_primitive_sha256=primitive.hexdigest())
+
+def global_contract(manifest):
+    return dict(family='baseline5stageComplex',m=110,live=14692,physical=24127,
+        stage_recipe=[dict(stage=j,window=f'G{j}',orientation=o,active_pair=p,
+            bank_owner='d' if j==0 else f'r{j}(t)^(-1)(d)',helper_owner='d' if j==0 else f's{j}(d)',
+            exterior_subset='empty' if j==0 else f'qS bs{j} l',
+            native_frame=f'(G{j} d).X.Phi(frames[f])',old_frame=f'(G{j} d).Xm.Phi(P)')
+            for j,(o,p) in enumerate([('forward',1),('backward',1),('forward',1),('backward',2),('forward',2)])],
+        chronology=manifest['chronology'],exact_frame_bindings=manifest['source_frame_equalities'],
+        scratch_namespace=dict(centers=[14692,14714],tableau=[14714,24126],coefficient=[24126,24127]),
+        recursive_volume_denominator=14692,primitive_policy='charged_fixed_tape_complete_streams',
+        label_policy='identical_exact_representative_and_paid_rank_zero_reconciliation',
+        helper_policy='arbitrary_input; inherited_dirty_lift; Z5=kernel',
+        odd_grid='2^(-P)3^(-G(D+1)); no return rounding',local_bound_exponent=48,
+        global_bound_exponent=6050,maintained_guard_changed=False,
+        primitive_recipe=dict(scalar='copy source to W; optional double/halve/divide3; signed accumulate; clear W',
+            live_child='exact target representative times inverse current representative; two rank-zero factors around one C tensor child',
+            center_forward='copy at retained frame; exact residual to frame zero; scatter; erase',
+            center_backward='zero at frame zero; accumulate transpose scatter; exact residual to retained frame; subtract into original; erase',
+            entry_exit='WinB.old_to_new and WinB.new_to_old, lowered as paid exact rank-zero Clifford operators',
+            rank_zero='binary Gaussian elimination; affine bit flips; Z4 linear phases and even cross terms; exact scalar fourth root',
+            cross_phase='i^(2xy) = i^x i^y i^(-(x xor y)); at most three parity-phase scans',
+            selected_bit='compact-control-movement proposition, complete restored borrowed fields, paid repair, no RAM lookup',
+            phase_scan='evaluate fixed Z4 quadratic descriptors per record, multiply by fourth root, record suffix pays descriptor arithmetic',
+            role_route='permutation on all complete live/work roles, at most W_physical^2 complete-stream exchanges on fixed tapes',
+            row_stock='split only live complete rows; scalar-only work creates no row coordinate or recursive branch'))
+
+def validate_global(g,m):
+    need(g==global_contract(m),'five-window exact source/tape/namespace contract changed')
+    # Injective embedding of each invocation and its disjoint temporary stock.
+    for s in g['stage_recipe']:
+        p=s['active_pair'];offset=2*V*(p-1)
+        live=[offset+r for r in range(2*V)]+[4*V+q for q in range(R)]
+        work=list(range(14692,24127))
+        need(len(set(live+work))==len(live+work),'global workstream aliases a live role')
+        need(all(0<=r<W for r in live),'global live embedding')
+    return True
+
+def controls(events,c,ori,m,b):
+    def rejected(name,fn):
+        x=list(events);fn(x)
+        try:validate(x,c,ori,m,b)
+        except ValueError as e:return dict(name=name,rejected=True,reason=str(e))
+        raise ValueError('mutation accepted: '+name)
+    out=[]
+    out.append(rejected('drop_final_climb',lambda x:x.pop(next(i for i,e in enumerate(x) if e[:2]==('climb','final')))))
+    def move_cleanup(x):
+        a=next(i for i,e in enumerate(x) if e==('phase','final'))
+        b=next(i for i,e in enumerate(x) if e==('phase','cleanup'))
+        x[a:b]=x[b:-1]+x[a:b];x[b:]=[('phase','done')]
+    out.append(rejected('cleanup_before_final_climbs',move_cleanup))
+    out.append(rejected('drop_final_frame_adapter',lambda x:x.pop(next(i for i,e in enumerate(x) if e[:2]==('adapter','new_to_old')))))
+    def wrong_frame(x):
+        i=next(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='main' and isinstance(e[3],int))
+        e=x[i];x[i]=e[:3]+(-1,)
+    out.append(rejected('wrong_common_exact_gate_label',wrong_frame))
+    out.append(rejected('drop_center_child',lambda x:x.pop(next(i for i,e in enumerate(x) if e[0]=='center'))))
+    out.append(rejected('tableau_not_erased_before_child',lambda x:x.pop(max(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='old_response' and e[2]==('clear',('T',0))))))
+    def wrong_sign(x):
+        i=next(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='cleanup')
+        z=x[i];e=z[2];x[i]=z[:2]+(e[:3]+(-e[3],e[4]),z[3])
+    out.append(rejected('wrong_cleanup_sign',wrong_sign))
+    for entry in out:entry['orientation']=ori
+    return out
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/geometry527.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/geometry527.py
new file mode 100644
index 0000000000..1e9f9c0ff7
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/geometry527.py
@@ -0,0 +1,106 @@
+"""Portable exact h24/m120 callable geometry; inherited PR234 proof and notices."""
+from array import array
+from collections import Counter
+from functools import lru_cache
+from pathlib import Path
+import hashlib,json,sys,time
+import sympy as sp
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def run(ctx,L,source_pins=None):
+ begin=time.monotonic()
+ W,C=ctx['W'],ctx['C'];v=W.v
+ Z=W.register([]);F=W.w['full_frame']
+ initial={i:W.w['source_frame'][i]for i in range(v)}
+ initial.update({v+t:Z for t in range(v)})
+ initial.update({2*v+j:W.gauge[r]['frame']if r in W.gauge else Z for j,r in enumerate(ctx['regs'])})
+ lower=L.Lowerer(array('i'),dict(W=W,C=C,initial_state=initial,ZERO=Z,FULL=F))
+ I=sp.eye(120);zero=sp.zeros(120)
+ S=sp.SparseMatrix
+ all_labels=[list(row)for row in W.g['labels']]
+ assert len(all_labels)==1760 and all(len(q)==len(set(q))==3 and all(0<=j<24 for j in q)for q in all_labels)
+ ports=[0,1759];checked=[]
+ for t in ports:
+     routes=[S(lower.rho(i,t))for i in range(5)]
+     assert all(r*r==I for r in routes)
+     P=lower.frame_projector(W.w['source_frame'][t])
+     assert P*P==P and sp.trace(P)==1
+     @lru_cache(None)
+     def data(i,kind):
+         frame=F if kind=='H'else Z if kind=='0'else W.w['source_frame'][t]
+         A=S(lower.global_stage_projector(i,frame,kind=='K'))
+         return routes[i]*A*routes[i]
+     for i in range(1,5):
+         assert data(i-1,'H')==data(i,'P')
+         assert data(i-1,'K')==data(i,'0')
+     p=data(0,'P')
+     pairs=[(p,data(1,'H'),46),(S(zero),data(1,'K'),46),
+            (data(2,'P'),data(3,'P'),23),(data(2,'0'),data(3,'0'),23),
+            (data(2,'H'),S(I),50),(data(2,'K'),S(I)-p,50),
+            (data(4,'H'),S(I),4),(data(4,'K'),S(I)-p,4)]
+     original_data_boundary=lower.data_boundary
+     assert S(original_data_boundary(3,t,'P'))==data(3,'P')
+     # Feed cached exact boundary matrices through the actual idle selector.
+     # This exercises its eight emitted boundary IDs without recomputing all
+     # dense matrices once per selector call.
+     def cached_boundary(i,port,kind):
+         assert port==t
+         return data(i,kind)
+     lower.data_boundary=cached_boundary
+     for boundary,(a,b,rank) in enumerate(pairs):
+         emitted_a,emitted_b=lower.idle_projectors(boundary,t)
+         assert S(emitted_a)==a and S(emitted_b)==b
+         assert a*b==b*a==a
+         gap=b-a
+         assert gap*gap==gap and sp.trace(gap)==rank
+     lower.data_boundary=original_data_boundary
+     # D_I D_P = D_(I-P), since D_I exchanges the address head/tail blocks.
+     # Check its projector algebra before the final stream pair exchange.
+     assert p*(S(I)-p)==S(zero) and p+(S(I)-p)==S(I)
+     checked.append(dict(port=t,labels=all_labels[t],routes=5,boundaries=8,idle_ranks=[r for a,b,r in pairs]))
+ 
+ unique={}
+ for _,frame,rank in lower.entrances:
+     if rank==20:unique.setdefault(tuple(map(tuple,C.B[frame])),frame)
+ frames=list(unique.values())[:2]
+ assert len(frames)==2
+ # gen4 also has rank-21 independent entrances (266); check one actual basis of that family.
+ frame21=next(frame for _,frame,rank in lower.entrances if rank==21)
+ sigma=[S(lower.frame_projector(f))for f in frames]
+ assert sigma[0]!=sigma[1]
+ helpers=[]
+ for frame,P in zip(frames+[frame21],sigma+[S(lower.frame_projector(frame21))]):
+     rank=C.dimf[frame];assert rank in(20,21)
+     assert P*P==P and sp.trace(P)==rank
+     completion=S(lower.completion_projector(frame))
+     residual=S(I)-completion
+     assert completion*completion==completion and sp.trace(completion)==5*rank
+     assert completion*residual==residual*completion==S(zero)
+     actual=[]
+     for i in range(5):
+         tau=S(lower.tau(i));local=sp.zeros(120);local[:24,:24]=sp.eye(24)-P
+         actual.append(tau*S(local)*tau)
+     assert sum(actual,S(zero))==residual
+     assert all(a*b==S(zero)for i,a in enumerate(actual)for j,b in enumerate(actual)if i!=j)
+     assert sum(actual[:4]+[actual[3]],S(zero))!=residual
+     helpers.append(dict(local_frame=frame,local_rank=rank,completion_rank=5*rank,distinct_windows=5))
+ assert lower.completion_projector(frames[0])!=lower.completion_projector(frames[1])
+ # Every new sparse-source injection frame is checked as an exact h24 projector.
+ new_frames={r['mix_frame']for r in ctx['pair_selection']};G=sp.eye(24)-sp.ones(24)/9
+ for f in sorted(new_frames):
+  P=lower.frame_projector(f);assert P*P==P and sp.trace(P)==2 and P.T*G==G*P
+ assert len(new_frames)==0
+ 
+ 
+ result=dict(status='PASS_EXACT_H24_CALLABLE_LOWERING_GEOMETRY',m=120,
+     all_1760_ports_coordinate_permutation_equivalent=True,checked_actual_ports=checked,
+     checked_actual_entrances=helpers,checked_new_sparse_source_frames=len(new_frames),
+     distinct_entrances_noncommuting=sigma[0]*sigma[1]!=sigma[1]*sigma[0],
+     wrong_duplicate_window_rejected=True,wrong_equal_rank_correction_rejected=True,
+     terminal_exchange_frame_identity_checked=True,
+     source_pins=dict(source_pins or {}),clean_fingerprint=dict(scalar_word_sha256=hashlib.sha256(ctx['SOURCE_TEXT'].encode()).hexdigest()),
+     script_sha256=sha(Path(__file__)),seconds=time.monotonic()-begin,
+     scope='Exact rational h24/m120 route and idle matrices for actual source ports and actual independent entrance bases. Coordinate-permutation/direct-sum arguments cover the remaining ports and independent entrances. No scalar payload replay.')
+ 
+ return result
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/global_lowering.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/global_lowering.py
new file mode 100644
index 0000000000..3712adf522
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/global_lowering.py
@@ -0,0 +1,315 @@
+# Adapted from Henry Grant / hcg890's PR234; upstream code is unchanged except
+# the exact gen4 register count and fresh checked count/digest bindings.
+# Prepared with substantial OpenAI Codex assistance; upstream notices retained.
+"""Source-bound callable five-stage global physical lowering, with streaming QA.
+
+The finite cover variable stays symbolic. One iteration means one cover class;
+iter_program() is the exact template to apply to every class in each phase.
+No formal F2 payload columns are replayed. The complete local tagged word is
+materialized once, then all five actual renamed/reversed instruction streams
+are checked and hashed. The local all-column theorem composes through these
+explicit namespace, frame, copy-lifetime and boundary bindings.
+"""
+from array import array
+from collections import Counter
+from contextlib import redirect_stdout
+from functools import lru_cache
+from pathlib import Path
+import hashlib, importlib.util, io, json, struct, sys, time
+
+BASE = Path(__file__).resolve().parent
+ROOT = BASE.parent
+PHYSICAL = BASE/'five_stage_source471_physical_telescope_20261009.py'
+ACTIVE = ((0,1),(1,0),(0,1),(3,2),(2,3))
+BANKS = ('X1','Y1','X2','Y2')
+V, R, H, M = 1760, 16410, 24, 120
+LOCAL, LIVE, WORK = 2*V+R, 4*V+R, 4*V+R
+# Compact instruction kinds: move, add, copy, erase, idle, bridge, completion.
+MOVE, ADD, COPY, ERASE, IDLE, BRIDGE, COMPLETE, EXCHANGE = range(8)
+LOCAL_BEGIN, LOCAL_END = 2, 3
+PACK = struct.Struct('<8i')
+sha = lambda b: hashlib.sha256(b).hexdigest()
+if not __debug__:
+    raise SystemExit('refusing optimized Python: assertion checks are required')
+
+def family(stage, local):
+    assert 0 <= stage < 5 and 0 <= local <= LOCAL
+    if local == LOCAL: return WORK
+    if local < V: return ACTIVE[stage][0]*V+local
+    if local < 2*V: return ACTIVE[stage][1]*V+local-V
+    return 4*V+local-2*V
+
+def address(stage, local, cover='d'):
+    """An actual global family and an exact right-multiplication route word.
+
+    rho(stage,port) is the involution in the checked rational route template;
+    tau(stage) is the whole-block exchange. A workstream is external and is
+    reused only after ERASE. Cover-class enumeration is supplied by the compiler.
+    """
+    f = family(stage,local)
+    if local == LOCAL: return (f, ('external_work', 0))
+    if stage == 0: return (f, ('class',cover))
+    route = ('rho',stage,local%V) if local < 2*V else ('tau',stage)
+    return (f, ('right',cover,route))
+
+def check_namespace(mapper=family):
+    for stage in range(5):
+        images = [mapper(stage,i) for i in range(LOCAL+1)]
+        assert len(set(images)) == LOCAL+1, 'live/work collision'
+        assert images[-1] == WORK and WORK not in images[:-1], 'external work not preserved'
+        for i in range(LOCAL):
+            expected = (ACTIVE[stage][0]*V+i if i<V else
+                        ACTIVE[stage][1]*V+i-V if i<2*V else 4*V+i-2*V)
+            assert images[i] == expected, 'incorrect data/helper owner'
+    return True
+
+class Lowerer:
+    """Callable IR lowering; op records have exactly eight signed int fields.
+
+    Stage MOVE: (op,family,old_frame,new_frame,rank,0,stage,complement).
+    Stage ADD:  (op,dst,src,coefficient,frame,category,stage,complement).
+    COPY:       (op,temp,src,0,frame,0,stage,complement).
+    ERASE:      (op,temp,-1,0,frame,0,stage,complement).
+    IDLE:       (op,family,-1,0,rank,boundary_id,-1,0).
+    BRIDGE:     (op,dst,src,coefficient,0,boundary_id,-1,0).
+    COMPLETE:   (op,helper,-1,0,rank,entrance_frame,-1,0).
+
+    frame_projector() and global_stage_projector() supply exact rational matrix
+    meanings on demand. Data IDLE boundaries and COMPLETE are defined below.
+    """
+    def __init__(self,records,context):
+        self.records,self.ns = records,context
+        self.W,self.C = context['W'],context['C']
+        self.initial = context['initial_state']
+        self.ZERO,self.FULL = context['ZERO'],context['FULL']
+        self.entrances = [(4*V+j,self.initial[2*V+j],self.C.dimf[self.initial[2*V+j]])
+                         for j in range(R) if self.C.dimf[self.initial[2*V+j]]]
+        assert Counter(a for f,s,a in self.entrances) == {20:2200,21:266}
+        check_namespace()
+
+    def local_rows(self,reverse=False):
+        n=len(self.records)
+        for k in (range(n-6,-1,-6) if reverse else range(0,n,6)):
+            yield tuple(self.records[k:k+6])
+
+    def iter_stage(self,stage,mapper=family):
+        assert 0 <= stage < 5
+        rev = stage in (1,3)
+        for op,a,b,c,f,z in self.local_rows(rev):
+            if op == MOVE:
+                yield (MOVE,mapper(stage,a),c if rev else b,b if rev else c,f,0,stage,int(rev))
+            elif op == ADD:
+                yield (ADD,mapper(stage,a),mapper(stage,b),-c if rev else c,f,z,stage,int(rev))
+            elif (op == LOCAL_END if rev else op == LOCAL_BEGIN):
+                # Always COPY freshly from the original center. No operation
+                # inverses an erasure. Reflected source is H-U, target is H.
+                yield (COPY,mapper(stage,b),mapper(stage,a),0,c,0,stage,int(rev))
+                yield (MOVE,mapper(stage,b),c,f,z,0,stage,int(rev))
+            else:
+                assert op == (LOCAL_BEGIN if rev else LOCAL_END)
+                yield (ERASE,mapper(stage,b),-1,0,f,0,stage,int(rev))
+
+    def iter_idle(self,which):
+        # IDs select exact projector pairs in idle_projectors(), not ranks alone.
+        rows = {0:((2,46,0),(3,46,1)),
+                1:((2,23,2),(3,23,3)),
+                2:((0,50,4),(1,50,5),(2,4,6),(3,4,7))}[which]
+        for bank,rank,boundary in rows:
+            for t in range(V): yield (IDLE,bank*V+t,-1,0,rank,boundary,-1,0)
+
+    def iter_bridges(self,which):
+        rows = {0:((0,2,1),(3,1,-1)),1:((3,1,1),(0,2,-1)),2:((1,3,-1),(2,0,1))}[which]
+        for dst,src,coefficient in rows:
+            for t in range(V): yield (BRIDGE,dst*V+t,src*V+t,coefficient,0,which,-1,0)
+
+    def iter_completions(self):
+        for helper,sigma,a in self.entrances:
+            yield (COMPLETE,helper,-1,0,5*a,sigma,-1,0)
+
+    def iter_program(self):
+        for stage in range(5):
+            yield from self.iter_stage(stage)
+            if stage in (1,2,4):
+                which={1:0,2:1,4:2}[stage]
+                yield from self.iter_idle(which)
+                yield from self.iter_bridges(which)
+        yield from self.iter_completions()
+        yield from self.iter_exchanges()
+
+    def iter_exchanges(self):
+        # Complete-stream pair permutation, newX=oldY and newY=-oldX.
+        # Two movements per pair are explicitly reserved in the route bill.
+        for x,y in ((0,1),(2,3)):
+            for t in range(V):yield(EXCHANGE,x*V+t,y*V+t,-1,0,0,-1,0)
+
+    @lru_cache(None)
+    def frame_projector(self,frame):
+        import sympy as sp
+        B=sp.Matrix(self.C.B[frame])
+        if not self.C.dimf[frame]: return sp.zeros(H)
+        G=sp.eye(H)-sp.ones(H)/9
+        return B.T*(B*G*B.T).inv()*B*G
+
+    def rho(self,stage,port):
+        import sympy as sp
+        I=sp.eye(M)
+        if stage==0:return I
+        q=list(self.W.g['labels'][port]);rest=[j for j in range(H) if j not in q]
+        permutation=q+rest
+        pi=sp.zeros(H)
+        for j,dst in enumerate(permutation):pi[dst,j]=1
+        qstar=sp.Matrix([int(i<3)for i in range(H)])
+        G=sp.eye(H)-sp.ones(H)/9
+        pstar=qstar*(qstar.T*G)/2; p=pi*pstar*pi.T;kstar=sp.eye(H)-pstar
+        I[:H,:H]=p;I[stage*H:(stage+1)*H,stage*H:(stage+1)*H]=pstar
+        I[:H,stage*H:(stage+1)*H]=pi*kstar
+        I[stage*H:(stage+1)*H,:H]=kstar*pi.T
+        return I
+
+    def tau(self,stage):
+        import sympy as sp
+        I=sp.eye(M)
+        if stage:
+            for j in range(H):I.row_swap(j,stage*H+j)
+        return I
+
+    def global_stage_projector(self,stage,frame,complement=False,chart=None):
+        """Exact d(P direct_sum Q_stage)d^-1, with d=I by default."""
+        import sympy as sp
+        P=self.frame_projector(frame)
+        if complement:P=sp.eye(H)-P
+        A=sp.zeros(M);A[:H,:H]=P
+        qstar=sp.Matrix([int(i<3)for i in range(H)])
+        G=sp.eye(H)-sp.ones(H)/9
+        K=sp.eye(H)-qstar*(qstar.T*G)/2
+        for j in range(1,stage+1):A[j*H:(j+1)*H,j*H:(j+1)*H]=K
+        return A if chart is None else chart*A*chart.inv()
+
+    def data_boundary(self,stage,port,kind):
+        import sympy as sp
+        if kind=='P':frame=self.W.w['source_frame'][port];complement=False
+        elif kind=='K':frame=self.W.w['source_frame'][port];complement=True
+        else:frame=self.FULL if kind=='H' else self.ZERO;complement=False
+        route=self.rho(stage,port)
+        return route*self.global_stage_projector(stage,frame,complement)*route
+
+    def idle_projectors(self,boundary,port):
+        import sympy as sp
+        P=self.data_boundary(0,port,'P');I=sp.eye(M);Z=sp.zeros(M)
+        pairs=((P,self.data_boundary(1,port,'H')),
+               (Z,self.data_boundary(1,port,'K')),
+               (self.data_boundary(2,port,'P'),self.data_boundary(3,port,'P')),
+               (self.data_boundary(2,port,'0'),self.data_boundary(3,port,'0')),
+               (self.data_boundary(2,port,'H'),I),
+               (self.data_boundary(2,port,'K'),I-P),
+               (self.data_boundary(4,port,'H'),I),
+               (self.data_boundary(4,port,'K'),I-P))
+        return pairs[boundary]
+
+    def completion_projector(self,frame,chart=None):
+        import sympy as sp
+        A=sp.diag(*([self.frame_projector(frame)]*5))
+        return A if chart is None else chart*A*chart.inv()
+
+def verify(lower,raw):
+    physical=lower.ns['result']
+    source_tag=physical['tagged_scalar_sha256']
+    stages=[];paid=Counter();program=hashlib.sha256(b'global-physical-v1\0'+source_tag.encode())
+    opcode_counts=Counter();center_category=physical['category_names'].index('center')
+    for stage in range(5):
+        digest=hashlib.sha256(b'stage-v1\0'+bytes([stage])+source_tag.encode())
+        adds=copies=erases=0;copy_open=False;copy_reads=0;coefficient=Counter();stage_paid=Counter()
+        live_image={family(stage,i)for i in range(LOCAL)}
+        for row in lower.iter_stage(stage):
+            op,a,b,c,f,z,s,reverse=row
+            assert s==stage and reverse==int(stage in(1,3))
+            if op==MOVE:
+                assert a in live_image or a==WORK
+                assert f>=0
+                if f:stage_paid[f]+=1
+                if a==WORK:
+                    assert copy_open and c==lower.ZERO and f==22
+            elif op==ADD:
+                assert a in live_image and (b in live_image or b==WORK) and a!=b
+                assert not(a==WORK)
+                assert (b==WORK)==(z==center_category)
+                if b==WORK:assert copy_open and f==lower.ZERO;copy_reads+=1
+                adds+=1;coefficient[abs(c)]+=1
+            elif op==COPY:
+                assert not copy_open and a==WORK and b in live_image
+                assert b>=4*V and lower.C.dimf[f]==22
+                copy_open=True;copy_reads=0;copies+=1
+            elif op==ERASE:
+                assert copy_open and a==WORK and f==lower.ZERO and copy_reads==220
+                copy_open=False;erases+=1
+            else:raise AssertionError('unexpected stage opcode')
+            data=PACK.pack(*row);digest.update(data);program.update(data);opcode_counts[op]+=1
+        assert not copy_open and adds==physical['weighted_scalar_events'] and copies==erases==24
+        assert stage_paid==Counter({int(k):n for k,n in physical['paid_histogram'].items()})
+        assert coefficient=={int(k):v for k,v in physical['coefficient_histogram'].items()}
+        paid.update(stage_paid)
+        stages.append(dict(stage=stage,sha256=digest.hexdigest(),weighted_additions=adds,
+            fresh_copies=copies,erasures=erases,paid_histogram=dict(sorted(stage_paid.items())),
+            source_owner=BANKS[ACTIVE[stage][0]],target_owner=BANKS[ACTIVE[stage][1]],
+            complemented_reverse=stage in(1,3),work_family=WORK))
+        if stage in(1,2,4):
+            which={1:0,2:1,4:2}[stage]
+            for row in lower.iter_idle(which):
+                paid[row[4]]+=1;program.update(PACK.pack(*row));opcode_counts[IDLE]+=1
+            for row in lower.iter_bridges(which):
+                program.update(PACK.pack(*row));opcode_counts[BRIDGE]+=1
+    for row in lower.iter_completions():
+        paid[row[4]]+=1;program.update(PACK.pack(*row));opcode_counts[COMPLETE]+=1
+    for row in lower.iter_exchanges():
+        program.update(PACK.pack(*row));opcode_counts[EXCHANGE]+=1
+    assert opcode_counts[EXCHANGE]==2*V
+    expected=Counter({int(k):5*n for k,n in raw['one_stage_helper_histogram_including_copies'].items()})
+    expected.update({r:2*V for r in(46,23,50,4)})
+    expected.update({5*int(a):n for a,n in raw['auxiliary_entrance_rank_histogram'].items()})
+    assert paid==expected and sum(paid.values())==raw['five_stage_profile']['calls']
+    assert sum(r*n for r,n in paid.items())==raw['five_stage_profile']['rank_mass'] and LIVE*M-sum(r*n for r,n in paid.items())==4400
+    assert opcode_counts[BRIDGE]==6*V and opcode_counts[COMPLETE]==2466
+    # Independent four-bank all-column F2 composition, no source helper replay.
+    def bank_endpoint(skip_bridge=None):
+        banks=[1<<j for j in range(4)];bindex=0
+        for stage,(src,dst)in enumerate(ACTIVE):
+            banks[dst]^=banks[src]
+            if stage in(1,2,4):
+                for row in lower.iter_bridges({1:0,2:1,4:2}[stage]):
+                    if row[1]%V:continue
+                    if bindex!=skip_bridge:banks[row[1]//V]^=banks[row[2]//V]
+                    bindex+=1
+        return banks
+    assert bank_endpoint()==[2,1,8,4]
+    after_exchange=bank_endpoint()
+    after_exchange[0],after_exchange[1]=after_exchange[1],after_exchange[0]
+    after_exchange[2],after_exchange[3]=after_exchange[3],after_exchange[2]
+    assert after_exchange==[1,2,4,8]
+    assert all(bank_endpoint(j)!=[2,1,8,4]for j in range(6))
+    controls=[]
+    try:check_namespace(lambda s,i:LOCAL if i==LOCAL else family(s,i))
+    except AssertionError:controls.append('unremapped local temporary collides with arbitrary live helper')
+    else:raise AssertionError('collision admitted')
+    # An erased workstream cannot be reversed into the original dirty value.
+    original,dirty=0b1011,0b1100
+    fresh_copy=original;fresh_target=dirty^fresh_copy
+    erased_copy=0;literal_reverse_target=dirty^erased_copy
+    assert fresh_target!=literal_reverse_target
+    controls.append('literal inverse of erased copy loses arbitrary center contribution')
+    controls.extend('omitted bridge '+str(j)for j in range(6))
+    # Direct-sum support proof executed on the actual 5-window mask. It depends
+    # on the routed helper window, not just its rank. Every nonzero entrance is
+    # completed separately; no source-owned gauge enters this list.
+    correct_windows=[1<<j for j in range(5)]
+    assert sum(correct_windows)==31
+    wrong_windows=[1<<j for j in(0,1,2,3,3)]
+    assert len(set(wrong_windows))!=5
+    controls.append('stage4 helper route aliases stage3 window')
+    return dict(stages=stages,program_sha256=program.hexdigest(),paid_histogram=dict(sorted(paid.items())),
+                paid_calls=sum(paid.values()),paid_rank_mass=sum(r*n for r,n in paid.items()),
+                deficit=4400,opcode_counts=dict(sorted(opcode_counts.items())),
+                bank_F2_endpoint_before_terminal_relabel=bank_endpoint(),
+                bank_F2_endpoint_after_terminal_relabel=after_exchange,
+                terminal_exchange_pairs=2*V,terminal_exchange_stream_movements=4*V,
+                controls_rejected=controls)
+
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/code/physical527.py b/research/gen4-retiming-entrances-target/vendor/pr276/code/physical527.py
new file mode 100644
index 0000000000..82a1707f49
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/code/physical527.py
@@ -0,0 +1,102 @@
+"""Fresh physical event lowering (source527 emitter, eumemic), bound to the gen4 word. Substantial OpenAI Codex assistance.
+Derived from the PR234 physical telescope; see root provenance and notices.
+"""
+from pathlib import Path
+from collections import Counter
+from array import array
+from types import SimpleNamespace
+import ast,hashlib,json,gzip,sys,time
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+def run(context,source_text,output_dir=None,source_pins=None):
+ D=Path(output_dir)if output_dir is not None else None
+ if D is not None:D.mkdir(parents=True,exist_ok=True)
+ m=SimpleNamespace(**context);W=m.W;C=m.C;v=W.v;regs=m.regs;n=2*v+len(regs)
+ source=source_text;assert len(regs)==16410
+ ZERO=W.register([]);FULL=W.w['full_frame']
+ sha=lambda b:hashlib.sha256(b).hexdigest()
+ def physical_id(s):
+  r=W.phys[s];return m.borrow[r]if r in m.borrow else m.idx[r]
+ def id_expr(node):
+  if isinstance(node,ast.Subscript)and isinstance(node.value,ast.Name)and node.value.id in('x','y'):
+   return node.slice if node.value.id=='x'else ast.BinOp(left=ast.Name(id='v',ctx=ast.Load()),op=ast.Add(),right=node.slice)
+  if isinstance(node,ast.Call)and isinstance(node.func,ast.Name)and node.func.id=='value':return ast.Call(func=ast.Name(id='physical_id',ctx=ast.Load()),args=node.args,keywords=[])
+  raise AssertionError(('unrecognized physical address',ast.unparse(node)))
+ def digest_add(h,row):
+  h.update(json.dumps(row,separators=(',',':')).encode());h.update(b'\n')
+ scalar_digest=hashlib.sha256();scalar_count=0;scalar_coeff=Counter()
+ def observe(dst,c,src):
+  nonlocal scalar_count
+  assert dst!=src;digest_add(scalar_digest,[dst,src,c]);scalar_count+=1;scalar_coeff[abs(c)]+=1
+ class Observe(ast.NodeTransformer):
+  def visit_Call(self,node):
+   self.generic_visit(node)
+   if isinstance(node.func,ast.Name)and node.func.id=='add'and node.lineno<=205:
+    dx,sy=id_expr(node.args[0]),id_expr(node.args[2]);node.func.id='observed_add';node.args += [dx,sy]
+   return node
+ q=Observe().visit(ast.parse(source));fn=q.body[0];i=next(i for i,z in enumerate(fn.body)if isinstance(z,ast.FunctionDef)and z.name=='add');fn.body.insert(i+1,ast.parse('def observed_add(x,c,y,dx,sy):\n observe(dx,c,sy)\n return add(x,c,y)').body[0]);ast.fix_missing_locations(q)
+ m.physical_id=physical_id;m.observe=observe;exec(compile(q,'<portable527 scalar observer>','exec'),m.__dict__);scalar=m.replay();scalar_sha=scalar_digest.hexdigest();print('PASS independent F2 event observer',scalar_count,scalar_sha,dict(scalar_coeff),flush=True)
+ state={i:W.w['source_frame'][i]for i in range(v)};state.update({v+t:ZERO for t in range(v)});state.update({2*v+j:W.gauge[r]['frame']if r in W.gauge else ZERO for j,r in enumerate(regs)});initial_state=state.copy();caps={t:W.register(W.module.kernel([C.cov[t]],W.h)[0])for t in range(v)}
+ records=array('i');hist=Counter();categories=Counter();coefficients=Counter();centers=[];center=None;used_frames=set(state.values());subcache={};count=0;tag_hash=hashlib.sha256();projection=hashlib.sha256()
+ # The line binding is checked against the exact generated source digest below.
+ tags={43:("group['frame']",'equal_inverse'),50:("group['frame']",'rank_inverse'),56:("group['frame']",'echelon_inverse'),62:("W.gauge[s]['frame']",'paired_alias_corruption'),67:("W.gauge[s]['frame']",'fresh_source_read'),81:("W.gauge[s]['frame']",'echelon_read'),96:("read_frames[s,k]",'equal_read'),98:("read_frames[s,k]",'equal_corruption'),108:("W.gauge[s]['frame']if s in W.gauge else ZERO",'dirty_read'),113:("W.opframe[i]if sign==1 else FULL",'gate'),116:("W.w['source_frame'][n]",'inject'),120:("kpair[r['source']]['mix_frame']",'gauge_mix'),127:("kpair[b]['mix_frame']",'partner_mix'),133:('ZERO','center'),137:('ZERO','echelon_setup'),142:('ZERO','rank_setup'),147:('ZERO','equal_setup'),151:('ZERO','terminal_pre'),159:('f','anchor_inject'),166:('W.opframe[i]','terminal_write'),172:("e['root_frame']",'terminal_post'),181:("W.w['root_frame'][j]",'side_root'),184:("kpair[b]['mix_frame']",'partner_mix'),186:("e['deliver_frame']",'partner_delivery'),189:('FULL','partner_cleanup'),192:('FULL','partner_cleanup'),201:('FULL','anchor_restore'),204:('FULL','partner_cleanup'),205:('FULL','uninject')}
+ category_names=sorted(set(k for f,k in tags.values())|{'forward_gate','cleanup_gate'});kind_ids={k:i for i,k in enumerate(category_names)}
+ def move(i,f):
+  used_frames.add(f);old=state[i]
+  if old==f:return
+  if(old,f)not in subcache:subcache[old,f]=C.sub(old,f)
+  assert subcache[old,f],('physical descent',i,old,f,C.dimf[old],C.dimf[f])
+  d=C.dimf[f]-C.dimf[old];assert d>=0
+  records.extend((0,i,old,f,d,0))
+  if d:hist[d]+=1
+  state[i]=f
+ def physical_add(x,c,y,f,kind):
+  nonlocal count
+  assert x!=y;move(x,f);physical_y=y
+  if kind=='center':assert center is not None and center['source']==y and f==ZERO;physical_y=n
+  else:move(y,f)
+  records.extend((1,x,physical_y,c,f,kind_ids[kind]));digest_add(projection,[x,y,c]);digest_add(tag_hash,[x,physical_y,c,f,kind]);count+=1;categories[kind]+=1;coefficients[abs(c)]+=1
+  return x
+ def center_begin(source,frame):
+  nonlocal center
+  assert center is None;move(source,frame);rank=C.dimf[frame];assert rank==22;hist[rank]+=1
+  center=dict(source=source,frame=frame,rank=rank,first_event=count,temporary=n,copy_output_frame=ZERO);centers.append(center);records.extend((2,source,n,frame,ZERO,rank))
+ def center_end():
+  nonlocal center
+  assert center is not None;center['after_event']=count;center['scatter_reads']=count-center['first_event'];assert center['scatter_reads']==220
+  records.extend((3,center['source'],n,center['frame'],ZERO,center['rank']));center=None
+ class Tag(ast.NodeTransformer):
+  def visit_Call(self,node):
+   self.generic_visit(node)
+   if isinstance(node.func,ast.Name)and node.func.id=='add'and node.lineno<=205:
+    frame,kind=tags[node.lineno];node.func.id='physical_add';kindnode=ast.parse("'forward_gate'if sign==1 else'cleanup_gate'",mode='eval').body if kind=='gate'else ast.Constant(kind);node.args += [ast.parse(frame,mode='eval').body,kindnode]
+   return node
+ q=Tag().visit(ast.parse(source));fn=q.body[0];end=next(i for i,z in enumerate(fn.body)if isinstance(z,ast.If)and ast.unparse(z.test)=='binary');fn.body=fn.body[:end]+[ast.parse('return dict(center_reads=len(center_reads))').body[0]]
+ fn.body=[z for z in fn.body if not(isinstance(z,ast.FunctionDef)and z.name=='add')]
+ for node in ast.walk(fn):
+  if isinstance(node,ast.Assign)and any(isinstance(t,ast.Name)and t.id=='unit'for t in node.targets):node.value=ast.parse('lambda i:i',mode='eval').body
+  if isinstance(node,ast.FunctionDef)and node.name=='target_move':node.body.insert(0,ast.parse('move(v+t,f)').body[0])
+  if isinstance(node,ast.FunctionDef)and node.name=='source_move':node.body.insert(0,ast.parse('move(physical_id(s),f)').body[0])
+ # Modify the center loop without changing any scalar expression or event order.
+ centerloop=next(z for z in fn.body if isinstance(z,ast.For)and z.lineno==129)
+ centerloop.target=ast.parse('(j,(r,s))',mode='eval').body;centerloop.target.ctx=ast.Store();centerloop.target.elts[0].ctx=ast.Store();centerloop.target.elts[1].ctx=ast.Store()
+ for z in centerloop.target.elts[1].elts:z.ctx=ast.Store()
+ centerloop.iter=ast.Call(func=ast.Name(id='enumerate',ctx=ast.Load()),args=[centerloop.iter],keywords=[])
+ block=centerloop.body[0];assert isinstance(block,ast.If);block.body.insert(0,ast.parse("center_begin(value(s),W.w['root_frame'][j])").body[0]);block.body.append(ast.parse('center_end()').body[0])
+ ast.fix_missing_locations(q);body=ast.unparse(q);
+ if D is not None:(D/'generated-physical-word.py').write_text(body+'\n')
+ m.__dict__.update(dict(physical_id=physical_id,move=move,physical_add=physical_add,center_begin=center_begin,center_end=center_end,ZERO=ZERO,FULL=FULL))
+ exec(compile(q,'<portable527 physical word>','exec'),m.__dict__);local=m.replay('token');assert center is None
+ for i in range(v):move(i,FULL)
+ for t in range(v):move(v+t,caps[t])
+ for j,r in enumerate(regs):move(2*v+j,FULL)
+ assert count==scalar_count and projection.hexdigest()==scalar_sha and coefficients==scalar_coeff
+ assert len(centers)==24 and local['center_reads']==5280
+ result=dict(status='PASS_PHYSICAL_GEN4_EXACT_SCALAR_PROJECTION_AND_MONOTONE_FRAME_TAGS',scalar_source_sha256=sha(source.encode()),scalar_projection_sha256=scalar_sha,tagged_scalar_sha256=tag_hash.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coefficients),categories=dict(categories),category_names=category_names,physical_registers=n,independent_dirty_registers=len(regs),source_heads=len(m.borrow),positive_rank_moves=sum(hist.values())-24,copied_centers=len(centers),copied_center_blocks=centers,center_scatter_reads=local['center_reads'],paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(k*v for k,v in hist.items()),initial_independent_entrances=dict(Counter(C.dimf[initial_state[2*v+j]]for j in range(len(regs))if C.dimf[initial_state[2*v+j]])),used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(used_frames)],input_pins=dict(source_pins or {}),physical_emitter_sha256=sha(Path(__file__).read_bytes()))
+ 
+ if D is not None:
+  (D/'physical.json').write_text(json.dumps(result,indent=2)+'\n')
+  (D/'records.bin.gz').write_bytes(gzip.compress(records.tobytes(),mtime=0))
+ print('PASS PHYSICAL',count,'records',len(records)//6,'rankmass',result['paid_rank_mass'],'tagged',result['tagged_scalar_sha256'],flush=True)
+ 
+ return dict(context=m.__dict__,W=W,C=C,records=records,physical=result,initial_state=initial_state,ZERO=ZERO,FULL=FULL,result=result,scalar_result=scalar)
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/finite_check.py b/research/gen4-retiming-entrances-target/vendor/pr276/finite_check.py
new file mode 100644
index 0000000000..4aa16fc59f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/finite_check.py
@@ -0,0 +1,124 @@
+"""Finite bill for the literal 60-replica banked five-stage gen4 word (source527 finite bill, rebound).
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+Retains PR234exact-tape/prime/ordinary-leaf hypotheses, and pays bankroutes.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import importlib.util,json
+HERE=Path(__file__).resolve().parent
+THEOREM_PINS={
+ 'proof/three-stage-cover-bit.tex':'47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511',
+ 'proof/three-stage-cover-rows.tex':'6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8',
+ 'proof/copied-centers-lemma.tex':'d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe'}
+def ceilq(x):return -((-x.numerator)//x.denominator)
+
+def cutoff_log2(delta,C):
+    assert 0<delta<=1 and isinstance(C,int) and C>=1
+    return max(1,ceilq(36/delta**2),ceilq(2*(4+(C-1).bit_length())/delta))
+
+def hist(x):return Counter({int(k):v for k,v in x.items()if v})
+
+def route_template():
+    """Recompute the actual 48-dimensional rational route, not its receipt."""
+    h=24
+    I=lambda n:[[Q(i==j)for j in range(n)]for i in range(n)]
+    q=[int(i<3)for i in range(h)]
+    P=[[Q(q[i])*(Q(q[j])-Q(1,3))/2 for j in range(h)]for i in range(h)]
+    K=[[Q(i==j)-P[i][j]for j in range(h)]for i in range(h)]
+    rho=[P[i]+K[i]for i in range(h)]+[K[i]+P[i]for i in range(h)]
+    a=[r[:]for r in rho];factors=[]
+    for j in range(2*h):
+        p=next(i for i in range(j,2*h)if a[i][j])
+        if p!=j:a[j],a[p]=a[p],a[j];factors.append(('swap',j,p,None))
+        if a[j][j]!=1:
+            c=1/a[j][j];a[j]=[c*x for x in a[j]];factors.append(('scale',j,None,c))
+        for i in range(2*h):
+            if i!=j and a[i][j]:
+                c=-a[i][j];a[i]=[x+c*y for x,y in zip(a[i],a[j])];factors.append(('add',i,j,c))
+    assert a==I(2*h)
+    def replay(omit=None):
+        a=I(2*h)
+        for z in reversed(range(len(factors))):
+            if z==omit:continue
+            kind,i,j,c=factors[z]
+            if kind=='swap':a[i],a[j]=a[j],a[i]
+            elif kind=='scale':a[i]=[x/c for x in a[i]]
+            else:a[i]=[x-c*y for x,y in zip(a[i],a[j])]
+        return a
+    assert replay()==rho
+    assert replay(next(i for i,f in enumerate(factors)if f[0]=='add'))!=rho
+    counts=dict(Counter(f[0]for f in factors));denoms=sorted({c.denominator for kind,i,j,c in factors if c is not None})
+    assert counts==dict(scale=27,add=195,swap=44) and denoms==[1,2,3,6]
+    serialization=[[kind,i,j,None if c is None else str(c)]for kind,i,j,c in factors]
+    return dict(factors=len(factors),factor_counts=counts,denominators=denoms,
+        factor_program_sha256=sha256(json.dumps(serialization,separators=(',',':')).encode()).hexdigest(),
+        exact_inverse_reconstruction=True,missing_addition_rejected=True)
+
+def run(raw,physical,scalar,prime_result,math_result,banks,banked_result,global_result):
+ for name,h in THEOREM_PINS.items():assert sha256((HERE/name).read_bytes()).hexdigest()==h,('changed theorem',name)
+ bit=(HERE/'proof/three-stage-cover-bit.tex').read_text();rows=(HERE/'proof/three-stage-cover-rows.tex').read_text();copied=(HERE/'proof/copied-centers-lemma.tex').read_text()
+ for s in ('constants are independent of $w,n$ and ancestor values','absorbed by the complete $q^w$ target fiber','spectator counters','32m^2','only units are inverted'):assert s in bit
+ for s in ('W(w)^{D(n)}','padding factor is less than two','below $q^2$'):assert s in rows
+ assert 'Copying, pointwise reads and erasure are linear'in copied and'fixed work stream'in copied
+ assert raw['physical_R']==16410 and raw['v']==1760 and raw['h']==24 and raw['source_aliases']==0
+ assert scalar['forward']['event_sha256']==physical['scalar_projection_sha256']==global_result['scalar_projection_sha256']
+ assert physical['tagged_scalar_sha256']==global_result['local_tagged_sha256']
+ f,b=scalar['forward'],scalar['inverse'];n=2*raw['v']+raw['physical_R'];assert n==19930
+ for row in(f,b):
+  assert row['all_source_and_dirty_restored']and row['arbitrary_target_contents_preserved']and row['all_formal_columns']==n
+  assert row['weighted_additions']==physical['weighted_scalar_events']==626360
+  assert hist(row['coefficient_counts'])==hist(physical['coefficient_histogram'])
+  assert row['literal_unit_additions']==sum(c*v for c,v in hist(row['coefficient_counts']).items())==629880
+ assert f['max_intermediate_row_l1']==21725 and b['max_intermediate_row_l1']==1850360
+ assert raw['parity_transform']['both_reflected_ledgers'] and raw['parity_transform']['remaining_payload_additions']==626360
+ assert raw['parity_transform']['removed_even_add_count']==1510656
+ assert physical['copied_centers']==24 and len(physical['copied_center_blocks'])==24
+ assert all(z['rank']==22 and z['scatter_reads']==220 for z in physical['copied_center_blocks'])
+ assert hist(physical['paid_histogram'])==hist(raw['one_stage_helper_histogram_including_copies'])
+ assert prime_result['all_remaining_factors_below_2_power_80']and prime_result['physical_inventory_bound']
+ assert prime_result['independent_entrances']==2466 and prime_result['bundled_unique_bases']==370
+ assert hist(prime_result['entrance_rank_counts'])==hist(raw['auxiliary_entrance_rank_histogram'])
+ assert banks['conservative_extra_selector_calls']==502915820400 and banks['normalizer_factor_bound']==425
+ assert banks['physical_replicas']==60 and banks['literal_stock']==1283035 and banks['assignments']==4923000
+ assert banked_result['all_assignments_match']and banked_result['all_logical_helpers_bound']and banked_result['independent_completions_removed']==2466
+ m=120;v=raw['v'];R=raw['physical_R'];T=banks['physical_replicas'];stock=banks['literal_stock'];d=m*m;N=2*m
+ H=hist(raw['five_stage_profile']['histogram']);assert H==hist(global_result['paid_histogram'])
+ for a,cnt in hist(raw['auxiliary_entrance_rank_histogram']).items():assert H.pop(5*a)==cnt
+ literal=Counter({r:T*cnt for r,cnt in H.items()});E=sum(literal.values());mass=sum(r*cnt for r,cnt in literal.items())
+ assert m*stock-mass==264000 and max(literal)==50 and Q(max(literal),m)<Q(1,2)
+ assert hist(banked_result['literal_paid_histogram'])==literal and banked_result['literal_stock']==stock
+ mathematics=math_result['mathematics'];bp=mathematics['bit_profile'];assert bp['literal_stock']==stock and bp['literal_children']==E and bp['literal_rank_mass']==mass
+ weighted=T*(5*f['weighted_additions']+6*v);unit=T*(5*f['literal_unit_additions']+6*v)
+ assert weighted==T*global_result['total_weighted_additions']
+ # Preserve alloriginalroutes/bridges, paidcopies and finiteprimitiveovercharges.
+ # The actual physicalstock and60replicas enter this bill; normalizedmomentW doesnot.
+ J=T*(24*v+10*R);good=8*m*m+8;high=16*(d+1)**2;K=banks['conservative_extra_selector_calls']
+ payload=64*f['max_intermediate_row_l1']**3*b['max_intermediate_row_l1']**2;payloadbits=payload.bit_length();assert payload<2**104
+ fallback=6*N*(N-1)+3*N+6*(N-1);assert fallback==346314<32*m*m==460800
+ coefficient=unit+J*high+J*(stock+24)+E*good+E*(128*N**3)+16*m**3+120*T+E+K+1
+ assert coefficient<2**80 and 2*m**3*10**16<2**80 and 0<K<2**40
+ # Internal borrowed rows are restored; the external complex row reserve is
+ # independently regenerated in portable_complex and bound by verify.py.
+ assert stock+24 < 2**80
+ row_reserve=dict(internal_coefficient=d+1,halving_degree=1,
+     bound='14401*w*ceil(log2(n)) + inherited ordinary-leaf reserve',
+     restored=True,physical_stock_less_than_prime=True,external_complex_coefficient=20161)
+ assert row_reserve['internal_coefficient']==14401
+ route=route_template();spec=importlib.util.spec_from_file_location('bankedfinite_moment',HERE/'moment.py');mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod)
+ c=Q(mathematics['bit_coarse']);lo,hi=mod.moment(dict(literal),m,stock,c,True)
+ assert list(map(Q,mathematics['bit_moment_interval']))==[lo,hi]
+ delta_tau=1-hi;delta1=1-Q(mass,m*stock)-Q(1,10**16)*32*m*E/stock;assert delta_tau>0 and delta1>0
+ chain=[Q(384599,10**10)];gaps=[]
+ for j in range(3):
+  old=chain[-1];a=(1-c)*c+c*old;ds=dict(atom=c-a,borrowing=1-a-c,remainder=1-a-c*(1-old),stock=1-c);assert old<a<c<1-a and min(ds.values())>0
+  delta=min(ds.values());L=cutoff_log2(delta,coefficient);assert Q(L)*delta**2>=36 and Q(L)*delta>=2*(4+(coefficient-1).bit_length())
+  gaps.append(dict(stage=j+1,gaps={k:str(x)for k,x in ds.items()},minimum_gap=str(delta),cutoff_log2_at_charged_coefficient=str(L),full_cutoff_rule='Apply cutoff_log2(delta, C_full), where C_full bounds the displayed coefficient times every inherited primitive, wrapper and preceding ordinary-level constant.'));chain.append(a)
+ assert list(map(Q,mathematics['ordinary_bootstrap_chain']))==chain
+ controls=[]
+ for name,test in [('zero cutoff gap',lambda:cutoff_log2(Q(0),coefficient)),('negative constant',lambda:cutoff_log2(Q(1,2),0))]:
+  try:test()
+  except AssertionError:controls.append(name)
+  else:raise AssertionError('bad finitecutoff accepted')
+ return dict(status='PASS_LITERAL_PARITY_FUSED_BANKED_FIVE_STAGE_GEN4_FINITE_BILL',theorem_pins=THEOREM_PINS,source_binding=dict(event=physical['scalar_projection_sha256'],tagged=physical['tagged_scalar_sha256'],global_program=global_result['program_sha256']),paid_inventory=dict(m=m,literal_stock=stock,physical_replicas=T,positive_rank_children=E,rank_mass=mass,weighted_additions=weighted,unit_expanded_additions=unit,bridge_additions=T*6*v,route_families=J,terminal_exchange_stream_movements=T*4*v,high_affine_factors=J*high,low_transposition_coefficient=J*(stock+24),generic_wrappers=E*good,matrix_preparation=E*128*N**3,copy_erase_episodes=120*T,fallback_per_child=32*m*m,extra_bank_selector_calls=K,normalizer_factor_bound=banks['normalizer_factor_bound'],simultaneous_extra_work_streams=1,payload_prefix_upper=payload,payload_prefix_bits=payloadbits),q_power_bound=dict(coefficient=coefficient,low_matrix_power=14400,strict_upper='q^14401'),rational_route=route,row_reserve=row_reserve,moment=dict(coarse=str(c),tau=str(1-c),delta_tau_lower=str(delta_tau),delta_linear=str(delta1),fallback_added_in_full=True),recurrence=dict(bound='A*(n+n^(1-c)*w^(1-a_j))',A='C*(1+1/delta_linear+1/delta_tau)',halving_degree=1,one_level_histogram=True),bootstrap=dict(chain=list(map(str,chain)),ordinary=str(chain[-1]),gaps=gaps),rejected_controls=controls,scope='Actual60replicas/literalbankstock andallfixedbanknormalizerschargedbefore finiteordinaryleaf absorption. Inheritedweightedcompiler,commonancestorchart,restoredrow,routing,prime,recoveryandanalyticinterfacesremainconditional.')
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/NOTICE-PR200 b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/NOTICE-PR200
new file mode 100644
index 0000000000..c2d7935d7f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/NOTICE-PR200
@@ -0,0 +1,60 @@
+Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI
+Codex assistance. Apache-2.0. Inherited files retain their original notices
+and assistance disclosures. This package claims no exclusive priority over
+concurrent work.
+
+Retained sources and lineage:
+- icekylinx: PR144 paired cubes, signed decoder, shared-core accounting,
+  original compiler, configurable local channels and finite bridge;
+  PR130/generalized Clifford frames.
+- eumemic: PR117 module infrastructure; PR155/157 scalar modules, physical
+  frames/reuse and partner-pair bit word; PR161 output merging and searched
+  p12 module; PR168 annealed pair, triple and all-but-one modules on both
+  words, nested-prefix schedules, the L1 local circuits this package varies,
+  fused outputs, bundle descent, both physical layers, the terminal-sink
+  gate and the physical bit word, pinned at
+  4a3c769e5c5430e7114c4d3e099ff34664677f17. Their Anthropic Claude and
+  OpenAI Codex disclosures are retained. PR131/143 supply frame/reuse and
+  late-read lineage; PR154 supplies isolated snapshot verification.
+- DaysSky: PR162 generalized carrier extension (`compile_closure` and the
+  extension rule reused here on the new graph) and full-intersection
+  compiler lineage. The selected graph retains the PR168 nested schedule.
+- jamesyc / James Chang: PR124 compensated birth cuts, PR34 balanced
+  assembly, and PR166 terminal-output accumulation and exact simultaneous
+  target-chain checking. The PR166 proof is retained in references/pr166.
+- GamingPuzzled / Joel Pulikkan: PR160 searched-bit-module composition.
+- gupt1156 PR148 and Abhinav Ramachandran/geckods PR158 (Hermes assistance):
+  paid atom-toll re-instantiation, including PR158 at
+  6e086603f936dbb95c6d7171132ed943cc024db9.
+- jacklightChen / Zhihao Chen: PR23/29 ordinary supplier; Rohan Arun
+  (rohanarun): PR100/103 paid positional layout and deferred signed words.
+- Earlier bit lineage retained by the prerequisite: Zhihao Chen PR97,
+  Swapnil Jain's round-seven checkers, an664 PR128, DaysSky PR150, hpst3r
+  PR147, SovereignSteak PR122, and the source-notice contributors.
+
+This package contributes, on the complex side, a random-restart and
+coordinate search over PR144's configurable local channel circuit on the
+PR168 v4 word, selecting face diagonals for A[0,0], A[0,1] and A[1,1] and
+fixed-coordinate differences for three G channels so that the carrier
+closure gains 1,485 arcs; our own legal-edge Hopcroft-Karp carrier matching with PR162's
+extension; endpoint frame descent and compensated handoffs for the new
+graph; independent complete admission of the resulting physical word and
+its 44 terminal deletions; independent physical-bit admission and exact
+prime witnesses for every used bit frame; and, on the bit side, a fixed-coordinate/face-diagonal variant of PR168's bit
+local circuit (A[0,0], A[0,1], A[2,0], A[2,1] face diagonals; A[1,*]
+direction-0 edges; G[0,1,0] fixed-coordinate differences), our own carrier
+matching, gauge selection and complete physical layer (endpoint frame descent and 1,760 compensated handoffs) for
+that graph, with 34 PR166 terminal deletions on face0 roots, independently
+admitted with exact prime witnesses for every used bit frame;
+and the fully paid balanced composition with finer positive backoffs. Scalar virtual stock, physical
+handoffs, terminal removals and every external row reserve remain
+distinct. The complete 47-inequality body is source-normalized to PR141.
+Prerequisite constructions, the configurable circuit itself and the
+terminal-compilation concept are not claimed as original here.
+
+The package is based on main (3b6b66891c0ac888521cf591fe306c6286601d4f),
+which integrates Dugongue's PR186 entrance-bank construction and already
+carries PR175's retired-register update. references/pr168-v4 holds
+byte-identical copies of the twelve PR168 v4 files this package executes or
+pins (icekylinx/eumemic/DaysSky lineage as noted in those files), with
+their digests in references/pr168-v4/SOURCE.json.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/README.md b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/README.md
new file mode 100644
index 0000000000..911da50b1c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/README.md
@@ -0,0 +1,74 @@
+# gen4: the paired-cube bit word
+
+The word is PR168's p = 12 paired-cube bit word (h = 24, v = 1,760 ports), with three structural changes.
+The roots, decoder and partner-pair source mixing are unchanged. Its virtual profile is:
+
+- R = 17,904 (= c + q − |M| = 23,380 + 6,624 − 12,100);
+- W = 21,424 and deficit 1,936;
+- 3,960 gauges, 2,200 of rank 20 and 1,760 of rank 21.
+
+PR200's word has R = 18,908 and main's PR168 word has R = 19,788.
+
+| region | additions − carrier arcs, PR168 (L1) | gen4 |
+| --- | ---: | ---: |
+| local channels (220 cubes) | 220 × 22 | 220 × 16 |
+| pair module + centre (24) | 24 × 191 | 24 × 184 |
+| all-but-one module (132) | 132 × 15 | 132 × 12 |
+| merges u/w, roots | 1,760 + 6,624 | 1,760 + 6,624 |
+| **total R** | **19,788** | **17,904** |
+
+## 1. Arc-aware local design
+
+`local_design()` builds every per-cube plane channel by a recipe tree. The tree is any binary tree of
+support-disjoint additions over the cube's sources, not only the edge, face-diagonal or fixed-coordinate
+options of PR144, PR189 and PR200.
+
+Each cube uses 29 additions, against 26 for L1. Those additions create 13 in-place carrier arcs, against
+4, so the per-cube debt drops from 22 to 16:
+
+- 5 partner-root arcs. The flip01 face-diagonal pairs feed only G01 and hand their control source to its
+  partner root.
+- 8 chain arcs. A dimension-2 edge pair hands a source on to its direct use at dimension 4.
+
+A CP-SAT model over all 15 recipe trees per plane, with exact initial frames and creation-order ties,
+proves 16 is the minimum. Of the 120 annealed designs at debt 16, seed 4 has the best saving.
+
+## 2. Re-annealed all-but-one module
+
+The module has 34 additions and 22 carrier arcs, so its debt is 12 against 15 before. It was annealed with
+split-function moves against a one-instance compile of the generator.
+
+## 3. Centre-sharing pair module
+
+The pair module's 56th root is the sum of all 55 inputs, star(2i + bit). It costs 10 extra additions on
+existing module nodes. `finish()` uses that root as the copied centre instead of a separate tree of 34
+additions. Pair-plus-centre debt drops from 191 to 184.
+
+The centre closure (phase one) grows but stays disjoint from every gauge. `prepare.py` checks this, and so
+do PR200's classes and the PR168 checker.
+
+## Physical layer
+
+`producer/make_physical.py` adds 1,494 compensated reuse pairs. Each pairs a rank-21 gauged recipient,
+read right before its first operation, with a dead ungauged non-root non-source donor whose last frame
+lies in the recipient gauge. The pairing is a maximum Hopcroft–Karp matching. PR200's word has 1,760 such
+pairs; gen4 has fewer because its leaner circuit leaves fewer dead registers.
+
+`producer/descent.py` moves equal-frame connected operation groups to the join of their incoming frames
+and node spans, or to the meet of their outgoing frames, repairing degenerate endpoints by one row. Gauge,
+root, source and target frames stay fixed. A move is accepted only when the five-stage first-order cost
+Σ r·ln(120/r) over all physical chains decreases. The result is 1,802 changed operation frames.
+
+Physical R = 16,410.
+
+## Reproduce
+
+```sh
+python3 -B gen4bit/producer/regenerate.py --work /new/scratch/dir
+```
+
+This runs the generator on frozen arcs, then both producers. It checks that all five pinned files in
+`selected/bit` are reproduced exactly, and takes about two minutes. The generator is
+`producer/paired_cube_bit_word.py`: eumemic's PR168 generator as integrated on main, plus `local_design()`
+and the centre patch in `finish()`. It reads only the four p = 12 data files in `producer/data`.
+`verify.py` never runs a producer; the pinned files are the mathematical inputs.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/bit/base_word.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/bit/base_word.py
new file mode 100644
index 0000000000..044f278fbe
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/bit/base_word.py
@@ -0,0 +1,202 @@
+#!/usr/bin/env python3
+"""Reusable independent formal checks for a physical partner-pair bit word.
+
+The supplied frozen inputs are source-pinned. This never runs their producer.
+The Z check is of the defining integer decoder; only its F2 reduction is I.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from collections import Counter, defaultdict
+import importlib.util
+import json
+from pathlib import Path
+import sys
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[2]
+BASE = HERE.parent / 'references/pr168-v4/research/paired-cube-bit'
+P = 12
+if sys.flags.optimize: raise SystemExit('refusing -O')
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+class Candidate:
+    def exact_frames(self):
+        C = self.C
+        C.decoder(); C.geometry()
+        for i in self.changed_frames:
+            f = self.opframe[i]; x = self.ops[i][2]; bits = C.sup[x]
+            need(C.nondeg(f), 'replacement operation frame nondegenerate')
+            while bits:
+                low = bits&-bits; s=low.bit_length()-1; bits-=low
+                need(C.in_frame(C.chi[s],f), 'value span in replacement operation frame')
+        for b, d in self.pairs:
+            need(C.sub(self.endframe[d], self.gauge[b]['frame']), 'exact Q donor-to-birth containment')
+            need(C.nondeg(self.endframe[d]) and C.nondeg(self.gauge[b]['frame']), 'handoff endpoints nondegenerate')
+
+    def register(self, rows):
+        C = self.C
+        B,_ = self.module.reduce_rows(rows,self.h if hasattr(self,'h') else C.h)
+        B = tuple(sorted(map(tuple,B),key=lambda r:next(i for i,x in enumerate(r) if x)))
+        if not hasattr(self,'frame_ids'):
+            self.frame_ids = {}
+        if B in self.frame_ids: return self.frame_ids[B]
+        f=max(C.B)+1; A,_=self.module.kernel(B,C.h)
+        C.B[f],C.A[f],C.dimf[f]=B,A,len(B);self.frame_ids[B]=f
+        return f
+
+
+    def row(self):
+        C,h,v=self.C,self.h,self.v
+        _,baseline_Y,src,_=C.chains()
+        seq=defaultdict(list)
+        for i,(a,b,x) in enumerate(self.ops):
+            seq[a].append(self.opframe[i]);seq[b].append(self.opframe[i])
+        for j,s in enumerate(self.w['rootroles']):seq[s].append(self.w['root_frame'][j])
+        start={b:self.w['source_frame'][x] for x,b in self.source.items()}
+        start.update({b:z['frame'] for b,z in self.gauge.items()})
+        recipient={d:b for b,d in self.pairs}
+        H=Counter()
+        for s in range(self.R):
+            if s in self.donor:continue
+            chain=list(seq[s])
+            if s in recipient:
+                b=recipient[s];chain += [self.gauge[b]['frame']]+seq[b]
+            chain.append(self.w['full_frame'])
+            prev=start.get(s);dp=0 if prev is None else C.dimf[prev]
+            if s in self.source.values():H[1]+=1
+            for f in chain:
+                need(prev is None or C.sub(prev,f),'physical role chain nested')
+                d=C.dimf[f]
+                if d>dp:H[d-dp]+=1
+                prev,dp=f,d
+        for j,r in enumerate(self.g['roots']):
+            if r['kind']=='center':H[C.dimf[self.w['root_frame'][j]]]+=1
+        Y=Counter();current=[None]*v
+        def read(t,f):
+            old=current[t];d=0 if old is None else C.dimf[old]
+            need(old is None or C.sub(old,f),'actual target frame chronology')
+            if C.dimf[f]>d:Y[C.dimf[f]-d]+=1
+            current[t]=f
+        for b in sorted(self.order,key=lambda b:self.readtime[b]):
+            for t in self.gauge[b]['targets']:read(t,self.gauge[b]['frame'])
+        deliveries=defaultdict(list)
+        for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e)
+        for j,r in enumerate(self.g['roots']):
+            if r['kind']!='center':
+                for t in r['targets']:read(t,self.w['root_frame'][j])
+            for e in deliveries[j]:
+                for t in e['receivers']:read(t,e['deliver_frame'])
+        for t,f in enumerate(current):
+            need(f is not None and all(self.module.dot(C.cov[t],b)==0 for b in C.B[f]),'final target cap')
+            gap=h-1-C.dimf[f]
+            if gap:Y[gap]+=1
+        need(sum(r*n for r,n in Y.items())==v*(h-1),'target rank mass')
+        hist=Counter()
+        for part in (H,Y,src):
+            for r,n in part.items():
+                if r and n:hist[r]+=3*n
+        for b,z in self.gauge.items():
+            if b not in self.donor:hist[3*z['dim']]+=1
+        hist[2]+=2*v
+        hist={r:n for r,n in sorted(hist.items()) if n}
+        need(all(0<r<3*h and n>0 for r,n in hist.items()),'positive proper child bins')
+        R=self.R-len(self.pairs);W=2*v+R;mass=sum(r*n for r,n in hist.items());m=3*h
+        need(W*m-mass==C.prof['deficit_per_vertex'],'reuse preserves telescoping deficit')
+        return dict(h=h,v=v,R=R,virtual_R=self.R,reused_registers=len(self.pairs),W_per_vertex=W,m=m,
+            loss=C.prof['loss'],rank_per_vertex=mass,deficit_per_vertex=W*m-mass,
+            child_histogram=hist,maxchild=max(hist),selected_roles=len(self.gauge)-len(self.pairs),
+            selected_rank_histogram=dict(Counter(z['dim'] for b,z in self.gauge.items() if b not in self.donor)),
+            changed_operation_frames=len(self.changed_frames),
+            frames_not_contained_in_original=sum(not C.sub(self.opframe[i],self.original_opframe[i]) for i in self.changed_frames),
+            physical_target_histogram=dict(Y),physical_internal_histogram=dict(H),
+            foreign_producer_replays=0)
+
+    def adjoint(self):
+        adj = [dict() for _ in range(self.R)]
+        for r,s in zip(self.g['roots'], self.w['rootroles']):
+            for t in r['targets']: adj[s][t] = adj[s].get(t,0)+1
+        for a,b,_ in reversed(self.ops):
+            for t,c in adj[a].items(): adj[b][t] = adj[b].get(t,0)+c
+        return adj
+
+    def formal(self, ring, tamper=None):
+        """All source, target and dirty-register columns; no random sampling."""
+        v, phys = self.v, self.phys
+        regs = sorted(set(phys.values())); index = {r:2*v+j for j,r in enumerate(regs)}
+        if ring == 2:
+            unit = lambda i: 1<<i
+            def accum(dst,val,c): return dst ^ val if c&1 else dst
+        else:
+            unit = lambda i: {i:1}
+            def accum(dst,val,c):
+                out = dict(dst)
+                for i,z in val.items():
+                    k = out.get(i,0)+c*z
+                    if k: out[i]=k
+                    else: out.pop(i,None)
+                return out
+        x = [unit(s) for s in range(v)]; y = [unit(v+t) for t in range(v)]
+        a = {r:unit(index[r]) for r in regs}
+        adj = self.adjoint()
+        at = defaultdict(list)
+        for b in self.order: at[self.readtime[b]].append(b)
+        done = []
+        stale_used = False
+        def read(b):
+            nonlocal stale_used
+            if tamper == 'omit_compensation' and b == self.order[0]: return
+            value = a[phys[b]]
+            if tamper == 'stale' and b in self.donor and not stale_used:
+                value = unit(index[phys[b]]); stale_used = True
+            for t,c in adj[b].items(): y[t] = accum(y[t],value,-c)
+        def op(i,sign):
+            b,d,_ = self.ops[i]
+            a[phys[b]] = accum(a[phys[b]],a[phys[d]],sign)
+        for b in range(self.R):
+            if b not in self.gauge: read(b)
+        for s,b in self.source.items(): a[phys[b]] = accum(a[phys[b]],x[s],1)
+        for i in self.phase1: op(i,1); done.append(i)
+        for r,b in zip(self.g['roots'],self.w['rootroles']):
+            if r['kind']=='center':
+                for t in r['targets']:y[t]=accum(y[t],a[phys[b]],1)
+        for j,i in enumerate(self.rest):
+            for b in at[j]: read(b)
+            op(i,1); done.append(i)
+        for b in at[len(self.rest)]: read(b)
+        deliveries=defaultdict(list)
+        for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e)
+        broken=False
+        for j,(r,b) in enumerate(zip(self.g['roots'],self.w['rootroles'])):
+            if r['kind']!='center':
+                for t in r['targets']: y[t] = accum(y[t],a[phys[b]],1)
+            for e in deliveries[j]:
+                c,d = e['carrier'],e['passive']
+                x[c] = accum(x[c],x[d],1)
+                for t in e['receivers']:
+                    if tamper == 'missing_partner' and not broken: broken=True;continue
+                    y[t] = accum(y[t],x[c],1)
+        for e in self.k['entries']:
+            x[e['carrier']] = accum(x[e['carrier']],x[e['passive']],-1)
+        for i in reversed(done): op(i,-1)
+        for s,b in self.source.items(): a[phys[b]] = accum(a[phys[b]],x[s],-1)
+        need(all(a[r] == unit(index[r]) for r in regs), 'all dirty register columns restored')
+        need(all(x[s] == unit(s) for s in range(v)), 'all source columns restored')
+        if ring == 2:
+            want = [accum(unit(v+t),unit(t),1) for t in range(v)]
+        else:
+            # Integer lift: the exact defining decoder, whose reduction is I over F2.
+            support = [{s:1} for s in range(v)]
+            for aa,bb in self.g['args'][v:]: support.append(accum(support[aa],support[bb],1))
+            want = [unit(v+t) for t in range(v)]
+            for r in self.g['roots']:
+                for t in r['targets']: want[t] = accum(want[t],support[r['node']],1)
+            for e in self.k['entries']:
+                for t in e['receivers']:
+                    want[t] = accum(want[t],unit(e['carrier']),1)
+                    want[t] = accum(want[t],unit(e['passive']),1)
+        need(y == want, 'all target columns equal defining decoder')
+        return dict(ring=str(ring),formal_variables=2*v+len(regs),
+            target_contract='F2 identity' if ring==2 else 'integer defining decoder',
+            identity=ring==2,defining_decoder=True,all_dirty_and_source_columns_restored=True)
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/bit/word.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/bit/word.py
new file mode 100644
index 0000000000..6b8d96043a
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/bit/word.py
@@ -0,0 +1,104 @@
+"""Independent complete formal admission of the PR168-v4 physical bit word with our own physical layer (endpoint descent and reuse pairs) and terminal sinks.
+
+Retains eumemic's exact integer linear algebra and original decoder/geometry
+predicates. Physical chains, chronological formal columns and paid moments
+use our separate verifier. No producer or foreign aggregate checker runs.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from hashlib import sha256
+import gzip,importlib.util,json,sys,time
+HERE=Path(__file__).resolve().parent
+SOURCE=HERE.parent/'references/pr168-v4'
+PKG=HERE.parent
+def module(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m
+def read(p):
+    raw=p.read_bytes();return json.loads(gzip.decompress(raw) if p.suffix=='.gz' else raw)
+old=module('own_frozen_word',PKG/'bit/base_word.py');need=old.need
+
+class Candidate(old.Candidate):
+    def __init__(self):
+        self.module=backend=module('exact_integer_backend',SOURCE/'research/paired-cube-bit/check_paired_cube_bit.py')
+        C=backend.Checker.__new__(backend.Checker);self.C=C;C.mut=None
+        B=F=PKG/'selected/bit'
+        self.input_paths=[B/'graph_p12.json',B/'profile_p12.json',F/'word_p12.json.gz',F/'frames_p12.json.gz',F/'kchron_p12.json']
+        C.g,C.prof,C.w,C.fr,C.k=map(read,self.input_paths)
+        C.h=C.g['h'];C.v=C.g['v'];C.frames()
+        self.h,self.v,self.R=C.h,C.v,C.prof['R'];self.w,self.g,self.k=C.w,C.g,C.k
+        self.ops=self.w['ops'];self.nf={int(n):f for n,f in self.w['node_frame'].items()}
+        self.source={int(n):s for n,s in self.w['sources'].items()};self.gauge={z['role']:z for z in self.w['gauges']}
+        need(len(self.gauge)==len(self.w['gauges']),'unique gauge roles')
+        self.original_opframe=tuple(self.nf[n] for a,b,n in self.ops);self.opframe=self.w['op_frame'][:]
+        need(len(self.opframe)==len(self.ops),'complete operation frame vector')
+        self.changed_frames=[i for i,(a,b) in enumerate(zip(self.original_opframe,self.opframe)) if a!=b]
+        self.phase1=sorted(self.w['phase1']);phase=set(self.phase1)
+        self.rest=[i for i in range(len(self.ops)) if i not in phase];order=self.phase1+self.rest
+        self.position={i:p for p,i in enumerate(order)};pos={i:p for p,i in enumerate(self.rest)}
+        self.order=[z['role'] for z in reversed(self.w['gauges'])]
+        self.role_ops=defaultdict(list)
+        for i in order:
+            for s in self.ops[i][:2]:self.role_ops[s].append(i)
+        need(all(xs==sorted(xs) for xs in self.role_ops.values()),'execution order preserves every role chronology')
+        self.first={s:pos.get(xs[0],-1) for s,xs in self.role_ops.items()}
+        self.last={s:pos.get(xs[-1],-1) for s,xs in self.role_ops.items()}
+        self.endframe={s:self.opframe[xs[-1]] for s,xs in self.role_ops.items()}
+        self.rootroles=set(self.w['rootroles']);self.rootkind={s:r['kind'] for s,r in zip(self.w['rootroles'],self.g['roots'])}
+        need(len(self.rootroles)==len(self.w['rootroles']),'unique root roles')
+        reads={int(s):p for s,p in self.w['reads'].items()}
+        need(set(reads)<=set(self.gauge),'only gauges have explicit reads')
+        self.readtime={s:reads.get(s,len(self.phase1))-len(self.phase1) for s in self.order}
+        need(all(0<=self.readtime[s]<=self.first[s] for s in self.order),'all gauge reads after centre phase and before first use')
+        self.pairs=[[b,a] for a,b in self.w['pairs']];self.donor=dict(self.pairs)
+        need(len(self.donor)==len(self.pairs)==len(set(self.donor.values())),'one-to-one aliases')
+        need(not set(self.donor)&set(self.donor.values()),'disjoint donor recipient sets')
+        for b,d in self.pairs:
+            need(d not in self.gauge and d not in self.rootroles and b in self.gauge,'ungauged non-root donor and gauged recipient')
+            need(self.last[d]<self.readtime[b],'donor dead before recipient read')
+        self.phys={s:self.donor.get(s,s) for s in range(self.R)}
+        need(len(set(self.phys.values()))==self.R-len(self.pairs),'physical slot count')
+        need(all(self.phys[a]!=self.phys[b] for a,b,n in self.ops),'distinct physical gate ports')
+        C.chains=self.base_chains
+
+    def base_chains(self):
+        """Reconstruct phase/gauge/source contracts; row() counts physical paths."""
+        C,w,h,v=self.C,self.w,self.h,self.v
+        order=self.phase1+self.rest
+        roleprev={};pred=[]
+        for i,(a,b,n) in enumerate(self.ops):
+            pred.append((roleprev.get(a,-1),roleprev.get(b,-1)));roleprev[a]=roleprev[b]=i
+        pending=[roleprev[s] for s in self.rootroles if self.rootkind[s]=='center' and s in roleprev];closure=set()
+        while pending:
+            i=pending.pop()
+            if i not in closure:closure.add(i);pending.extend(j for j in pred[i] if j>=0)
+        need(closure==set(self.phase1),'phase one is exactly centre closure')
+        content=[0]*self.R
+        for n,s in self.source.items():content[s]=1<<n
+        for i in order:
+            a,b,n=self.ops[i];args=self.g['args'][n]
+            if content[a]:need(args is not None and {content[a],content[b]}=={C.sup[t] for t in args},'actual addition operands')
+            else:need(content[b]==C.sup[n],'actual copied node value')
+            content[a]|=content[b]
+        co=[set() for _ in range(self.R)]
+        for r,s in zip(self.g['roots'],w['rootroles']):co[s].update(r['targets'])
+        for i in reversed(order):
+            a,b,n=self.ops[i];co[b].update(co[a])
+        touched={s for i in self.phase1 for s in self.ops[i][:2]}
+        for s,z in self.gauge.items():
+            need(s not in self.source.values() and s not in touched,'gauge untouched in phase one and source injection')
+            need(set(z['targets'])==co[s] and C.dimf[z['frame']]==z['dim']>0,'gauge dimension and complete response support')
+        src=Counter();members=Counter();labels=list(map(set,self.g['labels']))
+        for e in self.k['entries']:
+            c,d,f,cap=e['carrier'],e['passive'],e['mix_frame'],e['deliver_frame']
+            need(len(labels[c]&labels[d])==1,'orthogonal partner pair')
+            need(C.dimf[f]==2 and C.in_frame(C.chi[c],f) and C.in_frame(C.chi[d],f),'partner mix span')
+            need(C.sub(f,cap) and all(self.module.dot(C.cov[t],u)==0 for t in e['receivers'] for u in C.B[cap]),'partner mix delivery cap')
+            need(e['carrier_chain']==[w['source_frame'][c],f,cap,w['full_frame']] and e['passive_chain']==[w['source_frame'][d],f,w['full_frame']],'exact partner chains')
+            root=self.g['roots'][e['deliver_after_root']]
+            need(root['kind']=='side' and sorted(e['receivers'])==sorted(root['targets']),'partner delivery at own receiver root')
+            for chain in (e['carrier_chain'],e['passive_chain']):
+                for a,b in zip(chain,chain[1:]):
+                    need(C.sub(a,b),'nested source chronology');src[C.dimf[b]-C.dimf[a]]+=1
+            members[c]+=1;members[d]+=1
+        need(all(members[s]==1 for s in range(v)),'every source in one partner pair')
+        return Counter(),Counter(),src,self.R
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/arcs_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/arcs_p12.json
new file mode 100644
index 0000000000..983973aa70
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/arcs_p12.json
@@ -0,0 +1 @@
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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/local_design_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/local_design_p12.json
new file mode 100644
index 0000000000..66ce6682bb
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/local_design_p12.json
@@ -0,0 +1 @@
+{"design":[[["A",0,0],[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1]]]],[["A",0,1],[[[1,0,0],[1,1,0]],[[1,0,1],[1,1,1]]]],[["A",1,0],[[[[0,0,1],[1,0,0]],[0,0,0]],[1,0,1]]],[["A",1,1],[[[0,1,0],[1,1,0]],[[0,1,1],[1,1,1]]]],[["A",2,0],[[[[1,0,0],[1,1,0]],[0,1,0]],[0,0,0]]],[["A",2,1],[[[[0,0,1],[0,1,1]],[1,1,1]],[1,0,1]]],[["G",0,1,0],[[[0,0,0],[1,1,0]],[[0,0,1],[1,1,1]]]],[["G",0,1,1],[[[0,1,0],[1,0,0]],[[0,1,1],[1,0,1]]]],[["G",0,2,0],[[[0,0,0],[0,1,0]],[[1,0,1],[1,1,1]]]],[["G",0,2,1],[[[[0,0,1],[1,0,0]],[0,1,1]],[1,1,0]]],[["G",1,2,0],[[[0,0,0],[1,0,0]],[[0,1,1],[1,1,1]]]],[["G",1,2,1],[[[0,0,1],[1,0,1]],[[0,1,0],[1,1,0]]]]],"provenance":{"adds_per_cube":29,"arcs_per_cube":13,"source":"agent-helpers local_search.py seed 4 (simulated annealing on additions minus feasible carrier arcs per cube)"}}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/pair_module_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/pair_module_p12.json
new file mode 100644
index 0000000000..57809df44b
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/pair_module_p12.json
@@ -0,0 +1 @@
+{"args":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,[23,24],[1,55],[56,26],[22,21],[19,20],[58,59],[57,60],[52,7],[62,53],[62,16],[24,64],[46,45],[29,35],[47,67],[66,68],[9,8],[70,54],[0,1],[10,72],[26,18],[17,25],[74,75],[73,76],[71,77],[23,15],[78,79],[51,50],[53,81],[6,7],[83,49],[52,84],[82,85],[80,86],[16,87],[88,24],[33,32],[30,31],[2,91],[90,92],[93,11],[89,94],[19,95],[96,29],[14,22],[48,5],[99,47],[98,100],[101,66],[97,102],[38,32],[104,25],[17,105],[106,8],[50,107],[24,16],[79,109],[110,49],[91,37],[112,36],[111,113],[114,6],[115,7],[116,52],[108,117],[2,3],[72,119],[20,12],[121,10],[27,122],[19,123],[11,124],[120,125],[118,126],[42,46],[40,128],[45,129],[49,130],[131,41],[132,110],[60,1],[134,25],[12,11],[136,18],[137,17],[138,13],[4,5],[140,83],[141,132],[142,110],[34,35],[29,144],[145,28],[146,14],[58,13],[147,148],[149,125],[150,113],[151,133],[25,26],[28,34],[70,140],[155,83],[47,43],[131,157],[82,52],[54,159],[158,160],[48,44],[161,162],[163,41],[156,164],[76,165],[14,148],[73,167],[168,110],[166,169],[90,39],[171,38],[134,153],[27,119],[38,174],[175,171],[173,176],[98,5],[66,178],[179,67],[48,180],[9,126],[33,39],[18,183],[184,26],[182,185],[186,7],[187,115],[51,53],[188,189],[181,190],[15,14],[192,13],[0,16],[193,194],[76,54],[196,172],[157,40],[162,198],[197,199],[200,150],[52,53],[201,202],[21,59],[25,204],[10,167],[206,110],[76,207],[37,31],[128,209],[8,126],[211,197],[9,212],[213,117],[140,199],[149,215],[213,216],[25,57],[218,22],[219,59],[69,99],[220,221],[140,40],[149,223],[224,126],[157,225],[29,28],[19,11],[227,228],[229,32],[33,30],[230,231],[164,208],[232,233],[31,234],[8,157],[50,52],[236,237],[238,38],[4,43],[240,154],[36,37],[242,144],[41,243],[227,91],[244,245],[131,246],[247,141],[248,174],[189,162],[250,9],[249,251],[86,71],[242,253],[176,254],[91,255],[57,256],[257,205],[3,239],[210,109],[203,260],[39,38],[121,3],[262,263],[264,77],[242,262],[144,266],[267,3],[165,218],[269,22],[268,270],[138,194],[15,272],[273,255],[143,168],[275,75],[276,259],[30,36],[227,92],[279,90],[280,269],[273,14],[41,42],[44,283],[241,284],[258,285],[199,145],[28,287],[155,54],[288,289],[176,290],[291,139],[292,14],[293,194],[185,162],[182,224],[295,296],[297,45],[278,15],[299,23],[6,300],[41,51],[301,302],[298,303],[21,20],[271,305],[189,283],[307,188],[13,21],[309,154],[44,310],[311,4],[308,312],[153,60],[23,314],[27,172],[163,246],[316,317],[315,318],[319,24],[17,18],[194,321],[193,322],[165,323],[209,53],[325,62],[326,128],[327,294],[136,195],[17,238],[329,330],[264,35],[242,332],[267,164],[121,334],[335,208],[65,325],[6,36],[45,81],[339,41],[338,340],[341,30],[290,342],[152,105],[241,283],[126,309],[345,346],[291,327],[173,348],[199,289],[350,167],[351,77],[230,2],[352,353],[33,354],[63,16],[24,356],[46,357],[42,358],[355,359],[193,16],[265,351],[362,35],[243,121],[364,277],[240,311],[366,212],[9,337],[42,368],[367,369],[87,102],[371,333],[301,50],[213,373],[374,51],[250,39],[183,137],[17,361],[74,9],[101,45],[380,67],[176,317],[382,156],[256,222],[104,174],[385,248],[386,238],[387,55],[388,135],[65,107],[210,390],[23,340],[299,150],[392,393],[43,284],[310,395],[343,177],[213,101],[302,374],[399,366],[221,256],[282,401],[309,395],[403,4],[88,404],[263,405],[341,34],[54,26],[408,59],[72,409],[174,410],[6,340],[79,412],[413,231],[143,120],[151,415],[372,109],[275,379],[418,250],[31,360],[292,0],[192,421],[422,342],[179,127],[424,68],[349,24],[411,251],[427,330],[377,195],[429,252],[252,183],[266,34],[24,432],[207,428],[105,434],[377,435],[108,301],[45,41],[157,438],[225,439],[440,437],[91,285],[442,274],[13,443],[398,67],[445,46],[446,337],[114,124],[448,159],[11,197],[449,450],[396,451],[37,42],[406,433],[144,453],[358,362],[455,456],[248,436],[152,185],[276,238],[460,92],[3,156],[462,323],[364,3],[418,464],[376,465],[137,318],[28,19],[404,95],[468,469],[48,69],[451,471],[98,472],[414,354],[375,381],[19,58],[79,407],[226,391],[260,53],[7,479],[480,297],[363,477],[347,118],[280,11],[484,324],[386,331],[33,279],[459,250],[157,237],[17,489],[344,490],[334,12],[463,492],[397,23],[230,461],[61,431],[214,82],[419,228],[200,394],[498,487],[467,378],[281,476]],"input_count":55,"input_labels":[[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8],[1,9],[1,10],[2,3],[2,4],[2,5],[2,6],[2,7],[2,8],[2,9],[2,10],[3,4],[3,5],[3,6],[3,7],[3,8],[3,9],[3,10],[4,5],[4,6],[4,7],[4,8],[4,9],[4,10],[5,6],[5,7],[5,8],[5,9],[5,10],[6,7],[6,8],[6,9],[6,10],[7,8],[7,9],[7,10],[8,9],[8,10],[9,10]],"kind":"pair_disjoint","n":11,"provenance":{"additions":448,"extra_root":"centre star sum (all inputs)","mini_cost":61303.4564024385,"source":"agent-helpers modsa2/modsa3: simulated annealing of the pair-disjoint module WITH the centre star sum as an extra root (last root = all 55 inputs), started from data/pair_module_p12.json; objective = exact ledger cost of a one-instance mini-graph compile (minimod.py) with the seed-4 local design"},"roots":[320,501,336,235,473,452,261,499,488,491,383,306,502,384,286,426,494,496,389,493,485,402,444,328,423,430,486,170,417,454,457,482,466,365,103,470,420,474,500,495,497,447,475,191,425,370,400,313,483,217,481,478,304,441,416,458]}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/qmod_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/qmod_p12.json
new file mode 100644
index 0000000000..22bb0927cf
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/data/qmod_p12.json
@@ -0,0 +1 @@
+{"args":[null,null,null,null,null,null,null,null,null,null,[1,0],[3,1],[2,5],[5,7],[6,8],[7,9],[8,9],[10,2],[7,12],[14,9],[3,17],[19,4],[16,13],[20,4],[20,5],[7,21],[23,5],[13,21],[26,6],[15,24],[21,18],[28,7],[30,0],[27,11],[31,8],[28,15],[19,26],[22,23],[20,25],[29,14],[30,10],[33,0],[32,3],[11,30]],"input_count":10,"provenance":{"additions":34,"mini_cost":11348.829514317798,"source":"agent-helpers modsa.py seed 1: simulated annealing (split-function moves) of the all-but-one module from data/qmod_p12.json, objective = exact ledger cost of a one-instance mini-graph compile (minimod.py) with the seed-4 local design"},"roots":[43,42,41,40,39,38,37,36,35,34]}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/descent.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/descent.py
new file mode 100644
index 0000000000..6bdafeb1db
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/descent.py
@@ -0,0 +1,259 @@
+#!/usr/bin/env python3
+"""Endpoint frame descent for a physical paired-cube bit word (PR200 physical-layer rules).
+
+Moves equal-frame connected groups of operations to the join of their incoming frames and node value
+spans, or to the meet of their outgoing frames (degenerate endpoints repaired by one row), accepting a move
+only when the five-stage first-order cost  sum r*ln(120/r)  over all physical role chains decreases.
+Gauge, root, source, target and full frames are fixed; alias splices (donor -> recipient gauge) are kept.
+
+usage: descent.py PKGDIR OUTDIR   (PKGDIR = PR200-layout package whose selected/bit holds the word)
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import sys, json, gzip, math, time
+from pathlib import Path
+from collections import defaultdict, Counter
+
+pkg = Path(sys.argv[1]); out = Path(sys.argv[2]); out.mkdir(parents=True, exist_ok=True)
+sys.path.insert(0, str(pkg / 'bit'))
+from word import Candidate
+
+t0 = time.time()
+W = Candidate(); C = W.C; mod = W.module; h = W.h
+C.decoder(); C.geometry()
+FULL = W.w['full_frame']
+ops = W.ops; nops = len(ops)
+opframe = list(W.opframe)
+
+# ---------------------------------------------------------------- frame registry helpers
+key_of = {}
+def bkey(B): return tuple(sorted(map(tuple, B)))
+for f, B in C.B.items():
+    key_of.setdefault(bkey(B), f)
+
+def register(rows):
+    B, _ = mod.reduce_rows(rows, h)
+    B = [tuple(r) for r in B]
+    k = bkey(B)
+    if k in key_of: return key_of[k]
+    f = max(C.B) + 1
+    A, _ = mod.kernel(B, h)
+    C.B[f], C.A[f], C.dimf[f] = B, A, len(B)
+    key_of[k] = f
+    return f
+
+join_cache = {}
+def join(fs):
+    fs = tuple(sorted(set(fs)))
+    if len(fs) == 1: return fs[0]
+    r = join_cache.get(fs)
+    if r is None:
+        rows = [b for f in fs for b in C.B[f]]
+        r = join_cache[fs] = register(rows)
+    return r
+
+meet_cache = {}
+def meet(fs):
+    fs = tuple(sorted(set(fs)))
+    if len(fs) == 1: return fs[0]
+    r = meet_cache.get(fs)
+    if r is None:
+        ann = [a for f in fs for a in C.A[f]]
+        B, _ = mod.kernel(ann, h) if ann else ([tuple(int(i == j) for j in range(h)) for i in range(h)], None)
+        r = meet_cache[fs] = register(B)
+    return r
+
+nd_cache = {}
+def nondeg(f):
+    r = nd_cache.get(f)
+    if r is None: r = nd_cache[f] = C.nondeg(f)
+    return r
+
+def sub(a, b): return C.sub(a, b)
+
+# node value spans
+span_cache = {}
+def node_span(n):
+    r = span_cache.get(n)
+    if r is None:
+        bits = C.sup[n]; rows = []
+        while bits:
+            low = bits & -bits; s = low.bit_length() - 1; bits -= low
+            rows.append(C.chi[s])
+        r = span_cache[n] = register(rows)
+    return r
+
+def repair_up(L, U):
+    """smallest nondegenerate frame containing L inside U: L itself or L + one row of U."""
+    if nondeg(L): return L
+    for b in C.B[U]:
+        f = register(list(C.B[L]) + [b])
+        if C.dimf[f] == C.dimf[L] + 1 and nondeg(f): return f
+    return None
+
+def repair_down(L, U):
+    """largest nondegenerate frame inside U containing L: U itself or U minus one row (kernel of A_U + 1 row)."""
+    if nondeg(U): return U
+    # hyperplanes of U containing L: add one annihilator row vanishing on L but not on U
+    BL = C.B[L]
+    cand = []
+    for e in range(h):
+        a = [int(i == e) for i in range(h)]
+        cand.append(a)
+    # project candidate covectors to vanish on L: use combinations orthogonal to B_L via kernel of B_L
+    K, _ = mod.kernel(BL, h) if BL else ([tuple(int(i == j) for j in range(h)) for i in range(h)], None)
+    for a in K:
+        rows = list(C.A[U]) + [a]
+        B, _ = mod.kernel(rows, h)
+        f = register(B)
+        if C.dimf[f] == C.dimf[U] - 1 and sub(L, f) and nondeg(f): return f
+    return None
+
+# ---------------------------------------------------------------- physical chains
+recipient = {d: b for b, d in W.pairs}           # donor -> recipient
+roots = defaultdict(list)
+for j, s in enumerate(W.w['rootroles']): roots[s].append(W.w['root_frame'][j])
+start = {b: W.w['source_frame'][x] for x, b in W.source.items()}
+start.update({b: z['frame'] for b, z in W.gauge.items()})
+seq = defaultdict(list)
+for i, (a, b, x) in enumerate(ops):
+    seq[a].append(i); seq[b].append(i)
+
+chains = []   # list of element lists: ('f', frame) fixed or ('o', op)
+for s in range(W.R):
+    if s in W.donor: continue    # recipients are spliced into their donor's chain
+    el = []
+    st = start.get(s)
+    el.append(('f', st) if st is not None else ('z', None))
+    el += [('o', i) for i in seq[s]] + [('f', f) for f in roots[s]]
+    if s in recipient:
+        b = recipient[s]
+        el += [('f', W.gauge[b]['frame'])] + [('o', i) for i in seq[b]] + [('f', f) for f in roots[b]]
+    el.append(('f', FULL))
+    chains.append(el)
+pos = defaultdict(list)    # op -> [(chain, index)]
+for c, el in enumerate(chains):
+    for k, (t, x) in enumerate(el):
+        if t == 'o': pos[x].append((c, k))
+assert all(len(v) == 2 for v in pos.values()) and len(pos) == nops
+
+def fr(e):
+    t, x = e
+    if t == 'o': return opframe[x]
+    return x
+
+def dim(f): return 0 if f is None else C.dimf[f]
+
+LN = [0.0] + [r * math.log(120 / r) for r in range(1, 121)]
+def cost_pair(a, b):
+    d = dim(b) - dim(a)
+    assert d >= 0
+    return LN[d]
+
+def total_cost():
+    tot = 0.0
+    for el in chains:
+        for k in range(len(el) - 1):
+            tot += cost_pair(fr(el[k]), fr(el[k + 1]))
+    return tot
+
+def check_nested():
+    for el in chains:
+        for k in range(len(el) - 1):
+            a, b = fr(el[k]), fr(el[k + 1])
+            assert a is None or sub(a, b), ('nest', el[k], el[k + 1])
+
+check_nested()
+c0 = total_cost()
+print('loaded', round(time.time() - t0, 1), 's; chains', len(chains), 'cost', round(c0, 1), flush=True)
+
+# ---------------------------------------------------------------- group moves
+def groups():
+    parent = list(range(nops))
+    def find(x):
+        while parent[x] != x: parent[x] = parent[parent[x]]; x = parent[x]
+        return x
+    for el in chains:
+        for k in range(len(el) - 1):
+            if el[k][0] == 'o' and el[k + 1][0] == 'o' and opframe[el[k][1]] == opframe[el[k + 1][1]]:
+                ra, rb = find(el[k][1]), find(el[k + 1][1])
+                if ra != rb: parent[ra] = rb
+    g = defaultdict(list)
+    for i in range(nops): g[find(i)].append(i)
+    return list(g.values())
+
+def evaluate(G):
+    Gs = set(G); F = opframe[G[0]]
+    inc, outg = [], []
+    for i in G:
+        for c, k in pos[i]:
+            el = chains[c]
+            p = el[k - 1]
+            if not (p[0] == 'o' and p[1] in Gs): inc.append(fr(p))
+            q = el[k + 1]
+            if not (q[0] == 'o' and q[1] in Gs): outg.append(fr(q))
+    spans = {node_span(ops[i][2]) for i in G}
+    L = join([f for f in inc if f is not None] + list(spans))
+    U = meet(outg)
+    if not sub(L, U): return None
+    def delta(Fn):
+        d = 0.0
+        for f in inc: d += LN[dim(Fn) - dim(f)] - LN[dim(F) - dim(f)]
+        for f in outg: d += LN[dim(f) - dim(Fn)] - LN[dim(f) - dim(F)]
+        return d
+    best = (0.0, None)
+    cands = set()
+    lo = repair_up(L, U)
+    if lo is not None: cands.add(lo)
+    hi = repair_down(L, U)
+    if hi is not None: cands.add(hi)
+    for f in inc + outg:
+        if f is not None and sub(L, f) and sub(f, U) and nondeg(f): cands.add(f)
+    for Fn in cands:
+        if C.dimf[Fn] == C.dimf[F] and sub(Fn, F): continue
+        d = delta(Fn)
+        if d < best[0] - 1e-9: best = (d, Fn)
+    return best
+
+it = 0
+while True:
+    it += 1; moved = 0; gain = 0.0
+    gs = groups()
+    gs.sort(key=len, reverse=True)
+    for G in gs:
+        # frames may have changed for neighbours; G still has a common frame since only whole groups move
+        if len({opframe[i] for i in G}) != 1: continue
+        r = evaluate(G)
+        if r is None or r[1] is None: continue
+        d, Fn = r
+        for i in G: opframe[i] = Fn
+        moved += 1; gain += d
+    c = total_cost()
+    print('iter', it, 'groups', len(gs), 'moved', moved, 'gain', round(gain, 1), 'cost', round(c, 1), round(time.time() - t0, 1), 's', flush=True)
+    if moved == 0 or it >= 40: break
+
+check_nested()
+for i in range(nops):
+    f = opframe[i]
+    assert nondeg(f)
+    assert sub(node_span(ops[i][2]), f)
+changed = sum(1 for i in range(nops) if opframe[i] != W.original_opframe[i])
+print('changed op frames', changed, 'final cost', round(total_cost(), 1), 'from', round(c0, 1))
+
+# ---------------------------------------------------------------- write outputs
+w = dict(W.w); w['op_frame'] = opframe
+w['descent'] = 'op_frame[i]: equal-frame connected groups moved to the join of incoming frames and node spans or the meet of outgoing frames (one-row repair), five-stage first-order cost decrease'
+src = pkg / 'selected/bit'
+frames = json.loads(gzip.decompress((src / 'frames_p12.json.gz').read_bytes()))
+used = set(opframe)
+for f in sorted(C.B):
+    if str(f) in frames['frames'] or f not in used: continue
+    B, A = C.B[f], C.A[f]
+    frames['frames'][str(f)] = dict(dim=len(B), b=[list(r) for r in B]) if len(B) <= len(A) else dict(dim=len(B), a=[list(r) for r in A])
+used = set(opframe)
+print('frames now', len(frames['frames']))
+for name in ('graph_p12.json', 'kchron_p12.json', 'profile_p12.json', 'sinks.json'):
+    (out / name).write_bytes((src / name).read_bytes())
+wj = json.dumps(w, sort_keys=True).encode(); fj = json.dumps(frames, sort_keys=True).encode()
+(out / 'word_p12.json').write_bytes(wj); (out / 'word_p12.json.gz').write_bytes(gzip.compress(wj, mtime=0))
+(out / 'frames_p12.json').write_bytes(fj); (out / 'frames_p12.json.gz').write_bytes(gzip.compress(fj, mtime=0))
+print('wrote', out)
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/make_physical.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/make_physical.py
new file mode 100644
index 0000000000..a6f79038ed
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/make_physical.py
@@ -0,0 +1,136 @@
+#!/usr/bin/env python3
+"""Physical layer producer for a raw paired-cube bit word (PR168 format): compensated late reuse pairs.
+
+Input dir: graph_p12.json word_p12.json frames_p12.json kchron_p12.json profile_p12.json (raw generator output).
+Output dir: same names, word gains op_frame (= node frames unless --descent), pairs [[donor, recipient]],
+reads {recipient: absolute execution position}; frames/word also written gzipped for PR200's Candidate.
+
+Pair rules (PR200 bit/word.py + base_word.py): recipient gauged, read right before its first op; donor
+ungauged, non-root, non-source, last op strictly before that read; donor last op frame inside the recipient
+gauge frame; both nondegenerate; one-to-one; per-target gauge read times monotone along the nested chain.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import argparse, gzip, json, sys, importlib.util, time
+from collections import defaultdict, Counter
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+CHK = HERE.parent / 'references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py'
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(spec); spec.loader.exec_module(m); return m
+
+
+def hopcroft_karp(adj, nleft):
+    INF = 1 << 30
+    matchL = [-1] * nleft; matchR = {}
+    from collections import deque
+    while True:
+        dist = [INF] * nleft; q = deque()
+        for u in range(nleft):
+            if matchL[u] < 0: dist[u] = 0; q.append(u)
+        found = False
+        while q:
+            u = q.popleft()
+            for w in adj[u]:
+                v2 = matchR.get(w, -1)
+                if v2 < 0: found = True
+                elif dist[v2] == INF: dist[v2] = dist[u] + 1; q.append(v2)
+        if not found: break
+        sys.setrecursionlimit(100000)
+        def dfs(u):
+            for w in adj[u]:
+                v2 = matchR.get(w, -1)
+                if v2 < 0 or (dist[v2] == dist[u] + 1 and dfs(v2)):
+                    matchL[u] = w; matchR[w] = u; return True
+            dist[u] = INF; return False
+        for u in range(nleft):
+            if matchL[u] < 0: dfs(u)
+    return matchL
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument('--src', required=True); ap.add_argument('--out', required=True)
+    ap.add_argument('--ranks', default='21', help='gauge dims allowed as recipients, comma list')
+    a = ap.parse_args()
+    src, out = Path(a.src), Path(a.out); out.mkdir(parents=True, exist_ok=True)
+    mod = load('chk', CHK)
+    C = mod.Checker(src, 12)
+    C.frames(); C.decoder(); C.geometry()
+    g, w = C.g, C.w
+    ops = w['ops']; v = g['v']
+    R = 1 + max(max(x, y) for x, y, _ in ops)
+    nf = {int(k): f for k, f in w['node_frame'].items()}
+    opframe = [nf[n] for _, _, n in ops]
+    phase1 = sorted(w['phase1']); ph = set(phase1)
+    rest = [i for i in range(len(ops)) if i not in ph]
+    pos = {i: p for p, i in enumerate(rest)}
+    role_ops = defaultdict(list)
+    for i in phase1 + rest:
+        for s in ops[i][:2]: role_ops[s].append(i)
+    assert all(xs == sorted(xs) for xs in role_ops.values())
+    first = {s: pos.get(xs[0], -1) for s, xs in role_ops.items()}
+    last = {s: pos.get(xs[-1], -1) for s, xs in role_ops.items()}
+    endframe = {s: opframe[xs[-1]] for s, xs in role_ops.items()}
+    gauge = {z['role']: z for z in w['gauges']}
+    roots = set(w['rootroles']); sources = set(w['sources'].values())
+    allowed = {int(x) for x in a.ranks.split(',')}
+    # per-target chain order of gauges (time order = reversed selection order)
+    chain = defaultdict(list)
+    for z in reversed(w['gauges']):
+        for t in z['targets']: chain[t].append(z['role'])
+    # recipients: allowed dims; a recipient must be the LAST gauge of each of its targets' chains unless
+    # every later gauge on that target is also a recipient (resolved iteratively below: start with tops)
+    recips = [b for b in gauge if gauge[b]['dim'] in allowed]
+    def ok(b):
+        fb = gauge[b]['frame']
+        for t in gauge[b]['targets']:
+            later = chain[t][chain[t].index(b) + 1:]
+            if any(not (C.sub(gauge[x]['frame'], fb) and C.sub(fb, gauge[x]['frame'])) for x in later): return False
+        return True
+    recips = [b for b in recips if ok(b)]
+    donors = [s for s in range(R) if s not in gauge and s not in roots and s not in sources and s in role_ops]
+    print('roles', R, 'gauges', len(gauge), 'recipient candidates', len(recips), 'donor candidates', len(donors), flush=True)
+    t0 = time.time()
+    nd_cache = {}
+    def nondeg(f):
+        r = nd_cache.get(f)
+        if r is None: r = nd_cache[f] = C.nondeg(f)
+        return r
+    # group donors by end frame to share containment tests
+    by_frame = defaultdict(list)
+    for d in donors:
+        if nondeg(endframe[d]): by_frame[endframe[d]].append(d)
+    print('donor end frames', len(by_frame), 'nondeg donors', sum(map(len, by_frame.values())), flush=True)
+    adj = []
+    for b in recips:
+        gb = gauge[b]['frame']; rt = first[b]
+        lst = []
+        if nondeg(gb):
+            for f, ds in by_frame.items():
+                if C.dimf[f] > C.dimf[gb]: continue
+                cand = [d for d in ds if last[d] < rt]
+                if cand and C.sub(f, gb): lst.extend(cand)
+        adj.append(lst)
+    print('edges', sum(map(len, adj)), 'recipients with an edge', sum(1 for x in adj if x), 'secs', round(time.time() - t0, 1), flush=True)
+    m = hopcroft_karp(adj, len(recips))
+    pairs = [[m[i], b] for i, b in enumerate(recips) if m[i] >= 0]
+    print('pairs', len(pairs), flush=True)
+    reads = {str(b): len(phase1) + first[b] for d, b in pairs}
+    W = dict(w); W['op_frame'] = opframe; W['pairs'] = pairs; W['reads'] = reads
+    W['descent'] = 'none: op_frame[i] = node_frame[ops[i][2]]'
+    W['reuse'] = 'late compensated reuse: recipient slot is the donor register; recipient old-value read right before its first op, after the donor last op'
+    for name in ('graph', 'frames', 'kchron', 'profile'):
+        (out / ('%s_p12.json' % name)).write_text((src / ('%s_p12.json' % name)).read_text())
+    (out / 'word_p12.json').write_text(json.dumps(W, sort_keys=True))
+    for name in ('word', 'frames'):
+        raw = (out / ('%s_p12.json' % name)).read_bytes()
+        (out / ('%s_p12.json.gz' % name)).write_bytes(gzip.compress(raw, mtime=0))
+    (out / 'sinks.json').write_text('[]')
+    print(json.dumps(dict(pairs=len(pairs), physical_R=R - len(pairs), dims=Counter(gauge[b]['dim'] for _, b in pairs))))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/paired_cube_bit_word.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/paired_cube_bit_word.py
new file mode 100644
index 0000000000..7b0d575f7e
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/paired_cube_bit_word.py
@@ -0,0 +1,996 @@
+#!/usr/bin/env python3
+# Modified copy of eumemic's PR168 paired-cube bit generator (research/paired-cube-bit/paired_cube_bit_word.py
+# as integrated on main; Apache-2.0). Changes for gen4 (DreamingOfClouds, with Anthropic Claude assistance):
+# local_design() recipe-tree local channels read from data/local_design_p12.json; the centre-sharing pair
+# module patch in finish() (the pair module's extra root is the copied centre star); build() reads the
+# optional design file. New data: local_design_p12.json, pair_module_p12.json, qmod_p12.json, arcs_p12.json.
+# The rest of the generator, its compiler and its ledger are unchanged.
+"""Paired-cube BIT local word with partner-pair source mixing: deterministic generator and rank compiler.
+
+Ports are the triples of [h] (h = 2p) taking one coordinate from each of three distinct coordinate pairs
+(v = 8*C(p,3)); bit labels chi_S in Q^h with H0 = (I - J/9)/2, so H0(chi_S, chi_T) = (|S cap T| - 1)/2.
+Payload F2. Mod-2 decoder, for every target T:
+    x_T = sum_{c in T} star(c)                         (2p copied point-star centres, frames of dim h-2)
+        + face channels  P'(J,i,eta_i)                  (cubes sharing exactly pair i, matching selector)
+        + edge channels  Q'(J,i,j,mode)                 (cubes sharing pairs i,j, exactly one selector match)
+        + partner        x_{T'}, T' = T with the selectors of cube pairs 1,2 flipped (single-source root)
+        + partner-pair sum of the opposite pair of T's parity class, mixed on two SOURCE registers and
+          delivered at the shared cap of {T, T'} (no auxiliary role).
+At p = 12 each cube merges its face-1 and edge-01 outputs into u(b0,b1) and its face-2 and edge-02 outputs into
+w(b0,b2) (variant u); each merged node is read by two single roots and the mod-2 sums are unchanged. Its local
+channels use the L1 association (local_l1): three of the six G sums add long face diagonals instead of edges.
+Its all-but-one modules are the pinned annealed module data/qmod_p12.json (pinned_all_but_one).
+Compiler: the PR #144 frames.py/gauges.py ledger on rational frames (target cap ker(3 chi_T - 1), centre frame =
+span of the star), coordinate-padded maximum carrier matching (frozen arcs), plain frames span(n) for additions of
+span dimension <= PLAIN (closed under operands; a linked donor's span must lie in the plain target), PR #144
+chronological partial gauges with a G-nondegeneracy filter, PR #144 bit ledger (m = 3h, W = 2v + R).
+Linear algebra is exact: ranks are computed modulo the Mersenne prime 2^127-1, which exceeds the Hadamard bound
+of every minor that occurs (see README.md); G-nondegeneracy is certified by integer Gram determinants.
+
+Usage: python3 paired_cube_bit_word.py --p 12 [--out DIR] [--check] [--solve-matching]
+Standard library only. Run without -O.
+"""
+import argparse, gzip, hashlib, json, math, os, sys, time
+from collections import Counter, defaultdict, deque
+from itertools import combinations, product
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P = (1 << 127) - 1
+PLAIN = 8
+L1_DIAGONAL = {(0, 1, 0), (0, 1, 1), (1, 2, 1)}  # (cube positions j < k, mode) of the diagonal G sums at p = 12
+MODULES = {11: 'pair_module_p11.json', 12: 'pair_module_p12.json', 13: 'pair_module_p13.json'}
+QMODULES = {12: 'qmod_p12.json'}
+
+
+def require(cond, msg):
+    if not cond:
+        raise SystemExit('FAIL: ' + msg)
+
+
+# ----------------------------------------------------------------------------- exact subspaces of F_P^h
+def rref(rows, h):
+    piv = {}
+    for r in rows:
+        x = [a % P for a in r]
+        for c, y in piv.items():
+            if x[c]:
+                f = x[c]
+                x = [(a - f * b) % P for a, b in zip(x, y)]
+        nz = next((j for j in range(h) if x[j]), None)
+        if nz is None:
+            continue
+        inv = pow(x[nz], P - 2, P)
+        x = [(a * inv) % P for a in x]
+        for c in list(piv):
+            y = piv[c]
+            if y[nz]:
+                f = y[nz]
+                piv[c] = [(a - f * b) % P for a, b in zip(y, x)]
+        piv[nz] = x
+    return tuple(tuple(piv[c]) for c in sorted(piv))
+
+
+def kernel(S, h):
+    pivs = [next(j for j in range(h) if row[j]) for row in S]
+    ps = set(pivs)
+    out = []
+    for f in range(h):
+        if f in ps:
+            continue
+        u = [0] * h
+        u[f] = 1
+        for row, c in zip(S, pivs):
+            u[c] = (-row[f]) % P
+        out.append(u)
+    return rref(out, h)
+
+
+class Table:
+    """Interned subspaces (canonical RREF) with memoized joins; id 0 is the zero space."""
+    def __init__(self, h):
+        self.h = h
+        self.rows = [()]
+        self.index = {(): 0}
+        self.jc = {}
+        self.pc = {}
+
+    def intern(self, rows):
+        S = rref(rows, self.h)
+        i = self.index.get(S)
+        if i is None:
+            i = len(self.rows)
+            self.rows.append(S)
+            self.index[S] = i
+        return i
+
+    def dim(self, i):
+        return len(self.rows[i])
+
+    def join(self, i, j):
+        if i == j or j == 0:
+            return i
+        if i == 0:
+            return j
+        if i > j:
+            i, j = j, i
+        k = self.jc.get((i, j))
+        if k is None:
+            A, B = self.rows[i], self.rows[j]
+            k = i if len(A) == self.h else j if len(B) == self.h else self.intern(A + B)
+            self.jc[(i, j)] = k
+        return k
+
+    def join_many(self, ids):
+        k = 0
+        for i in ids:
+            k = self.join(k, i)
+        return k
+
+    def contained(self, i, j):
+        return self.join(i, j) == j
+
+    def perp(self, i):
+        k = self.pc.get(i)
+        if k is None:
+            k = self.intern(kernel(self.rows[i], self.h))
+            self.pc[i] = k
+        return k
+
+
+class Geometry:
+    """Bit geometry: source line <chi_S>; target cap annihilated by 3 chi_T - 1 (the H0 = (I-J/9)/2 cap)."""
+    def __init__(self, h, labels):
+        self.h = h
+        self.T = Table(h)
+        self.src = [self.T.intern([[1 if j in lab else 0 for j in range(h)]]) for lab in labels]
+        self.tcov = [self.T.intern([[(3 if j in lab else 0) - 1 for j in range(h)]]) for lab in labels]
+        self.coord = [self.T.intern([[1 if k == j else 0 for k in range(h)]]) for j in range(h)]
+
+    def join(self, a, b): return self.T.join(a, b)
+    def join_many(self, ids): return self.T.join_many(ids)
+    def dim(self, a): return self.T.dim(a)
+    def perp(self, a): return self.T.perp(a)
+    def contained(self, a, b): return self.T.contained(a, b)
+
+
+def gram_nondegenerate_frame(rows, h):
+    """G = I - J/9 nondegenerate on the F_P-subspace with basis rows (exact sound test: an integer determinant
+    nonzero mod P is nonzero over Q; frames here are reductions of rational frames of the same dimension)."""
+    k = len(rows)
+    if k == 0:
+        return True
+    inv9 = pow(9, P - 2, P)
+    sums = [sum(s) % P for s in rows]
+    M = [[(sum(a * b for a, b in zip(rows[i], rows[j])) - inv9 * sums[i] * sums[j]) % P for j in range(k)] for i in range(k)]
+    return len(rref(M, k)) == k
+
+
+# ----------------------------------------------------------------------------- graph
+class BitGraph:
+    def __init__(self, p):
+        self.p, self.h = p, 2 * p
+        self.cubes = list(combinations(range(p), 3))
+        self.labels = [tuple(2 * i + b for i, b in zip(I, bits)) for I in self.cubes for bits in product(range(2), repeat=3)]
+        self.a = [None] * len(self.labels)
+        self.s = [1 << i for i in range(len(self.labels))]
+        self.intern = {}
+        self.source = {(I, bits): 8 * j + k for j, I in enumerate(self.cubes) for k, bits in enumerate(product(range(2), repeat=3))}
+        self.A, self.G = {}, {}
+        self.root, self.centers, self.mix = [], [], []
+
+    def add(self, a, b):
+        if a is None:
+            return b
+        if b is None:
+            return a
+        if a > b:
+            a, b = b, a
+        if (a, b) not in self.intern:
+            require(not self.s[a] & self.s[b], 'support-disjoint addition')
+            self.intern[a, b] = len(self.a)
+            self.a.append([a, b])
+            self.s.append(self.s[a] | self.s[b])
+        return self.intern[a, b]
+
+    def sum(self, xs):
+        xs = [x for x in xs if x is not None]
+        while len(xs) > 1:
+            xs = [self.add(xs[i], xs[i + 1]) if i + 1 < len(xs) else xs[i] for i in range(0, len(xs), 2)]
+        return xs[0] if xs else None
+
+    def module(self, data, inputs):
+        image = list(inputs)
+        n = data['input_count']
+        require(len(image) == n, 'module arity')
+        for pair in data['args'][n:]:
+            image.append(self.add(image[pair[0]], image[pair[1]]))
+        return [image[x] for x in data['roots']]
+
+    def local_channels(self):
+        for I in self.cubes:
+            src = lambda bits: self.source[I, tuple(bits)]
+            edges = {}
+            for ii, jj in combinations(range(3), 2):
+                kk = 3 - ii - jj
+                for a, b in product(range(2), repeat=2):
+                    b0 = [0] * 3
+                    b0[ii], b0[jj] = a, b
+                    b1 = b0[:]
+                    b1[kk] = 1
+                    edges[ii, jj, a, b] = self.add(src(b0), src(b1))
+                self.G[I, I[ii], I[jj], 0] = self.add(edges[ii, jj, 0, 0], edges[ii, jj, 1, 1])
+                self.G[I, I[ii], I[jj], 1] = self.add(edges[ii, jj, 0, 1], edges[ii, jj, 1, 0])
+            for ii in range(3):
+                jj = next(j for j in range(3) if j != ii)
+                for a in range(2):
+                    ids = [edges[(ii, jj, a, b) if ii < jj else (jj, ii, b, a)] for b in range(2)]
+                    self.A[I, I[ii], a] = self.add(*ids)
+
+    def local_l1(self):
+        """L1 local-channel association (eumemic, Claude assistance): the G sums listed in L1_DIAGONAL add the two
+        long diagonals of their cube face, the other G sums and the A sums add two edges; same supports as
+        local_channels, with the nodes created in channel order."""
+        for I in self.cubes:
+            def at(bits):
+                b = [0] * 3
+                for q, x in bits.items():
+                    b[q] = x
+                return self.source[I, tuple(b)]
+
+            def edge(d, fixed):
+                return self.add(at({**fixed, d: 0}), at({**fixed, d: 1}))
+            for j, k in combinations(range(3), 2):
+                r = 3 - j - k
+                for mode in range(2):
+                    if (j, k, mode) in L1_DIAGONAL:
+                        node = self.add(self.add(at({j: 0, k: mode, r: 0}), at({j: 1, k: 1 - mode, r: 1})),
+                                        self.add(at({j: 0, k: mode, r: 1}), at({j: 1, k: 1 - mode, r: 0})))
+                    else:
+                        node = self.add(edge(r, {j: 0, k: mode}), edge(r, {j: 1, k: 1 - mode}))
+                    self.G[I, I[j], I[k], mode] = node
+            for i in range(3):
+                j, k = [q for q in range(3) if q != i]
+                for a in range(2):
+                    self.A[I, I[i], a] = self.add(edge(k, {i: a, j: 0}), edge(k, {i: a, j: 1}))
+
+    def local_design(self, design):
+        """Design-driven local channels (agent-helpers search): every plane channel of every cube is built by the
+        recipe tree of `design` (a list of [plane key, tree] in creation order; a plane key is ['A', i, a] for the
+        sources with selector a at cube position i, or ['G', j, k, m] for the sources with s_j ^ s_k = m; a tree is a
+        3-bit selector (leaf) or a pair of trees).  Equal supports must have equal recipes (checked)."""
+        def members(key):
+            allb = list(product(range(2), repeat=3))
+            if key[0] == 'A':
+                return {b for b in allb if b[key[1]] == key[2]}
+            return {b for b in allb if b[key[1]] ^ b[key[2]] == key[3]}
+        for I in self.cubes:
+            def build(t):
+                if isinstance(t[0], int):
+                    return self.source[I, tuple(t)], {tuple(t)}
+                (a, sa), (b, sb) = build(t[0]), build(t[1])
+                require(not sa & sb, 'design support-disjoint')
+                return self.add(a, b), sa | sb
+            for key, tree in design:
+                node, sup = build(tree)
+                require(sup == members(key), 'design plane support')
+                if key[0] == 'A':
+                    self.A[I, I[key[1]], key[2]] = node
+                else:
+                    self.G[I, I[key[1]], I[key[2]], key[3]] = node
+
+    def finish(self, pair, allbut, merge=False, l1=False, design=None):
+        p = self.p
+        if design is not None:
+            self.local_design(design)
+        else:
+            self.local_l1() if l1 else self.local_channels()
+        Pm, Qm = {}, {}
+        cen = {}
+        for i in range(p):
+            pairs = list(combinations([a for a in range(p) if a != i], 2))
+            for bit in range(2):
+                outs = self.module(pair, [self.A[tuple(sorted((i, *K))), i, bit] for K in pairs])
+                for K, node in zip(pairs, outs):
+                    Pm[tuple(sorted((i, *K))), i, bit] = node
+                if len(outs) == len(pairs) + 1:
+                    # centre-sharing pair module (agent-helpers): the extra root sums all inputs = star(2i+bit)
+                    cen[2 * i + bit] = outs[-1]
+        for i, j in combinations(range(p), 2):
+            others = [a for a in range(p) if a not in (i, j)]
+            for mode in range(2):
+                for k, node in zip(others, self.module(allbut, [self.G[tuple(sorted((i, j, k))), i, j, mode] for k in others])):
+                    Qm[tuple(sorted((i, j, k))), i, j, mode] = node
+        allb = list(product(range(2), repeat=3))
+
+        def emit(I, bl, node, channel):
+            self.root.append(dict(node=node, targets=[self.source[I, b] for b in bl], kind='side', channel=channel))
+        for I in self.cubes:
+            for a in range(2):
+                emit(I, [b for b in allb if b[0] == a], Pm[I, I[0], a], 'face0')
+            for a in range(2):
+                for m12 in range(2):
+                    emit(I, [b for b in allb if b[0] == a and (b[1] ^ b[2]) == m12], Qm[I, I[1], I[2], 1 - m12], 'edge12')
+            if merge:
+                # variant u output merge (eumemic, Claude assistance): u(b0,b1) = face1 + edge01 and
+                # w(b0,b2) = face2 + edge02, each read by two single roots, replace the four single reads
+                u = {(b0, b1): self.add(Pm[I, I[1], b1], Qm[I, I[0], I[1], 1 - (b0 ^ b1)]) for b0 in range(2) for b1 in range(2)}
+                w = {(b0, b2): self.add(Pm[I, I[2], b2], Qm[I, I[0], I[2], 1 - (b0 ^ b2)]) for b0 in range(2) for b2 in range(2)}
+            for b in allb:
+                if merge:
+                    emit(I, [b], u[b[0], b[1]], 'u01')
+                    emit(I, [b], w[b[0], b[2]], 'w02')
+                else:
+                    emit(I, [b], Pm[I, I[1], b[1]], 'face1')
+                    emit(I, [b], Qm[I, I[0], I[1], 1 - (b[0] ^ b[1])], 'edge01')
+                    emit(I, [b], Pm[I, I[2], b[2]], 'face2')
+                    emit(I, [b], Qm[I, I[0], I[2], 1 - (b[0] ^ b[2])], 'edge02')
+                emit(I, [b], self.source[I, (b[0], 1 - b[1], 1 - b[2])], 'partner')
+            # partner-pair source mixing: in each parity class the pair with selector a on cube pair 0
+            # (carrier = smaller bits, passive = its partner) is delivered to the opposite pair of the class.
+            for par in range(2):
+                for a in range(2):
+                    pair_ = sorted(b for b in allb if sum(b) % 2 == par and b[0] == a)
+                    recv = sorted(b for b in allb if sum(b) % 2 == par and b[0] == 1 - a)
+                    self.mix.append(dict(carrier=self.source[I, pair_[0]], passive=self.source[I, pair_[1]],
+                                         receivers=[self.source[I, r] for r in recv]))
+        for i in range(p):
+            for e in range(2):
+                if 2 * i + e in cen:
+                    self.centers.append(cen[2 * i + e])
+                else:
+                    self.centers.append(self.sum(self.A[I, i, e] for I in self.cubes if i in I))
+        for coordinate, node in enumerate(self.centers):
+            self.root.append(dict(node=node, targets=[t for t, lab in enumerate(self.labels) if coordinate in lab],
+                                  kind='center', coordinate=coordinate))
+        return dict(p=p, h=self.h, v=len(self.labels), labels=[list(l) for l in self.labels], args=self.a,
+                    roots=self.root, partner_mix=self.mix)
+
+
+def check_decoder(g):
+    v, args = g['v'], g['args']
+    sup = [1 << i for i in range(v)] + [0] * (len(args) - v)
+    for x in range(v, len(args)):
+        a, b = args[x]
+        require(not sup[a] & sup[b], 'disjoint supports')
+        sup[x] = sup[a] | sup[b]
+    acc = [0] * v
+    for r in g['roots']:
+        for t in r['targets']:
+            acc[t] ^= sup[r['node']]
+    for mx in g['partner_mix']:
+        for t in mx['receivers']:
+            acc[t] ^= (1 << mx['carrier']) | (1 << mx['passive'])
+    return sum(acc[t] != 1 << t for t in range(v))
+
+
+# ----------------------------------------------------------------------------- matching
+def hopcroft_karp(adj, nleft, nright):
+    INF = 1 << 30
+    mL, mR = [-1] * nleft, [-1] * nright
+    while True:
+        dist = [INF] * nleft
+        dq = deque(u for u in range(nleft) if mL[u] < 0)
+        for u in dq:
+            dist[u] = 0
+        found = False
+        while dq:
+            u = dq.popleft()
+            for w in adj[u]:
+                m = mR[w]
+                if m < 0:
+                    found = True
+                elif dist[m] == INF:
+                    dist[m] = dist[u] + 1
+                    dq.append(m)
+        if not found:
+            return mL
+        it = [0] * nleft
+        for u0 in range(nleft):
+            if mL[u0] >= 0:
+                continue
+            stack = [u0]
+            while stack:
+                u = stack[-1]
+                if it[u] < len(adj[u]):
+                    w = adj[u][it[u]]
+                    it[u] += 1
+                    m = mR[w]
+                    if m < 0:
+                        ws = w
+                        for uu in reversed(stack):
+                            prev = mL[uu]
+                            mL[uu], mR[ws] = ws, uu
+                            ws = prev
+                        break
+                    if dist[m] == dist[u] + 1:
+                        stack.append(m)
+                else:
+                    dist[u] = INF
+                    stack.pop()
+
+
+# ----------------------------------------------------------------------------- compiler
+def compile_word(g, frozen=None, plain_k=PLAIN, log=lambda *a: None):
+    h, v = g['h'], g['v']
+    geo = Geometry(h, [tuple(l) for l in g['labels']])
+    args = [None] + [None if a is None else [x + 1 for x in a] for a in g['args']]  # node 0 reserved
+    roots = [dict(r, node=r['node'] + 1) for r in g['roots']]
+    n, q = len(args), len(roots)
+    sup = [0] * n
+    for i in range(v):
+        sup[i + 1] = 1 << i
+    spans = [0] * n
+    for i in range(v):
+        spans[i + 1] = geo.src[i]
+    for x in range(v + 1, n):
+        a, b = args[x]
+        spans[x] = geo.join(spans[a], spans[b])
+        sup[x] = sup[a] | sup[b]
+    rframe, rann, ell = [], [], 0
+    Y, targetH = [0] * v, Counter()
+    for r in roots:
+        x = r['node']
+        if r['kind'] == 'center':
+            U = spans[x]; A = geo.perp(U); ell += geo.dim(U)
+        else:
+            A = geo.join_many(geo.tcov[t] for t in r['targets']); U = geo.perp(A)
+            for t in r['targets']:
+                require(geo.contained(Y[t], U), 'target retreat')
+                targetH[geo.dim(U) - geo.dim(Y[t])] += 1
+                Y[t] = U
+        require(geo.contained(spans[x], U), 'root physical compatibility')
+        rframe.append(U); rann.append(A)
+    for t in range(v):
+        require(geo.contained(Y[t], geo.perp(geo.tcov[t])), 'target cap')
+        targetH[h - 1 - geo.dim(Y[t])] += 1
+    active, todo = set(range(1, v + 1)), [r['node'] for r in roots]
+    while todo:
+        x = todo.pop()
+        if x not in active:
+            active.add(x)
+            if args[x]:
+                todo.extend(args[x])
+    succ0, cons = [[] for _ in args], [[] for _ in args]
+    for x in sorted(active):
+        if args[x]:
+            for y in args[x]:
+                succ0[y].append(x)
+    for j, r in enumerate(roots):
+        cons[r['node']].append(rann[j])
+    preann, initial = [0] * n, [0] * n
+    for x in sorted(active, reverse=True):
+        preann[x] = geo.join_many(cons[x] + [preann[y] for y in succ0[x]])
+        cover = 0
+        s = sup[x]
+        while s:
+            b = s & -s; s ^= b
+            for j in g['labels'][b.bit_length() - 1]:
+                cover |= 1 << j
+        initial[x] = geo.join_many([preann[x]] + [geo.coord[j] for j in range(h) if not cover >> j & 1])
+    order = sorted(active, key=lambda x: (h - geo.dim(initial[x]), x))
+    position = {x: i for i, x in enumerate(order)}
+    uses, usevalue, usetarget, useann, usecode = [[] for _ in args], [], [], [], []
+    for x in order:
+        if args[x]:
+            for j, y in enumerate(args[x]):
+                uses[y].append(len(usevalue)); usevalue.append(y); usetarget.append(x); useann.append(initial[x]); usecode.append(['op', x - 1, j])
+    for j, r in enumerate(roots):
+        x = r['node']
+        uses[x].append(len(usevalue)); usevalue.append(x); usetarget.append(n + j); useann.append(rann[j]); usecode.append(['root', j])
+    donors = [x for x in order if args[x]]
+    code_index = {tuple(c): u for u, c in enumerate(usecode)}
+    if frozen is not None:
+        arcs = {d + 1: code_index[tuple(c)] for d, c in frozen}
+    else:
+        dindex = {x: i for i, x in enumerate(donors)}
+        adj = [[] for _ in donors]
+        for x in donors:
+            for y in args[x]:
+                for u in uses[y]:
+                    t = usetarget[u]
+                    if t == x or (t < n and position[t] <= position[x]):
+                        continue
+                    if geo.contained(useann[u], initial[x]):
+                        adj[dindex[x]].append(u)
+        mL = hopcroft_karp(adj, len(donors), len(usevalue))
+        arcs = {donors[i]: u for i, u in enumerate(mL) if u >= 0}
+    for x, u in arcs.items():
+        t = usetarget[u]
+        require(usevalue[u] in args[x] and (t >= n or position[t] > position[x]), 'arc order')
+        require(geo.contained(useann[u], initial[x]), 'arc frame')
+    succ, direct = [[] for _ in args], [[] for _ in args]
+    for x in order:
+        if args[x]:
+            for y in args[x]:
+                succ[y].append(x)
+    for j, r in enumerate(roots):
+        direct[r['node']].append(rann[j])
+    for x, u in arcs.items():
+        t = usetarget[u]
+        (succ[x].append(t) if t < n else direct[x].append(rann[t - n]))
+    ann, rank = [0] * n, [0] * n
+    for x in reversed(order):
+        ann[x] = geo.join_many(direct[x] + [ann[y] for y in succ[x]])
+        rank[x] = h - geo.dim(ann[x])
+        require(geo.contained(ann[x], geo.perp(spans[x])), 'span inside frame')
+    # plain frames span(n): leaves and small additions, closed under operands; a linked donor must be plain and
+    # its span must lie in the plain target's span
+    cand = set(x for x in active if not args[x])
+    for x in sorted(active):
+        if args[x] and geo.dim(spans[x]) <= plain_k and all(y in cand for y in args[x]):
+            cand.add(x)
+    arcin, users = defaultdict(list), defaultdict(list)
+    for x, u in arcs.items():
+        if usetarget[u] < n:
+            arcin[usetarget[u]].append(x)
+    for x in active:
+        if args[x]:
+            for y in args[x]:
+                users[y].append(x)
+    changed = True
+    while changed:
+        changed = False
+        for t in sorted(cand):
+            if t in cand and any(x not in cand or not geo.contained(spans[x], spans[t]) for x in arcin[t]):
+                cand.discard(t); changed = True
+                st = [t]
+                while st:
+                    z = st.pop()
+                    for w in users[z]:
+                        if w in cand:
+                            cand.discard(w); st.append(w)
+    plain = sorted(cand)
+    for x in plain:
+        ann[x] = geo.perp(spans[x]); rank[x] = h - geo.dim(ann[x])
+    H = Counter()
+    for x in order:
+        r, deg = rank[x], len(uses[x])
+        require(deg > 0, 'unused node')
+        H[r] += deg - 1
+        if args[x]:
+            H[h - r] += 1
+            for y in args[x]:
+                require(geo.contained(ann[x], ann[y]), 'operand nesting')
+                H[r - rank[y]] += 1
+        else:
+            H[1] += 1; H[r - 1] += 1
+    for j, root in enumerate(roots):
+        x = root['node']; r = rank[x]; rt = geo.dim(rframe[j])
+        require(r <= rt, 'root climb')
+        if root['kind'] == 'center':
+            require(r == rt, 'centre frame')
+            H[r] += 1; H[h - r] += 1
+        else:
+            H[rt - r] += 1; H[h - rt] += 1
+    for x, u in arcs.items():
+        val, t = usevalue[u], usetarget[u]
+        rv, rd = rank[val], rank[x]
+        rt = rank[t] if t < n else geo.dim(rframe[t - n])
+        require(rt >= rd >= rv, 'arc ranks')
+        H[h - rd] -= 1; H[rv] -= 1; H[rt - rv] -= 1; H[rt - rd] += 1
+    require(min(H.values()) >= 0, 'nonnegative ledger')
+    R = len(donors) + q - len(arcs)
+    require(sum(r * c for r, c in H.items()) == h * R + ell, 'mass identity')
+    prof = dict(h=h, v=v, R=R, q=q, c=len(donors), matched=len(arcs), loss=ell, plain=len(plain))
+    wit = dict(geo=geo, args=args, roots=roots, n=n, order=order, arcs=arcs, ann=ann, rank=rank, uses=uses,
+               usevalue=usevalue, usetarget=usetarget, usecode=usecode, rframe=rframe, rann=rann, spans=spans,
+               plain=plain, H=H, targetH=targetH)
+    return prof, wit
+
+
+def nondeg_id(geo, f, cache):
+    if f not in cache:
+        cache[f] = gram_nondegenerate_frame(list(geo.T.rows[f]), geo.h)
+    return cache[f]
+
+
+def select_gauges(g, prof, wit, trial_a=0.00065):
+    """PR #144 gauges.select, exactly, plus the bit G-nondegeneracy filter on sigma."""
+    geo = wit['geo']; h, v = prof['h'], prof['v']
+    args, roots, n, order, ann, arcs = wit['args'], wit['roots'], wit['n'], wit['order'], wit['ann'], wit['arcs']
+    usevalue, usetarget = wit['usevalue'], wit['usetarget']
+    incoming = set(arcs.values())
+    uses, opuse, rootuse = [[] for _ in args], {}, {}
+    for u, (val, t) in enumerate(zip(usevalue, usetarget)):
+        uses[val].append(u)
+        if t < n:
+            opuse[t, 0 if args[t][0] == val else 1] = u
+        else:
+            rootuse[t - n] = u
+    assign, sources, ops, R = {}, {}, [], 0
+    for x in order:
+        if args[x]:
+            aa, bb = args[x]
+            dest, control = assign[opuse[x, 0]], assign[opuse[x, 1]]
+            if x in arcs:
+                u = arcs[x]
+                if usevalue[u] == aa:
+                    dest, control = control, dest
+                require(u not in assign, 'arc use assigned once')
+                assign[u] = control
+            ops.append((dest, control, x))
+        else:
+            dest = R; R += 1; sources[x] = dest
+        free = [u for u in uses[x] if u not in incoming]
+        require(free, 'free use')
+        for j, u in enumerate(free):
+            if j == 0:
+                assign[u] = dest
+            else:
+                t = R; R += 1; assign[u] = t; ops.append((t, dest, x))
+    require(R == prof['R'], 'role count')
+    rootroles = [assign[rootuse[j]] for j in range(len(roots))]
+    prev, pred, first = [-1] * R, [], [None] * R
+    for i, (a, b, x) in enumerate(ops):
+        pred.append((prev[a], prev[b])); prev[a] = prev[b] = i
+        if first[a] is None:
+            first[a] = x
+        if first[b] is None:
+            first[b] = x
+    stack = [prev[s] for r, s in zip(roots, rootroles) if r['kind'] == 'center' and prev[s] >= 0]
+    phase = set()
+    while stack:
+        i = stack.pop()
+        if i not in phase:
+            phase.add(i); stack.extend(j for j in pred[i] if j >= 0)
+    touched = set(sources.values())
+    for i in phase:
+        touched.update(ops[i][:2])
+    co = [0] * R
+    for r, s in zip(roots, rootroles):
+        co[s] |= sum(1 << t for t in r['targets'])
+    for a, b, x in reversed(ops):
+        co[b] |= co[a]
+    limit = [None] * v
+    for r in roots:
+        if r['kind'] != 'center':
+            A = geo.join_many(geo.tcov[t] for t in r['targets'])
+            for t in r['targets']:
+                if limit[t] is None:
+                    limit[t] = A
+    for t in range(v):
+        if limit[t] is None:
+            limit[t] = geo.tcov[t]
+    H = Counter(wit['H'])
+    gauges, selected, cache = Counter(), [], {}
+    cands = sorted((s for s in range(R) if s not in touched and first[s] is not None),
+                   key=lambda s: (geo.dim(ann[first[s]]), bin(co[s]).count('1'), s))
+
+    def excess(t):
+        return t * math.expm1(trial_a * math.log(3 * h / t)) if t else 0.
+    for s in cands:
+        A, targets, bits = ann[first[s]], [], co[s]
+        while bits:
+            low = bits & -bits; t = low.bit_length() - 1; bits ^= low; targets.append(t)
+            A = geo.join(A, limit[t])
+            if geo.dim(A) == h:
+                break
+        if geo.dim(A) == h:
+            continue
+        r, d = h - geo.dim(ann[first[s]]), h - geo.dim(A)
+        delta = 3 * (excess(r - d) - excess(r)) + excess(3 * d)
+        delta += 3 * math.fsum(excess(d) + excess(h - geo.dim(limit[t]) - d) - excess(h - geo.dim(limit[t])) for t in targets)
+        if delta >= -1e-12 or not nondeg_id(geo, geo.perp(A), cache):
+            continue
+        H[r] -= 1; H[r - d] += 1; gauges[d] += 1
+        require(H[r] >= 0, 'gauge ledger')
+        for t in targets:
+            limit[t] = A
+        selected.append(dict(role=s, first=first[s] - 1, targets=targets, dim=d, ann=A))
+    Yh, cur = Counter(), [0] * v
+    for z in reversed(selected):
+        U = geo.perp(z['ann'])
+        for t in z['targets']:
+            require(geo.contained(cur[t], U), 'gauge target chain')
+            Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U
+    for r in roots:
+        if r['kind'] != 'center':
+            U = geo.perp(geo.join_many(geo.tcov[t] for t in r['targets']))
+            for t in r['targets']:
+                require(geo.contained(cur[t], U), 'side target chain')
+                Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U
+    for t in range(v):
+        Yh[h - 1 - geo.dim(cur[t])] += 1
+    word = dict(ops=[[a, b, x - 1] for a, b, x in ops], sources={str(x - 1): s for x, s in sources.items()},
+                rootroles=rootroles, phase1=sorted(phase), gauges=[{k: z[k] for k in ('role', 'first', 'targets', 'dim')} for z in selected],
+                _gauge_ann=[z['ann'] for z in selected])
+    return gauges, H, Yh, word
+
+
+def profile(prof, gauges, H, Y):
+    h, v, R, ell = prof['h'], prof['v'], prof['R'], prof['loss']
+    m, W = 3 * h, 2 * v + R
+    source = Counter({1: v, h - 4: v // 2, 2: v // 2, h - 2: v // 2})
+    C = Counter()
+    for part in (H, source, Y):
+        for r, c in part.items():
+            if r and c:
+                C[r] += 3 * c
+    for d, c in gauges.items():
+        C[3 * d] += c
+    C[2] += 2 * v
+    mass = sum(r * c for r, c in C.items())
+    require(W * m - mass == 2 * v - 3 * ell, 'shared-core telescoping deficit')
+    srt = lambda c: {str(k): c[k] for k in sorted(c) if c[k]}
+    return dict(h=h, v=v, R=R, c=prof['c'], q=prof['q'], matched=prof['matched'], loss=ell, plain_frames=prof['plain'],
+                m=m, W_per_vertex=W, rank_per_vertex=mass, deficit_per_vertex=W * m - mass,
+                selected_roles=sum(gauges.values()), selected_rank_histogram=srt(gauges),
+                remaining_internal_histogram=srt(H), source_data_histogram=srt(source), target_data_histogram=srt(Y),
+                child_histogram=srt(C), maxchild=max(C))
+
+
+def float_root(child, W, m):
+    items = [(int(t), c) for t, c in child.items()]
+    lo, hi = 0., .1
+    for _ in range(80):
+        a = (lo + hi) / 2
+        if math.fsum(c * (t / m) ** (1 - a) for t, c in items) < W:
+            lo = a
+        else:
+            hi = a
+    return lo
+
+
+def ratrec(r):
+    """Rational reconstruction a/b of a residue mod P with |a|, b < sqrt(P/2)."""
+    r %= P
+    if r == 0:
+        return 0, 1
+    bound = math.isqrt(P // 2)
+    r0, r1, s0, s1 = P, r, 0, 1
+    while r1 > bound:
+        qq = r0 // r1
+        r0, r1 = r1, r0 - qq * r1
+        s0, s1 = s1, s0 - qq * s1
+    require(abs(s1) <= bound and s1 != 0, 'rational reconstruction')
+    a, b = (r1, s1) if s1 > 0 else (-r1, -s1)
+    require((a - r * b) % P == 0, 'reconstruction residue')
+    return a, b
+
+
+def primitive(row):
+    from fractions import Fraction
+    fr = [Fraction(*ratrec(x)) for x in row]
+    den = 1
+    for f in fr:
+        den = den * f.denominator // math.gcd(den, f.denominator)
+    ints = [int(f * den) for f in fr]
+    gg = 0
+    for x in ints:
+        gg = math.gcd(gg, abs(x))
+    ints = [x // gg for x in ints] if gg else ints
+    first = next((x for x in ints if x), 1)
+    return [-x for x in ints] if first < 0 else ints
+
+
+def frame_record(geo, ann_id):
+    """Exact integer description of the frame perp(ann): 'a' = integer annihilator rows (frame = common kernel)
+    when codim <= dim, else 'b' = integer basis rows. Both are primitive rows of the rational RREF."""
+    h = geo.h
+    A = geo.T.rows[ann_id]
+    codim = len(A)
+    if codim <= h - codim:
+        rows = [primitive(r) for r in A]
+        return dict(dim=h - codim, a=rows)
+    B = geo.T.rows[geo.perp(ann_id)]
+    return dict(dim=h - codim, b=[primitive(r) for r in B])
+
+
+def dumps(obj):
+    return json.dumps(obj, sort_keys=True, separators=(',', ':')) + '\n'
+
+
+def build(p, frozen_arcs=None, log=print):
+    mod = json.loads((HERE / 'data' / MODULES[p]).read_text())
+    abo = pinned_all_but_one(QMODULES[p], p - 2) if p in QMODULES else all_but_one(p - 2)
+    dpath = HERE / 'data' / ('local_design_p%d.json' % p)
+    design = json.loads(dpath.read_text())['design'] if dpath.exists() else None
+    g = BitGraph(p).finish(mod, abo, merge=p == 12, l1=p == 12, design=design)
+    require(check_decoder(g) == 0, 'mod-2 decoder identity')
+    t0 = time.time()
+    prof, wit = compile_word(g, frozen=frozen_arcs)
+    log('compiled p=%d in %.1fs: R=%d arcs=%d plain=%d' % (p, time.time() - t0, prof['R'], prof['matched'], prof['plain']))
+    gauges, H, Y, word = select_gauges(g, prof, wit)
+    prf = profile(prof, gauges, H, Y)
+    arcs = sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items())
+    cache = {}
+    geo = wit['geo']
+    deg = sum(1 for x in wit['order'] if not nondeg_id(geo, geo.perp(wit['ann'][x]), cache))
+    deg += sum(1 for U in wit['rframe'] if not nondeg_id(geo, U, cache))
+    require(deg == 0, 'G-nondegenerate node and root frames')
+    out = dict(graph=dict(p=p, h=g['h'], v=g['v'], labels=g['labels'], args=g['args'], roots=g['roots'],
+                          partner_mix=g['partner_mix'], pair_module_sha256=hashlib.sha256((HERE / 'data' / MODULES[p]).read_bytes()).hexdigest()),
+               compile=dict(plain_threshold=PLAIN, order=[x - 1 for x in wit['order']], plain=[x - 1 for x in wit['plain']], arcs=arcs),
+               word={k: v for k, v in word.items() if not k.startswith('_')})
+    exp = export(p, g, prof, wit, word, prf)
+    return out, prf, arcs, exp
+
+
+def export(p, g, prof, wit, word, prf):
+    """Plain-JSON gate files: graph, word (selection.json shape), exact frames, partial-K chronology."""
+    geo, h, v = wit['geo'], g['h'], g['v']
+    n, roots = wit['n'], wit['roots']
+    ann = wit['ann']
+    frames = {}
+
+    def fid(a):
+        if a not in frames:
+            frames[a] = None
+        return a
+    node_frame = {str(x - 1): fid(ann[x]) for x in wit['order']}
+    root_frame = [fid(a) for a in wit['rann']]
+    gauges = []
+    for z, A in zip(word['gauges'], word['_gauge_ann']):
+        gauges.append(dict(z, frame=fid(A)))
+    lab = g['labels']
+    src_ann = [fid(geo.perp(geo.src[i])) for i in range(v)]
+    full = fid(0)
+    level2 = {}
+    for j, r in enumerate(g['roots']):
+        if r['kind'] == 'side' and len(r['targets']) == 2:
+            level2[tuple(sorted(r['targets']))] = j
+    kchron = []
+    for mx in g['partner_mix']:
+        c, d = mx['carrier'], mx['passive']
+        mixf = fid(geo.perp(geo.join(geo.src[c], geo.src[d])))
+        j = level2[tuple(sorted(mx['receivers']))]
+        capf = root_frame[j]
+        require(geo.contained(capf, mixf), 'mix frame inside receivers cap')
+        kchron.append(dict(carrier=c, passive=d, receivers=mx['receivers'], mix_frame=mixf, deliver_frame=capf,
+                           deliver_after_root=j, undo_frame=full,
+                           carrier_chain=[src_ann[c], mixf, capf, full], passive_chain=[src_ann[d], mixf, full],
+                           carrier_ranks=[1, h - 4, 2], passive_ranks=[1, h - 2]))
+    table = {str(a): frame_record(geo, a) for a in sorted(frames)}
+    conv = dict(target_covector='3*chi_T - 1 (target cap = {u : (3 chi_T - 1).u = 0} = H0-orthogonal complement of chi_T)',
+                gram='G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested for G',
+                frame_ids='frame id = id of the canonical annihilator; record "a" lists integer annihilator rows (frame ='
+                          ' common kernel), record "b" lists integer basis rows; id 0 (empty "a") is the full space Q^h',
+                ops='[dest, control, node]: dest ^= control at the frame of node (copies: dest is the fresh role)',
+                nodes='zero-based graph nodes; nodes < v are the source leaves (port index)')
+    graph = dict(p=p, h=h, v=v, labels=g['labels'], args=g['args'],
+                 roots=[dict(r, coefficient=1) for r in g['roots']], partner_mix=g['partner_mix'],
+                 decoder='mod 2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T;'
+                         ' side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T;'
+                         ' equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} x_S')
+    wordj = dict(ops=word['ops'], sources=word['sources'], rootroles=word['rootroles'], phase1=word['phase1'],
+                 gauges=gauges, order=[x - 1 for x in wit['order']], arcs=sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items()),
+                 plain=[x - 1 for x in wit['plain']], node_frame=node_frame, root_frame=root_frame,
+                 source_frame=src_ann, full_frame=full, conventions=conv,
+                 schedule='old-value reads of non-gauged roles (frame 0); V injections at <chi_S>; ops in order (phase1 ops'
+                          ' are those listed); centre copies read at 0; gauged old-value reads at their gauge frames'
+                          ' (ascending per target); side root reads in root order; partial-K deliveries right after'
+                          ' root deliver_after_root; undo at full frame; inverse ops; V removal')
+    return dict(graph=graph, word=wordj, frames=dict(h=h, P_used_for_ranks='2^127-1', conventions=conv, frames=table),
+                kchron=dict(h=h, entries=kchron, conventions=conv))
+
+
+def nested_prefix(n):
+    """Nested-prefix all-but-one module (QMOD lane; eumemic, Claude assistance): prefix p_{k+1} = p_k + x_k, suffix
+    s_k = x_k + s_{k+1}; y_0 = s_1, y_{n-1} = p_{n-1}, y_{i+1} = p_i + (x_i + s_{i+2}). Each prefix is used twice with
+    nested supports, which gives the carrier matching more links than the balanced tree. Contract-checked. It is the
+    seed of the pinned p = 12 module data/qmod_p12.json."""
+    args = [None] * n
+
+    def add(a, b):
+        args.append([a, b])
+        return len(args) - 1
+    pre = {1: 0}
+    for k in range(1, n - 1):
+        pre[k + 1] = add(pre[k], k)
+    suf = {n - 1: n - 1}
+    for k in range(n - 2, 0, -1):
+        suf[k] = add(k, suf[k + 1])
+    roots = [None] * n
+    roots[0], roots[n - 1] = suf[1], pre[n - 1]
+    roots[1] = add(0, suf[2])
+    for i in range(1, n - 2):
+        roots[i + 1] = add(pre[i], add(i, suf[i + 2]))
+    support = []
+    for x, a in enumerate(args):
+        if a is None:
+            support.append(1 << x)
+        else:
+            require(0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'nested prefix disjoint')
+            support.append(support[a[0]] | support[a[1]])
+    full = (1 << n) - 1
+    require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'nested prefix all-but-one roots')
+    return dict(input_count=n, args=args, roots=roots)
+
+
+def pinned_all_but_one(name, n):
+    """Pinned all-but-one module {input_count, args, roots} in data/ (eumemic, Claude assistance). The p = 12
+    module was annealed from nested_prefix(10) by split-function moves, scored by the p = 12 bit word.
+    Contract-checked: disjoint supports, root i sums every input but i."""
+    mod = json.loads((HERE / 'data' / name).read_text())
+    args, roots = mod['args'], mod['roots']
+    require(mod['input_count'] == n == len(roots) and args[:n] == [None] * n, 'pinned all-but-one arity')
+    support = [1 << x for x in range(n)]
+    for x, a in enumerate(args[n:], n):
+        require(a and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'pinned all-but-one disjoint')
+        support.append(support[a[0]] | support[a[1]])
+    full = (1 << n) - 1
+    require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'pinned all-but-one roots')
+    return dict(input_count=n, args=args, roots=roots)
+
+
+def all_but_one(n):
+    """PR #144 modules.all_but_one (balanced binary tree upward sums and complementary downward sums)."""
+    args, support = [None] * n, [1 << i for i in range(n)]
+    by = {s: i for i, s in enumerate(support)}
+
+    def add(a, b):
+        if a is None:
+            return b
+        if b is None:
+            return a
+        s = support[a] | support[b]
+        if s not in by:
+            by[s] = len(args); args.append([a, b]); support.append(s)
+        return by[s]
+
+    def tree(lo, hi):
+        if hi - lo == 1:
+            return (lo, None, None)
+        mid = (lo + hi) // 2
+        L, Rr = tree(lo, mid), tree(mid, hi)
+        return (add(L[0], Rr[0]), L, Rr)
+    roots = [None] * n
+
+    def walk(t, outside):
+        x, L, Rr = t
+        if L is None:
+            roots[x] = outside
+            return
+        walk(L, add(outside, Rr[0])); walk(Rr, add(outside, L[0]))
+    walk(tree(0, n), None)
+    active, stack = set(range(n)), list(roots)
+    while stack:
+        x = stack.pop()
+        if x not in active:
+            active.add(x)
+            if args[x] is not None:
+                stack.extend(args[x])
+    ids = sorted(active); ren = {x: i for i, x in enumerate(ids)}
+    return dict(input_count=n, args=[None if args[x] is None else [ren[y] for y in args[x]] for x in ids], roots=[ren[x] for x in roots])
+
+
+def main():
+    require(not sys.flags.optimize, 'run without -O')
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--p', type=int, default=12)
+    ap.add_argument('--out', type=Path, default=HERE / 'out')
+    ap.add_argument('--check', action='store_true', help='regenerate from frozen arcs and compare byte-identically')
+    ap.add_argument('--solve-matching', action='store_true', help='recompute the carrier matching (Hopcroft-Karp)')
+    a = ap.parse_args()
+    a.out.mkdir(parents=True, exist_ok=True)
+    arcs_path = HERE / 'data' / ('arcs_p%d.json' % a.p)
+    frozen = None if a.solve_matching or not arcs_path.exists() else json.loads(arcs_path.read_text())
+    out, prf, arcs, exp = build(a.p, frozen)
+    root = float_root(prf['child_histogram'], prf['W_per_vertex'], prf['m'])
+    word_bytes = gzip.compress(dumps(out).encode(), mtime=0)
+    prof_bytes = dumps(prf).encode()
+    names = {'word_p%d.json.gz' % a.p: word_bytes, 'profile_p%d.json' % a.p: prof_bytes}
+    for k, obj in exp.items():
+        names['%s_p%d.json' % (k, a.p)] = dumps(obj).encode()
+    if a.check:
+        for name, data in names.items():
+            old = (a.out / name).read_bytes()
+            if name.endswith('.gz'):  # gzip bytes depend on the zlib build; compare the compressed content
+                old, data = gzip.decompress(old), gzip.decompress(data)
+            require(old == data, 'byte-identical regeneration of ' + name)
+        require(frozen is not None, 'frozen arcs present')
+        print('PASS p=%d: word and profile regenerate byte-identically (sha256 %s, %s)' % (
+            a.p, hashlib.sha256(word_bytes).hexdigest()[:16], hashlib.sha256(prof_bytes).hexdigest()[:16]))
+    else:
+        for name, data in names.items():
+            (a.out / name).write_bytes(data)
+        if frozen is None:
+            arcs_path.write_text(dumps(arcs))
+        print('wrote p=%d: R=%d R/v=%.3f loss=%d deficit=%d W=%d gauges=%d float a_b=%.7e' % (
+            a.p, prf['R'], prf['R'] / prf['v'], prf['loss'], prf['deficit_per_vertex'], prf['W_per_vertex'],
+            prf['selected_roles'], root))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/regenerate.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/regenerate.py
new file mode 100644
index 0000000000..aacaae266f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/producer/regenerate.py
@@ -0,0 +1,38 @@
+#!/usr/bin/env python3
+"""Rebuild gen4bit/selected/bit from the generator and the two physical-layer producers, and compare.
+
+    python3 -B gen4bit/producer/regenerate.py --work /new/scratch/dir      (about 2 minutes)
+
+1. paired_cube_bit_word.py --p 12 (frozen arcs data/arcs_p12.json) writes the virtual word;
+2. make_physical.py adds the compensated reuse pairs and late recipient reads;
+3. descent.py moves operation frames (PR200 physical-layer rules) and writes the physical word.
+The five pinned files must be reproduced exactly (gzip members compared after decompression).
+This is provenance only: verify.py admits the pinned files themselves and never runs a producer.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import argparse, gzip, shutil, subprocess, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+BIT = HERE.parent
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__); ap.add_argument('--work', type=Path, required=True)
+    a = ap.parse_args(); work = a.work.resolve(); assert not work.exists(), 'work dir must be new'
+    raw, phys, pkg, final = work/'raw', work/'phys', work/'pkg', work/'final'
+    py = [sys.executable, '-B']
+    subprocess.run(py + [str(HERE/'paired_cube_bit_word.py'), '--p', '12', '--out', str(raw)], check=True)
+    subprocess.run(py + [str(HERE/'make_physical.py'), '--src', str(raw), '--out', str(phys)], check=True)
+    (pkg/'selected').mkdir(parents=True)
+    shutil.copytree(BIT/'bit', pkg/'bit'); shutil.copytree(BIT/'references', pkg/'references')
+    shutil.copytree(phys, pkg/'selected/bit')
+    subprocess.run(py + [str(HERE/'descent.py'), str(pkg), str(final)], check=True)
+    pinned = BIT/'selected/bit'
+    for name in ('graph_p12.json', 'kchron_p12.json', 'profile_p12.json'):
+        assert (final/name).read_bytes() == (pinned/name).read_bytes(), name
+    for name in ('word_p12.json.gz', 'frames_p12.json.gz'):
+        assert gzip.decompress((final/name).read_bytes()) == gzip.decompress((pinned/name).read_bytes()), name
+    print('PASS gen4 regeneration: all five pinned bit-word files reproduced exactly')
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/references/pr168-v4/SOURCE.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/references/pr168-v4/SOURCE.json
new file mode 100644
index 0000000000..c57edcae25
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/references/pr168-v4/SOURCE.json
@@ -0,0 +1,20 @@
+{
+  "commit": "4a3c769e5c5430e7114c4d3e099ff34664677f17",
+  "files": {
+    "certificates/paired-cube-network.json": "05b253a21dc526b6039f56d1068162a19a8a4f29291ad94eb892656b88e9142d",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "research/paired-cube-bit/check_paired_cube_bit.py": "4d7c86cd999a1519e0dfb6dcf33a8f26e442a353c3665a0f06881216a260fbf3",
+    "scripts/certify.py": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e",
+    "scripts/paired_cube/__init__.py": "b5fb17c79fd41a75c0648e7a5f99076f9f42a619857d5e34e71699bf00ef0c91",
+    "scripts/paired_cube/closure.py": "e4b3086f4b5663297fe06f4646e1349f10d8647997989f17eef6ec4e84aec693",
+    "scripts/paired_cube/frames.py": "7d897418dbfee47de0723ea4983098a982610ccba45e1bac9000a79626d8421c",
+    "scripts/paired_cube/gauges.py": "8a501c66e1330f054e0e11a35e9321d2deea7b51cd03ca56b6a41765e43fe061",
+    "scripts/paired_cube/graph.py": "d10478ba509c7d8abcefcaaf7c5e0b580b9cd9cbe7777b3e49b2fe24620985c8",
+    "scripts/paired_cube/modules.py": "6c134f3d24c6cd9aca03763050aaf600005c126c09b35ac0ff5f040e0e29db87",
+    "scripts/paired_cube/verify.py": "b1eb42a91381ae031d97879f7c43e6c00fc4787e132ed60eb3e124994bdb7d35",
+    "scripts/paired_cube_physical.py": "9c9ea1ea29e551ab6116d7c8ca09f4703ff9e2fa102032d5055327fde07ba319"
+  },
+  "pr": 168,
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "scope": "Byte-identical copies of the PR168 v4 files this package executes or pins (compiler frames/closure/gauges/graph/modules, physical checkers, package bit checker, parent certificate, frame theorem note), so the package is self-contained on main."
+}
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py
new file mode 100644
index 0000000000..69d535a6c2
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py
@@ -0,0 +1,465 @@
+#!/usr/bin/env python3
+"""Standalone checker for subset-port bit words with broadcast roots (paired-cube bit word with partner-pair
+source mixing).  Standard library only; independent of the generator (own exact integer linear algebra, own
+register simulation).  Refuses to run under python -O.
+
+Inputs (plain JSON written by paired_cube_bit_word.py): graph_pP.json, word_pP.json, frames_pP.json,
+kchron_pP.json, profile_pP.json.  Checks:
+  1. exact frames: every frame record (integer annihilator rows 'a' or integer basis rows 'b') is completed to
+     the other representation by exact integer elimination; A.B^T = 0 exactly and rank A + rank B = h;
+  2. the mod-2 decoder: supports of all additions are disjoint; for every target the deliveries (star roots,
+     side roots, partner singles, partner-pair sums) XOR to {T}; stars read are exactly the c in T and the
+     side part is exactly sum_{|S cap T|=1} x_S;
+  3. geometry: source frames are the lines <chi_S>; side root frames lie in every receiver's cap
+     ker(3 chi_T - 1) and equal the common cap of the group; centre frames are the star spans; the frame of
+     every addition contains its operands' frames; every root node's frame lies in its root frame;
+  4. every role chain (start -> each op frame -> root frame -> full) is nested, including gauged starts
+     (sigma inside the first op frame, gauged roles untouched in phase one); every target chain (gauge reads
+     ascending, side root caps in root order, partner-pair delivery at the level-2 cap, final cap) is nested;
+     the partner-pair chronology: mix frame span{chi_c,chi_d} with H0-Gram I_2, contained in the receivers'
+     level-2 cap, carrier chain [<chi_c>, mix, cap, full] and passive chain [<chi_d>, mix, full] nested;
+  5. G = I - J/9 nondegenerate on every frame used (exact integer determinant test);
+  6. literal F2 replay with arbitrary dirty scratch: y = y0 + x, scratch and sources restored;
+  7. independent ledger recount from the role chains equals the saved child histogram (PR #144 bit ledger);
+  8. mutation controls (must all be REJECTED): broken partner mix, delivery outside the shared cap (full
+     frame), delivery below the level (face cap without span{chi_c,chi_d}), dropped star, non-nested role chain.
+Usage: python3 check_paired_cube_bit.py --dir out --p 12
+"""
+import argparse, json, random, sys
+from collections import Counter, defaultdict
+from math import gcd
+from operator import mul
+from pathlib import Path
+
+if sys.flags.optimize:
+    raise SystemExit('refusing to run under python -O: assertions are part of the check')
+
+
+class Fail(Exception):
+    pass
+
+
+def need(cond, msg):
+    if not cond:
+        raise Fail(msg)
+
+
+# ------------------------------------------------------------------ exact integer linear algebra
+def prim(v):
+    g = 0
+    for x in v:
+        g = gcd(g, abs(x))
+    if g > 1:
+        v = [x // g for x in v]
+    f = next((x for x in v if x), 0)
+    return tuple(-x for x in v) if f < 0 else tuple(v)
+
+
+def reduce_rows(rows, h):
+    """Integer reduced echelon form: returns (rows, pivot columns); each pivot column is zero outside its row."""
+    rows = [list(r) for r in rows]
+    out, pivs = [], []
+    for r in rows:
+        for pr, pc in zip(out, pivs):
+            if r[pc]:
+                a, b = pr[pc], r[pc]
+                r = [x * a - y * b for x, y in zip(r, pr)]
+        r = list(prim(r))
+        c = next((j for j in range(h) if r[j]), None)
+        if c is None:
+            continue
+        for i, (pr, pc) in enumerate(zip(out, pivs)):
+            if pr[c]:
+                a, b = r[c], pr[c]
+                out[i] = list(prim([x * a - y * b for x, y in zip(pr, r)]))
+        out.append(r); pivs.append(c)
+    return out, pivs
+
+
+def kernel(rows, h):
+    red, pivs = reduce_rows(rows, h)
+    ps = set(pivs)
+    basis = []
+    for f in range(h):
+        if f in ps:
+            continue
+        D = 1
+        for r, c in zip(red, pivs):
+            if r[f]:
+                D = D * abs(r[c]) // gcd(D, abs(r[c]))
+        v = [0] * h
+        v[f] = D
+        for r, c in zip(red, pivs):
+            if r[f]:
+                v[c] = -r[f] * D // r[c]
+        basis.append(prim(v))
+    return basis, len(red)
+
+
+def rank(rows, h):
+    return len(reduce_rows(rows, h)[0])
+
+
+def dot(a, b):
+    return sum(map(mul, a, b))
+
+
+# ------------------------------------------------------------------ checker
+class Checker:
+    def __init__(self, d, p, mutate=None):
+        self.mut = mutate
+        rd = lambda name: json.loads((d / ('%s_p%d.json' % (name, p))).read_text())
+        self.g, self.w, self.fr, self.k, self.prof = rd('graph'), rd('word'), rd('frames'), rd('kchron'), rd('profile')
+        self.h, self.v = self.g['h'], self.g['v']
+        if mutate == 'dropped_star':
+            j = next(i for i, r in enumerate(self.g['roots']) if r['kind'] == 'center')
+            self.g['roots'][j]['targets'] = []
+        if mutate == 'broken_mix':
+            self.k['entries'][0]['skip_mix'] = True
+        if mutate == 'outside_cap':
+            # raise the mixed carrier past the receivers' shared cap (to the full frame) and deliver there
+            e = self.k['entries'][0]
+            e['deliver_frame'] = self.w['full_frame']
+            e['carrier_chain'][2] = e['deliver_frame']
+        if mutate == 'below_level':
+            # deliver at the receivers' level-1 (face) cap, which does not contain span{chi_c, chi_d}
+            e = self.k['entries'][0]
+            face = next(j for j, r in enumerate(self.g['roots']) if r['kind'] == 'side' and set(e['receivers']) < set(r['targets']))
+            e['deliver_frame'] = self.w['root_frame'][face]
+            e['carrier_chain'][2] = e['deliver_frame']
+        if mutate == 'non_nested':
+            # move one addition's frame down to the frame of its smallest operand's source line
+            x = next(int(k) for k, f in sorted(self.w['node_frame'].items(), key=lambda kv: int(kv[0])) if int(k) >= self.v and str(int(k)) not in set(map(str, self.w['plain'])))
+            self.w['node_frame'][str(x)] = self.w['source_frame'][0]
+
+    # ---------------- frames
+    def frames(self):
+        h = self.h
+        self.A, self.B, self.dimf = {}, {}, {}
+        for key, rec in self.fr['frames'].items():
+            f = int(key)
+            if 'a' in rec:
+                A = [tuple(r) for r in rec['a']]
+                need(rank(A, h) == len(A), 'independent annihilator rows %d' % f)
+                B, _ = kernel(A, h)
+            else:
+                B = [tuple(r) for r in rec['b']]
+                need(rank(B, h) == len(B), 'independent basis rows %d' % f)
+                A, _ = kernel(B, h)
+            need(len(A) + len(B) == h and len(B) == rec['dim'], 'dimensions of frame %d' % f)
+            need(all(dot(a, b) == 0 for a in A for b in B), 'A.B = 0 for frame %d' % f)
+            self.A[f], self.B[f], self.dimf[f] = A, B, len(B)
+        self.cc = {}
+        return len(self.A)
+
+    def sub(self, f1, f2):
+        """frame f1 contained in frame f2 (exact)"""
+        if f1 == f2:
+            return True
+        key = (f1, f2)
+        r = self.cc.get(key)
+        if r is None:
+            B1, A2 = self.B[f1], self.A[f2]
+            r = len(B1) <= len(self.B[f2]) and all(dot(a, b) == 0 for a in A2 for b in B1)
+            self.cc[key] = r
+        return r
+
+    def in_frame(self, vec, f):
+        return all(dot(a, vec) == 0 for a in self.A[f])
+
+    def nondeg(self, f):
+        h = self.h
+        B, A = self.B[f], self.A[f]
+        if not B or len(B) == h:
+            return True
+        if len(B) <= len(A):
+            s = [sum(b) for b in B]
+            M = [[9 * dot(B[i], B[j]) - s[i] * s[j] for j in range(len(B))] for i in range(len(B))]
+            return rank(M, len(B)) == len(B)
+        s = [sum(a) for a in A]
+        M = [[(9 - h) * dot(A[i], A[j]) + s[i] * s[j] for j in range(len(A))] for i in range(len(A))]
+        return rank(M, len(A)) == len(A)
+
+    # ---------------- decoder
+    def decoder(self):
+        g, v = self.g, self.v
+        args = g['args']
+        lab = [frozenset(l) for l in g['labels']]
+        sup = [1 << i for i in range(v)] + [0] * (len(args) - v)
+        for x in range(v, len(args)):
+            a, b = args[x]
+            need(not sup[a] & sup[b], 'support-disjoint addition %d' % x)
+            sup[x] = sup[a] | sup[b]
+        self.sup = sup
+        acc, stars, side = [0] * v, [set() for _ in range(v)], [0] * v
+        for r in g['roots']:
+            need(r.get('coefficient', 1) == 1, 'mod-2 unit coefficients')
+            for t in r['targets']:
+                acc[t] ^= sup[r['node']]
+                if r['kind'] == 'center':
+                    stars[t].add(r['coordinate'])
+                else:
+                    side[t] ^= sup[r['node']]
+        for e in self.k['entries']:
+            for t in e['receivers']:
+                acc[t] ^= (1 << e['carrier']) | (1 << e['passive'])
+                side[t] ^= (1 << e['carrier']) | (1 << e['passive'])
+        for t in range(v):
+            need(acc[t] == 1 << t, 'decoder identity at target %d' % t)
+            need(stars[t] == set(lab[t]), 'stars read by target %d' % t)
+            orth = sum(1 << s for s in range(v) if len(lab[s] & lab[t]) == 1)
+            need(side[t] == orth, 'side part = sum over |S cap T| = 1 at target %d' % t)
+        for r in g['roots']:
+            if r['kind'] == 'center':
+                c = r['coordinate']
+                need(sup[r['node']] == sum(1 << s for s in range(v) if c in lab[s]), 'star support %d' % c)
+
+    # ---------------- geometry and chains
+    def geometry(self):
+        g, w, h, v = self.g, self.w, self.h, self.v
+        lab = g['labels']
+        chi = [tuple(1 if j in l else 0 for j in range(h)) for l in lab]
+        cov = [tuple((3 if j in l else 0) - 1 for j in range(h)) for l in lab]
+        nf = {int(k): f for k, f in w['node_frame'].items()}
+        rf = w['root_frame']
+        full = w['full_frame']
+        need(self.dimf[full] == h, 'full frame')
+        for s in range(v):
+            f = w['source_frame'][s]
+            need(self.dimf[f] == 1 and self.in_frame(chi[s], f), 'source line <chi_S>')
+        args = g['args']
+        for x, f in nf.items():
+            if x < v:
+                need(self.in_frame(chi[x], f), 'leaf label inside its frame')
+            else:
+                for y in args[x]:
+                    need(self.sub(nf[y], f), 'operand frame inside node frame (%d <- %d)' % (x, y))
+        loss = 0
+        for j, r in enumerate(g['roots']):
+            f = rf[j]
+            need(self.sub(nf[r['node']], f), 'root node frame inside root frame %d' % j)
+            if r['kind'] == 'center':
+                c = r['coordinate']
+                S = [chi[s] for s in range(v) if c in lab[s]]
+                need(all(self.in_frame(x, f) for x in S) and rank(S, h) == self.dimf[f], 'centre frame = star span')
+                loss += self.dimf[f]
+            else:
+                need(all(dot(cov[t], b) == 0 for t in r['targets'] for b in self.B[f]), 'root frame inside caps')
+                need(self.dimf[f] == h - rank([cov[t] for t in r['targets']], h), 'root frame = common cap')
+        need(loss == self.prof['loss'], 'copied-centre loss')
+        self.chi, self.cov, self.nf, self.rf = chi, cov, nf, rf
+
+    def chains(self):
+        """Role chains of the physical word and target chains; returns the recounted child histogram."""
+        g, w, h, v = self.g, self.w, self.h, self.v
+        nf, rf, full = self.nf, self.rf, w['full_frame']
+        ops, rootroles = w['ops'], w['rootroles']
+        R = 1 + max(max(a, b) for a, b, _ in ops)
+        R = max(R, 1 + max(rootroles), 1 + max(w['sources'].values()))
+        need(R == self.prof['R'], 'role count')
+        start = {}
+        for leaf, s in w['sources'].items():
+            start[s] = w['source_frame'][int(leaf)]
+        phase1 = set(w['phase1'])
+        touched_p1 = set()
+        for i in phase1:
+            touched_p1.update(ops[i][:2])
+        # phase one = closure of the centre roots' last ops under per-role precedence (recomputed)
+        prev_op, pred = {}, []
+        for i, (a, b, _) in enumerate(ops):
+            pred.append((prev_op.get(a, -1), prev_op.get(b, -1)))
+            prev_op[a] = prev_op[b] = i
+        stack = [prev_op[s] for r, s in zip(g['roots'], rootroles) if r['kind'] == 'center' and s in prev_op]
+        closure = set()
+        while stack:
+            i = stack.pop()
+            if i not in closure:
+                closure.add(i); stack.extend(j for j in pred[i] if j >= 0)
+        need(closure == phase1, 'phase one is the centre closure')
+        # conservative response support of every role (union incidence through the XOR word)
+        co = [0] * R
+        for j, (r, s) in enumerate(zip(g['roots'], rootroles)):
+            for t in r['targets']:
+                co[s] |= 1 << t
+        for a, b, _ in reversed(ops):
+            co[b] |= co[a]
+        gauge_of = {}
+        for z in w['gauges']:
+            need(sum(1 << t for t in z['targets']) == co[z['role']], 'gauge targets = response support of its role')
+            s = z['role']
+            need(s not in start, 'gauged role is not a source role')
+            need(s not in touched_p1, 'gauged role untouched in phase one')
+            need(self.dimf[z['frame']] == z['dim'] and z['dim'] > 0, 'gauge dimension')
+            need(self.nondeg(z['frame']), 'gauge frame nondegenerate')
+            start[s] = z['frame']; gauge_of[s] = z
+        seq = defaultdict(list)
+        for i, (a, b, x) in enumerate(ops):
+            f = nf[x]
+            seq[a].append(f); seq[b].append(f)
+        for j, s in enumerate(rootroles):
+            seq[s].append(rf[j])
+        H = Counter()
+        for s in range(R):
+            chain = [start.get(s)] + seq[s] + [full]
+            prev = chain[0]
+            dprev = 0 if prev is None else self.dimf[prev]
+            if prev is not None and s not in gauge_of:
+                H[1] += 1          # source role: injection frame <chi_S> (entrance child of width 1)
+            for f in chain[1:]:
+                if prev is not None:
+                    need(self.sub(prev, f), 'nested role chain (role %d)' % s)
+                d = self.dimf[f]
+                need(d >= dprev, 'ascending role chain (role %d)' % s)
+                if d > dprev:
+                    H[d - dprev] += 1
+                prev, dprev = f, d
+        for j, r in enumerate(g['roots']):
+            if r['kind'] == 'center':
+                H[self.dimf[rf[j]]] += 1   # copied-centre transform
+        # partner-pair chronology
+        src = Counter()
+        lab = [set(l) for l in g['labels']]
+        for e in self.k['entries']:
+            c, d = e['carrier'], e['passive']
+            need(len(lab[c] & lab[d]) == 1, 'carrier and passive orthogonal (H0-Gram I_2)')
+            mf, cf = e['mix_frame'], e['deliver_frame']
+            need(self.dimf[mf] == 2 and self.in_frame(self.chi[c], mf) and self.in_frame(self.chi[d], mf), 'mix frame = span{chi_c, chi_d}')
+            need(self.nondeg(mf), 'mix frame nondegenerate')
+            need(self.sub(mf, cf), 'mix frame inside the receivers shared cap')
+            need(all(dot(self.cov[t], b) == 0 for t in e['receivers'] for b in self.B[cf]), 'delivery frame inside receiver caps')
+            need(e['carrier_chain'][0] == w['source_frame'][c] and e['passive_chain'][0] == w['source_frame'][d], 'chains start at source lines')
+            need(e['carrier_chain'][1:] == [mf, cf, w['full_frame']] and e['passive_chain'][1:] == [mf, w['full_frame']], 'chain shape')
+            for ch in (e['carrier_chain'], e['passive_chain']):
+                for f1, f2 in zip(ch, ch[1:]):
+                    need(self.sub(f1, f2), 'nested source-register chain')
+                for f1, f2 in zip(ch, ch[1:]):
+                    src[self.dimf[f2] - self.dimf[f1]] += 1
+        # target chains: gauge reads (time order = reverse selection order), side caps in root order,
+        # partner-pair delivery at the level-2 cap right after its root, final cap
+        events = defaultdict(list)
+        for z in reversed(w['gauges']):
+            for t in z['targets']:
+                events[t].append(z['frame'])
+        deliveries = defaultdict(list)
+        for e in self.k['entries']:
+            deliveries[e['deliver_after_root']].append(e)
+        for j, r in enumerate(g['roots']):
+            if r['kind'] == 'center':
+                continue
+            for t in r['targets']:
+                events[t].append(rf[j])
+            for e in deliveries.get(j, []):
+                need(sorted(e['receivers']) == sorted(r['targets']), 'delivery after the receivers own level-2 root')
+                for t in e['receivers']:
+                    events[t].append(e['deliver_frame'])
+        Y = Counter()
+        cap = {}
+        for t in range(v):
+            capf = None
+            prev, dprev = None, 0
+            for f in events[t]:
+                if prev is not None:
+                    need(self.sub(prev, f), 'nested target chain (target %d)' % t)
+                need(all(dot(self.cov[t], b) == 0 for b in self.B[f]), 'target frame inside cap (target %d)' % t)
+                if self.dimf[f] > dprev:
+                    Y[self.dimf[f] - dprev] += 1
+                prev, dprev = f, self.dimf[f]
+            need(dprev <= h - 1, 'target chain below the cap')
+            Y[h - 1 - dprev] += 1 if h - 1 - dprev else 0
+        # every source register is in exactly one mixing pair
+        members = Counter()
+        for e in self.k['entries']:
+            members[e['carrier']] += 1; members[e['passive']] += 1
+        need(all(members[s] == 1 for s in range(v)), 'each source in exactly one partner pair')
+        for f in set(self.nf.values()) | set(self.rf):
+            need(self.nondeg(f), 'G-nondegenerate frame %d' % f)
+        return H, Y, src, R
+
+    # ---------------- replay
+    def replay(self, seeds=3):
+        g, w, v = self.g, self.w, self.v
+        ops, rootroles = w['ops'], w['rootroles']
+        R = self.prof['R']
+        srcmap = {int(k): s for k, s in w['sources'].items()}
+        roots = g['roots']
+        for seed in range(seeds):
+            rng = random.Random(1000 + seed)
+            x = [rng.getrandbits(1) for _ in range(v)]
+            y0 = [rng.getrandbits(1) for _ in range(v)]
+            z0 = [rng.getrandbits(1) for _ in range(R)]
+            X, Yv, z = x[:], y0[:], z0[:]
+            # y <- y - J M z (old-value response of the dirty scratch)
+            zd = z0[:]
+            for a, b, _ in ops:
+                zd[a] ^= zd[b]
+            for j, r in enumerate(roots):
+                for t in r['targets']:
+                    Yv[t] ^= zd[rootroles[j]]
+            for leaf, s in srcmap.items():      # z <- z + V x  (at the rank-one source lines)
+                z[s] ^= X[leaf]
+            for a, b, _ in ops:                  # z <- M z
+                z[a] ^= z[b]
+            for j, r in enumerate(roots):        # y <- y + J z
+                for t in r['targets']:
+                    Yv[t] ^= z[rootroles[j]]
+            for e in self.k['entries']:          # partner-pair sums on the source registers
+                if not e.get('skip_mix'):
+                    X[e['carrier']] ^= X[e['passive']]
+                for t in e['receivers']:
+                    Yv[t] ^= X[e['carrier']]
+            for e in self.k['entries']:          # undo at the full frame
+                if not e.get('skip_mix'):
+                    X[e['carrier']] ^= X[e['passive']]
+            for a, b, _ in reversed(ops):        # z <- M^-1 z
+                z[a] ^= z[b]
+            for leaf, s in srcmap.items():       # z <- z - V x
+                z[s] ^= X[leaf]
+            need(all(Yv[t] == y0[t] ^ x[t] for t in range(v)), 'replay: y = y0 + x (seed %d)' % seed)
+            need(z == z0 and X == x, 'replay: scratch and sources restored (seed %d)' % seed)
+
+    def run(self):
+        nfr = self.frames()
+        self.decoder()
+        self.geometry()
+        H, Y, src, R = self.chains()
+        self.replay()
+        h, v = self.h, self.v
+        m, W = 3 * h, 2 * v + R
+        C = Counter()
+        for part in (H, Y, src):
+            for r, c in part.items():
+                if r and c:
+                    C[r] += 3 * c
+        for z in self.w['gauges']:
+            C[3 * z['dim']] += 1
+        C[2] += 2 * v
+        saved = {int(k): c for k, c in self.prof['child_histogram'].items()}
+        need(dict(C) == saved, 'independent recount equals the saved child histogram')
+        mass = sum(r * c for r, c in C.items())
+        need(W == self.prof['W_per_vertex'] and W * m - mass == 2 * v - 3 * self.prof['loss'] == self.prof['deficit_per_vertex'],
+             'W = 2v + R and deficit 2v - 3 ell')
+        return dict(frames=nfr, roles=R, W=W, m=m, deficit=W * m - mass, children=sum(C.values()))
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--dir', type=Path, default=Path(__file__).resolve().parent / 'out')
+    ap.add_argument('--p', type=int, default=12)
+    ap.add_argument('--no-controls', action='store_true')
+    a = ap.parse_args()
+    res = Checker(a.dir, a.p).run()
+    print('PASS p=%d: %s' % (a.p, res))
+    if a.no_controls:
+        return
+    for m in ('broken_mix', 'outside_cap', 'below_level', 'dropped_star', 'non_nested'):
+        try:
+            Checker(a.dir, a.p, mutate=m).run()
+        except Fail as e:
+            print('control %-13s REJECTED: %s' % (m, e))
+            continue
+        raise SystemExit('FAIL: control %s was accepted' % m)
+    print('PASS: all 5 mutation controls rejected')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/frames_p12.json.gz b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/frames_p12.json.gz
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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/graph_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/graph_p12.json
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+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/graph_p12.json
@@ -0,0 +1 @@
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2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T; side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T; equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} 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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/kchron_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/kchron_p12.json
new file mode 100644
index 0000000000..f39b02e3f7
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/kchron_p12.json
@@ -0,0 +1 @@
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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/profile_p12.json b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/profile_p12.json
new file mode 100644
index 0000000000..da422014b7
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/profile_p12.json
@@ -0,0 +1 @@
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index 0000000000..6db28abe95
Binary files /dev/null and b/research/gen4-retiming-entrances-target/vendor/pr276/gen4bit/selected/bit/word_p12.json.gz differ
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/LICENSE b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
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+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/LICENSE
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+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
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+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
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+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
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+      incurred by, or claims asserted against, such Contributor by reason
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+
+   APPENDIX: How to apply the Apache License to your work.
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+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
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+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+       http://www.apache.org/licenses/LICENSE-2.0
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+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/NOTICE b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/NOTICE
new file mode 100644
index 0000000000..63aa295646
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/NOTICE
@@ -0,0 +1,290 @@
+Walsh-Hadamard power saving (wht-power-saving-lean)
+Copyright 2026 Jacob Sussman
+
+Repository: https://github.com/jacobalansussman/wht-power-saving-lean
+
+This repository is not a project of OpenAI. OpenAI did not write, review or
+endorse it. The package name "OAI" and the namespace "OAI.PowerSaving" are
+those of openai/math and are kept only because the new files extend that
+development.
+
+This repository is not a project of CrocSwap/integer-mult-bounds either. Its
+authors did not write, review or endorse it. Section 6 says what is taken
+from their repository.
+
+This repository contains files from, and files derived from, the repository
+"openai/math" (https://github.com/openai/math), family 130, "Exact Fourier
+transforms below n log n", at commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
+That repository is published under the Apache License, Version 2.0. A copy of
+the licence is in the file LICENSE. The upstream repository has no NOTICE file
+and its licence text names no copyright holder; the files are attributed here
+to the authors of openai/math (OpenAI).
+
+1. Unmodified upstream files.
+   The 89 files under OAI/Computability/ are byte-for-byte copies of the files
+   with the same paths under lean/ in openai/math at the commit above. They
+   have not been changed. Modified copies of some of them are under
+   Work/Fourier/ and are listed in section 7.
+   One more file of openai/math is here unchanged, outside the Lean build:
+   third-party/openai-math/lean/ComparatorChallenges/UniformFourier.lean is a
+   byte-for-byte copy of lean/ComparatorChallenges/UniformFourier.lean at the
+   commit above (the statement of OpenAI's Fourier challenge). It is included
+   so that the modified copy named in section 2 can be compared with it.
+
+2. Files that contain upstream text.
+   - Work/CarrierCheck/ChallengeB2Ke16x.lean,
+     Work/CarrierCheck/ChallengeB2Ke16xR.lean,
+     Work/GCert/Data/ChallengeB2Gp193x.lean and the text template
+     tools/gen/templates/ChallengeB2L16x.lean.txt each contain, as their
+     lines 22-270, lines 9-257 of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the RAM cost
+     model), unchanged. Everything else in these files was written for this
+     repository.
+   - Work/Fourier/UniformFourierChallenge.lean is a modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the
+     statement of OpenAI's Fourier challenge, 336 lines). Changes: a comment
+     was added at the top; the exponent 1 - 1/(10^(13:ℕ)) was replaced by
+     1 - 7474546/(10^(10:ℕ)); seven names received the suffix "Z"
+     (decimalExponent, decimalTime, TimeBounds, DFTGoal, ConvGoal,
+     transform_main, convolution_main). Everything else in the file is the
+     upstream text, unchanged. See section 7.
+   - Work/Scratch/Engine.lean and Work/Block/Engine.lean contain copies of
+     proofs of openai/math, changed for this repository: sections 1, 2 and 5
+     of Work/Scratch/Engine.lean are upstream proofs with the batch layout
+     renamed, and both files contain a copy of the private upstream theorem
+     "hills_project" (lean/OAI/Computability/FourierTransform/
+     TensorProgram.lean) with its envelope generalised. The comments in the
+     two files mark these places.
+   - lakefile.lean is adapted from lean/lakefile.lean of openai/math: the same
+     package name, toolchain, package option and Mathlib pin; every other
+     dependency was removed and the libraries of this repository were added.
+     lean-toolchain is a byte-for-byte copy of lean/lean-toolchain.
+     lake-manifest.json lists Mathlib and its dependencies at the revisions of
+     lean/lake-manifest.json.
+   - RELATED-WORK.md reproduces the BibTeX entries of two manuscripts of
+     openai/math.
+
+3. New files that build on upstream proofs.
+   The other files under WHTCheck/ and Work/ were written for this
+   repository. They import the upstream files, and several of them generalise
+   or adapt proofs of upstream files (for example Work/Block/Recursion.lean,
+   which says so in its header). They are changes and additions made for this
+   repository and are not part of openai/math.
+
+4. How the new files were made.
+   Jacob Sussman made the new files on 2026-10-08 and 2026-10-09 by directing
+   a team of AI agents (Claude). The agents wrote the new Lean files, the
+   certificate data and the generator scripts. See README.md, section 4.
+
+5. Ideas taken from other public work.
+   The network of the first result uses ideas published by others, among them
+   the helper circuit "NStar3" (Swapnil-jain/integer-mult-kappa, which credits
+   CrocSwap pull request #36 and Paureel for parts of it), its transfer to
+   family 130 (shea256/fourier-transform-below-nlogn), and "carrier links" and
+   "whole-residual batching" (pull requests to CrocSwap/integer-mult-bounds).
+   No file of Swapnil-jain/integer-mult-kappa or of
+   shea256/fourier-transform-below-nlogn is included here. One comment in
+   Work/Scratch/Engine.lean quotes three counts reported in
+   Swapnil-jain/integer-mult-kappa and names that source. The general frame
+   lemma that Work/GFrame proves is stated in
+   notes/general-clifford-frames.tex of CrocSwap/integer-mult-bounds; its Lean
+   proof was written for this repository. The credits, with links, are in
+   RELATED-WORK.md.
+
+6. Data derived from CrocSwap/integer-mult-bounds (second result).
+   The helper circuit of the second result is the paired-cube circuit of the
+   repository "CrocSwap/integer-mult-bounds"
+   (https://github.com/CrocSwap/integer-mult-bounds), in the state of its pull
+   request #193. It is the design of that community: icekylinx (pull requests
+   #144 and #184), eumemic (#168, and #117 behind its modules), ikeboy /
+   Avi Eisenberg (#191 and #193), with an664 (#128) credited there for the
+   workspace-sharing principle. That repository is published under the Apache
+   License, Version 2.0 (the same licence text as the file LICENSE). Its
+   NOTICE file begins "A sharper exponent for integer multiplication /
+   Copyright 2026 Douglas Colkitt" and says that the community release "is
+   not solely Douglas Colkitt's work". A complete copy of that NOTICE file, as
+   it is at the head of pull request #193, is in
+   third-party/CrocSwap-integer-mult-bounds/NOTICE.
+
+   The data were taken from these files of that repository. They were loaded
+   as data by programs written for this repository; no program of that
+   repository was run, and none is included here.
+   - at the head of pull request #168 (eumemic),
+     4a3c769e5c5430e7114c4d3e099ff34664677f17:
+       references/paired-cube/sources/local_L1.json
+       references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json
+       references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json
+       references/paired-cube/sources/qmod_climb3u_best.json
+       references/paired-cube/selected-module/matching-arcs.json
+       references/paired-cube/physical/frames.json
+   - at the head of pull request #193 (ikeboy),
+     187e1010ac8b259af8e9b5166f68b64bc27b4b47:
+       research/source-assisted-v4/data/physical-pairs.json
+
+   Files of this repository that contain data derived from them:
+   tools/certificate/gcert1-p11-pr193.json.gz and the Lean data modules
+   generated from it, Work/GCert/Data/Gen/P193*.lean and the files they import
+   from Work/GCert/Data/Gen/P193/; its block counts are also in the generated
+   modules Work/GCert/Data/P193Price.lean, RateB2Gp193.lean, RateB2Gp193x.lean
+   and InstB2Gp193.lean.
+   Changes made: the circuit was rebuilt from those data as one explicit,
+   renumbered list of additions with a table of frames, in the certificate
+   format "gcert/1" of this repository; its 1,980 in-place steps were written
+   as pairs of additions with rescaled coefficients; the Lean data modules
+   were generated from that list. No file of that repository is included
+   unchanged, except the copy of its NOTICE file named above.
+
+   Notices of that NOTICE file that pertain to these data, quoted:
+
+     Paired-cube and shared-core extension, 9 October 2026
+     Copyright 2026 icekylinx
+
+     Source-assisted common-frame extension (2026-10-09)
+     Copyright 2026 icekylinx. Apache-2.0.
+     Substantial dependency: eumemic PR168,
+     fd25adb7fbaa12ee761d02c733c54d1d2a7687ee
+
+   The full text of both notices, and the notices of the work they build on,
+   are in the copy named above. The credits, with links and with the words of
+   pull request #193 about its own sources, are in README.md ("Whose circuit
+   this is") and in RELATED-WORK.md, section 1.
+
+7. Modified copies of upstream files (third result).
+   The files listed below are copies of files of openai/math at the commit
+   above, changed for this repository. Each begins with a comment that names
+   the upstream file it is derived from and states what was changed. The
+   upstream originals under lean/OAI/Computability/ are in this repository
+   as well, unchanged (section 1), and the copies import them. The upstream
+   challenge file lean/ComparatorChallenges/UniformFourier.lean is in this
+   repository in both forms: unchanged under third-party/openai-math/
+   (section 1) and modified (section 2).
+
+   - Work/Fourier/ArbitraryLength.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ArbitraryLength.lean (224
+     lines; 159 of them unchanged in the copy). Changes: identifiers renamed
+     on 64 lines (18 names: 15 with the suffix Z, 3 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Asymptotics.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Asymptotics.lean (187 lines;
+     112 of them unchanged in the copy). Changes: identifiers renamed on 74
+     lines (32 names: 26 with the suffix Z, 6 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/Axioms.lean: written for this repository (not a copy of an
+     upstream file).
+   - Work/Fourier/ConvolutionProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ConvolutionProgram.lean (100
+     lines; 77 of them unchanged in the copy). Changes: identifiers renamed
+     on 22 lines (10 names: 9 with the suffix Z, 1 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Goal.lean: written for this repository; contains lines of
+     upstream files: of its 7 code lines, 6 are lines of
+     lean/OAI/Computability/FourierTransform/Goal.lean (original lines 35,
+     75-77, 79, 81): unchanged: its lines 25; with identifiers renamed: its
+     lines 21, 24, 26, 28, 30.
+   - Work/Fourier/Main.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Main.lean (151 lines; 90 of
+     them unchanged in the copy). Changes: identifiers renamed on 59 lines
+     (40 names: 35 with the suffix Z, 5 with Z inserted); 1 import line
+     replaced by 2; 24 comment lines added; other code lines changed: 1 of
+     the original, 1 of the copy (copy line 59).
+   - Work/Fourier/Seam.lean: written for this repository; contains lines of
+     upstream files: of its 122 code lines, 15 are lines of
+     lean/OAI/Computability/FourierTransform/TensorProgram.lean (original
+     lines 36-37, 95-96): unchanged: its lines 93-94, 113-114, 141-142,
+     163-164, 185-187, 194-196; with identifiers renamed: its lines 184; 3
+     are lines of lean/OAI/Computability/FourierTransform/TensorSaving.lean
+     (original lines 83-84, 114): with identifiers renamed: its lines 45-46,
+     59; 1 is a line of lean/OAI/Computability/FourierTransform/Main.lean
+     (original line 60): with identifiers renamed: its lines 213.
+   - Work/Fourier/SectorAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SectorAlgorithm.lean (224
+     lines; 162 of them unchanged in the copy). Changes: identifiers renamed
+     on 61 lines (17 names: 13 with the suffix Z, 4 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/SynchronizedAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SynchronizedAlgorithm.lean (126
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 31 lines (12 names: 10 with the suffix Z, 1 with Z inserted, 1
+     other), the other being "canopy" to "Grove.canopy" (5 lines); 1 import
+     line replaced by 1; 16 comment lines added; no other change to the
+     code.
+   - Work/Fourier/TransformProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/TransformProgram.lean (146
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 51 lines (21 names: 19 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/UniformBounds.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/UniformBounds.lean (183 lines;
+     115 of them unchanged in the copy). Changes: identifiers renamed on 67
+     lines (29 names: 25 with the suffix Z, 4 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/UniformFourierChallenge.lean: modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean (336 lines; 328 of them
+     unchanged in the copy). Changes: identifiers renamed on 7 lines (7
+     names: 7 with the suffix Z); 12 comment lines added; other code lines
+     changed: 1 of the original, 1 of the copy (copy line 281).
+   - Work/Fourier/WorkingCompiler.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingCompiler.lean (153
+     lines; 104 of them unchanged in the copy). Changes: identifiers renamed
+     on 48 lines (14 names: 14 with the suffix Z); 1 import line replaced by
+     1; 15 comment lines added; no other change to the code.
+   - Work/Fourier/WorkingPreparation.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingPreparation.lean (212
+     lines; 156 of them unchanged in the copy). Changes: identifiers renamed
+     on 55 lines (30 names: 28 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/WorkingTransform.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingTransform.lean (119
+     lines; 91 of them unchanged in the copy). Changes: identifiers renamed
+     on 27 lines (9 names: 8 with the suffix Z, 1 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+
+   Changes made to the eleven copied proof files: every declaration received
+   the letter "Z" in its name (as a suffix of its own name, or of the name
+   of the declaration it belongs to), so that it does not collide with the
+   upstream declaration of the same name; the upstream exponent "alpha"
+   (1 - 2/10^11) and the bound "hills" defined from it were replaced by
+   "alphaZ" (1 - 7474547/10^10) and "hillsZ", which are defined in
+   Work/Fourier/Seam.lean, and the single use of the upstream theorem
+   "hills_program" by "hillsZ_program"; the five definitions of the upstream
+   statement that contain its exponent (decimalExponent, decimalTime,
+   TimeBounds, DFTGoal, ConvGoal) were replaced by the versions of
+   Work/Fourier/Goal.lean, whose exponent is 1 - 7474546/(10^(10:ℕ));
+   the import lines point to the copies; a header comment was added.
+      Two further changes: in the copy of Main.lean the same constant stands
+   once as the literal 2/10^11 and was replaced there too, and the two
+   final theorems of that copy received a documentation comment; in the
+   copy of SynchronizedAlgorithm.lean the name "canopy" was written out as
+   "Grove.canopy" in 5 places, because the short name is shadowed in the
+   larger environment of the copy. The script also renamed three names
+   inside upstream comments; the comments are otherwise the upstream ones
+   and describe the upstream network.
+   The proofs are those of openai/math. The copies were made by the script
+   tools/fourier/mkchain.py of this repository.
+
+   Work/Fourier/Goal.lean contains copies of those five definitions of
+   lean/OAI/Computability/FourierTransform/Goal.lean, with the exponent
+   replaced and the suffix "Z" on the five names.
+
+   Work/Fourier/Seam.lean was written for this repository. It repeats the
+   statement of the upstream theorem "hills_program" (TensorProgram.lean) and
+   the definition of "hills" (TensorSaving.lean) with the two names replaced;
+   its header says so.
+
+   The work of others that the third result follows (danadran01, shea256,
+   eumemic) is credited in README.md ("Whose reduction this is") and in
+   RELATED-WORK.md, section 1. No file of their repositories is included
+   here.
+
+Not included in this repository and fetched by the build: Mathlib
+(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its
+dependencies. The comparator (https://github.com/leanprover/comparator) is a
+separate tool and is not included.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/gcert1-p11-pr193.json.gz b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/gcert1-p11-pr193.json.gz
new file mode 100644
index 0000000000..a98026a72f
Binary files /dev/null and b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/gcert1-p11-pr193.json.gz differ
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/FINITE_BRIDGE.txt b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/FINITE_BRIDGE.txt
new file mode 100644
index 0000000000..c1a8843611
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/FINITE_BRIDGE.txt
@@ -0,0 +1,141 @@
+FINITE ROUTER, ROW-STOCK, AND SEMANTIC BRIDGE FOR ROUND 13
+
+Prepared for icekylinx by GPT-6 Astra, 9 October 2026. Apache-2.0.
+
+This bridge applies to a completed, physically proved round-13 profile.
+It cannot make a numerically attractive but unconstructed profile valid.
+The local source/target flags, controlled injections, old-response
+subtraction, inverse cleanup, and retained alias boundaries are separate
+construction obligations. assemble_profiles.py records their role as
+proof dependencies and independently checks the exact arithmetic.
+
+1. The inherited uniform interfaces
+
+Retain the three completed-core cover of PR144/PR168 and all of its
+analytic and fixed-tape assumptions. The complex cover is O(m,2), m<=72,
+with order V<2^(m*m)<=2^5184. No new independent cover coordinates are
+introduced by common-frame scalar lifts or source-controlled local
+rewrites. Every stage still uses one completed invocation at each vertex.
+
+For a supplied profile with W0<10^7 roles per cover vertex, the full
+physical stock W=V W0 is less than2^5208. Its total rank s is less
+than mW<2^5215. The profile's actual proper-child maximum is retained;
+the selected complex maximum must be less than m/2. The script checks
+these inequalities rather than assuming that fewer auxiliary rows imply
+a better contraction or a shorter recursion.
+
+The bit word uses the same weighted q-adic frame interface and the same
+internally borrowed selectors as its pinned parent. New source controls
+must use existing nondegenerate source-meeting planes or separately
+certified new frames. All zero-rank adapters remain charged scalar work.
+The group-size factor is not omitted and is not inserted into an external
+polynomial row reserve. The inherited ordinary leaf saving is exactly
+384599/10^10. The bad-row allowance is1/10^16; the charged fallback per
+edge is32m^2. Its inequality2m^3/2^80<1/10^16 is checked explicitly.
+
+2. A deliberately loose finite scalar bound
+
+The pinned words and round-13 modifications are finite straight-line
+programs with fewer than2^40 stored nodes, roles, coefficients, and
+boundary entries. Scalar sum/difference lifts use actual invertible
+matrices and are executed pointwise at common frame representatives.
+For the selected dyadic rewrite, new elementary coefficients are
+dyadic; the inherited center scatters retain their fixed odd divisor3.
+No unrecorded new odd denominator may be included under this bridge.
+
+Fixed integer multipliers can be expanded into scalar doublings and
+additions; dyadic divisions can be expanded into halvings. The explicit
+low words and full-frame inverses are much smaller than2^4096 primitive
+scalar/movement groups per invocation. Even constructing their fixed
+old-response matrices by exact elimination is dominated by this bound:
+matrix order is below2^40, original finite-word coefficient bit lengths
+are below2^80, and the elementary elimination and coefficient expansion
+bounds are below2^1024. No input-size-dependent dense elimination is
+being performed. These are constants of the chosen finite construction.
+
+Consequently all3V invocation words, endpoint adapters, and finite role
+bookkeeping fit within K<2^9300 logical groups. The retained universal
+router is overcharged by a full W-role permutation for every group:
+
+    64 (m+1)^3 (K+1) (W+1)^2 < 2^20000.
+
+Choose the exact dominating scalar/router budget G=2^30000. This also
+dominates the primitive arithmetic required to realize the fixed scalar
+coefficients and source-controlled inverse cleanup. The router still
+uses a fixed number of tapes, with sequential reuse of row stock.
+
+3. Explicit semantic constants
+
+Choose the exact integer E=2^100000 and put B=s+E. Then
+
+    2 G W^2 + 8s + 4W + 4 + 32m < 2^40500 < E,
+    E <= B < 2^100001.
+
+For the actual maximum child r<m, the induction gap obeys
+
+    2B(m-r)-s-E >= s+E >= 1.
+
+Choose C0=2^210000 and C1=1. These dominate both the retained semantic
+requirement32m B^2 and2B+18. The reported strict_literal_gap=1 and
+induction_gap_lower=1 are proved lower bounds on the positive actual
+integer gaps; they are not claims that those gaps equal one.
+
+Use the inherited common dyadic grid with fixed3^(-K') exposure and
+retain its precision/rounding contract. No child receives an independent
+rounding allowance and no source-controlled injection is treated as an
+unpaid numerical operation.
+
+4. External rows and stopping
+
+The complex child maximum below m/2 gives halving degree1, while
+log2 W<5208<10000. Keep the deliberately conservative inherited bit
+coarse reserve9909 and ordinary-leaf reserve252. Thus the external
+row coefficient is bounded by
+
+    A=10000+9909+252=20161.
+
+Choose degree D=1000000 and suffix slope4D. The exact row gap is
+
+    D - (51/25)A > 0.
+
+The q-adic selector fields and source-control labels remain internally
+borrowed and restored. Increasing these finite overcharges changes
+constants and the all-size bridge, not the selected exponent saving.
+
+5. Exact supplier moments and balanced assembly
+
+For each actual histogram, assemble_profiles.py proves
+
+    sum_r n_r r exp(a log(m/r))/(mW0) + bad_allowance < 1
+
+using rational upper bounds, with upward rounding on the2^120 grid.
+The bit atom stop is the first10^(-12) grid point above
+a/(1+a-old), which implies both required strict toll inequalities.
+Its effective saving is(1-beta)a+beta*old. This stopping rule is the
+already reviewed PR158 edge rule, not a new local-word contribution.
+
+The final assembly uses the substantial PR168 balanced-prefix adapter,
+with eta=10^(-8) and phase stop10^(-9), retaining all47 strict
+constraints and all7 margins. The selected final kappa is rounded
+down on the10^(-10) grid below the minimum complete margin. The
+script checks every constraint exactly and reports whether the fixed
+target0.0009218338 is reached.
+
+This is a conditional bound of the retained theorem form
+
+    T(n)=O(n (log n)^(1-kappa)).
+
+The improvement ratio refers to kappa, the logarithmic exponent saving.
+It is not a measurement of practical multiplication throughput.
+
+Credits
+
+The base supplier, scalar/frame verification, and actual profiles are
+pinned to PR168 fd25adb7fbaa12ee761d02c733c54d1d2a7687ee, eumemic
+(Anthropic Claude assistance), building on icekylinx's PR144. The
+balanced prefix is RaD/hipotures; the semantic constraints are retained
+from the reviewed PR23 line; completed-core sharing is credited to
+an664 PR128; the atom-edge stop is credited to geckods PR158. Existing
+source notices retain their more detailed upstream attributions.
+The new source-controlled boundary construction, this conservative
+bridge, and its integration are GPT-6 Astra's round-13 work.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/compact-control-layout.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/compact-control-layout.tex
new file mode 100644
index 0000000000..16f4d23347
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/compact-control-layout.tex
@@ -0,0 +1,118 @@
+\paragraph{Rows and complete compact fields.}
+Let $m,W,s$ denote the complex network constants and keep the layer's global
+$p,d,K$ at every node. Put
+\[
+ G=4\lceil\log_2p\rceil+6,\quad H=dG,\quad
+ q_F=\left\lceil\frac{2H}{K}\right\rceil,\quad
+ q_B=\left\lceil\frac{H}{K}\right\rceil,
+\]
+\[
+ q_0=\lceil\log_2W\rceil\lceil\log_m(2d)\rceil,
+ \quad k_0=\lceil\log_m d\rceil,\quad Q_0=q_0+q_F+q_B.
+\]
+If $D\le Q_0$, apply all $D$ selected kernels individually. Otherwise,
+process individually the first $q_0+q_F$ and last $q_B$ selected axes.
+This uses existing coordinates only. The remaining active axes are a
+consecutive middle block of length $D-Q_0$.
+
+Regard the first $q_0$ chunks as the row index. Immediately after it, the
+next $q_F$ chunks have at least $2H$ bits. Reinterpret these consecutive
+bits as two $H$-bit front fields and a spectator remainder; a remainder
+of length zero is omitted. The last $q_B$ chunks similarly supply one
+$H$-bit back field and a spectator remainder. These reinterpretations move
+no records and preserve the total address space. For a call with $f$ axes
+per slot, carve $nG=(f-1)G\le H$ consecutive bits from each of these
+fields; collapse their unused bits into spectators. The resulting field
+list has a fixed number of entries. Both front fields precede all active
+slots and the back field follows them, so the compact-control proposition
+applies to every ordered pair of slots. For $f=1$ no compact fields are used.
+
+The original row range has length $R_{\rm row}=2^{q_0K}\ge W^{k_0}$.
+For each original prefix, pad this row range to the next multiple of
+$W^{k_0}$ by adding zero rows. A row includes the entire complete front
+fields, active middle block, back field, all spectator coordinates and
+polynomial record suffix. Padding adds whole such rows, so increases total
+volume by at most two and does not change any within-row range.
+
+At a node write the row index as $u=Wg+w$, $0\le w<W$, and send the entire
+row to role $w$. The index $u$ consists solely of the first row region:
+\emph{no compact-field bit is included in it}. Each role therefore has
+the same complete within-row address set and exactly $1/W$ of the parent
+volume. At depth $j$ the remaining row count is divisible by $W^{k_0-j}$.
+This invariant survives further splits, padding, and reassembly. Pointwise
+gates on different roles have aligned $g$ and every remaining coordinate.
+All compact operations restore the temporary fields before a scalar gate,
+recursive child, or returned result uses that layout.
+
+The fixed-tape scheduler is unchanged: park only the other role streams at
+the active stack top, execute the child on a complete role stream, and restore
+the parked streams on return. Every child has its own current logical volume;
+copying, parking, rewinds and clearing cost a fixed multiple of that volume.
+The constant number of compact operations per edge use fixed work areas.
+Descriptors include the global $p,d,K,G,H$ and the carved field lengths;
+all have $O(p)$ bits and there are a fixed number of fields. The existing
+record suffix absorbs polynomial setup at every node and per record.
+
+Each completed invocation acts as the desired $C$ tensor on its active axes
+and as identity on the reserved and spectator coordinates. It therefore
+commutes with the earlier individual kernels, including those on bits now
+interpreted as compact fields. Restoring the row permutation returns the
+result to each original row separately. A padded zero row is consequently
+zero at completion and can be deleted exactly as before. Neither temporary
+field contents nor intermediate scratch payloads were assumed to be zero.
+
+The number of individually processed axes is at most $Q_0$, including the
+fallback $D\le Q_0$. For large $p$, $K\ge d^c/2$ and
+\[
+ q_F+q_B\le\frac{3dG}{K}+2\le6d^{1-c}G+2.
+\]
+Thus preprocessing, padding and reservation cost
+\[
+ O\bigl(V(\log(2d)+d^{\max\{1-c,0\}}\log p+1)\bigr).
+\]
+All reserved axes lie within the original $D$ axes; in particular their
+total number never exceeds $d$. This fact also bounds their coefficient
+dependency depth by the same $8d$ allowance used in the guard proof.
+
+\paragraph{Unrolling the compact-control recurrence.}
+Fix rational $0<\beta<1$. Choose $0<\tau<1$ and
+$\max\{0,\log_m(s/W)\}<\sigma<1$. Stop when $e<d^\beta$ and apply
+the remaining kernels individually. With $F(e)$ denoting time per current
+logical volume, the exact row split gives
+\[
+ F(e)\le(s/W)F(e/m)+O(G^\tau e^\tau+1),\qquad
+ F(e)=O(e)\quad(e<d^\beta).
+\]
+Here $G$ and the compact reservations are global parameters, not rebuilt
+at each node. This is why no factor $K^\tau$ appears in the overhead.
+Repair costs are already included in the node overhead.
+
+Write $b=s/W$. At level $j$ the internal contribution is bounded by
+$O(G^\tau e^\tau(b/m^\tau)^j)$. Summing through the stopping depth gives
+\[
+ O(G^\tau\log(2d)d^\chi),\qquad
+ \chi=\tau+(1-\beta)\max\{\sigma-\tau,0\}.
+\]
+Indeed if $\sigma\le\tau$ the root bounds every summand; otherwise the
+last internal level costs at most the root bound times a fixed constant
+and $d^{(1-\beta)(\sigma-\tau)}$. The additive $1$ is absorbed by
+$G^\tau e^\tau$ at internal nodes. The leaf contribution is at most
+$O(d^{\sigma+\beta(1-\sigma)})$, by the original volume-weighted argument.
+
+Partition $D-Q_0$ into consecutive powers of $m$, using its base-$m$
+expansion. There are $O(\log(2d))$ pieces. Include their costs and the
+reservation cost to obtain, per original volume,
+\[
+ O\!\left((\log p)^3
+ [d^\chi+d^{\sigma+\beta(1-\sigma)}+d^{\max\{1-c,0\}}+1]\right).
+\]
+We used $\log d=\Theta(\log p)$ and $G=O(\log p)$ for each fixed
+$d=\Theta(p^\epsilon)$ family. Any fixed rational exponents satisfying
+\[
+ \max\{\tau,\sigma,\chi\}<\lambda<\lambda'<1,\qquad
+ \max\{\sigma+\beta(1-\sigma),1-c,0\}<\lambda'
+\]
+therefore give the complete $O(Vd^{\lambda'})$ layer bound. The strict gaps
+absorb the logarithms. The small-$D$ fallback obeys the same bound.
+For fixed rational $\beta=u/v$, implement stopping by the integer test
+$e^v<d^u$; its polynomial descriptor cost is already included.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/compact-control-movement.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/compact-control-movement.tex
new file mode 100644
index 0000000000..06b6a9ef24
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/compact-control-movement.tex
@@ -0,0 +1,167 @@
+\subsection{Compact dirty controls for selected-bit additions}
+\label{sec:compact-control-movement}
+The following replacement for the wide-slot packed operation moves only
+compact control fields. Temporary address fields have arbitrary contents;
+they are complete ranges of existing address bits, not newly allocated
+independent coordinates. Their availability in every recursive call is
+proved separately below.
+
+\begin{lemma}[Controlled rotations with record-paid offset work]
+\label{lem:record-paid-rotation}
+Consider $M$ records of $R$ bits on a complete rectangular address set, of
+volume $V=MR$. Its fixed number of field lengths and controls have at most
+$A=\lceil\log_2(2V)\rceil$ bits each. A binary target field follows all its
+controls. Suppose its rotation offset, independent of that target, is
+computable from the controls and descriptors in $O(A^C)$ tape steps for
+some fixed $C$. Then the rotation can be performed on fixed tapes in
+$O(V+MA^{C'})$ time for a fixed $C'$. In particular, this is $O(V)$ when
+$A=O(p)$ and $R$ exceeds every fixed power of $p$.
+\end{lemma}
+\begin{proof}
+Fix the prefix before the target. If its range is $Q$ and each target block
+has $B$ suffix bits, rotate by $a$ through the two-piece split at $Q-a$ and
+merge in the opposite piece order. This is the controlled-rotation
+construction from the ordered-affine streaming lemma. Each data bit is
+copied a bounded number of times. There are at most $M$ prefix fibers, since
+every fiber contains at least one complete record. At each fiber, compute
+the offset, initialize its two piece lengths, and reset the finite collection
+of counters; recompute the offset at the merge. Ordinary binary arithmetic
+and descriptor copies cost a fixed polynomial in $A$ per fiber. The controls
+can be wider than the target: their lengths are bounded by $A$, not by the
+target width. Local suffix-length copies and ripple counters are charged as
+in the original streaming proof, so no growing descriptor is scanned per
+payload bit. Two piece tapes, output and fixed arithmetic work tapes suffice;
+rewinds and clearing are over the regions just written. This gives the stated
+bound. Finally $MA^{C'}/V=A^{C'}/R=o(1)$ in the specified record regime.
+\end{proof}
+
+Let $x,y$ be disjoint slots of $fK$ bits, with corresponding selected
+positions $j_i=\rho+iK$, $0\le i<f$, $0\le\rho<K$. Put $n=f-1$.
+For $f=1$ use the elementary two-bit XOR. Otherwise fix a positive integer
+$G$, put $B=2^G$, and assume two disjoint complete $nG$-bit fields $u,t$
+precede both slots and a third such field $b$ follows both slots. Arbitrary
+spectator fields may intervene. Each compact field has $n$ radix-$B$ digits.
+The selected-bit operation will preserve these three entire fields.
+
+\paragraph{Earlier source.}
+Suppose $x$ precedes $y$. The unused field $u$ is a spectator. For an integer
+target segment $v$, a bit $z$, and an arbitrary integer temporary $w$, perform
+\[
+ v\gets v+2zw,\qquad w\gets w+(v\bmod2),\qquad
+ v\gets v+z(1-2w),\qquad w\gets w-((v\bmod2)\mathbin\oplus z).
+\]
+Writing the original parity as $a$, the first update leaves it unchanged.
+The final values are $v+z(1-2a)$ and the original $w$. Thus this toggles
+only the parity of $v$ when $z=1$, and restores the dirty temporary.
+
+Apply these four updates simultaneously, with $z_i=x_{j_i}$, to the low
+$n$ selected segments of $y$ and the digits $t_i$ of $t$. A target-slot
+update is one modular rotation of $y$, whose offsets are respectively
+\[
+ \sum_{i<n}2x_{j_i}t_i2^{j_i},\qquad
+ \sum_{i<n}x_{j_i}(1-2t_i)2^{j_i} \pmod{2^{fK}}.
+\]
+Both control fields precede $y$. For a temporary update, swap $t$ with $b$,
+rotate the back field by the packed selected bits of the current $y$, and
+swap back. For unloading, use minus the packed bits
+$y_{j_i}\mathbin\oplus x_{j_i}$. These controls precede the back field.
+There are four width-$nG$ swaps and four rotations. The arbitrary original
+contents of $b$ return after each pair of swaps.
+
+\paragraph{Later source.}
+If $x$ follows $y$, first execute the earlier-source construction with control
+bits $u_i\bmod2$. Load the selected bits of $x$ into $u$ by swapping $u,b$,
+rotating the back field by their packed radix-$B$ representation, and swapping
+back. Repeat the earlier-source construction with the new parities of $u$,
+then unload the selected bits of $x$ from $u$ by the inverse load.
+When the digit loads do not overflow, the two control parities differ by
+exactly $x_{j_i}$. The resulting target update is the required XOR, with
+$u,t,b$ restored. This version uses twelve compact swaps and ten rotations.
+Every offset depends on a fixed number of fields preceding its target.
+
+\paragraph{Guards and deterministic repair.}
+Temporarily omit the highest selected position. The low $n$ segments
+$[j_i,j_i+K)$ are disjoint and fit inside $y$, including when $\rho=K-1$.
+Write each initial segment as $2g_i+a_i$, $a_i\in\{0,1\}$.
+Declare an address bad if a $t$ digit is $B-1$, or a target guard fails
+\[
+ 2B\le g_i<2^{K-1}-2B.
+\]
+For a later source also declare it bad if any $u$ digit is $B-1$.
+On a good address each temporary load stays within its digit, and the target
+displacement is at most $2B$ in either execution of the four-step identity.
+The conservative guard interval therefore prevents every carry or borrow
+between the wide segments. After each completed identity the guard is
+unchanged. Induction through the later-source sequence proves the desired
+map on the good set, including restoration of every temporary and every
+unselected address bit.
+
+Uniform complete ranges give the common bound
+\[
+ \delta=\min\{1,n(2\cdot2^{-G}+8\cdot2^{G-K})\}
+\]
+on the bad fraction; for an earlier source the first factor 2 can be omitted.
+The ideal map $T$ changes only the selected target parities, so it preserves
+the bad set. The actual sequence $S$ is a bijection on the entire rectangle:
+each rotation is independent of its target and all swaps are bijections.
+Since $S=T$ off the bad set, $S$ preserves that set too. Thus $TS^{-1}$ is
+supported there, exactly as in the original exceptional-stream repair.
+
+Extract the bad records, retaining marked holes in the full stream. For each
+extracted address $q$, reverse the swaps and modular rotations to compute
+$S^{-1}q$, then compute $T(S^{-1}q)$. All fields and descriptors have $O(A)$
+bits. A constant number of offset calculations each scan at most $n\le A$
+digits and combine shifted integers of $O(A)$ bits. Integer arithmetic,
+mixed-radix decoding, inverse offsets and the destination key can consequently
+be computed in $O(A^3)$ per record. Sort only the extracted records by their
+$O(A)$-bit destination keys, using stable binary radix passes, then reinsert
+them in their marked holes. Keys are distinct and fill precisely those holes
+because $TS^{-1}$ permutes the bad set. This uses fixed tapes and costs
+\[
+ O(V+MA^3+\delta MA(R+A)).
+\]
+Every inverse offset is evaluated on the current inverse controls; modular
+overflow on bad addresses is handled exactly, rather than treated as an
+integer identity. Finally, supply the omitted highest selected position
+through the elementary two-bit XOR in $O(V)$ time.
+
+\begin{proposition}[Compact-control selected-bit addition]
+\label{prop:compact-selected-addition}
+Under the stated complete-field hypotheses, take
+\[
+ G=4\lceil\log_2 p\rceil+6,\quad f\le p,\quad A=O(p),
+ \quad K/\log p\longrightarrow\infty,
+\]
+and let $R$ exceed every fixed power of $p$. The exact selected-bit row
+addition, with all temporary fields restored, costs
+\[
+ O\bigl(V((f\log p)^\tau+1)\bigr)
+\]
+on a fixed number of tapes, for either order of the two slots. Constants and
+cutoffs are uniform within each fixed parameter family of the layer theorem.
+\end{proposition}
+\begin{proof}
+Use the retained arbitrary-width chunk-swap primitive for the at most twelve
+swaps, each of width $nG$. Its padding, cleanup and all spectator intervals
+are covered by that interface. For every rotation, apply
+Lemma~\ref{lem:record-paid-rotation}; its offset arithmetic is polynomial
+in $A$. No new record volume is introduced by describing the compact fields.
+For $\ell_p=\lceil\log_2 p\rceil$, eventually
+$K\ge G+4\ell_p+10$. Then
+\[
+ \delta\le \frac{5}{128p^3},\qquad
+ \frac{A^3}{R}=o(1),\qquad
+ \delta A(1+A/R)=O(p^{-2}).
+\]
+The repair is therefore $O(V)$ per call, including predicate scans and key
+arithmetic. The elementary highest-bit operation costs $O(V)$. All calls
+reuse their fixed work tapes and finish in the declared physical field order.
+\end{proof}
+
+\paragraph{Application to a fixed binary change of basis.}
+The original phase-frame construction expresses each binary basis change
+as a fixed number of row additions on $m$ slots of $f=e/m$ axes. Use the
+two slots of each addition as $x,y$ and the reserved front/back compact
+fields as controls. The complete basis change and its inverse cost
+$O(V((e\log p)^\tau+1))$. The reservations below guarantee their complete
+ranges, independently of which slots are involved, at every recursive node.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/copied-centers-assembly.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/copied-centers-assembly.tex
new file mode 100644
index 0000000000..b0c69166c3
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/copied-centers-assembly.tex
@@ -0,0 +1,118 @@
+\subsection{Selected semantic guard and product rows}
+For each local producer retain
+\[
+ g_h=4(c_h+v_h)+10v_h+4hv_h+4h^2+8h+8.
+\]
+The two-stage literal scalar count includes two additional groups per
+copied center and one endpoint-addition group per data pair:
+\[
+ G=N_c+2v(g_{28}+2\cdot28)=4793351472.
+\]
+These are local scalar charges; the recursive copied transformations
+are already included in $s_c$. Set
+\[
+\begin{aligned}
+ E&=64(W_c+m_c+G+1)^3=9696565176891520488192506033216,\\
+ \mathcal E&=2GW_c^2+8s_c+4W_c+4+32m_c\\
+           &=2771683137698171397039558468<E,\\
+ B_{
m guard}&=s_c+E,\qquad C_0=32m_cB_{
m guard}^2.
+\end{aligned}
+\]
+A completed $u$-axis child has coefficients in $2^{-u}\mathbb Z[i]$
+and absolute row sum at most $2^u$. Its internal excess stays local;
+other streams, including originals of active copies, are parked.
+No return rounding or encoding change is performed. A copied input
+has the same incoming magnitude/grid bound as its original, and its
+completed output obeys the same semantic bound. Consequently, with
+$f=\lfloor e/m_c\rfloor$,
+\[
+ A(e)\le A(756f)+s_cf+E\le2B_{
m guard}e,
+\]
+using $2B_{
m guard}(m_c-756)\ge s_c+E$ and the direct-leaf bound
+$A(e)\le8e$. Prefix kernels, phases and normalization add the retained
+$18e$, which is less than $C_0e-2B_{
m guard}e$. Thus $C_1=1$,
+with the fixed fine-grid precision proof of RaD/PR23 unchanged.
+
+The actual least halving degrees and wire bitlengths are
+\[
+ (t_b,w_b)=(9,28),\qquad(t_c,w_c)=(20,30),
+\]
+where $m_j^{t_j}>2r_j^{t_j}$ for largest children $r_b=529,r_c=756$.
+At width $e$ reserve the product
+$Q=W_c^{D_c(e)}W_b^{D_b(e)}$, with
+$D_j(e)=t_j\lceil\log_2e\rceil$. Its coefficient is
+$9\cdot28+20\cdot30=852$, and
+\[
+ 2000>\frac{51}{25}\,852.
+\]
+The sufficient stock is therefore $p^{2000}$, supplied by the retained
+physically preceding transformed prefix and a single complete-row
+padding. Nested bit stock is restored before another complex child.
+Sequential copies introduce no independent row field. The supplementary
+suffix condition $b_{\rm in}^{1-\epsilon}>8000(\log_2b_{\rm in}+8)$
+is eventual for fixed $\epsilon<1$.
+
+\subsection{Exact conditional assembly}
+Use the analytic proof map in
+\path{notes/structured-bulk-assembly.tex}: arbitrary-source routing
+with active masking and paid repair scans; one rounded phase-cell
+matrix with preserved period cuts and downward-weight error bounds;
+persistent target halos, sequential overlap tapes and factor pages;
+Baker--Harman--Pintz prime packing; and the retained exact-recovery
+interface. Their full costs are unchanged. In particular the bulk
+bound retains the terms
+\[
+ O\!\left(Tp\left[p^\tau\operatorname{polylog}p+
+ d\operatorname{polylog}p+dp^\delta+w^2p^\delta+
+ dw^2p^\delta/L\right]\right)+n^{o(1)},
+\]
+with $L=2^{\lceil8\log_2p\rceil}$,
+$w^2=O(p^{1-r})$, and normalization exponent requiring
+$\epsilon+r<1$. These arguments, not a change of arithmetic model,
+justify the seven margins below.
+
+\begin{theorem}[Conditional fixed-tape multiplication bound]
+Under the retained analytic and fixed-tape interfaces of PR23/PR29
+and the preceding proof map, the selected copied-center networks give
+\[
+ T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+ \boxed{\kappa=\frac{384569}{10000000000}=3.84569\times10^{-5}}.
+\]
+\end{theorem}
+\begin{proof}
+Take the strict finite savings $a=a_b=384599/10^{10}$ and
+$b=a_c=717/10^7$, with $\tau=1-a$, $\sigma=1-b$, and put
+\[
+\begin{gathered}
+ \eta=10^{-8},\quad\beta=\tfrac14,\quad q=a(1-2\eta),\quad
+ c=q(1+\eta),\quad\epsilon=\frac{1-\eta}{1+c+q},\\
+ \lambda'=1-q,\quad\lambda=(\tau+\lambda')/2,\quad
+ g=\epsilon q,\quad r=(g+1-\epsilon)/2,\quad\delta=\eta/8.
+\end{gathered}
+\]
+The stopped complex leaf saving $(1-\beta)b=53.775\times10^{-6}$
+is strictly above $a$, so paid internal adapters use exponent $\tau$
+and both layer exponents lie below $\lambda'$. The exact certificate
+checks all 47 strict constraints of the retained semantic/bulk
+composition, using the new literal scalar charge and product-row gap.
+These include compact reservations, geometry, the linear guard,
+$\epsilon+r<1$, phase-cell/band separation, prime packing, short-record
+fallback and artificial-boundary allowances.
+
+The seven final savings are
+\[
+ 1-\epsilon(1+c),\quad a,\quad g,\quad a,\quad
+ \min(1-\epsilon-\delta,r-\delta),\quad
+ 1-\epsilon-\delta,\quad\epsilon.
+\]
+Their minimum is exactly $g$ and the prefix margin equals $g+\eta$.
+Exact rational comparison gives
+\[
+ g-\frac{384569}{10^{10}}>4.0746056580\times10^{-11}>0.
+\]
+These positive gaps absorb fixed logarithms. The all-size conclusion
+retains constructive finite setup, descriptor and catalogue domination,
+prime existence and analytic recovery as eventual thresholds. The
+strict bit and complex moments, copied-stream recurrence contracts and
+these assembly inequalities prove the claimed conditional bound.
+\end{proof}
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/copied-centers-lemma.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/copied-centers-lemma.tex
new file mode 100644
index 0000000000..8933aaf508
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/copied-centers-lemma.tex
@@ -0,0 +1,103 @@
+\subsection{Scalar, frame and temporary-stream contracts}
+The retained source-copy, reversible mixer and scatter maps satisfy
+$JLV=I$. Over $\mathbb F_2$ the chronological word
+\[
+ L,\ J,\ L^{-1},\ V,\ L,\ J,\ L^{-1},\ V
+\]
+adds the input to the target and restores every arbitrary auxiliary.
+Over Gaussian dyadics use its corresponding old-value subtraction and
+new-value addition. A designated retained output has a distinct terminal
+output-use carrier: a matching may feed that carrier, but cannot merge
+two designated terminals or append a later middle-producer consumer.
+Its remaining uses before cleanup are its scatter reads, all of which
+leave its scalar value unchanged.
+
+Within one tensor invocation suppress the fixed future line and put
+\[
+ D_0=B\otimes F_h,\quad D_1=A\otimes F_h,\quad
+ A=B\mathbin{\perp}P,\quad D_U=D_0\mathbin{\perp}(P\otimes U),
+\]
+where $P$ and the suppressed future factor are one-dimensional and
+$U$ is a nondegenerate retained-center space of dimension $r$.
+Thus a local change of rank $d$ has ambient rank $d$.
+Write $\mathcal F_Q$ for the address frame: it is the rational partial
+swap $D_Q$ in the bit construction, and the binary phase $C_Q$ in the
+complex construction. Changing a copy from frame $Q_1$ to $Q_2$ means
+applying $\mathcal F_{Q_2}\mathcal F_{Q_1}^{-1}$ to its physical stream.
+Orthogonal backgrounds cancel in this quotient.
+
+Copies use Paureel's retained copy/transform/read/discard interface
+\cite{paureel,pr29}. A copy has precisely the original complete role
+stream, including all control and spectator ranges, and volume $V/W$.
+It is processed while inactive original streams are parked on the fixed
+depth-first stack tapes. Copying, pointwise reads and erasure are linear
+in that stream's volume. Sequential processing needs one additional
+fixed work stream, not an independently varying row coordinate.
+
+\begin{lemma}[Copied retained-center schedule]
+In either invocation orientation a designated retained center's
+physical rank profile can be changed from $z^r+z^h$ to
+$z^r+z^{h-r}$, with the same scalar action, original role endpoints,
+and arbitrary-scratch restoration. The rank-$r$ transform on the copy
+is included in the recursive call list.
+\end{lemma}
+\begin{proof}
+In the forward orientation the original center has scalar value $w$
+at frame $D_U$ after the middle mixer. Its old sequence was
+$D_U\to D_0\to D_1$: scatter at $D_0$, then cleanup at $D_1$,
+with ranks $r,h$.
+Keep the original at $D_U$, copy its physical stream, and transform
+only the copy to $D_0$, paying rank $r$. Supply every scatter read
+from that transformed copy while its data targets remain at their
+unchanged common frame $D_0$, then erase the temporary. The reads
+are exactly those of $w$ in the old schedule. Since they do not change
+$w$, move the original directly from $D_U$ to $D_1$ before its first
+cleanup incidence; this costs $h-r$. Every subsequent original gate
+therefore receives the same scalar value at its required frame.
+
+In the reverse complementary orientation the old sequence was
+$D_0\to D_1\to D_{U^\perp}$, with ranks $h,r$ and scatter at $D_1$.
+After the preceding all-$D_0$ operations, advance the original directly
+to $D_{U^\perp}=D_0\mathbin{\perp}(P\otimes U^\perp)$, paying
+$h-r$. Copy it and transform the copy to $D_1$, paying $r$.
+Use that copy for all early scatter reads, then erase it. The original
+already has the exact frame and unchanged scalar value required by the
+following inverse mixer. Terminal output-use separation ensures no
+intervening producer consumer has been bypassed.
+
+For partial swaps either direction of the rank-$r$ change is the same
+involution. For complex phases the forward copy uses $C_U^{-1}$,
+the direct original growth uses $C_{U^\perp}$, and the reverse copy
+uses $C_FC_{U^\perp}^{-1}=C_U$. These are the same charged ranks,
+implemented by the retained forward/inverse residual interface.
+All tensor backgrounds cancel as stated. Every original scalar
+incidence, final source-copy cancellation and auxiliary source/sink
+operator is unchanged. Thus the scalar identity and all endpoints
+remain exact on arbitrary initial auxiliary values.
+\end{proof}
+
+For the selected centers $r=h-1$, and there are $h$ distinct retained
+output uses per invocation. Their old histogram has rank mass
+$hR_h+2\ell_h$, where $\ell_h=h(h-1)$. The new histogram is exactly
+\[
+ H'_{h,1}=H_{h,1}+h,\qquad H'_{h,h}=H_{h,h}-h,
+ \qquad H'_{h,r}=H_{h,r}\quad(r\ne1,h),
+\]
+and hence $\sum_r rH'_{h,r}=hR_h+\ell_h$.
+Every old rank-$(h-1)$ residual remains as a paid transform of a copy;
+its projector and ordinary bit pivot profile are unchanged. Only the
+full-rank original transition becomes the rank-one complement.
+The physical role count $R_h$ is unchanged.
+
+For two factors, put $N=v_av_b$, $B_a=v_bR_a$, $B_b=v_aR_b$,
+$W=2N+B_a+B_b$ and $L=v_b\ell_a+v_a\ell_b$.
+All exterior, data-front and endpoint-correction calls remain in place.
+The resulting complete rank mass is
+\[
+ s=Wm-N+L,\qquad Wm-s=N-L.
+\]
+This follows by subtracting exactly $L$ from the retained two-stage
+physical mass $Wm-N+2L$. The $N$ rank-one endpoint-copy calls are
+separate and remain fully charged. Because center copies retain the
+same complete role-volume fraction $1/W$, the existing complete-row,
+integer-width remainder and fixed-tape recurrence proofs apply.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/endpoint-gauge-complex.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/endpoint-gauge-complex.tex
new file mode 100644
index 0000000000..907a0ceda8
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/endpoint-gauge-complex.tex
@@ -0,0 +1,225 @@
+\subsection{A normal form for every nondegenerate binary residual}
+Let $E$ have binary basis matrix $V$ and nonsingular Gram matrix
+$G=V^tV$. In dual Fourier coordinates put
+$q(z)=\operatorname{wt}(VG^{-1}z)\pmod4$.
+Its polarization is $2z^tG^{-1}w$. The same argument applies to mixed
+signs on orthogonal summands, since reversing a sign preserves this
+polarization. Write $S_q=\sum_z i^{q(z)}$. Completing the square gives
+\[
+\begin{aligned}
+K(x,y)&=2^{-r}\sum_z i^{q(z)}(-1)^{z^t(x+y)}\\
+ &=2^{-r}S_q\,i^{-q(Gx)}(-1)^{x^tGy}i^{-q(Gy)}.
+\end{aligned}
+\]
+The scaled Walsh kernel in the middle is a binary permutation of
+$H_0^{\otimes r}$, where
+\[
+ H_0=\tfrac12\begin{pmatrix}1&1\\1&-1\end{pmatrix}
+     =bSCS,\qquad b=(1-i)/2,\quad S=\operatorname{diag}(1,i).
+\]
+The remaining scalar $S_qb^r$ is a fourth root of unity. To verify
+this, decompose the nondegenerate quadratic module into odd
+one-dimensional and alternating two-dimensional blocks. Their Gauss
+sums are $1\pm i$ and $\pm2$, respectively; multiplying by $b$ and
+$b^2$ gives a fourth root in each case. This is a proof device, not
+an orthonormal-basis assumption on $E$.
+
+Consequently one rank-$r$ child suffices, with binary address changes,
+diagonal fourth-root phases, and one scalar fourth-root phase.
+On $f$ parallel columns it is one $C^{\otimes rf}$ child, the scalar
+raised to power $f$, and columnwise quadratic phases modulo four.
+The retained packed address operations evaluate these fixed formulas.
+These wrappers have modulus one and introduce no denominator loss.
+
+\subsection{The selected Gaussian-dyadic producer}
+Use paired triple exclusion with base threshold two, complete unsplit
+disjoint and pair-star sums, and sharing by actual ordinary support.
+For an ordinary support with at least two common points use the span
+of its triple indicators; these form an orthonormal common-pair star.
+Otherwise use the coordinate space of its union. Support inclusion
+preserves these labels: losing the common pair enters a containing
+coordinate space. Source lines use ordinary triple containment.
+
+Retain every full pair-star $P_{uv}=\sum_{w\ne u,v}X_{uvw}$ and form
+$B_u=\sum_{v\ne u}P_{uv}=2\sum_{T\ni u}X_T$.
+For even $h$ label these central additions by the nondegenerate
+hyperplane $E_u=\{x:\sum_{j\ne u}x_j=0\}$; every contributing star
+lies in it. Retain the global total $T$ with full-space label.
+The central correction at target $S$ is
+\[
+ \frac14\sum_{u\in S}B_u-\frac12T
+       =\sum_U\frac{|S\cap U|-1}{2}X_U.
+\]
+Adding half the disjoint sum and subtracting half the intersection-two
+sum gives exactly $X_S$. All coefficients are Gaussian dyadic.
+The transparent retained-output wrapper and oriented carrier compiler
+apply to these nested nondegenerate labels. The $h$ hyperplane centers
+lose $h(h-1)$ and the global center loses $h$, so loss is $h^2$.
+The selected counts, including all point centers, are
+\[
+\begin{array}{c|rrrrrr}
+h&v_h&c_h&q_h&|\mathcal M_h|&R_h&\text{loss}\\\hline
+32&4960&122512&19873&19241&123144&1024\\
+30&4060&99153&16271&15873&99551&900\\
+40&9880&252023&39561&37642&253942&1600
+\end{array}
+\]
+Their internal histograms satisfy $\sum_r rH_{h,r}=hR_h+2h^2$.
+They are distinct from the bit histograms.
+
+\subsection{Endpoint normalization and the complex characteristic}
+For nondegenerate $U$, Fourier phases give
+\[
+ C_U^2=X_{P_U\mathbf1},\qquad
+ C_{U^\perp}C_U^{-1}=C_FX_{P_U\mathbf1}.
+\]
+Put $v=P_U\mathbf1$. On coordinates in $v$, this endpoint has
+$C^{-1}$ instead of $C$. The identity $C^{-1}=-iZCZ$ shows that
+conjugating by $Z_v$ and multiplying by $i^{\operatorname{wt}(v)}$
+normalizes it to $C_F$; for $f$ columns the exponent is
+$f\operatorname{wt}(v)$. These are diagonal wrappers without a child.
+
+Choose stage-two source $C_{D_0}$ and sink $C_{D_0^\perp}$, where
+$D_1=D_0\mathbin{\perp} A$ and $\dim A=b$. The same refined copy
+schedule removes the entrance on every auxiliary role. With
+$R=D_1^\perp$, the exit is $C_RC_{D_0}^{-1}$ on
+$E=R\mathbin{\perp}D_0=A^\perp$. Its rank is $m-b$ and its
+nondegenerate polar form is unchanged by the mixed signs. The normal
+form above executes it as one child. Arbitrary auxiliary restoration
+justifies the endpoint normalization on the entire $B_2$ bank.
+
+Use the complex counts to define $B_i=NR_{h_i}/v_{h_i}$, and now
+\[
+\begin{aligned}
+W&=2N+B_2+B_3=10390178240000,\\
+L&=\sum_i(N/v_{h_i})h_i^2=117399987200,\\
+s&=Wm-2N+2L=398982681296998400.
+\end{aligned}
+\]
+The whole-residual macro list is
+\[
+\begin{array}{c|rrrrr}
+t&38328&38360&38370&37401&899\\\hline
+n_t&B_1&B_3-B_1&B_2&2N&2N.
+\end{array}
+\]
+Add $(N/v_h)H_{h,r}$ rank-$r$ children for each positive internal rank.
+Leave the remaining physical-data rank, 39393978624000, as singleton
+calls. The resulting list has weighted rank exactly $s$.
+For $a_c=3/125000$ and $\sigma=1-a_c$, the rational logarithm bounds
+above and $e^u\le(1-u)^{-1}$, $0\le u<1$, give
+\[
+ \Psi_c(\sigma)\le\sum_t\frac{n_tt}{Wm(1-a_c\ell_t)}
+ <1-\frac{792981575160764}{10^{23}}.
+\]
+
+\subsection{The dependency-path guard}
+Before gauging, nested producer labels telescope along every arithmetic
+path, including wire switches at common-frame scalar gates. Retained
+center drops occur on one return frontier per stage, crossed at most
+once by a path, and each costs at most that axis dimension. Carrier
+reuse adds only increasing continuations. This gives
+$q_0=m+2(a+b+k)$. Gauging removes an early edge and adds $ab-b$ at
+a late stage-two edge. A path meets at most one such edge, since it
+terminates that stage-two role, which is not shared across stages.
+Thus the conservative total rank budget is
+\[
+ q=m+2(a+b+k)+ab=39564.
+\]
+Every child except the four large macros is at most 899; two large
+macros cannot fit within $q$. Set $\rho=19/10$, $\gamma=9997/10000$.
+The integer comparisons $m^{19}>500000000^{10}$ and
+$899^9<460^{10}$ give $m^\rho>500000000$ and
+$899^{\rho-1}<460$.
+If a path has one large child $t$, its moment is at most
+\[
+ (t/m)^\rho+(q-t)899^{\rho-1}/m^\rho.
+\]
+This expression increases over the large-child range, since its
+numerator derivative is $\rho t^{\rho-1}-899^{\rho-1}>0$.
+Use $t=m-b$ and the concavity bound
+$(1-x)^{19/10}\le1-19x/10+9x^2/10$ to obtain
+\[
+ \sum_{\rm path}(r/m)^\rho
+ <1-\frac{19}{12800}+\frac9{10\cdot1280^2}
+       +\frac{1194\cdot460}{500000000}
+ =\frac{51180270301}{51200000000}<\gamma.
+\]
+Without a large macro the bound is $227493/6250000<\gamma$.
+
+For coefficient-depth accounting take $E_0=128(W+m+1)^3$.
+There are at most $s$ positive-rank residual calls and $W$ endpoint
+normalizations. Combining the quadratic phases with the $S$ factors,
+each uses at most two diagonal phase passes and one scalar phase.
+The inherited gate and remainder count is therefore bounded conservatively by
+\[
+ 36W^3+16s+16W+8m+4<E_0.
+\]
+Binary address changes only permute coefficients; descriptor evaluation
+is paid by the retained packed record work and does not increase
+coefficient depth.
+Stop below width $d^\beta$, where $\beta=1/1000$.
+For $e=mf+r$, $0\le r<m$, recurse on $tf$ and treat the remainder
+individually. For sufficiently large $d$, a leaf descending from an
+internal node has width at least $d^\beta/(2m)$. Choose
+$C_{\rm dep}\ge16m$ and
+$(1-\gamma)C_{\rm dep}\ge E_0+16m+1$.
+The retained elementary-kernel bound $A(e)\le8e$ and strong induction
+using the path moment imply
+\[
+ A(e)\le C_{\rm dep}d^{-\beta(\rho-1)}e^\rho.
+\]
+At a leaf the lower width bound proves this inequality, while at an
+internal node the unused $1-\gamma$ fraction covers local work.
+Small roots are handled directly. With $\zeta=1/10000$ take
+\[
+ C_1=\rho-(\rho-1)\beta+\zeta=\frac{1187}{625},\quad
+ C_0=\left\lceil128m(1+1/\zeta)C_{\rm dep}\right\rceil,
+ \quad\Delta=\lceil C_0d^{C_1}\rceil.
+\]
+The retained exact denominator/magnitude-depth induction gives
+$p+\Delta$ fractional bits and $\Delta+3$ integer/sign bits.
+All selected scalar coefficients are Gaussian dyadic and the new
+wrappers have modulus one, so that induction still applies.
+For $\epsilon C_1<1$ their total width is $O(p)$.
+\subsection{Rows, stopping, and transfer to the layer interface}
+Let $t_*<m$ be the largest child and compute
+$D(e)=0$ for $e<m$ and $D(e)=1+D(t_*\lfloor e/m\rfloor)$ otherwise.
+It is $O(\log e)$ and bounds every descendant depth.
+With the retained compact-control parameters, reserve
+\[
+ q_0=\lceil\log_2W\rceil D(d),\qquad Q_0=q_0+q_F+q_B.
+\]
+Process the first $q_0+q_F$ and last $q_B$ selected axes individually;
+if at most $Q_0$ axes exist, process them all individually. Otherwise
+the middle active interval is consecutive. Only the $q_0$ row chunks
+supply row indices, separate from the two compact fields. Pad their
+count once to a multiple of $W^{D(d)}$, by a factor below two.
+Every child retains complete compact and spectator ranges and has
+exactly $1/W$ of its parent's volume. No internal padding is needed.
+The reserved-axis bound remains
+\[
+ Q_0=O(\log(2d)+d^{\max\{1-c,0\}}\log p+1).
+\]
+Remainders commute with the completed tensor map and cost $O(V)$ per
+node. The fixed-tape depth-first scheduler and complete-row argument
+of the bit construction apply with the retained compact descriptors.
+
+Since $\Psi_c(\sigma)<1$, the total leaf $\sigma$-weighted width,
+including the volume factor $W^{-j}$ at depth $j$, is at most
+$d^\sigma$. Thus leaf work is
+$O(d^{\sigma+\beta(1-\sigma)})$. Internal compact operations cost
+$O(G^\tau e^\tau+1)$ per current volume. Summing the strict moments
+gives the retained complete normalized layer bound
+\[
+ O\!\left((\log p)^3\left[
+ d^\chi+d^{\sigma+\beta(1-\sigma)}+d^{\max\{1-c,0\}}+1
+ \right]\right),\qquad
+ \chi=\tau+(1-\beta)\max\{\sigma-\tau,0\}.
+\]
+For $\sigma\le\tau$, use $\Psi_c(\tau)\le\Psi_c(\sigma)$;
+otherwise use $e^\tau\le d^{\beta(\tau-\sigma)}e^\sigma$ at each
+internal node. These arguments do not assume equal leaf depth.
+The usual strict conditions on $\lambda,\lambda'$ therefore give
+the retained $O(Vd^{\lambda'})$ layer interface, now with the new
+moment and the new $C_{\rm dep}$.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/general-clifford-frames.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/general-clifford-frames.tex
new file mode 100644
index 0000000000..0367eeb005
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/general-clifford-frames.tex
@@ -0,0 +1,102 @@
+\subsection{Preimage frames for arbitrary binary subspaces}
+This frame construction is due to icekylinx with OpenAI GPT-6 Astra assistance;
+the present exposition and integration use Codex.
+Let $H=\mathbb F_2^h$ with the standard dot product. In the binary
+symplectic space $H\oplus H$ put
+\[
+ L_0=\{(0,z)\},\qquad
+ F=\begin{pmatrix}I&I\\0&I\end{pmatrix},\qquad
+ L_F=FL_0=\{(z,z)\}.
+\]
+We also write $F$ for the exact Gaussian-dyadic operator $C^{\otimes h}$.
+Its exact square is a Pauli translation; only its binary symplectic square
+is the identity. For an exact Clifford operator $T$ the frame label is
+$L(T)=T^{-1}L_0$. The physical transition from $T$ to $S$ is $ST^{-1}$,
+and its Fourier rank is
+$d(L(S),L(T))$, where $d(L,L')=h-\dim(L\cap L')$.
+This follows by transporting the intersection by $S$: the intersection
+with $L_0$ computes the kernel dimension of the $B$ block of $ST^{-1}$.
+
+\begin{lemma}
+For every subspace $U\subseteq H$, including degenerate subspaces,
+\[
+ L_U=\{(u,u+v):u\in U,\ v\in U^\perp\}
+\]
+is Lagrangian, and
+\[
+ d(L_U,L_V)=\dim U+\dim V-2\dim(U\cap V),\qquad
+ FL_U=L_{U^\perp}.
+\]
+\end{lemma}
+\begin{proof}
+The displayed parametrization is injective and has dimension $h$.
+Its symplectic pairing is $u\cdot v'+v\cdot u'=0$.
+In an intersection, $u$ belongs to $U\cap V$ and $v$ to
+$(U+V)^\perp$, giving the asserted dimension and distance.
+Finally $F(u,u+v)=(v,u+v)$ proves the complement identity.
+\end{proof}
+
+\subsection{Exact representatives and nested children}
+Choose a deterministic invertible binary matrix $G$ carrying the first
+$r=\dim U$ coordinate space $E_r$ to $U$, and set
+\[
+ K_G=\begin{pmatrix}G&0\\G+G^{-T}&G^{-T}\end{pmatrix},\qquad
+ T_U=K_G T_{E_r}K_G^{-1}.
+\]
+Here $T_{E_r}$ is the exact coordinate $C$ operator, and the $K_G$ are
+exact Gaussian-dyadic Clifford lifts. The matrix $K_G$ is symplectic
+because $G^TG+I$ is symmetric. It fixes both $L_0,L_F$ and maps $L_V$
+to $L_{GV}$. Thus both $K_G$ and $FK_GF^{-1}$ have Fourier rank zero;
+their lifts are fixed binary address permutations with unit quadratic
+phases. In particular,
+\[
+ L(T_U)=L_U,\quad \operatorname{rank}B(T_U)=r,\quad
+ \operatorname{rank}B(FT_UF^{-1})=r,\quad T_U^2\text{ is Pauli}.
+\]
+Set $V_U=GE_r^\perp$, a direct complement of $U$. The binary action gives
+$T_U^{-1}L_F=L_{V_U}$ and hence
+$\operatorname{rank}B(FT_U^{-1})=h-r$.
+No assertion $V_U=U^\perp$ is needed.
+For the norm-one source lines and their orthogonal target hyperplanes,
+retain the inherited exact representatives; set $T_0=I,T_H=F$.
+At every common scalar gate use one identical exact representative on all
+incident registers. If separately transported representatives have the
+same preimage, their physical ratio has rank zero and is implemented as
+an actual left adapter before the gate.
+
+For $U\subseteq V$, the exact transition $T_VT_U^{-1}$ has rank
+$\dim V-\dim U$. Clifford elimination expresses it as two rank-zero
+adapters surrounding that many coordinate Fourier factors. These factors
+are a single $C^{\otimes r}$ child: the scaled Hadamard satisfies
+\[
+ \frac{1+i}{2}\begin{pmatrix}1&1\\1&-1\end{pmatrix}
+   =SCS,\qquad S=\operatorname{diag}(1,i).
+\]
+Thus no new irrational field is introduced. All adapters are charged
+finite movement and scalar operations. Exact transitions telescope;
+commutativity between distinct $T_U$ is unnecessary.
+
+\subsection{Dirty tails and reverse/complement words}
+A dirty role entering with gauge $T_\sigma$ and whose last active frame
+is $T_U$, with $\sigma\subseteq U$, is assigned terminal gauge
+$FT_\sigma$. Its logical value is restored by the complete transparent
+scalar word, so its physical action is exactly $F$. The tail is
+$FT_\sigma T_U^{-1}$. Its rank is
+\[
+ d(L_U,L_{V_\sigma})=h-\dim U+\dim\sigma.
+\]
+Indeed $H=\sigma\oplus V_\sigma$ and $U\supseteq\sigma$ imply
+$\dim(U\cap V_\sigma)=\dim U-\dim\sigma$.
+An inactive exterior adds $m-h$, giving $m-\dim U+\dim\sigma$.
+
+For the complete time-reversed word use
+\[
+ D_U=T_UF^{-1},\qquad L(D_U)=L_{U^\perp},\qquad
+ D_UD_V^{-1}=T_UT_V^{-1}.
+\]
+The last equality is exact, so reversal preserves every inverse transition
+rank. Reverse the scalar signs and the whole transparent word, including
+old-value corrections and final cleanup. The endpoints $D_0=F^{-1}$
+and $F$ differ by a Pauli, and the inherited norm-one endpoints are
+reconciled by actual rank-zero adapters. Neither equality of binary
+matrices nor equality of frame cosets substitutes for these operators.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/stopped-product-complex.tex b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/stopped-product-complex.tex
new file mode 100644
index 0000000000..4a9037137c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/retained/stopped-product-complex.tex
@@ -0,0 +1,137 @@
+\subsection{All-disjoint retained centers}
+Use two factors $h=24$. For triple inputs write $G=\sum_TX_T$,
+$T_i=\sum_{T\ni i}X_T$, and retain all $A_i=G-T_i$.
+Each input triple avoids exactly 21 points, so
+\[
+ \sum_{i=1}^{24}A_i=21G,\qquad G=\frac1{21}\sum_i A_i.
+\]
+For a target triple $S$ the central correction is
+\[
+ G-\frac12\sum_{i\in S}A_i
+       =\frac{\sum_{i\in S}T_i-G}{2}.
+\]
+An input triple meeting $S$ in $j$ points has central coefficient
+$(j-1)/2$. Adding half the disjoint sum and subtracting half the
+intersection-two sum leaves coefficient one exactly when $j=3$.
+The scalar source-to-scatter transfer is therefore the identity.
+The transparent old-value subtraction and new-value addition use this
+identity only on fresh contributions and restore arbitrary old values.
+
+The base-two paired exclusion and aligned pair-star producer retains
+nested binary labels: common-pair supports have their orthonormal triple
+span, other ordinary sums have their coordinate cover. Each retained
+$A_i$ has the nondegenerate coordinate hyperplane excluding $i$,
+of dimension 23. Hence all copied-center arguments and general
+nondegenerate binary residuals of the preceding proof apply. The
+selected local counts are
+\[
+ v=2024,\quad c_h=45764,\quad q_h=8120,\quad
+ |\mathcal M|=8966,\quad R=44918,\quad\ell=552.
+\]
+The old internal histogram, starting at rank zero, is
+\begin{small}\begin{align*}
+[&8930,49042,30844,15972,11883,8272,6399,4356,6682,2263,\\
+ &5109,1808,5317,1733,5391,1757,4908,3290,6233,4363,\\
+ &4056,264,564,24,24].
+\end{align*}\end{small}
+It has rank mass $24R+2\ell$. Replace 24 rank-24 original transitions
+by 24 rank-one transitions; all rank-23 copied transforms remain.
+The new mass is $24R+\ell$.
+
+\subsection{Physical endpoints and strict complex moment}
+The copied-center two-stage complex contract in
+\path{notes/copied-centers-complex.tex} is unchanged by the scalar
+center decoding. For the tensor triple line $U$, let
+$T=C_U$, $F=C_I$, $E=C_{U^\perp}=FT^{-1}$.
+The two data outputs are $A=-Fy$ and $B=FT^{-2}x+Ey$.
+Add $T^{-1}$ applied to a copy of $A$ into $B$, paying one rank-one
+child per data pair. The inherited input/output $Z$ phases and
+$i^{9f}$ scalar normalize $FT^{-2}$ to $F$; sign and bank corrections
+complete the exact tensor $C$. Auxiliary source/sink operators remain
+$C_{D_0}$ and $FC_{D_0}$ in the second stage. Every original role
+therefore returns the exact selected-axis tensor operation on arbitrary
+inputs. This algebraic statement holds over $\mathbb Q(i)$ as well as
+over Gaussian dyadics.
+
+With $m_c=576$, $N_c=v^2=4096576$, $B_c=vR=90914032$, put
+\[
+ W_c=2N_c+2B_c=190021216,\quad L_c=2v\ell=2234496,
+\]
+\[
+ s_c=W_cm_c-N_c+L_c=109450358336,\qquad N_c-L_c=1862080.
+\]
+The complete list is $2B_c$ width-552 auxiliary exteriors,
+$2N_c$ width-529 data macros, $2vH'_r$ width-$r$ internal children,
+$4N_c$ width-23 data fronts, and $N_c$ width-one endpoint copies.
+These disjoint classes include both kinds of paid copies and sum to
+$s_c$. All binary residuals, including alternating forms, use the retained
+one-child Gauss normal form with paid bit adapters and unit phases.
+At $a_c=1949/25000000$ the exact rational enclosure gives
+\[
+ \sum_r\frac{n_r}{W_c}(r/m_c)^{1-a_c}
+ <1-1.3338373969\times10^{-10}.
+\]
+
+\subsection{One exact odd-denominator grid}
+The only new odd divisor is 21. Let $d$ bound the root axis count,
+$D$ bound its maximum complex recursion depth, and $G_0$ bound the
+number of grouped scalar operations per node. Choose
+\[
+ K=G_0(D+1),\qquad \text{common grid }2^{-P}21^{-K}.
+\]
+Root inputs and arbitrary dirty auxiliaries start Gaussian dyadic.
+Multiply their integer numerators by $21^K$ once at the outer boundary.
+Every local coefficient contains at most one factor 21 in its denominator,
+so a local finite program adds at most $G_0$ to the odd-denominator
+exponent. A completed $u$-axis child has Gaussian-dyadic coefficients
+and therefore preserves its input's existing odd-denominator exponent;
+it adds no new odd factor. Only the active chain of unfinished calls
+can accumulate new factors. Its length is at most $D+1$, proving that
+all intermediates lie on the common grid and every local division by
+21 is an exact integer division of its encoded numerator.
+
+This divisibility claim uses the root dyadic-input invariant, not an
+assumption about arbitrary numerators on the finest grid. Internal values
+may have odd denominators. They are neither rounded nor re-encoded when
+a child returns. At the completed outer return the operator is the exact
+Gaussian-dyadic tensor on root dyadic inputs, so the final numerators
+are divisible by $21^K$; exact unscaling restores dyadic encoding.
+
+Since the largest child is $552<576$, $D=O(\log d)$ and
+$K=O(\log d)$ with fixed constants. Constant-divisor long division
+is linear in numerator length. Initial and final scaling by $K$
+successive constant multiplications/divisions cost $O(V\log d)$ and
+occur only at the outer boundary. The extra numerator length is
+$O(\log d)$, preserving the retained $O(p)$ word bound. This overhead
+is subordinate to the positive-power complex layer bound.
+
+For explicit semantic constants use
+\[
+ g_h=4(c_h+v)+10v+4hv+4h^2+8h+8=408200,
+\]
+\[
+ G_0=N_c+2v(g_h+2h)=1656684480,
+\]
+where endpoint additions and copied-center scalar work are included.
+The complete child contributes at most $u$ binary denominator bits
+and row-norm factor $2^u$, with no additional odd exponent. A local
+21-division contributes fewer than five denominator-height bits,
+covered by the fixed scalar charge. Set
+\[
+\begin{aligned}
+ E_0&=64(W_c+m_c+G_0+1)^3=403063477262941121443761178688,\\
+ \mathcal E&=2G_0W_c^2+8s_c+4W_c+4+32m_c\\
+           &=119639333593035096270287748<E_0,\\
+ B_0&=s_c+E_0,\qquad C_0=32m_cB_0^2.
+\end{aligned}
+\]
+With $f=\lfloor e/m_c\rfloor$, the completed-child induction is
+\[
+ A(e)\le A(552f)+s_cf+E_0\le2B_0e,
+\]
+since $2B_0(m_c-552)\ge s_c+E_0$. It counts total denominator height
+and magnitude, including the local odd factor. The retained prefix and
+normalization allowance $18e$ fits inside $C_0e$. Together with the
+$O(\log d)$ common-grid encoding overhead this gives $C_1=1$ and
+$O(p)$ records for $d=\lfloor b_{\rm in}^{\epsilon}\rfloor$,
+$p=6b_{\rm in}$, fixed $\epsilon<1$.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/source-pins.json b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/source-pins.json
new file mode 100644
index 0000000000..5cb04b0c72
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/source-pins.json
@@ -0,0 +1,215 @@
+{
+  "schema": "primary-complex-input-pins/1",
+  "certificate": {
+    "compressed_sha256": "15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633",
+    "uncompressed_sha256": "c64d2a95431c3cf24452de7391cce780bd71521da44ce23923ebb235f6c7962c",
+    "path": "inputs/complex/gcert1-p11-pr193.json.gz"
+  },
+  "files": {
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+      "upstream": "Work/Bridge/Cert.lean",
+      "source_pin": "f010392c923279e3dd59ef3aa5fedad23affc5fd",
+      "url": "https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/Bridge/Cert.lean"
+    },
+    "inputs/complex/sources/Work__Bridge__Net.lean": {
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+    },
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+      "sha256": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+      "upstream": "notes/general-clifford-frames.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/endpoint-gauge-complex.tex": {
+      "sha256": "dfee33b0281e5551bb6927f757ff0240abade60ae1800f715afd88853ae0191e",
+      "upstream": "notes/endpoint-gauge-complex.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/copied-centers-lemma.tex": {
+      "sha256": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe",
+      "upstream": "notes/copied-centers-lemma.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/copied-centers-assembly.tex": {
+      "sha256": "00117892971ae766188ace0af03030c44164fda105e42b70d84f52c3339a7dcb",
+      "upstream": "notes/copied-centers-assembly.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/stopped-product-complex.tex": {
+      "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a",
+      "upstream": "notes/stopped-product-complex.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/compact-control-layout.tex": {
+      "sha256": "2bc28e50f3eb092195294cafa81213e520f6d42e7935e9905ad8a6199e2a7c87",
+      "upstream": "notes/compact-control-layout.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/compact-control-movement.tex": {
+      "sha256": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+      "upstream": "notes/compact-control-movement.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/FINITE_BRIDGE.txt": {
+      "sha256": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46",
+      "upstream": "research/source-assisted/global/FINITE_BRIDGE.txt",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    }
+  }
+}
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Bridge__Cert.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Bridge__Cert.lean
new file mode 100644
index 0000000000..f7bdc3d903
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Bridge__Cert.lean
@@ -0,0 +1,241 @@
+import Work.Bridge.Net
+
+/-!
+# (key: bridge-net) The certificate of the BRIDGED five-stage network B_2
+
+The three layers of free gates between twins, the signed exchange, and
+
+    theorem bridge2_certificate (N : Bridge2 H T Sl C α Γ) :
+        BCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) (fun φ => card Γ * N.unit φ)
+
+Scalar chain of one class (`x1 y1 x2 y2` on `X1 Y1 X2 Y2`), as in `bridged-word.md`:
+
+    stage 0  F on pair 1     Y1 = y1 + x1
+    stage 1  B on pair 1     X1 = -y1
+    gates A  X1 += X2,  Y2 -= Y1
+    stage 2  F on pair 1     Y1 = x1 + x2
+    gates B  Y2 += Y1,  X1 -= X2          (X1 = -y1, Y2 = y2 - y1 + x2)
+    stage 3  B on pair 2     X2 = y1 - y2
+    stage 4  F on pair 2     Y2 = x2
+    gates C  Y1 -= Y2,  X2 += X1          (X1 = -y1, X2 = -y2, Y1 = x1, Y2 = x2)
+    exchange X_i := Y_i, Y_i := -X_i
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace BR
+open Binary Matrix Finset RAM SS CB RF
+noncomputable section
+
+section Gates
+variable {Γ T Sl C : Type}
+
+/-- source of the gates of the layers A and B: `X1 ← X2`, `Y2 ← Y1`. -/
+def pAB : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kX2 (g,t)) (fun g t => kY1 (g,t)) (fun g t => kX2 (g,t))
+    (fun g t => kY1 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+/-- layer A: `X1 += X2`, `Y2 -= Y1`. -/
+def kA : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => -1) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- layer B: `X1 -= X2`, `Y2 += Y1`. -/
+def kB : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => -1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- source of the gates of the layer C: `Y1 ← Y2`, `X2 ← X1`. -/
+def pC : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kX1 (g,t)) (fun g t => kY2 (g,t)) (fun g t => kX1 (g,t))
+    (fun g t => kY2 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+/-- layer C: `Y1 -= Y2`, `X2 += X1`. -/
+def kCc : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 0) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- scalar map of a gate layer. -/
+def gsc (p : BRole Γ T Sl C → BRole Γ T Sl C) (k : BRole Γ T Sl C → ℚ)
+    (x : BRole Γ T Sl C → ℂ) : BRole Γ T Sl C → ℂ := fun i => x i + (k i : ℂ) * x (p i)
+
+/-- the signed exchange `X_i := Y_i`, `Y_i := -X_i` on both pairs. -/
+def bpull : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kY1 (g,t)) (fun g t => kX1 (g,t)) (fun g t => kY2 (g,t))
+    (fun g t => kX2 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+def bsgn : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 1) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => 1)
+
+variable [Fintype Γ] [DecidableEq Γ] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+def brecM : Matrix (BRole Γ T Sl C) (BRole Γ T Sl C) ℚ :=
+  fun i j => if j = bpull i then bsgn i else 0
+
+lemma actPoint_brecM (x : BRole Γ T Sl C → ℂ) (i : BRole Γ T Sl C) :
+    actPoint brecM x i = (bsgn i : ℂ) * x (bpull i) := by
+  unfold actPoint
+  rw [sum_eq_single (bpull i)]
+  · simp [brecM]
+  · intro j _ hj; simp [brecM, hj]
+  · simp
+
+/-- the scalar map of the whole network before the exchange, on one class. -/
+def chain (x : BRole Γ T Sl C → ℂ) : BRole Γ T Sl C → ℂ :=
+  gsc pC kCc (lift2 GF (lift2 GB (gsc pAB kB (lift1 GF (gsc pAB kA (lift1 GB (lift1 GF x)))))))
+
+/-- **The scalar identity of the bridged chain**: `X_i = -y_i`, `Y_i = x_i` on both pairs,
+helper slots unchanged. -/
+lemma chain_eq (x : BRole Γ T Sl C → ℂ) (l : BLive Γ T Sl) :
+    chain x (Sum.inl l) = mkB (fun g t => -x (kY1 (g,t))) (fun g t => x (kX1 (g,t)))
+      (fun g t => -x (kY2 (g,t))) (fun g t => x (kX2 (g,t)))
+      (fun g q => x (kS (g,q))) (fun g c => x (kC (g,c))) (Sum.inl l) := by
+  rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+  all_goals
+    simp only [chain, gsc, lift1, lift2, GF, GB, mkB, mkS, pAB, pC, kA, kB, kCc, pos1, pos2,
+      kX1, kY1, kX2, kY2, kS, kC, jX, jY, jS, jC, Function.comp_apply]
+    first
+      | (push_cast; ring)
+      | (push_cast; done)
+      | ring
+
+end Gates
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : Bridge2 H T Sl C α Γ)
+
+/-- gate layer A, after stage 1 and the first idle climb of pair 2: twins have equal frames. -/
+lemma Bridge2.gateA : XRoute N.S3 N.S3 (gsc pAB kA) (fun _ => 0) := by
+  refine gateP pAB kA N.S3 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer B, after stage 2 and the second idle climb of pair 2. -/
+lemma Bridge2.gateB : XRoute N.S5 N.S5 (gsc pAB kB) (fun _ => 0) := by
+  refine gateP pAB kB N.S5 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact N.x23 g t
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (N.y23 g t).symm
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer C, after the final climbs. -/
+lemma Bridge2.gateC : XRoute N.S8 N.S8 (gsc pC kCc) (fun _ => 0) := by
+  refine gateP pC kCc N.S8 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact (hk rfl).elim
+  · rfl
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- the free shifts at the end. -/
+def Bridge2.corr : BRole Γ T Sl C → Space α :=
+  mkB (fun _ _ => 0) (fun g t => N.u g t) (fun _ _ => 0) (fun g t => N.u g t)
+    (fun _ _ => 0) (fun _ _ => 0)
+
+def Bridge2.S9 : BRole Γ T Sl C → CMat α := fun r => shift (N.corr r) * N.S8 r
+
+/-- the whole word before the exchange: five stages, three idle-climb layers, three gate
+layers. -/
+lemma Bridge2.route :
+    XRoute N.S0 N.S8 chain (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R := ((((((((((N.stage0.trans N.stage1).trans N.climbA).trans N.gateA).trans
+    N.stage2).trans N.climbB).trans N.gateB).trans N.stage3).trans N.stage4).trans
+    N.fin).trans N.gateC)
+  refine (R.castg ?_).cast (fun φ => ?_)
+  · rfl
+  · simp only [Bridge2.unit]
+    ring
+
+/-- **The scratch certificate of the bridged five-stage network with shared helper sets**,
+in whole blocks, with its exact price for every price list. -/
+theorem bridge2_certificate :
+    BCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C)
+      (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R2 : XRoute N.S8 N.S9 id (fun _ => 0) := XRoute.shifts N.hm N.S8 N.corr
+  have R3 : XRoute N.S9 (fun r => N.S9 (bpull r)) (actPoint brecM) (fun _ => 0) :=
+    XRoute.gate brecM N.S9 _ (fun i j h => by
+      have hj : j = bpull i := by
+        by_contra hne
+        exact h (by simp [brecM, hne])
+      rw [hj])
+  have Rt := ((N.route.trans R2).trans R3).cast (c' := fun φ => (Fintype.card Γ : ℝ) * N.unit φ)
+    (fun φ => by first | ring | simp)
+  have hSinv : ∀ r, ∃ M, N.S0 r * M = 1 := by
+    rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.M0 g).Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.M0 g).Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact ⟨1, Matrix.mul_one _⟩
+    · exact ⟨1, Matrix.mul_one _⟩
+  choose S' hS' using hSinv
+  have hT : ∀ l : BLive Γ T Sl, N.S9 (bpull (Sum.inl l)) = kernel α * N.S0 (Sum.inl l) := by
+    rintro (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.M0 g).Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.M0 g).Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.M0 g).Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.M0 g).Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (0 : Space α) * kernel α = kernel α * 1
+      rw [shift_zero, Matrix.one_mul, Matrix.mul_one]
+  have hg : ∀ x : BRole Γ T Sl C → ℂ,
+      (∀ s, (∀ l : BLive Γ T Sl, (Sum.inl l : BRole Γ T Sl C) ≠ s) → x s = 0) →
+      ∀ l : BLive Γ T Sl,
+        (actPoint brecM ∘ (id ∘ chain)) x (Sum.inl l) = x (Sum.inl l) := by
+    intro x _ l
+    change actPoint brecM (chain x) (Sum.inl l) = _
+    rw [actPoint_brecM]
+    rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX1 (g,t)) = x (kX1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY1 (g,t))) = x (kY1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX2 (g,t)) = x (kX2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY2 (g,t))) = x (kY2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inr (g,q))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kS (g,q)) = x (kS (g,q))
+      first | (push_cast; ring) | simp
+  exact XRoute.liveKernel (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) N.S0 S'
+    (fun r => N.S9 (bpull r)) hS' _ _ Rt hg hT
+
+end Net
+end
+end BR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BR.chain_eq
+#print axioms OAI.PowerSaving.BR.Bridge2.route
+#print axioms OAI.PowerSaving.BR.bridge2_certificate
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Bridge__Net.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Bridge__Net.lean
new file mode 100644
index 0000000000..204f6d9cf9
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Bridge__Net.lean
@@ -0,0 +1,345 @@
+import Work.Bridge.Inv
+
+/-!
+# (key: bridge-net) The BRIDGED five-stage network B_2 with shared helper sets, abstract form
+
+Generalises `RF.Fold3S` / `RF.fold3s_certificate` (`Work.Reframe.SCert`) to the bridged word
+of PLAN2.md B1: every class `(g,t)` has TWO bank pairs `(X1,Y1)`, `(X2,Y2)` with the same
+line; five stages of invocations
+
+    stage 0  forward   on pair 1      invocation of the class (g,t):  g
+    stage 1  backward  on pair 1                                      r1 t g
+    stage 2  forward   on pair 1                                      r2 t g
+    stage 3  backward  on pair 2                                      r3 t g
+    stage 4  forward   on pair 2                                      r4 t g
+
+and three layers of FREE gates between twins at equal frames:
+
+    after stage 1 (pair 2 has climbed to the frames of pair 1):   X1 += X2,  Y2 -= Y1
+    after stage 2 (pair 2 has climbed one more window):           Y2 += Y1,  X1 -= X2
+    after the final climbs (all four roles at their end frames):  Y1 -= Y2,  X2 += X1
+
+Result on both pairs: `X_i = -y_i`, `Y_i = x_i`; then the usual signed exchange.
+
+The idle pair does not move during a stage.  Its climbs are ONE block per role:
+`aX2`, `aY2` (pair 2 before the first gate layer, prices `caX`, `caY`; in B_2 ONE block of
+rank `2h-2` each),
+the window of stage 2 (pair 2 before the second gate layer, rank `card H - 1`, from the
+package: `Inv.climbX`, `Inv.climbY`), `fX1`, `fY1` (pair 1 at the end, prices `cX1`, `cY1`;
+in B_2 ONE block of rank `2h+2` each), `fX2`, `fY2` (pair 2 at the end, prices `cX2`, `cY2`;
+in B_2 one block of rank `4` each).  The prices are arbitrary functions of the price list, so
+a geometry that makes an idle climb in several blocks can be plugged in as well.
+
+`Bridge2 H T Sl C α Γ` is everything the wiring needs to know about the geometry;
+`bridge2_certificate`: a `BCert` on the live roles `BLive Γ T Sl`
+(`card Γ * (4 card T + card Sl)` of them, `BR.card_BLive`) whose price, for EVERY price
+list, is `card Γ * N.unit φ`,
+
+    N.unit φ = 5 * N.I.cost φ + card T * ((caX φ + caY φ) + 2 * bcost φ (card H - 1)
+                 + (cX1 φ + cY1 φ) + (cX2 φ + cY2 φ)).
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace BR
+open Binary Matrix Finset RAM SS CB RF
+noncomputable section
+
+/-- See the file header.  Fields in the style of `RF.Fold3S`; stages are numbered 0 to 4. -/
+structure Bridge2 (H T Sl C α Γ : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α] where
+  /-- the invocation (for a block circuit `X`: `X.inv`). -/
+  I : Inv H T Sl C
+  /-- frame maps of the invocations of the five stages. -/
+  M0 : Γ → XMap H α
+  M1 : Γ → XMap H α
+  M2 : Γ → XMap H α
+  M3 : Γ → XMap H α
+  M4 : Γ → XMap H α
+  /-- the class `(g,t)` is served by the invocation `g` in stage 0 and `r_l t g` in stage `l`. -/
+  r1 : T → Γ ≃ Γ
+  r2 : T → Γ ≃ Γ
+  r3 : T → Γ ≃ Γ
+  r4 : T → Γ ≃ Γ
+  /-- the invocation `d` of stage `l` uses the helper set (and the copies) `s_l d`. -/
+  s1 : Γ ≃ Γ
+  s2 : Γ ≃ Γ
+  s3 : Γ ≃ Γ
+  s4 : Γ ≃ Γ
+  /-- inverse of the frame of the base, and frame of the window, of every invocation. -/
+  N1 : Γ → CMat α
+  W1 : Γ → CMat α
+  N2 : Γ → CMat α
+  W2 : Γ → CMat α
+  N3 : Γ → CMat α
+  W3 : Γ → CMat α
+  N4 : Γ → CMat α
+  W4 : Γ → CMat α
+  u : Γ → T → Space α
+  YF : Γ → T → CMat α
+  hm : 2 ≤ Fintype.card α
+  /-- prices of the idle climbs, for every price list.  B_2 with merged climbs:
+  `caX = caY = fun φ => bcost φ (2h-2)`, `cX1 = cY1 = fun φ => bcost φ (2h+2)`,
+  `cX2 = cY2 = fun φ => bcost φ 4`. -/
+  caX : (ℕ → ℝ) → ℝ
+  caY : (ℕ → ℝ) → ℝ
+  cX1 : (ℕ → ℝ) → ℝ
+  cY1 : (ℕ → ℝ) → ℝ
+  cX2 : (ℕ → ℝ) → ℝ
+  cY2 : (ℕ → ℝ) → ℝ
+  inv0 : ∀ g t, ∃ N : CMat α, (M0 g).Φ (tt (I.tv t)) * N = 1
+  z0 : ∀ g, (M0 g).Φ 0 = 1
+  hN1 : ∀ d, (M1 d).Φ 0 * N1 d = 1
+  hW1 : ∀ d, (M1 d).Φ 1 = W1 d * (M1 d).Φ 0
+  hN2 : ∀ d, (M2 d).Φ 0 * N2 d = 1
+  hW2 : ∀ d, (M2 d).Φ 1 = W2 d * (M2 d).Φ 0
+  hN3 : ∀ d, (M3 d).Φ 0 * N3 d = 1
+  hW3 : ∀ d, (M3 d).Φ 1 = W3 d * (M3 d).Φ 0
+  hN4 : ∀ d, (M4 d).Φ 0 * N4 d = 1
+  hW4 : ∀ d, (M4 d).Φ 1 = W4 d * (M4 d).Φ 0
+  /-- the bank frames a stage leaves are the bank frames the next stage starts from. -/
+  x01 : ∀ g t, (M0 g).Φ 1 = (M1 (r1 t g)).Φ (tt (I.tv t))
+  y01 : ∀ g t, (M0 g).Φ (1 + tt (I.tv t)) = (M1 (r1 t g)).Φ 0
+  x12 : ∀ g t, (M1 (r1 t g)).Φ 1 = (M2 (r2 t g)).Φ (tt (I.tv t))
+  y12 : ∀ g t, (M1 (r1 t g)).Φ (1 + tt (I.tv t)) = (M2 (r2 t g)).Φ 0
+  x23 : ∀ g t, (M2 (r2 t g)).Φ 1 = (M3 (r3 t g)).Φ (tt (I.tv t))
+  y23 : ∀ g t, (M2 (r2 t g)).Φ (1 + tt (I.tv t)) = (M3 (r3 t g)).Φ 0
+  x34 : ∀ g t, (M3 (r3 t g)).Φ 1 = (M4 (r4 t g)).Φ (tt (I.tv t))
+  y34 : ∀ g t, (M3 (r3 t g)).Φ (1 + tt (I.tv t)) = (M4 (r4 t g)).Φ 0
+  /-- the five windows of a helper set make up the kernel. -/
+  sfin : ∀ g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) *
+    (W1 (s1.symm g) * (M0 g).Φ 1))) = kernel α
+  /-- pair 2, idle in stages 0 and 1: ONE block from its start frame to the frame of its
+  twin after stage 1. -/
+  aX2 : ∀ g t, XReach ((M0 g).Φ (tt (I.tv t))) ((M1 (r1 t g)).Φ 1) caX
+  aY2 : ∀ g t, XReach ((M0 g).Φ 0) ((M1 (r1 t g)).Φ (1 + tt (I.tv t))) caY
+  /-- pair 1, idle in stages 3 and 4: ONE block from its frame after stage 2 to the end. -/
+  fX1 : ∀ g t, XReach ((M2 (r2 t g)).Φ 1) (kernel α) cX1
+  fY1 : ∀ g t, XReach ((M2 (r2 t g)).Φ (1 + tt (I.tv t))) (YF g t) cY1
+  /-- pair 2 after stage 4: ONE final block. -/
+  fX2 : ∀ g t, XReach ((M4 (r4 t g)).Φ 1) (kernel α) cX2
+  fY2 : ∀ g t, XReach ((M4 (r4 t g)).Φ (1 + tt (I.tv t))) (YF g t) cY2
+  term : ∀ g t, kernel α * (M0 g).Φ (tt (I.tv t)) = shift (u g t) * YF g t
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : Bridge2 H T Sl C α Γ)
+
+/-- price of the blocks of one unit (one element of `Γ`): five invocations and the idle
+climbs of the four bank roles of every class. -/
+def Bridge2.unit (φ : ℕ → ℝ) : ℝ :=
+  5 * N.I.cost φ + (Fintype.card T : ℝ) * ((N.caX φ + N.caY φ)
+    + 2 * bcost φ (Fintype.card H - 1)
+    + (N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ))
+
+/-- scratch copies always enter and leave with the matrix `1` (also: the helper slots at the
+start, with `C := Sl`). -/
+def cOne (Γ C α : Type) [Fintype α] [DecidableEq α] : Γ → C → CMat α := fun _ _ => 1
+
+/-- the bank index of stage 0: the class `(g,t)` belongs to the invocation `g`. -/
+abbrev bid (Γ T : Type) : T → Γ ≃ Γ := fun _ => Equiv.refl Γ
+
+/-! bank frames of the class `(g,t)`: `xi l`, `yi l` at the START of stage `l`; `xo l`,
+`yo l` at the END of stage `l` (only where no next stage follows on that pair). -/
+def Bridge2.xi0 (g : Γ) (t : T) : CMat α := (N.M0 g).Φ (tt (N.I.tv t))
+def Bridge2.yi0 (g : Γ) (t : T) : CMat α := (N.M0 g).Φ 0
+def Bridge2.xi1 (g : Γ) (t : T) : CMat α := (N.M1 (N.r1 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi1 (g : Γ) (t : T) : CMat α := (N.M1 (N.r1 t g)).Φ 0
+def Bridge2.xi2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ 0
+def Bridge2.xo2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ 1
+def Bridge2.yo2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ (1 + tt (N.I.tv t))
+def Bridge2.xi3 (g : Γ) (t : T) : CMat α := (N.M3 (N.r3 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi3 (g : Γ) (t : T) : CMat α := (N.M3 (N.r3 t g)).Φ 0
+def Bridge2.xi4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ 0
+def Bridge2.xo4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ 1
+def Bridge2.yo4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ (1 + tt (N.I.tv t))
+
+/-- helper slots after the stages 0, 1, 2, 3, 4 (at the start: `cOne Γ Sl α`). -/
+def Bridge2.Z1 : Γ → Sl → CMat α := fun g _ => (N.M0 g).Φ 1
+def Bridge2.Z2 : Γ → Sl → CMat α := fun g q => N.W1 (N.s1.symm g) * N.Z1 g q
+def Bridge2.Z3 : Γ → Sl → CMat α := fun g q => N.W2 (N.s2.symm g) * N.Z2 g q
+def Bridge2.Z4 : Γ → Sl → CMat α := fun g q => N.W3 (N.s3.symm g) * N.Z3 g q
+def Bridge2.Z5 : Γ → Sl → CMat α := fun g q => N.W4 (N.s4.symm g) * N.Z4 g q
+
+/-- frames: at the start; after stage 0; after stage 1; after the first idle climb of pair 2
+(first gate layer here); after stage 2; after the second idle climb of pair 2 (second gate
+layer here); after stage 3; after stage 4; after the final climbs (third gate layer here). -/
+def Bridge2.S0 : BRole Γ T Sl C → CMat α := mkB N.xi0 N.yi0 N.xi0 N.yi0 (cOne Γ Sl α) (cOne Γ C α)
+def Bridge2.S1 : BRole Γ T Sl C → CMat α := mkB N.xi1 N.yi1 N.xi0 N.yi0 N.Z1 (cOne Γ C α)
+def Bridge2.S2 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi0 N.yi0 N.Z2 (cOne Γ C α)
+def Bridge2.S3 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi2 N.yi2 N.Z2 (cOne Γ C α)
+def Bridge2.S4 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi2 N.yi2 N.Z3 (cOne Γ C α)
+def Bridge2.S5 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi3 N.yi3 N.Z3 (cOne Γ C α)
+def Bridge2.S6 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi4 N.yi4 N.Z4 (cOne Γ C α)
+def Bridge2.S7 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xo4 N.yo4 N.Z5 (cOne Γ C α)
+def Bridge2.S8 : BRole Γ T Sl C → CMat α :=
+  mkB (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) (cOne Γ C α)
+
+/-- stage 0: forward on pair 1, every helper set starts at the matrix `1`. -/
+lemma Bridge2.stage0 :
+    XRoute N.S0 N.S1 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_fwd N.I (bid Γ T) (Equiv.refl Γ) N.M0 (fun _ => 1) (fun g => (N.M0 g).Φ 1)
+    (fun d => by rw [N.z0, Matrix.mul_one]) (fun d => by rw [N.z0, Matrix.mul_one])
+    (cOne Γ Sl α) (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv (bid Γ T) N.M0
+      (fun g (q : Sl) => (N.M0 ((Equiv.refl Γ).symm g)).Φ 1 * cOne Γ Sl α g q) (cOne Γ C α)
+      = mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x01 g t
+    · exact N.y01 g t
+    · show (N.M0 g).Φ 1 * 1 = (N.M0 g).Φ 1
+      rw [Matrix.mul_one]
+    · rfl
+  have h' : XRoute (bIn N.I.tv (bid Γ T) N.M0 (cOne Γ Sl α) (cOne Γ C α))
+      (mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α)) GF (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift1 N.xi0 N.yi0 h'
+
+/-- stage 1: backward on pair 1; the helper set `g` serves the invocation `s1⁻¹ g`. -/
+lemma Bridge2.stage1 :
+    XRoute N.S1 N.S2 (lift1 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_bwd N.I N.r1 N.s1 N.M1 N.N1 N.W1 N.hN1 N.hW1 N.Z1 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r1 N.M1 (fun g q => N.W1 (N.s1.symm g) * N.Z1 g q) (cOne Γ C α)
+      = mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x12 g t
+    · exact N.y12 g t
+    · rfl
+    · rfl
+  have h' : XRoute (bIn N.I.tv N.r1 N.M1 N.Z1 (cOne Γ C α))
+      (mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift1 N.xi0 N.yi0 h'
+
+/-- stage 2: forward on pair 1. -/
+lemma Bridge2.stage2 :
+    XRoute N.S3 N.S4 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  blift1 N.xi2 N.yi2
+    (istage_fwd N.I N.r2 N.s2 N.M2 N.N2 N.W2 N.hN2 N.hW2 N.Z2 (cOne Γ C α) (cOne Γ C α))
+
+/-- stage 3: backward on pair 2. -/
+lemma Bridge2.stage3 :
+    XRoute N.S5 N.S6 (lift2 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_bwd N.I N.r3 N.s3 N.M3 N.N3 N.W3 N.hN3 N.hW3 N.Z3 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r3 N.M3 (fun g q => N.W3 (N.s3.symm g) * N.Z3 g q) (cOne Γ C α)
+      = mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x34 g t
+    · exact N.y34 g t
+    · rfl
+    · rfl
+  have h' : XRoute (bIn N.I.tv N.r3 N.M3 N.Z3 (cOne Γ C α))
+      (mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift2 N.xo2 N.yo2 h'
+
+/-- stage 4: forward on pair 2. -/
+lemma Bridge2.stage4 :
+    XRoute N.S6 N.S7 (lift2 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  blift2 N.xo2 N.yo2
+    (istage_fwd N.I N.r4 N.s4 N.M4 N.N4 N.W4 N.hN4 N.hW4 N.Z4 (cOne Γ C α) (cOne Γ C α))
+
+/-- first idle climb of pair 2 (stages 0 and 1 in ONE block per role), to the frames of
+pair 1 after stage 1. -/
+lemma Bridge2.climbA :
+    XRoute N.S2 N.S3 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (N.caX φ + N.caY φ))) := by
+  have H1 := XRoute.reach_all N.S2 N.S3
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ => N.caX)
+      (fun _ _ => N.caY) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.M0 g).Φ (tt (N.I.tv t))) ((N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))) N.caX
+        rw [← N.x12 g t]
+        exact N.aX2 g t
+      · show XReach ((N.M0 g).Φ 0) ((N.M2 (N.r2 t g)).Φ 0) N.caY
+        rw [← N.y12 g t]
+        exact N.aY2 g t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- second idle climb of pair 2: the window of stage 2, ONE block of rank `card H - 1` per
+role, to the frames of pair 1 after stage 2. -/
+lemma Bridge2.climbB :
+    XRoute N.S4 N.S5 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (2 * bcost φ (Fintype.card H - 1)))) := by
+  have H1 := XRoute.reach_all N.S4 N.S5
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ φ => bcost φ (Fintype.card H - 1))
+      (fun _ _ φ => bcost φ (Fintype.card H - 1)) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))) ((N.M3 (N.r3 t g)).Φ (tt (N.I.tv t)))
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.x23 g t]
+        exact N.I.climbX (N.M2 (N.r2 t g)) t
+      · show XReach ((N.M2 (N.r2 t g)).Φ 0) ((N.M3 (N.r3 t g)).Φ 0)
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.y23 g t]
+        exact N.I.climbY (N.M2 (N.r2 t g)) t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- the final climbs: pair 1 from its frames after stage 2 (ONE block per role for the
+stages 3, 4 and the rest), pair 2 from its frames after stage 4; the helper slots are
+already at the kernel. -/
+lemma Bridge2.fin :
+    XRoute N.S7 N.S8 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * ((N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ)))) := by
+  have H1 := XRoute.reach_all N.S7 N.S8
+    (mkB (fun _ _ => N.cX1) (fun _ _ => N.cY1) (fun _ _ => N.cX2) (fun _ _ => N.cY2)
+      (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact N.fX1 g t
+      · exact N.fY1 g t
+      · exact N.fX2 g t
+      · exact N.fY2 g t
+      · show XReach (N.W4 (N.s4.symm g) * (N.W3 (N.s3.symm g) * (N.W2 (N.s2.symm g) *
+          (N.W1 (N.s1.symm g) * (N.M0 g).Φ 1)))) (kernel α) (fun _ => 0)
+        rw [N.sfin g]
+        exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+end Net
+end
+end BR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BR.Bridge2.stage0
+#print axioms OAI.PowerSaving.BR.Bridge2.stage1
+#print axioms OAI.PowerSaving.BR.Bridge2.stage2
+#print axioms OAI.PowerSaving.BR.Bridge2.stage3
+#print axioms OAI.PowerSaving.BR.Bridge2.stage4
+#print axioms OAI.PowerSaving.BR.Bridge2.climbA
+#print axioms OAI.PowerSaving.BR.Bridge2.climbB
+#print axioms OAI.PowerSaving.BR.Bridge2.fin
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Carrier__Live.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Carrier__Live.lean
new file mode 100644
index 0000000000..b8306527d6
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Carrier__Live.lean
@@ -0,0 +1,232 @@
+import Work.Carrier.Pack
+import Work.Carrier.Ring
+
+/-!
+# (key: carrier-thm) The live roles of an invocation, and the four dirt gates as matrices
+
+`L3 T Sl = (T ⊕ T) ⊕ Sl`: the bank roles `x` (`lX`), `y` (`lY`) and the helper slots (`lS`), all
+on the same footing (no scratch copies).  `PX`, `PY`: the coordinate projectors.
+
+For the matrix `M` of all gates of the main phase and its inverse `Mi`:
+
+    g1 M  = 1 - PY * M * PS      `y -= K s`            g1i M = 1 + PY * M * PS   (its inverse)
+    g8 Mi = PX + PY + PS * Mi    slot rows of `M⁻¹`    h8 M  = PX + PY + PS * M  (its inverse)
+
+(`PS = 1 - PX - PY`).  This file: unit rows / columns of these gates (hence between which roles
+their entries can be nonzero), the scatter with the copies eliminated (`scatM`), and the scalar
+maps of `1 + PY * M * PX` and of the transpose of `1 - PY * M * PX`.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace CR
+open Binary Matrix Finset RAM SS CB BR
+noncomputable section
+
+section Diag
+variable {ρ : Type*} [Fintype ρ] [DecidableEq ρ]
+
+lemma col_zero_of {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : G * Matrix.diagonal d = Matrix.diagonal d) {i j : ρ} (hj : d j = 1) (hij : i ≠ j) :
+    G i j = 0 := by
+  have e := congrFun (congrFun h i) j
+  rw [Matrix.mul_diagonal, Matrix.diagonal_apply_ne _ hij, hj, mul_one] at e
+  exact e
+
+lemma row_zero_of {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : Matrix.diagonal d * G = Matrix.diagonal d) {i j : ρ} (hi : d i = 1) (hij : i ≠ j) :
+    G i j = 0 := by
+  have e := congrFun (congrFun h i) j
+  rw [Matrix.diagonal_mul, Matrix.diagonal_apply_ne _ hij, hi, one_mul] at e
+  exact e
+
+lemma diag_mul_of_rows {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : ∀ i j, d i ≠ 0 → G i j = if i = j then 1 else 0) :
+    Matrix.diagonal d * G = Matrix.diagonal d := by
+  ext i j
+  rw [Matrix.diagonal_mul]
+  by_cases hd : d i = 0
+  · rw [hd, zero_mul]
+    by_cases hij : i = j
+    · subst hij; rw [Matrix.diagonal_apply_eq, hd]
+    · rw [Matrix.diagonal_apply_ne _ hij]
+  · rw [h i j hd]
+    by_cases hij : i = j
+    · subst hij; rw [if_pos rfl, mul_one, Matrix.diagonal_apply_eq]
+    · rw [if_neg hij, mul_zero, Matrix.diagonal_apply_ne _ hij]
+
+lemma mul_diag_of_cols {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : ∀ i j, d j ≠ 0 → G i j = if i = j then 1 else 0) :
+    G * Matrix.diagonal d = Matrix.diagonal d := by
+  ext i j
+  rw [Matrix.mul_diagonal]
+  by_cases hd : d j = 0
+  · rw [hd, mul_zero]
+    by_cases hij : i = j
+    · subst hij; rw [Matrix.diagonal_apply_eq, hd]
+    · rw [Matrix.diagonal_apply_ne _ hij]
+  · rw [h i j hd]
+    by_cases hij : i = j
+    · subst hij; rw [if_pos rfl, one_mul, Matrix.diagonal_apply_eq]
+    · rw [if_neg hij, zero_mul, Matrix.diagonal_apply_ne _ hij]
+
+/-- scalar map of a diagonal gate matrix. -/
+lemma act_diag (d : ρ → ℚ) (u : ρ → ℂ) :
+    actPoint (Matrix.diagonal d) u = fun i => ((d i : ℚ) : ℂ) * u i := by
+  funext i
+  show ∑ j, ((Matrix.diagonal d i j : ℚ) : ℂ) * u j = ((d i : ℚ) : ℂ) * u i
+  rw [Finset.sum_eq_single i]
+  · rw [Matrix.diagonal_apply_eq]
+  · intro j _ hj
+    rw [Matrix.diagonal_apply_ne _ (Ne.symm hj), Rat.cast_zero, zero_mul]
+  · intro h
+    exact absurd (Finset.mem_univ i) h
+
+lemma actPoint_mul (A B : Matrix ρ ρ ℚ) (u : ρ → ℂ) :
+    actPoint (A * B) u = actPoint A (actPoint B u) :=
+  ap_mul A B u
+
+end Diag
+
+section Live
+variable {T Sl : Type} [Fintype T] [DecidableEq T] [Fintype Sl] [DecidableEq Sl]
+
+/-- live roles of one invocation: `x`, `y`, helper slots. -/
+abbrev L3 (T Sl : Type) := (T ⊕ T) ⊕ Sl
+abbrev lX (t : T) : L3 T Sl := Sum.inl (Sum.inl t)
+abbrev lY (t : T) : L3 T Sl := Sum.inl (Sum.inr t)
+abbrev lS (q : Sl) : L3 T Sl := Sum.inr q
+
+/-- indicator of the x roles. -/
+def iX : L3 T Sl → ℚ := Sum.elim (Sum.elim (fun _ => 1) (fun _ => 0)) (fun _ => 0)
+/-- indicator of the y roles. -/
+def iY : L3 T Sl → ℚ := Sum.elim (Sum.elim (fun _ => 0) (fun _ => 1)) (fun _ => 0)
+
+def PX : Matrix (L3 T Sl) (L3 T Sl) ℚ := Matrix.diagonal iX
+def PY : Matrix (L3 T Sl) (L3 T Sl) ℚ := Matrix.diagonal iY
+
+lemma iX_cases (i : L3 T Sl) : iX i = 0 ∨ iX i = 1 := by
+  rcases i with ((t|t)|q)
+  · exact Or.inr rfl
+  · exact Or.inl rfl
+  · exact Or.inl rfl
+
+lemma iY_cases (i : L3 T Sl) : iY i = 0 ∨ iY i = 1 := by
+  rcases i with ((t|t)|q)
+  · exact Or.inl rfl
+  · exact Or.inr rfl
+  · exact Or.inl rfl
+
+lemma PX_sq : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PX = PX := by
+  unfold PX
+  have e : (fun i : L3 T Sl => iX i * iX i) = iX := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX]
+  rw [Matrix.diagonal_mul_diagonal, e]
+
+lemma PY_sq : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PY = PY := by
+  unfold PY
+  have e : (fun i : L3 T Sl => iY i * iY i) = iY := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iY]
+  rw [Matrix.diagonal_mul_diagonal, e]
+
+lemma PX_PY : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PY = 0 := by
+  unfold PX PY
+  rw [Matrix.diagonal_mul_diagonal]
+  have e : (fun i : L3 T Sl => iX i * iY i) = fun _ => 0 := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX, iY]
+  rw [e]
+  exact Matrix.diagonal_zero
+
+lemma PY_PX : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PX = 0 := by
+  unfold PX PY
+  rw [Matrix.diagonal_mul_diagonal]
+  have e : (fun i : L3 T Sl => iY i * iX i) = fun _ => 0 := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX, iY]
+  rw [e]
+  exact Matrix.diagonal_zero
+
+lemma PX_T : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ)ᵀ = PX := Matrix.diagonal_transpose _
+lemma PY_T : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ)ᵀ = PY := Matrix.diagonal_transpose _
+
+/-- "no gate into an x role": the x rows are unit rows. -/
+lemma PX_mul_of {M : Matrix (L3 T Sl) (L3 T Sl) ℚ}
+    (hx : ∀ t j, M (lX t) j = if lX t = j then 1 else 0) : PX * M = PX := by
+  unfold PX
+  apply diag_mul_of_rows
+  intro i j hi
+  rcases i with ((t|t)|q)
+  · exact hx t j
+  · exact absurd rfl hi
+  · exact absurd rfl hi
+
+/-- "no gate reads a y role": the y columns are unit columns. -/
+lemma mul_PY_of {M : Matrix (L3 T Sl) (L3 T Sl) ℚ}
+    (hy : ∀ i t, M i (lY t) = if i = lY t then 1 else 0) : M * PY = PY := by
+  unfold PY
+  apply mul_diag_of_cols
+  intro i j hj
+  rcases j with ((t|t)|q)
+  · exact absurd rfl hj
+  · exact hy i t
+  · exact absurd rfl hj
+
+/-! ### the four dirt gates -/
+
+def g1 (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  1 - PY * M * (1 - PX - PY)
+def g1i (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  1 + PY * M * (1 - PX - PY)
+def g8 (Mi : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  PX + PY + (1 - PX - PY) * Mi
+def h8 (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  PX + PY + (1 - PX - PY) * M
+
+/-- a gate with unit x rows and unit x columns joins two different roles only if neither is an
+x role. -/
+lemma offdiag_x {G : Matrix (L3 T Sl) (L3 T Sl) ℚ} (h1 : G * PX = PX) (h2 : PX * G = PX)
+    {i j : L3 T Sl} (hij : G i j ≠ 0) (e : i ≠ j) : iX i = 0 ∧ iX j = 0 := by
+  constructor
+  · by_contra h
+    exact hij (row_zero_of h2 ((iX_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (col_zero_of h1 ((iX_cases j).resolve_left h) e)
+
+/-- a gate with unit x rows, unit y rows and unit y columns: a nonzero entry off the diagonal
+is in a slot row and not in a y column. -/
+lemma offdiag_s {G : Matrix (L3 T Sl) (L3 T Sl) ℚ} (hx : PX * G = PX) (hy : PY * G = PY)
+    (hyc : G * PY = PY) {i j : L3 T Sl} (hij : G i j ≠ 0) (e : i ≠ j) :
+    iX i = 0 ∧ iY i = 0 ∧ iY j = 0 := by
+  refine ⟨?_, ?_, ?_⟩
+  · by_contra h
+    exact hij (row_zero_of hx ((iX_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (row_zero_of hy ((iY_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (col_zero_of hyc ((iY_cases j).resolve_left h) e)
+
+lemma g1_x (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : g1 M * PX = PX ∧ PX * g1 M = PX := by
+  unfold g1
+  constructor
+  · rw [sub_mul, one_mul, side_n_right (PX_sq (T := T) (Sl := Sl)) PY_PX, sub_zero]
+  · rw [mul_sub, mul_one, side_n_left (PX_PY (T := T) (Sl := Sl)), sub_zero]
+
+lemma g1i_x (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : g1i M * PX = PX ∧ PX * g1i M = PX := by
+  unfold g1i
+  constructor
+  · rw [add_mul, one_mul, side_n_right (PX_sq (T := T) (Sl := Sl)) PY_PX, add_zero]
+  · rw [mul_add, mul_one, side_n_left (PX_PY (T := T) (Sl := Sl)), add_zero]
+
+end Live
+end
+end CR
+end PowerSaving
+end OAI
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean
new file mode 100644
index 0000000000..305da15b5d
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean
@@ -0,0 +1,192 @@
+import Work.Carrier.Glue
+
+/-!
+# (key: carrier-thm) A carrier circuit given by its phases: hypotheses and scalar identities
+
+`Phased H T Sl C` is the hypothesis structure of the carrier invocation theorem in the general
+scope (any ordered mix of gates `(x, slot)`, `(slot, slot)`, `(x, y)`, `(slot, y)`):
+
+* phase A (before the scatter), phase B (after it) and the final climbs F are exact block routes
+  on the LIVE roles `L3 T Sl` (`x`, `y`, slots: all on the same footing), for every block frame
+  map, with the gate products `MA`, `MB` (and the transposed inverses for the backward word);
+* the scatter goes through the scratch copies: `c += Cc s` at the labels `cen`, the copies come
+  down, `y += Jr c` at 0;
+* `hx`: no gate INTO an x role, `hy`: no gate READS a y role, `hid`: the y roles receive exactly
+  the x roles — three facts about the ONE matrix `Mt = MB * scatM (Jr * Cc) * MA`.
+
+This file: `Mt`, its inverse `Mti`, and the scalar identities of the forward and of the backward
+word (`fwd_scalar`, `bwd_scalar`): with the two dirt gates `g1`, `g8` (resp. the transposes of
+`g1i`, `h8`) the word does `y += x` (resp. `x -= y`) for ARBITRARY slot contents.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace CR
+open Binary Matrix Finset RAM SS CB BR
+noncomputable section
+
+/-- labels of the live roles at the START of an invocation. -/
+def lab3 {H T Sl : Type} (tv : T → Space H) : L3 T Sl → Lbl H :=
+  Sum.elim (Sum.elim (fun t => lineL (tv t)) (fun _ => zeroL)) (fun _ => zeroL)
+
+/-- **The hypotheses of the carrier invocation theorem, by phases.**  See the file header. -/
+structure Phased (H T Sl C : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] where
+  tv : T → Space H
+  kx : ∀ t, Climb (lineL (tv t)) fullL
+  ky : ∀ t, Climb zeroL (perpL (tv t))
+  cen : C → Lbl H
+  kc : ∀ k, Climb zeroL (cen k)
+  Cc : Matrix C Sl ℚ
+  Jr : Matrix T C ℚ
+  labA : L3 T Sl → Lbl H
+  labB : L3 T Sl → Lbl H
+  labF : L3 T Sl → Lbl H
+  hAy : ∀ t, (labA (lY t)).P = 0
+  hAc : ∀ k q, Cc k q ≠ 0 → (cen k).P = (labA (lS q)).P
+  hFx : ∀ t, (labF (lX t)).P = 1
+  hFy : ∀ t, (labF (lY t)).P = 1 + tt (tv t)
+  hFs : ∀ q, (labF (lS q)).P = 1
+  MA : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MAi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MB : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MBi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  hAi : MAi * MA = 1
+  hBi : MBi * MB = 1
+  hx : ∀ t j, (MB * scatM (Jr * Cc) * MA) (lX t) j = if lX t = j then 1 else 0
+  hy : ∀ i t, (MB * scatM (Jr * Cc) * MA) i (lY t) = if i = lY t then 1 else 0
+  hid : ∀ S t, (MB * scatM (Jr * Cc) * MA) (lY S) (lX t) = if S = t then 1 else 0
+  rA : List ℕ
+  rB : List ℕ
+  rF : List ℕ
+  pA : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (lab3 tv r).P) (fun r => Xm.Φ (labA r).P) (actPoint MA)
+        (fun φ => rcost φ rA) ∧
+    XRoute (fun r => Xm.Φ (lab3 tv r).P) (fun r => Xm.Φ (labA r).P) (actPoint MAiᵀ)
+        (fun φ => rcost φ rA)
+  pB : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (labA r).P) (fun r => Xm.Φ (labB r).P) (actPoint MB)
+        (fun φ => rcost φ rB) ∧
+    XRoute (fun r => Xm.Φ (labA r).P) (fun r => Xm.Φ (labB r).P) (actPoint MBiᵀ)
+        (fun φ => rcost φ rB)
+  pF : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (labB r).P) (fun r => Xm.Φ (labF r).P) id (fun φ => rcost φ rF)
+
+section Alg
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+namespace Phased
+variable (K : Phased H T Sl C)
+
+/-- the product of ALL gates of the main phase (scatter with the copies eliminated). -/
+def Mt : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MB * scatM (K.Jr * K.Cc) * K.MA
+/-- its inverse. -/
+def Mti : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MAi * scatMi (K.Jr * K.Cc) * K.MBi
+
+/-- price of one invocation: the blocks of the three phases and one block per copy. -/
+def cost (φ : ℕ → ℝ) : ℝ :=
+  rcost φ K.rA + (∑ k, bcost φ (K.cen k).d) + rcost φ K.rB + rcost φ K.rF
+
+lemma im : K.Mti * K.Mt = 1 := by
+  unfold Mti Mt
+  have hB : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ, K.MBi * (K.MB * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, K.hBi, Matrix.one_mul]
+  have hS : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ,
+      scatMi (K.Jr * K.Cc) * (scatM (K.Jr * K.Cc) * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, scat_inv, Matrix.one_mul]
+  rw [Matrix.mul_assoc, Matrix.mul_assoc, Matrix.mul_assoc, hB, hS, K.hAi]
+
+lemma mi : K.Mt * K.Mti = 1 := mul_eq_one_comm.mp K.im
+
+lemma hxm : PX * K.Mt = PX := PX_mul_of (M := K.Mt) K.hx
+lemma hmy : K.Mt * PY = PY := mul_PY_of (M := K.Mt) K.hy
+lemma hiy : K.Mti * PY = PY := dirt_iy K.hmy K.im
+
+/-- **the dirt rule, forward**, for the matrices of the circuit. -/
+lemma hF : g8 K.Mti * K.Mt * g1 K.Mt = 1 + PY * K.Mt * PX := by
+  unfold g8 g1
+  exact dirt_fwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- **the dirt rule, backward.** -/
+lemma hB : g1i K.Mt * K.Mti * h8 K.Mt = 1 - PY * K.Mt * PX := by
+  unfold g1i h8
+  exact dirt_bwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- live part of the forward word before the scatter: `y -= K s`, then phase A. -/
+def f1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MA (actPoint (g1 K.Mt) u)
+/-- after the scatter: phase B, then the slot rows of the inverse. -/
+def f2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (g8 K.Mti) (actPoint K.MB u)
+/-- the same for the backward word (transposed inverses). -/
+def b1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u)
+def b2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ u)
+
+lemma fwd_live (u : L3 T Sl → ℂ) :
+    K.f2 (actPoint (scatM (K.Jr * K.Cc)) (K.f1 u)) = actPoint (1 + PY * K.Mt * PX) u := by
+  rw [← K.hF]
+  show actPoint (g8 K.Mti) (actPoint K.MB (actPoint (scatM (K.Jr * K.Cc))
+      (actPoint K.MA (actPoint (g1 K.Mt) u))))
+    = actPoint (g8 K.Mti * (K.MB * scatM (K.Jr * K.Cc) * K.MA) * g1 K.Mt) u
+  rw [actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma bwd_live (u : L3 T Sl → ℂ) :
+    K.b2 (actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 u))
+      = actPoint ((1 - PY * K.Mt * PX)ᵀ) u := by
+  rw [← K.hB]
+  show actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ (actPoint (scatMi (K.Jr * K.Cc))ᵀ
+      (actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u))))
+    = actPoint ((g1i K.Mt * (K.MAi * scatMi (K.Jr * K.Cc) * K.MBi) * h8 K.Mt)ᵀ) u
+  rw [Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul,
+    actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma liveAct_glue (φ : (L3 T Sl → ℂ) → (L3 T Sl → ℂ)) (u : L3 T Sl → ℂ) (c : C → ℂ) :
+    liveAct φ (glue u c) = glue (φ u) c :=
+  congrArg (fun v => glue (φ v) c) (glue_up u c)
+
+/-- **Scalar identity of the forward word**: `y += x`, slots restored, for ARBITRARY slot
+contents (the copies are erased before and after). -/
+theorem fwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.f2 (gateS bY bC K.Jr (gateS bC bS K.Cc (liveAct K.f1 (eraseC z)))))
+      = shearF z := by
+  have h1 : liveAct K.f1 (eraseC z) = glue (K.f1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bY bC K.Jr (gateS bC bS K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint (scatM (K.Jr * K.Cc)) (K.f1 (z ∘ upE)) := by
+    have h := scat_glue K.Jr K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.fwd_live, act_shear K.Mt K.hid]
+  exact glue_shearF z
+
+/-- **Scalar identity of the backward word**: `x -= y`, slots restored. -/
+theorem bwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.b2 (gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (liveAct K.b1 (eraseC z)))))
+      = shearB z := by
+  have h1 : liveAct K.b1 (eraseC z) = glue (K.b1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (glue (K.b1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 (z ∘ upE)) := by
+    have h := scat_glueT K.Jr K.Cc (glue (K.b1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.bwd_live, act_shearT K.Mt K.hid]
+  exact glue_shearB z
+
+end Phased
+end Alg
+end
+end CR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.CR.Phased.fwd_scalar
+#print axioms OAI.PowerSaving.CR.Phased.bwd_scalar
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean
new file mode 100644
index 0000000000..9aa06b5bf2
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean
@@ -0,0 +1,176 @@
+import Work.Fourier.Asymptotics
+import OAI.Computability.FourierTransform.RegisterBounds
+import Work.Fourier.Goal
+
+/-
+Modified copy of lean/OAI/Computability/FourierTransform/Main.lean of github.com/openai/math
+(commit fd4aeeb, Apache-2.0), generated by `tools/fourier/mkchain.py`. OpenAI's file itself is
+unmodified in this repository and still imported. Changed for this repository, all mechanically:
+  * every declaration of this file (and of the other 10 copied files) has the suffix `Z`
+    on its name, so that it does not collide with OpenAI's original;
+  * OpenAI's exponent `alpha = 1 - 2/10^11` and envelope `hills` are replaced by
+    `alphaZ = 1 - 7474547/10^10` and `hillsZ` (Work/Fourier/Seam.lean), and the single use of
+    OpenAI's `hills_program` by `hillsZ_program`;
+  * `decimalExponent`, `decimalTime`, `TimeBounds`, `DFTGoal`, `ConvGoal` are replaced by their
+    `Z` versions from Work/Fourier/Goal.lean (exponent `1 - 7474546/10^10`);
+  * imports point to the copies.
+  * literal `let d : ℝ := 2/(10:ℝ)^11` -> `let d : ℝ := 7474547/(10:ℝ)^10` (alpha_thetaZ: the local constant d must equal 1 - alphaZ)
+  * `theorem transform_mainZ : DFTGoalZ :=`: docstring added
+  * `theorem convolution_mainZ : ConvGoalZ :=`: docstring added
+Comments and docstrings below are OpenAI's and describe OpenAI's network, not ours.
+-/
+
+namespace OAI
+
+/-!
+Exact uniform Fourier transforms and convolution.
+
+The construction formalizes the exact arithmetic algorithms of
+*An explicit power saving for the exact discrete Fourier transform* (OpenAI).
+The finite phase network originates in the complex construction of
+*Integer multiplication below n log n*.
+
+`transform_mainZ` and `convolution_mainZ` give fixed finite RAM programs, including
+preparation and index work, polynomial storage bounds, and a canonical root whose
+order is computed from the input length. Each includes the paper exponent, decimal
+power saving, and little-o bound. The `_order` variants also specify the root order.
+
+The implementation uses a smaller concrete tensor network (32 binary coordinates
+per factor, 4060 triples, and a `2^50` role envelope) with a stronger saving that
+implies the stated paper constants. The general rational-algebra extraction,
+symbolic certificate search, circuit printer, and bounded-printer uniformization
+from the synthesis appendix are outside this formalization.
+-/
+namespace PowerSaving
+open RAM Bench Selection Filter Asymptotics Real
+noncomputable section
+namespace Skies
+
+lemma multiplier_rangeZ : 1 < paperMultiplier ∧ paperMultiplier < paperM := by
+  norm_num [paperMultiplier,paperM,paperDelta,paperW]
+
+lemma theta_ltZ : theta < 1 := by
+  have h := multiplier_rangeZ
+  have hg : 0<log paperM := Real.log_pos (lt_trans h.1 h.2)
+  rw [theta,div_lt_iff₀ hg,one_mul]
+  exact Real.log_lt_log (by linarith) h.2
+
+lemma alpha_thetaZ : alphaZ < theta := by
+  let d : ℝ := 7474547/(10:ℝ)^10
+  have hp : 0<d := by dsimp [d]; norm_num
+  have hm : 2 ≤ paperM := by norm_num [paperM]
+  have hx : 0<paperMultiplier := lt_trans zero_lt_one multiplier_rangeZ.1
+  have hu : 0<paperM := by linarith
+  have h2 := (Real.log_le_log (by norm_num : 0 < (2:ℝ)) hm)
+  have he := log2_minZ
+  have hh : 0<log paperM := by linarith
+  have hk := Real.log_le_sub_one_of_pos (show 0<paperM/paperMultiplier by positivity)
+  rw [log_div hu.ne' hx.ne'] at hk
+  have H : paperM/paperMultiplier-1 < d*(2/3) := by
+    norm_num [d,paperM,paperMultiplier,paperW,paperDelta]
+  rw [theta,lt_div_iff₀ hh]
+  change (1-d)*log paperM < log paperMultiplier
+  have H' := mul_le_mul_of_nonneg_left (he.trans h2) hp.le
+  have hy := hk.trans_lt (lt_of_lt_of_le H H')
+  rw [sub_mul,one_mul]
+  linarith only [hy]
+
+lemma decimal_rangeZ : alphaZ < decimalExponentZ ∧ decimalExponentZ < 1 := by
+  norm_num [decimalExponentZ,alphaZ]
+
+def speedZ (v : ℝ) (n : ℕ) := (n:ℝ)*(TmZ n)^v
+
+lemma flight_littleZ {v : ℝ} (h : alphaZ < v) :
+    flightZ =o[atTop] speedZ v := by
+  rw [isLittleO_iff]
+  intro c hc
+  filter_upwards [TtopZ.eventually_ge_atTop 1,dwarfZ TtopZ 2
+    (p:=v-alphaZ) (sub_pos.mpr h) hc] with n hn hh
+  have he : 0<TmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^alphaZ*QmZ n^2‖ ≤ c*‖(n:ℝ)*TmZ n^v‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity)]
+  calc
+    _ ≤ ((n:ℝ)*TmZ n^alphaZ)*(c*TmZ n^(v-alphaZ)) :=
+      mul_le_mul_of_nonneg_left hh (by positivity)
+    _ = c*((n:ℝ)*(TmZ n^alphaZ*TmZ n^(v-alphaZ))) := by ring
+    _ = _ := by rw [← rpow_add he, show alphaZ + (v-alphaZ)=v by ring] -- a+(v-a)
+
+lemma speed_littleZ {u v : ℝ} (h : u < v) :
+    speedZ u =o[atTop] speedZ v := by
+  rw [isLittleO_iff]
+  intro c hc
+  filter_upwards [TtopZ.eventually_ge_atTop 1,dwarfZ TtopZ 0
+    (p:=v-u) (sub_pos.mpr h) hc] with n hn hh
+  have he : 0<TmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^u‖ ≤ c*‖(n:ℝ)*TmZ n^v‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity)]
+  have hh' : 1 ≤ c * TmZ n^(v-u) := by simpa only [pow_zero] using hh
+  calc
+    _ = ((n:ℝ)*TmZ n^u)*1 := by ring
+    _ ≤ ((n:ℝ)*TmZ n^u)*(c*TmZ n^(v-u)) := mul_le_mul_of_nonneg_left hh' (by positivity)
+    _ = c*((n:ℝ)*(TmZ n^u*TmZ n^(v-u))) := by ring
+    _ = _ := by rw [← rpow_add he, show u+(v-u)=v by ring]
+
+theorem decimal_littleZ : decimalTimeZ =o[atTop] nlogn := by
+  have H := speed_littleZ decimal_rangeZ.2
+  have h : speedZ 1 = nlogn := funext fun n => by rw [speedZ,Real.rpow_one]; rfl
+  rw [h] at H; exact H
+
+lemma speed_paperZ : speedZ theta =O[atTop] paperTime := by
+  rw [isBigO_iff]
+  refine ⟨1,?_⟩
+  filter_upwards [TtopZ.eventually_ge_atTop 1,QtopZ.eventually_ge_atTop 1] with n hn hh
+  have he : 0<TmZ n := by linarith
+  have he' : 0<QmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^theta‖ ≤ 1*‖(n:ℝ)*TmZ n^theta*QmZ n^(4-theta)‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity),one_mul]
+  have hb := Real.one_le_rpow hh (show 0 ≤ 4-theta by linarith [theta_ltZ])
+  exact le_mul_of_one_le_right (by positivity) hb
+
+lemma time_boundZ {N} (h : ∀ n:ℕ,n ≤ N n ∧ N n ≤ 2*n) (a b : RationZ) :
+    TimeBoundsZ (lunchZ a b N) := by
+  have H := lunch_bigZ a b h
+  have hp := H.trans_isLittleO (flight_littleZ alpha_thetaZ)
+  have hd := H.trans_isLittleO (flight_littleZ decimal_rangeZ.1)
+  have ht : (fun n => (lunchZ a b N n:ℝ)) =O[atTop] decimalTimeZ := hd.isBigO
+  exact ⟨hp.isBigO.trans speed_paperZ,ht,ht.trans_isLittleO decimal_littleZ⟩
+
+end Skies
+
+/-! Main results. Provide formula for the order besides the existential specification. -/
+theorem transform_main_orderZ : ∃ order solve W,
+    DFTProgram order solve W ∧ TimeBoundsZ W ∧
+    ∀ n, 0<n → (run order n).val = receipt n ∧ (run order n).val < 8*n^3 := by
+  obtain ⟨o,s,a,b,hp,ho⟩ := flagshipOneZ
+  exact ⟨o,s,lunchZ a b id,hp,Skies.time_boundZ (N:=id) (fun n => ⟨le_rfl,by dsimp; omega⟩)
+    a b,fun n hn => ⟨ho n hn,(ho n hn).symm ▸ (receipt_bound n hn).2⟩⟩
+
+theorem convolution_main_orderZ : ∃ order solve W,
+    ConvProgram order solve W ∧ TimeBoundsZ W ∧
+    ∀ n, 0<n → (run order n).val = receipt (2*n-1) ∧ (run order n).val < 8*(2*n-1)^3 := by
+  obtain ⟨o,s,a,b,hp,ho⟩ := flagshipBothZ
+  have h (n : ℕ) : n ≤ stretchZ n ∧ stretchZ n ≤ 2*n := by unfold stretchZ; omega
+  exact ⟨o,s,lunchZ a b stretchZ,hp,Skies.time_boundZ h a b,fun n hn =>
+    ⟨ho n hn,(ho n hn).symm ▸ (receipt_bound _ (stretch_posZ hn)).2⟩⟩
+
+/-- **The discrete Fourier transform of every length in `O(n (log n)^(1 - 7474546/10^10))`.**
+OpenAI's `transform_main` (one fixed program, OpenAI's own `DFTProgram`, `paperTime` and `nlogn`)
+with the decimal exponent `1 - 1/10^13` replaced by `decimalExponentZ = 1 - 7474546/10^10`
+(Work/Fourier/Goal.lean). Sibling of the Walsh-Hadamard theorem `wht_main_block_B2Gp193x`: both
+follow from one kernel program, `RAM.hillsZ_program` (Work/Fourier/Seam.lean). -/
+theorem transform_mainZ : DFTGoalZ :=
+  let ⟨o,s,W,h,g,_⟩ := transform_main_orderZ
+  ⟨o,s,W,h,g⟩
+
+/-- **Convolution of every length with the same bounds** (OpenAI's `convolution_main`, same change). -/
+theorem convolution_mainZ : ConvGoalZ :=
+  let ⟨o,s,W,h,g,_⟩ := convolution_main_orderZ
+  ⟨o,s,W,h,g⟩
+
+lemma matrix_definitionZ (n : ℕ) (x : Vec n) : dft n x = Matrix.mulVec (dftMatrix n) x :=
+  rfl
+
+end
+end PowerSaving
+
+end OAI
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean
new file mode 100644
index 0000000000..eb4490af8b
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean
@@ -0,0 +1,210 @@
+import Work.GCert.Chain.NetCert
+import Work.GCert.Chain.WinB
+import Work.BridgeGeom.B2
+
+/-!
+# (key: gx-chain) THE NETWORK LEMMA (spec statement 6): the bridged word B_2 delivers a `GCert`
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/BridgeGeom/Net.lean (section Net):
+the geometry of `BG.geomBridge2`, word for word, with the windows `gwinB` (`.Xm = BG.fmapB`).
+
+`bridge2_gcert I hH`: for every generalised invocation package, a `GCert` on
+`card Γ * (4 card T + card Sl)` live roles, label dimension `5h`, unit price
+`5 * I.cost φ + card T * BG.bankPrice h φ` (unchanged).  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF BG
+noncomputable section
+
+section Net
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+variable (I : GInv H T Sl C) (base : T → OBase H) (l : H)
+  (hbase : ∀ t, I.tv t = (base t).v l) (hH : 1 ≤ Fintype.card H)
+include hbase
+
+lemma ggeom_x01 (g : Orth (L5 H)) (t : T) :
+    PhiB g ∅ 1 = PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) (tt (I.tv t)) := by
+  rw [hbase t]
+  exact bankT_x0 (base t) l (0 : Fin 4) g
+
+lemma ggeom_y01 (g : Orth (L5 H)) (t : T) :
+    PhiB g ∅ (1 + tt (I.tv t)) = PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) 0 := by
+  rw [hbase t]
+  exact bankT_y0 (base t) l (0 : Fin 4) g
+
+/-- consecutive stages `c ∈ bs`, `c' ∉ bs`: `X` leaves where it enters. -/
+lemma ggeom_xx (bs : Finset (Fin 4)) (c c' : Fin 4) (hc : c ∈ bs) (hc' : c' ∉ bs)
+    (g : Orth (L5 H)) (t : T) :
+    PhiB (RrB (base t) l c g) (qS bs l) 1
+      = PhiB (RrB (base t) l c' g) (qS (insert c' bs) l) (tt (I.tv t)) := by
+  rw [hbase t]
+  exact bankT_xx (base t) l bs c c' hc hc' g
+
+/-- consecutive stages: `Y` leaves where it enters. -/
+lemma ggeom_yy (bs : Finset (Fin 4)) (c c' : Fin 4) (hc : c ∈ bs) (hc' : c' ∉ bs)
+    (g : Orth (L5 H)) (t : T) :
+    PhiB (RrB (base t) l c g) (qS bs l) (1 + tt (I.tv t))
+      = PhiB (RrB (base t) l c' g) (qS (insert c' bs) l) 0 := by
+  rw [hbase t]
+  exact bankT_yy (base t) l bs c c' hc hc' g
+
+/-- terminal identity of the bank pairs of the class `(g,t)`. -/
+lemma ggeom_term5 (g : Orth (L5 H)) (t : T) :
+    kernel (L5 H) * PhiB g ∅ (tt (I.tv t))
+      = shift ((BBB (base t) g).v (Sum.inl l))
+          * frame (BBB (base t) g) (univ \ {Sum.inl l}) := by
+  rw [hbase t]
+  exact class_term (base t) l g
+
+include hH
+
+/-- pair 2 before the first gate layer, `X`: ONE block of rank `2h-2`. -/
+lemma ggeom_aX2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB g ∅ (tt (I.tv t))) (PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) 1)
+      (fun φ => bcost φ (2 * Fintype.card H - 2)) := by
+  rw [hbase t]
+  exact idle_X0 (base t) l hB4 hH (0 : Fin 4) g _ (by omega)
+
+/-- pair 2 before the first gate layer, `Y`: ONE block of rank `2h-2`. -/
+lemma ggeom_aY2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB g ∅ 0) (PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) (1 + tt (I.tv t)))
+      (fun φ => bcost φ (2 * Fintype.card H - 2)) := by
+  rw [hbase t]
+  exact idle_Y0 (base t) l hB4 hH (0 : Fin 4) g _ (by omega)
+
+/-- pair 1 at the end (idle in stages 3, 4, then the last four moves), `X`: ONE block `2h+2`. -/
+lemma ggeom_fX1 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (1 : Fin 4) g) (qS bs2 l) 1) (kernel (L5 H))
+      (fun φ => bcost φ (2 * Fintype.card H + 2)) :=
+  idle_Xend (base t) l hB4 hH bs2 (1 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs2, Fintype.card_fin]; omega)
+
+/-- pair 1 at the end, `Y`: ONE block of rank `2h+2`. -/
+lemma ggeom_fY1 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (1 : Fin 4) g) (qS bs2 l) (1 + tt (I.tv t)))
+      (frame (BBB (base t) g) (univ \ {Sum.inl l}))
+      (fun φ => bcost φ (2 * Fintype.card H + 2)) := by
+  rw [hbase t]
+  exact idle_Yend (base t) l hB4 hH bs2 (1 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs2, Fintype.card_fin]; omega)
+
+/-- pair 2 after stage 4, `X`: ONE block of rank `4`. -/
+lemma ggeom_fX2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (3 : Fin 4) g) (qS bs4 l) 1) (kernel (L5 H))
+      (fun φ => bcost φ 4) :=
+  idle_Xend (base t) l hB4 hH bs4 (3 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs4, Fintype.card_fin]; omega)
+
+/-- pair 2 after stage 4, `Y`: ONE block of rank `4`. -/
+lemma ggeom_fY2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (3 : Fin 4) g) (qS bs4 l) (1 + tt (I.tv t)))
+      (frame (BBB (base t) g) (univ \ {Sum.inl l})) (fun φ => bcost φ 4) := by
+  rw [hbase t]
+  exact idle_Yend (base t) l hB4 hH bs4 (3 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs4, Fintype.card_fin]; omega)
+
+/-- **The bridged word B_2 as a term of `BR.Bridge2`**: five stages on the label space
+`H ⊕ (Fin 4 × H)`, for any invocation package whose lines are the vectors of index `l` of
+orthonormal bases. -/
+def ggeomBridge2 : GBridge2 H T Sl C (L5 H) (Orth (L5 H)) where
+  I := I
+  G0 := fun g => gwinB hB4 hH g ∅
+  G1 := fun d => gwinB hB4 hH d (qS bs1 l)
+  G2 := fun d => gwinB hB4 hH d (qS bs2 l)
+  G3 := fun d => gwinB hB4 hH d (qS bs3 l)
+  G4 := fun d => gwinB hB4 hH d (qS bs4 l)
+  r1 := fun t => RrB (base t) l (0 : Fin 4)
+  r2 := fun t => RrB (base t) l (1 : Fin 4)
+  r3 := fun t => RrB (base t) l (2 : Fin 4)
+  r4 := fun t => RrB (base t) l (3 : Fin 4)
+  s1 := (Orth.colPerm (tauB (0 : Fin 4))).symm
+  s2 := (Orth.colPerm (tauB (1 : Fin 4))).symm
+  s3 := (Orth.colPerm (tauB (2 : Fin 4))).symm
+  s4 := (Orth.colPerm (tauB (3 : Fin 4))).symm
+  N1 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs1 l)) * d.1ᵀ)
+  W1 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N2 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs2 l)) * d.1ᵀ)
+  W2 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N3 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs3 l)) * d.1ᵀ)
+  W3 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N4 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs4 l)) * d.1ᵀ)
+  W4 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  u := fun g t => (BBB (base t) g).v (Sum.inl l)
+  YF := fun g t => frame (BBB (base t) g) (univ \ {Sum.inl l})
+  hm := two_le_card_LB hB4 hH
+  caX := fun φ => bcost φ (2 * Fintype.card H - 2)
+  caY := fun φ => bcost φ (2 * Fintype.card H - 2)
+  cX1 := fun φ => bcost φ (2 * Fintype.card H + 2)
+  cY1 := fun φ => bcost φ (2 * Fintype.card H + 2)
+  cX2 := fun φ => bcost φ 4
+  cY2 := fun φ => bcost φ 4
+  inv0 := fun g t => ⟨unframeM (g.1 * Matrix.fromBlocks (tt (I.tv t)) 0 0 (diagI ∅) * g.1ᵀ),
+    frameM_unframeM _⟩
+  z0 := fun g => PhiB_zero_empty g
+  hN1 := fun d => frameM_unframeM _
+  hW1 := fun d => PhiB_one d (qS bs1 l)
+  hN2 := fun d => frameM_unframeM _
+  hW2 := fun d => PhiB_one d (qS bs2 l)
+  hN3 := fun d => frameM_unframeM _
+  hW3 := fun d => PhiB_one d (qS bs3 l)
+  hN4 := fun d => frameM_unframeM _
+  hW4 := fun d => PhiB_one d (qS bs4 l)
+  x01 := fun g t => ggeom_x01 I base l hbase g t
+  y01 := fun g t => ggeom_y01 I base l hbase g t
+  x12 := fun g t => ggeom_xx I base l hbase bs1 0 1 (Finset.mem_singleton_self _) mem1 g t
+  y12 := fun g t => ggeom_yy I base l hbase bs1 0 1 (Finset.mem_singleton_self _) mem1 g t
+  x23 := fun g t => ggeom_xx I base l hbase bs2 1 2 (Finset.mem_insert_self _ _) mem2 g t
+  y23 := fun g t => ggeom_yy I base l hbase bs2 1 2 (Finset.mem_insert_self _ _) mem2 g t
+  x34 := fun g t => ggeom_xx I base l hbase bs3 2 3 (Finset.mem_insert_self _ _) mem3 g t
+  y34 := fun g t => ggeom_yy I base l hbase bs3 2 3 (Finset.mem_insert_self _ _) mem3 g t
+  sfin := fun g => helper_fin5 g
+  aX2 := fun g t => ggeom_aX2 I base l hbase hH g t
+  aY2 := fun g t => ggeom_aY2 I base l hbase hH g t
+  fX1 := fun g t => ggeom_fX1 I base l hbase hH g t
+  fY1 := fun g t => ggeom_fY1 I base l hbase hH g t
+  fX2 := fun g t => ggeom_fX2 I base l hbase hH g t
+  fY2 := fun g t => ggeom_fY2 I base l hbase hH g t
+  term := fun g t => ggeom_term5 I base l hbase g t
+
+end Net
+
+section End
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+/-- an orthonormal basis through a unit vector with a zero coordinate, at any index. -/
+theorem base_ex (z : Space H) (hz : dot z z = 1) (hg : ∃ p, z p = 0) (l : H) :
+    ∃ A : OBase H, z = A.v l := by
+  obtain ⟨p, hp⟩ := hg
+  obtain ⟨A, k, hA⟩ := exists_base_one z hz p hp
+  refine ⟨reindex A (Equiv.swap k l), ?_⟩
+  rw [← hA]
+  show A.v k = A.v (Equiv.swap k l l)
+  rw [Equiv.swap_apply_right]
+
+/-- **Generalised certificate of the bridged word B_2** for a generalised invocation package. -/
+theorem bridge2_gcert (I : GInv H T Sl C) (hH : 1 ≤ Fintype.card H) :
+    GCert (L5 H) (Sum.inl : BLive (Orth (L5 H)) T Sl → BRole (Orth (L5 H)) T Sl C)
+      (fun φ => (Fintype.card (Orth (L5 H)) : ℝ)
+        * (5 * I.cost φ + (Fintype.card T : ℝ) * bankPrice (Fintype.card H) φ)) := by
+  obtain ⟨l⟩ : Nonempty H := Fintype.card_pos_iff.mp (by omega)
+  have hb : ∀ t, ∃ A : OBase H, I.tv t = A.v l :=
+    fun t => base_ex (I.tv t) (I.hunit t) (I.hgap t) l
+  choose base hbase using hb
+  exact gbridge2_certificate (ggeomBridge2 I base l hbase hH)
+
+end End
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.ggeomBridge2
+#print axioms OAI.PowerSaving.GX.bridge2_gcert
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean
new file mode 100644
index 0000000000..d69fcb4992
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean
@@ -0,0 +1,164 @@
+import Work.GCert.Chain.Inv
+
+/-!
+# (key: gx-chain) THE CARRIER INVOCATION THEOREM on the generalised engine: `Lab.inv`
+
+`CR.Phased.inv` (`Work/Carrier/PhasedInv.lean`) with subspace labels and `GRoute`.  Forward word:
+
+    erase | y -= K s (old frame 0) | free adapters to the labels of the certificate | phase A |
+    c += Cc s | copies down | y += Jr c | phase B | final climbs | free adapters to the old
+    frames | slots := slot rows of the inverse (old frame 1) | erase
+
+The backward word is the transposed inverse, gate by gate, on the same labels.  The scalar
+identities are `Scal.fwd_scalar` / `Scal.bwd_scalar` (those of `CR.Phased`).
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB BR CR GF RF
+noncomputable section
+
+section Thm
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+variable {α : Type} [Fintype α] [DecidableEq α]
+variable {S : Scal T Sl C} (L : Lab H S) (W : GWin H α)
+
+/-- **Forward word on clean frames.** -/
+theorem Lab.fwd_erased (c0 c1 : C → CMat α) :
+    GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) shearF L.cost := by
+  have a1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (actPoint (g1 S.Mt)) (fun _ => 0) :=
+    GRoute.gate (g1 S.Mt) _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · obtain ⟨h1, h2⟩ := offdiag_x (g1_x S.Mt).1 (g1_x S.Mt).2 hij e
+        exact start_frames W.Xm L.tv i j h1 h2)
+  have b3 : GRoute (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (actPoint (g8 S.Mti)) (fun _ => 0) :=
+    GRoute.gate (g8 S.Mti) _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have f := g8_facts S.hiy
+        obtain ⟨h1, h2, h3⟩ := offdiag_s f.1 f.2.1 f.2.2 hij e
+        exact end_old W.Xm L.tv i j h1 h2 h3)
+  have seg1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun r => W.X.Φ (L.labA r))
+      S.f1 (fun φ => rcost φ L.rA) :=
+    ((a1.trans (L.ad0 W)).trans (L.pA W.X W.big).1).cast (fun φ => by simp)
+  have seg2 : GRoute (fun r => W.X.Φ (L.labA r)) (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      S.f2 (fun φ => rcost φ L.rB + rcost φ L.rF) :=
+    ((((L.pB W.X W.big).1.trans (L.pF W.X W.big)).trans (L.adF W)).trans b3).cast
+      (fun φ => by simp)
+  have e0 : GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (glue (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun k => W.X.Φ (L.cen k)))
+      eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have L1 := glift_live (fun k => W.X.Φ (L.cen k)) seg1
+  have m1 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (fun z => addBlk bC (ap S.Cc (z ∘ bS)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bC bS bS_inj S.Cc (fun k q h => congrArg W.X.Φ (L.hAc k q h)))
+  have m2 := L.cdown W (fun r => W.X.Φ (L.labA r))
+  have m3 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (fun z => addBlk bY (ap S.Jr (z ∘ bC)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bY bC bC_inj S.Jr (fun t k _ => congrArg W.X.Φ (L.hAy t)))
+  have L2 := glift_live (fun _ : C => W.X.Φ L.z0) seg2
+  have e1 : GRoute (glue (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r)) (fun _ : C => W.X.Φ L.z0))
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have tot := (((((e0.trans L1).trans m1).trans m2).trans m3).trans L2).trans e1
+  refine (tot.castg (g' := shearF) (funext fun z => S.fwd_scalar z)).cast (fun φ => ?_)
+  simp only [Lab.cost, zero_add, add_zero]
+  ring
+
+/-- **Backward word on clean frames**: the transposed inverse gates, same labels; the copies
+start at the zero frame and climb. -/
+theorem Lab.bwd_erased (c0 c1 : C → CMat α) :
+    GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) shearB L.cost := by
+  have a1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (actPoint (g1i S.Mt)ᵀ) (fun _ => 0) :=
+    GRoute.gate (g1i S.Mt)ᵀ _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have hij' : g1i S.Mt j i ≠ 0 := hij
+        obtain ⟨h1, h2⟩ := offdiag_x (g1i_x S.Mt).1 (g1i_x S.Mt).2 hij' (Ne.symm e)
+        exact start_frames W.Xm L.tv i j h2 h1)
+  have b3 : GRoute (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (actPoint (h8 S.Mt)ᵀ) (fun _ => 0) :=
+    GRoute.gate (h8 S.Mt)ᵀ _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have hij' : h8 S.Mt j i ≠ 0 := hij
+        have f := h8_facts S.hmy
+        obtain ⟨h1, h2, h3⟩ := offdiag_s f.1 f.2.1 f.2.2 hij' (Ne.symm e)
+        exact (end_old W.Xm L.tv j i h1 h2 h3).symm)
+  have seg1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun r => W.X.Φ (L.labA r))
+      S.b1 (fun φ => rcost φ L.rA) :=
+    ((a1.trans (L.ad0 W)).trans (L.pA W.X W.big).2).cast (fun φ => by simp)
+  have seg2 : GRoute (fun r => W.X.Φ (L.labA r)) (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      S.b2 (fun φ => rcost φ L.rB + rcost φ L.rF) :=
+    ((((L.pB W.X W.big).2.trans (L.pF W.X W.big)).trans (L.adF W)).trans b3).cast
+      (fun φ => by simp)
+  have e0 : GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (glue (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun _ : C => W.X.Φ L.z0))
+      eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have L1 := glift_live (fun _ : C => W.X.Φ L.z0) seg1
+  have m1 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (fun z => addBlk bC (ap S.Jrᵀ (z ∘ bY)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bC bY bY_inj S.Jrᵀ (fun k t _ => (congrArg W.X.Φ (L.hAy t)).symm))
+  have m2 := L.cup W (fun r => W.X.Φ (L.labA r))
+  have m3 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (fun z => addBlk bS (ap (-S.Ccᵀ) (z ∘ bC)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bS bC bC_inj (-S.Ccᵀ)
+      (fun q k h => (congrArg W.X.Φ (L.hAc k q (ne_of_negT S.Cc h))).symm))
+  have L2 := glift_live (fun k => W.X.Φ (L.cen k)) seg2
+  have e1 : GRoute (glue (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r)) (fun k => W.X.Φ (L.cen k)))
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have tot := (((((e0.trans L1).trans m1).trans m2).trans m3).trans L2).trans e1
+  refine (tot.castg (g' := shearB) (funext fun z => S.bwd_scalar z)).cast (fun φ => ?_)
+  simp only [Lab.cost, zero_add, add_zero]
+  ring
+
+/-- **THE CARRIER INVOCATION THEOREM on the generalised engine.**  The two halves of a
+certificate are an invocation package for the bridged network, with the price `L.cost`. -/
+def Lab.inv : GInv H T Sl C where
+  tv := L.tv
+  hunit := L.hunit
+  hgap := L.hgap
+  cost := L.cost
+  fwd := fun W N0 Wn hN hW Z c0 c1 =>
+    gdirty_of_erased W.Xm L.tv N0 Wn hN hW Z c0 c1 (L.fwd_erased W c0 c1)
+      (shearF_comm (fun _ => 1) (fun q => N0 * Z q) (fun _ => 1))
+  bwd := fun W N0 Wn hN hW Z c0 c1 =>
+    gdirty_of_erased W.Xm L.tv N0 Wn hN hW Z c0 c1 (L.bwd_erased W c0 c1)
+      (shearB_comm (fun _ => 1) (fun q => N0 * Z q) (fun _ => 1))
+
+@[simp] lemma Lab.inv_cost (φ : ℕ → ℝ) : L.inv.cost φ = L.cost φ := rfl
+@[simp] lemma Lab.inv_tv : L.inv.tv = L.tv := rfl
+
+end Thm
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.Lab.fwd_erased
+#print axioms OAI.PowerSaving.GX.Lab.bwd_erased
+#print axioms OAI.PowerSaving.GX.Lab.inv
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean
new file mode 100644
index 0000000000..6336ba0766
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean
@@ -0,0 +1,157 @@
+import Work.GCert.Chain.NetStage
+import Work.GFrame.Top.Assemble
+
+/-!
+# (key: gx-chain) The bridged word B_2 on the generalised engine: the certificate `GCert`
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Cert.lean (section Net).
+`gbridge2_certificate`: a `GCert` on the live roles `BLive Γ T Sl` with price `card Γ * N.unit φ`.
+The gate layers, the idle climbs and the exchange are the old routes (`GRoute.ofX`).  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- gate layer A, after stage 1 and the first idle climb of pair 2: twins have equal frames. -/
+lemma GBridge2.gateA : XRoute N.S3 N.S3 (gsc pAB kA) (fun _ => 0) := by
+  refine gateP pAB kA N.S3 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer B, after stage 2 and the second idle climb of pair 2. -/
+lemma GBridge2.gateB : XRoute N.S5 N.S5 (gsc pAB kB) (fun _ => 0) := by
+  refine gateP pAB kB N.S5 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact N.x23 g t
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (N.y23 g t).symm
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer C, after the final climbs. -/
+lemma GBridge2.gateC : XRoute N.S8 N.S8 (gsc pC kCc) (fun _ => 0) := by
+  refine gateP pC kCc N.S8 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact (hk rfl).elim
+  · rfl
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- the free shifts at the end. -/
+def GBridge2.corr : BRole Γ T Sl C → Space α :=
+  mkB (fun _ _ => 0) (fun g t => N.u g t) (fun _ _ => 0) (fun g t => N.u g t)
+    (fun _ _ => 0) (fun _ _ => 0)
+
+def GBridge2.S9 : BRole Γ T Sl C → CMat α := fun r => shift (N.corr r) * N.S8 r
+
+/-- the whole word before the exchange: five stages, three idle-climb layers, three gate
+layers. -/
+lemma GBridge2.route :
+    GRoute N.S0 N.S8 chain (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R := ((((((((((N.stage0.trans N.stage1).trans (GRoute.ofX N.climbA)).trans
+    (GRoute.ofX N.gateA)).trans N.stage2).trans (GRoute.ofX N.climbB)).trans
+    (GRoute.ofX N.gateB)).trans N.stage3).trans N.stage4).trans
+    (GRoute.ofX N.fin)).trans (GRoute.ofX N.gateC))
+  refine (R.castg ?_).cast (fun φ => ?_)
+  · rfl
+  · simp only [GBridge2.unit]
+    ring
+
+/-- **The scratch certificate of the bridged five-stage network with shared helper sets**,
+in whole blocks, with its exact price for every price list. -/
+theorem gbridge2_certificate :
+    GCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C)
+      (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R2 : GRoute N.S8 N.S9 id (fun _ => 0) := GRoute.shifts N.hm N.S8 N.corr
+  have R3 : GRoute N.S9 (fun r => N.S9 (bpull r)) (actPoint brecM) (fun _ => 0) :=
+    GRoute.gate brecM N.S9 _ (fun i j h => by
+      have hj : j = bpull i := by
+        by_contra hne
+        exact h (by simp [brecM, hne])
+      rw [hj])
+  have Rt := ((N.route.trans R2).trans R3).cast (c' := fun φ => (Fintype.card Γ : ℝ) * N.unit φ)
+    (fun φ => by first | ring | simp)
+  have hSinv : ∀ r, ∃ M, N.S0 r * M = 1 := by
+    rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.G0 g).Xm.Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.G0 g).Xm.Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact ⟨1, Matrix.mul_one _⟩
+    · exact ⟨1, Matrix.mul_one _⟩
+  have hT : ∀ l : BLive Γ T Sl, N.S9 (bpull (Sum.inl l)) = kernel α * N.S0 (Sum.inl l) := by
+    rintro (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.G0 g).Xm.Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.G0 g).Xm.Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.G0 g).Xm.Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.G0 g).Xm.Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (0 : Space α) * kernel α = kernel α * 1
+      rw [shift_zero, Matrix.one_mul, Matrix.mul_one]
+  have hg : ∀ x : BRole Γ T Sl C → ℂ,
+      (∀ s, (∀ l : BLive Γ T Sl, (Sum.inl l : BRole Γ T Sl C) ≠ s) → x s = 0) →
+      ∀ l : BLive Γ T Sl,
+        (actPoint brecM ∘ (id ∘ chain)) x (Sum.inl l) = x (Sum.inl l) := by
+    intro x _ l
+    change actPoint brecM (chain x) (Sum.inl l) = _
+    rw [actPoint_brecM]
+    rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX1 (g,t)) = x (kX1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY1 (g,t))) = x (kY1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX2 (g,t)) = x (kX2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY2 (g,t))) = x (kY2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inr (g,q))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kS (g,q)) = x (kS (g,q))
+      first | (push_cast; ring) | simp
+  exact gcert_of_groute (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) N.S0
+    (fun r => N.S9 (bpull r)) _ _ Rt hSinv hg hT
+
+end Net
+
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.route
+#print axioms OAI.PowerSaving.GX.gbridge2_certificate
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean
new file mode 100644
index 0000000000..c13042eb43
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean
@@ -0,0 +1,157 @@
+import Work.GCert.Chain.Stage
+
+/-!
+# (key: gx-chain) The bridged five-stage word B_2 on the generalised engine: data and frames
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Net.lean (`BR.Bridge2`): the
+invocation is a `GInv`, the frame maps of the stages are windows `GWin` (`G0 .. G4`; the old
+frame map of a window is `.Xm`).  Everything else word for word.  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+/-- See the file header.  Fields in the style of `RF.Fold3S`; stages are numbered 0 to 4. -/
+structure GBridge2 (H T Sl C α Γ : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α] where
+  /-- the invocation (for a block circuit `X`: `X.inv`). -/
+  I : GInv H T Sl C
+  /-- frame maps of the invocations of the five stages. -/
+  G0 : Γ → GWin H α
+  G1 : Γ → GWin H α
+  G2 : Γ → GWin H α
+  G3 : Γ → GWin H α
+  G4 : Γ → GWin H α
+  /-- the class `(g,t)` is served by the invocation `g` in stage 0 and `r_l t g` in stage `l`. -/
+  r1 : T → Γ ≃ Γ
+  r2 : T → Γ ≃ Γ
+  r3 : T → Γ ≃ Γ
+  r4 : T → Γ ≃ Γ
+  /-- the invocation `d` of stage `l` uses the helper set (and the copies) `s_l d`. -/
+  s1 : Γ ≃ Γ
+  s2 : Γ ≃ Γ
+  s3 : Γ ≃ Γ
+  s4 : Γ ≃ Γ
+  /-- inverse of the frame of the base, and frame of the window, of every invocation. -/
+  N1 : Γ → CMat α
+  W1 : Γ → CMat α
+  N2 : Γ → CMat α
+  W2 : Γ → CMat α
+  N3 : Γ → CMat α
+  W3 : Γ → CMat α
+  N4 : Γ → CMat α
+  W4 : Γ → CMat α
+  u : Γ → T → Space α
+  YF : Γ → T → CMat α
+  hm : 2 ≤ Fintype.card α
+  /-- prices of the idle climbs, for every price list.  B_2 with merged climbs:
+  `caX = caY = fun φ => bcost φ (2h-2)`, `cX1 = cY1 = fun φ => bcost φ (2h+2)`,
+  `cX2 = cY2 = fun φ => bcost φ 4`. -/
+  caX : (ℕ → ℝ) → ℝ
+  caY : (ℕ → ℝ) → ℝ
+  cX1 : (ℕ → ℝ) → ℝ
+  cY1 : (ℕ → ℝ) → ℝ
+  cX2 : (ℕ → ℝ) → ℝ
+  cY2 : (ℕ → ℝ) → ℝ
+  inv0 : ∀ g t, ∃ N : CMat α, (G0 g).Xm.Φ (tt (I.tv t)) * N = 1
+  z0 : ∀ g, (G0 g).Xm.Φ 0 = 1
+  hN1 : ∀ d, (G1 d).Xm.Φ 0 * N1 d = 1
+  hW1 : ∀ d, (G1 d).Xm.Φ 1 = W1 d * (G1 d).Xm.Φ 0
+  hN2 : ∀ d, (G2 d).Xm.Φ 0 * N2 d = 1
+  hW2 : ∀ d, (G2 d).Xm.Φ 1 = W2 d * (G2 d).Xm.Φ 0
+  hN3 : ∀ d, (G3 d).Xm.Φ 0 * N3 d = 1
+  hW3 : ∀ d, (G3 d).Xm.Φ 1 = W3 d * (G3 d).Xm.Φ 0
+  hN4 : ∀ d, (G4 d).Xm.Φ 0 * N4 d = 1
+  hW4 : ∀ d, (G4 d).Xm.Φ 1 = W4 d * (G4 d).Xm.Φ 0
+  /-- the bank frames a stage leaves are the bank frames the next stage starts from. -/
+  x01 : ∀ g t, (G0 g).Xm.Φ 1 = (G1 (r1 t g)).Xm.Φ (tt (I.tv t))
+  y01 : ∀ g t, (G0 g).Xm.Φ (1 + tt (I.tv t)) = (G1 (r1 t g)).Xm.Φ 0
+  x12 : ∀ g t, (G1 (r1 t g)).Xm.Φ 1 = (G2 (r2 t g)).Xm.Φ (tt (I.tv t))
+  y12 : ∀ g t, (G1 (r1 t g)).Xm.Φ (1 + tt (I.tv t)) = (G2 (r2 t g)).Xm.Φ 0
+  x23 : ∀ g t, (G2 (r2 t g)).Xm.Φ 1 = (G3 (r3 t g)).Xm.Φ (tt (I.tv t))
+  y23 : ∀ g t, (G2 (r2 t g)).Xm.Φ (1 + tt (I.tv t)) = (G3 (r3 t g)).Xm.Φ 0
+  x34 : ∀ g t, (G3 (r3 t g)).Xm.Φ 1 = (G4 (r4 t g)).Xm.Φ (tt (I.tv t))
+  y34 : ∀ g t, (G3 (r3 t g)).Xm.Φ (1 + tt (I.tv t)) = (G4 (r4 t g)).Xm.Φ 0
+  /-- the five windows of a helper set make up the kernel. -/
+  sfin : ∀ g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) *
+    (W1 (s1.symm g) * (G0 g).Xm.Φ 1))) = kernel α
+  /-- pair 2, idle in stages 0 and 1: ONE block from its start frame to the frame of its
+  twin after stage 1. -/
+  aX2 : ∀ g t, XReach ((G0 g).Xm.Φ (tt (I.tv t))) ((G1 (r1 t g)).Xm.Φ 1) caX
+  aY2 : ∀ g t, XReach ((G0 g).Xm.Φ 0) ((G1 (r1 t g)).Xm.Φ (1 + tt (I.tv t))) caY
+  /-- pair 1, idle in stages 3 and 4: ONE block from its frame after stage 2 to the end. -/
+  fX1 : ∀ g t, XReach ((G2 (r2 t g)).Xm.Φ 1) (kernel α) cX1
+  fY1 : ∀ g t, XReach ((G2 (r2 t g)).Xm.Φ (1 + tt (I.tv t))) (YF g t) cY1
+  /-- pair 2 after stage 4: ONE final block. -/
+  fX2 : ∀ g t, XReach ((G4 (r4 t g)).Xm.Φ 1) (kernel α) cX2
+  fY2 : ∀ g t, XReach ((G4 (r4 t g)).Xm.Φ (1 + tt (I.tv t))) (YF g t) cY2
+  term : ∀ g t, kernel α * (G0 g).Xm.Φ (tt (I.tv t)) = shift (u g t) * YF g t
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- price of the blocks of one unit (one element of `Γ`): five invocations and the idle
+climbs of the four bank roles of every class. -/
+def GBridge2.unit (φ : ℕ → ℝ) : ℝ :=
+  5 * N.I.cost φ + (Fintype.card T : ℝ) * ((N.caX φ + N.caY φ)
+    + 2 * bcost φ (Fintype.card H - 1)
+    + (N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ))
+
+/-- the bank index of stage 0: the class `(g,t)` belongs to the invocation `g`. -/
+abbrev bid (Γ T : Type) : T → Γ ≃ Γ := fun _ => Equiv.refl Γ
+
+/-! bank frames of the class `(g,t)`: `xi l`, `yi l` at the START of stage `l`; `xo l`,
+`yo l` at the END of stage `l` (only where no next stage follows on that pair). -/
+def GBridge2.xi0 (g : Γ) (t : T) : CMat α := (N.G0 g).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi0 (g : Γ) (t : T) : CMat α := (N.G0 g).Xm.Φ 0
+def GBridge2.xi1 (g : Γ) (t : T) : CMat α := (N.G1 (N.r1 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi1 (g : Γ) (t : T) : CMat α := (N.G1 (N.r1 t g)).Xm.Φ 0
+def GBridge2.xi2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ 0
+def GBridge2.xo2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ 1
+def GBridge2.yo2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ (1 + tt (N.I.tv t))
+def GBridge2.xi3 (g : Γ) (t : T) : CMat α := (N.G3 (N.r3 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi3 (g : Γ) (t : T) : CMat α := (N.G3 (N.r3 t g)).Xm.Φ 0
+def GBridge2.xi4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ 0
+def GBridge2.xo4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ 1
+def GBridge2.yo4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ (1 + tt (N.I.tv t))
+
+/-- helper slots after the stages 0, 1, 2, 3, 4 (at the start: `cOne Γ Sl α`). -/
+def GBridge2.Z1 : Γ → Sl → CMat α := fun g _ => (N.G0 g).Xm.Φ 1
+def GBridge2.Z2 : Γ → Sl → CMat α := fun g q => N.W1 (N.s1.symm g) * N.Z1 g q
+def GBridge2.Z3 : Γ → Sl → CMat α := fun g q => N.W2 (N.s2.symm g) * N.Z2 g q
+def GBridge2.Z4 : Γ → Sl → CMat α := fun g q => N.W3 (N.s3.symm g) * N.Z3 g q
+def GBridge2.Z5 : Γ → Sl → CMat α := fun g q => N.W4 (N.s4.symm g) * N.Z4 g q
+
+/-- frames: at the start; after stage 0; after stage 1; after the first idle climb of pair 2
+(first gate layer here); after stage 2; after the second idle climb of pair 2 (second gate
+layer here); after stage 3; after stage 4; after the final climbs (third gate layer here). -/
+def GBridge2.S0 : BRole Γ T Sl C → CMat α := mkB N.xi0 N.yi0 N.xi0 N.yi0 (cOne Γ Sl α) (cOne Γ C α)
+def GBridge2.S1 : BRole Γ T Sl C → CMat α := mkB N.xi1 N.yi1 N.xi0 N.yi0 N.Z1 (cOne Γ C α)
+def GBridge2.S2 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi0 N.yi0 N.Z2 (cOne Γ C α)
+def GBridge2.S3 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi2 N.yi2 N.Z2 (cOne Γ C α)
+def GBridge2.S4 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi2 N.yi2 N.Z3 (cOne Γ C α)
+def GBridge2.S5 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi3 N.yi3 N.Z3 (cOne Γ C α)
+def GBridge2.S6 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi4 N.yi4 N.Z4 (cOne Γ C α)
+def GBridge2.S7 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xo4 N.yo4 N.Z5 (cOne Γ C α)
+def GBridge2.S8 : BRole Γ T Sl C → CMat α :=
+  mkB (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) (cOne Γ C α)
+
+
+end Net
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.unit
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean
new file mode 100644
index 0000000000..670f4c6a84
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean
@@ -0,0 +1,186 @@
+import Work.GCert.Chain.NetDef
+
+/-!
+# (key: gx-chain) The bridged word B_2 on the generalised engine: the five stages and the idle climbs
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Net.lean.  The stages are
+`GRoute`s (`gistage_fwd` / `gistage_bwd`, `gblift1` / `gblift2`); the idle climbs of the bank
+roles are the OLD block routes, unchanged.  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- stage 0: forward on pair 1, every helper set starts at the matrix `1`. -/
+lemma GBridge2.stage0 :
+    GRoute N.S0 N.S1 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_fwd N.I (bid Γ T) (Equiv.refl Γ) N.G0 (fun _ => 1) (fun g => (N.G0 g).Xm.Φ 1)
+    (fun d => by rw [N.z0, Matrix.mul_one]) (fun d => by rw [N.z0, Matrix.mul_one])
+    (cOne Γ Sl α) (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv (bid Γ T) (fun d => (N.G0 d).Xm)
+      (fun g (q : Sl) => (N.G0 ((Equiv.refl Γ).symm g)).Xm.Φ 1 * cOne Γ Sl α g q) (cOne Γ C α)
+      = mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x01 g t
+    · exact N.y01 g t
+    · show (N.G0 g).Xm.Φ 1 * 1 = (N.G0 g).Xm.Φ 1
+      rw [Matrix.mul_one]
+    · rfl
+  have h' : GRoute (bIn N.I.tv (bid Γ T) (fun d => (N.G0 d).Xm) (cOne Γ Sl α) (cOne Γ C α))
+      (mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α)) GF (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift1 N.xi0 N.yi0 h'
+
+/-- stage 1: backward on pair 1; the helper set `g` serves the invocation `s1⁻¹ g`. -/
+lemma GBridge2.stage1 :
+    GRoute N.S1 N.S2 (lift1 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_bwd N.I N.r1 N.s1 N.G1 N.N1 N.W1 N.hN1 N.hW1 N.Z1 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r1 (fun d => (N.G1 d).Xm) (fun g q => N.W1 (N.s1.symm g) * N.Z1 g q) (cOne Γ C α)
+      = mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x12 g t
+    · exact N.y12 g t
+    · rfl
+    · rfl
+  have h' : GRoute (bIn N.I.tv N.r1 (fun d => (N.G1 d).Xm) N.Z1 (cOne Γ C α))
+      (mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift1 N.xi0 N.yi0 h'
+
+/-- stage 2: forward on pair 1. -/
+lemma GBridge2.stage2 :
+    GRoute N.S3 N.S4 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  gblift1 N.xi2 N.yi2
+    (gistage_fwd N.I N.r2 N.s2 N.G2 N.N2 N.W2 N.hN2 N.hW2 N.Z2 (cOne Γ C α) (cOne Γ C α))
+
+/-- stage 3: backward on pair 2. -/
+lemma GBridge2.stage3 :
+    GRoute N.S5 N.S6 (lift2 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_bwd N.I N.r3 N.s3 N.G3 N.N3 N.W3 N.hN3 N.hW3 N.Z3 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r3 (fun d => (N.G3 d).Xm) (fun g q => N.W3 (N.s3.symm g) * N.Z3 g q) (cOne Γ C α)
+      = mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x34 g t
+    · exact N.y34 g t
+    · rfl
+    · rfl
+  have h' : GRoute (bIn N.I.tv N.r3 (fun d => (N.G3 d).Xm) N.Z3 (cOne Γ C α))
+      (mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift2 N.xo2 N.yo2 h'
+
+/-- stage 4: forward on pair 2. -/
+lemma GBridge2.stage4 :
+    GRoute N.S6 N.S7 (lift2 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  gblift2 N.xo2 N.yo2
+    (gistage_fwd N.I N.r4 N.s4 N.G4 N.N4 N.W4 N.hN4 N.hW4 N.Z4 (cOne Γ C α) (cOne Γ C α))
+
+/-- first idle climb of pair 2 (stages 0 and 1 in ONE block per role), to the frames of
+pair 1 after stage 1. -/
+lemma GBridge2.climbA :
+    XRoute N.S2 N.S3 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (N.caX φ + N.caY φ))) := by
+  have H1 := XRoute.reach_all N.S2 N.S3
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ => N.caX)
+      (fun _ _ => N.caY) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.G0 g).Xm.Φ (tt (N.I.tv t))) ((N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))) N.caX
+        rw [← N.x12 g t]
+        exact N.aX2 g t
+      · show XReach ((N.G0 g).Xm.Φ 0) ((N.G2 (N.r2 t g)).Xm.Φ 0) N.caY
+        rw [← N.y12 g t]
+        exact N.aY2 g t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- second idle climb of pair 2: the window of stage 2, ONE block of rank `card H - 1` per
+role, to the frames of pair 1 after stage 2. -/
+lemma GBridge2.climbB :
+    XRoute N.S4 N.S5 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (2 * bcost φ (Fintype.card H - 1)))) := by
+  have H1 := XRoute.reach_all N.S4 N.S5
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ φ => bcost φ (Fintype.card H - 1))
+      (fun _ _ φ => bcost φ (Fintype.card H - 1)) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))) ((N.G3 (N.r3 t g)).Xm.Φ (tt (N.I.tv t)))
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.x23 g t]
+        exact N.I.climbX (N.G2 (N.r2 t g)).Xm t
+      · show XReach ((N.G2 (N.r2 t g)).Xm.Φ 0) ((N.G3 (N.r3 t g)).Xm.Φ 0)
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.y23 g t]
+        exact N.I.climbY (N.G2 (N.r2 t g)).Xm t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- the final climbs: pair 1 from its frames after stage 2 (ONE block per role for the
+stages 3, 4 and the rest), pair 2 from its frames after stage 4; the helper slots are
+already at the kernel. -/
+lemma GBridge2.fin :
+    XRoute N.S7 N.S8 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * ((N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ)))) := by
+  have H1 := XRoute.reach_all N.S7 N.S8
+    (mkB (fun _ _ => N.cX1) (fun _ _ => N.cY1) (fun _ _ => N.cX2) (fun _ _ => N.cY2)
+      (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact N.fX1 g t
+      · exact N.fY1 g t
+      · exact N.fX2 g t
+      · exact N.fY2 g t
+      · show XReach (N.W4 (N.s4.symm g) * (N.W3 (N.s3.symm g) * (N.W2 (N.s2.symm g) *
+          (N.W1 (N.s1.symm g) * (N.G0 g).Xm.Φ 1)))) (kernel α) (fun _ => 0)
+        rw [N.sfin g]
+        exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+end Net
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.stage0
+#print axioms OAI.PowerSaving.GX.GBridge2.stage1
+#print axioms OAI.PowerSaving.GX.GBridge2.stage2
+#print axioms OAI.PowerSaving.GX.GBridge2.stage3
+#print axioms OAI.PowerSaving.GX.GBridge2.stage4
+#print axioms OAI.PowerSaving.GX.GBridge2.climbA
+#print axioms OAI.PowerSaving.GX.GBridge2.climbB
+#print axioms OAI.PowerSaving.GX.GBridge2.fin
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean
new file mode 100644
index 0000000000..e68c42377f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean
@@ -0,0 +1,199 @@
+import Work.Carrier.Phases
+import Work.GFrame.Labels.All
+
+/-!
+# (key: gx-chain) The certificate as two halves: `Scal` (scalar half) and `Lab` (label half)
+
+`Scal T Sl C`: the scalar fields of `CR.Phased` (three facts about ONE matrix
+`Mt = MB * scatM (Jr * Cc) * MA`).  The scalar identities of the forward and of the backward
+word (`fwd_scalar`, `bwd_scalar`) are those of `Work/Carrier/Phases.lean`, word for word.
+
+`Lab H S`: subspace labels (`GF.SLbl H`), routes of the three phases on the generalised engine
+(`GF.GRoute`) through every stage-B frame map (`GF.BXMap H α`), and facts about dimensions at
+the two ends.  No projector, no `Climb`.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB BR CR GF
+noncomputable section
+
+/-- **The scalar half.** -/
+structure Scal (T Sl C : Type) [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] where
+  Cc : Matrix C Sl ℚ
+  Jr : Matrix T C ℚ
+  MA : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MAi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MB : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MBi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  hAi : MAi * MA = 1
+  hBi : MBi * MB = 1
+  hx : ∀ t j, (MB * scatM (Jr * Cc) * MA) (lX t) j = if lX t = j then 1 else 0
+  hy : ∀ i t, (MB * scatM (Jr * Cc) * MA) i (lY t) = if i = lY t then 1 else 0
+  hid : ∀ S t, (MB * scatM (Jr * Cc) * MA) (lY S) (lX t) = if S = t then 1 else 0
+
+/-- **The label half.**  See `checks/wht26/shared/gcert-interface.md`, section CHAIN. -/
+structure Lab (H : Type) [Fintype H] [DecidableEq H] {T Sl C : Type} [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] (S : Scal T Sl C) where
+  tv : T → Space H
+  hunit : ∀ t, dot (tv t) (tv t) = 1
+  hgap : ∀ t, ∃ p, tv t p = 0
+  lab0 : L3 T Sl → SLbl H
+  labA : L3 T Sl → SLbl H
+  labB : L3 T Sl → SLbl H
+  labF : L3 T Sl → SLbl H
+  cen : C → SLbl H
+  z0 : SLbl H
+  hz0 : z0.dim = 0
+  h0x : ∀ t, (lab0 (lX t)).dim = 1 ∧ (lab0 (lX t)).Mem (tv t)
+  h0y : ∀ t, (lab0 (lY t)).dim = 0
+  h0s : ∀ q, (lab0 (lS q)).dim = 0
+  hAy : ∀ t, labA (lY t) = z0
+  hAc : ∀ k q, S.Cc k q ≠ 0 → cen k = labA (lS q)
+  hcen : ∀ k, 0 < (cen k).dim
+  hFx : ∀ t, (labF (lX t)).dim = Fintype.card H
+  hFs : ∀ q, (labF (lS q)).dim = Fintype.card H
+  hFy : ∀ t, (labF (lY t)).dim + 1 = Fintype.card H ∧
+    ∀ x, (labF (lY t)).Mem x → dot (tv t) x = 0
+  rA : List ℕ
+  rB : List ℕ
+  rF : List ℕ
+  pA : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (lab0 r)) (fun r => X.Φ (labA r)) (actPoint S.MA)
+        (fun φ => rcost φ rA) ∧
+    GRoute (fun r => X.Φ (lab0 r)) (fun r => X.Φ (labA r)) (actPoint S.MAiᵀ)
+        (fun φ => rcost φ rA)
+  pB : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (labA r)) (fun r => X.Φ (labB r)) (actPoint S.MB)
+        (fun φ => rcost φ rB) ∧
+    GRoute (fun r => X.Φ (labA r)) (fun r => X.Φ (labB r)) (actPoint S.MBiᵀ)
+        (fun φ => rcost φ rB)
+  pF : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (labB r)) (fun r => X.Φ (labF r)) id (fun φ => rcost φ rF)
+
+/-- price of one invocation: the blocks of the three phases and one block per copy. -/
+def Lab.cost {H : Type} [Fintype H] [DecidableEq H] {T Sl C : Type} [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] {S : Scal T Sl C} (L : Lab H S)
+    (φ : ℕ → ℝ) : ℝ :=
+  rcost φ L.rA + (∑ k, bcost φ (L.cen k).dim) + rcost φ L.rB + rcost φ L.rF
+
+section Alg
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+namespace Scal
+variable (K : Scal T Sl C)
+
+/-- the product of ALL gates of the main phase (scatter with the copies eliminated). -/
+def Mt : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MB * scatM (K.Jr * K.Cc) * K.MA
+/-- its inverse. -/
+def Mti : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MAi * scatMi (K.Jr * K.Cc) * K.MBi
+
+
+lemma im : K.Mti * K.Mt = 1 := by
+  unfold Mti Mt
+  have hB : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ, K.MBi * (K.MB * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, K.hBi, Matrix.one_mul]
+  have hS : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ,
+      scatMi (K.Jr * K.Cc) * (scatM (K.Jr * K.Cc) * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, scat_inv, Matrix.one_mul]
+  rw [Matrix.mul_assoc, Matrix.mul_assoc, Matrix.mul_assoc, hB, hS, K.hAi]
+
+lemma mi : K.Mt * K.Mti = 1 := mul_eq_one_comm.mp K.im
+
+lemma hxm : PX * K.Mt = PX := PX_mul_of (M := K.Mt) K.hx
+lemma hmy : K.Mt * PY = PY := mul_PY_of (M := K.Mt) K.hy
+lemma hiy : K.Mti * PY = PY := dirt_iy K.hmy K.im
+
+/-- **the dirt rule, forward**, for the matrices of the circuit. -/
+lemma hF : g8 K.Mti * K.Mt * g1 K.Mt = 1 + PY * K.Mt * PX := by
+  unfold g8 g1
+  exact dirt_fwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- **the dirt rule, backward.** -/
+lemma hB : g1i K.Mt * K.Mti * h8 K.Mt = 1 - PY * K.Mt * PX := by
+  unfold g1i h8
+  exact dirt_bwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- live part of the forward word before the scatter: `y -= K s`, then phase A. -/
+def f1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MA (actPoint (g1 K.Mt) u)
+/-- after the scatter: phase B, then the slot rows of the inverse. -/
+def f2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (g8 K.Mti) (actPoint K.MB u)
+/-- the same for the backward word (transposed inverses). -/
+def b1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u)
+def b2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ u)
+
+lemma fwd_live (u : L3 T Sl → ℂ) :
+    K.f2 (actPoint (scatM (K.Jr * K.Cc)) (K.f1 u)) = actPoint (1 + PY * K.Mt * PX) u := by
+  rw [← K.hF]
+  show actPoint (g8 K.Mti) (actPoint K.MB (actPoint (scatM (K.Jr * K.Cc))
+      (actPoint K.MA (actPoint (g1 K.Mt) u))))
+    = actPoint (g8 K.Mti * (K.MB * scatM (K.Jr * K.Cc) * K.MA) * g1 K.Mt) u
+  rw [actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma bwd_live (u : L3 T Sl → ℂ) :
+    K.b2 (actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 u))
+      = actPoint ((1 - PY * K.Mt * PX)ᵀ) u := by
+  rw [← K.hB]
+  show actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ (actPoint (scatMi (K.Jr * K.Cc))ᵀ
+      (actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u))))
+    = actPoint ((g1i K.Mt * (K.MAi * scatMi (K.Jr * K.Cc) * K.MBi) * h8 K.Mt)ᵀ) u
+  rw [Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul,
+    actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma liveAct_glue (φ : (L3 T Sl → ℂ) → (L3 T Sl → ℂ)) (u : L3 T Sl → ℂ) (c : C → ℂ) :
+    liveAct φ (glue u c) = glue (φ u) c :=
+  congrArg (fun v => glue (φ v) c) (glue_up u c)
+
+/-- **Scalar identity of the forward word**: `y += x`, slots restored, for ARBITRARY slot
+contents (the copies are erased before and after). -/
+theorem fwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.f2 (gateS bY bC K.Jr (gateS bC bS K.Cc (liveAct K.f1 (eraseC z)))))
+      = shearF z := by
+  have h1 : liveAct K.f1 (eraseC z) = glue (K.f1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bY bC K.Jr (gateS bC bS K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint (scatM (K.Jr * K.Cc)) (K.f1 (z ∘ upE)) := by
+    have h := scat_glue K.Jr K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.fwd_live, act_shear K.Mt K.hid]
+  exact glue_shearF z
+
+/-- **Scalar identity of the backward word**: `x -= y`, slots restored. -/
+theorem bwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.b2 (gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (liveAct K.b1 (eraseC z)))))
+      = shearB z := by
+  have h1 : liveAct K.b1 (eraseC z) = glue (K.b1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (glue (K.b1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 (z ∘ upE)) := by
+    have h := scat_glueT K.Jr K.Cc (glue (K.b1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.bwd_live, act_shearT K.Mt K.hid]
+  exact glue_shearB z
+
+end Scal
+end Alg
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.Scal.fwd_scalar
+#print axioms OAI.PowerSaving.GX.Scal.bwd_scalar
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean
new file mode 100644
index 0000000000..951edde5cf
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean
@@ -0,0 +1,132 @@
+import Work.GCert.Chain.Win
+import Work.BridgeGeom.Stage
+
+/-!
+# (key: gx-chain) THE WINDOW LIFT (spec statement 3): the windows of the bridged geometry
+
+For the block frame map `BG.fmapB hB hH d q` of a stage of the bridged word (label space
+`LB B H = H ⊕ (B × H)`, old frame of the projector `P`: `PhiB d q P`) the stage-B frame map is
+`BXMap.ofConj d q` (`U ↦ d (U ⊕ span q)`, arbitrary subspaces `U` of `H`).  At a coordinate
+subspace of an orthonormal basis `A` of `H` the two name the SAME subspace of the address space
+(`insub_old_new`), so the old frame and the representative of any label of that subspace
+differ by a free factor (`frame_core_free`, `rep_change`): `old_to_new`, `new_to_old`.
+
+`gwinB hB hH d q : GWin H (LB B H)` with `(gwinB hB hH d q).Xm = fmapB hB hH d q` (`rfl`).
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR BG GF
+noncomputable section
+
+section
+variable {B H : Type} [Fintype B] [DecidableEq B] [Fintype H] [DecidableEq H]
+
+lemma blkT_mulVec (A : OBase H) (z : Space (LB B H)) (k : LB B H) :
+    ((blkB B A)ᵀ *ᵥ z) k = Sum.elim (fun i => dot (A.v i) (fun j => z (Sum.inl j)))
+      (fun b => z (Sum.inr b)) k := by
+  cases k with
+  | inl i =>
+    simp [blkB, Matrix.fromBlocks_transpose, Matrix.mulVec, dotProduct, Fintype.sum_sum_type,
+      cmat, dot]
+  | inr b =>
+    simp [blkB, Matrix.fromBlocks_transpose, Matrix.mulVec, dotProduct, Fintype.sum_sum_type,
+      Matrix.one_apply]
+
+/-- coordinates of `y` in the basis `d (A ⊕ std)`. -/
+lemma dot_cols (d : Orth (LB B H)) (A : OBase H) (y : Space (LB B H)) (k : LB B H) :
+    dot ((ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))).v k) y
+      = Sum.elim (fun i => dot (A.v i) (fun j => (d.1ᵀ *ᵥ y) (Sum.inl j)))
+          (fun b => (d.1ᵀ *ᵥ y) (Sum.inr b)) k := by
+  rw [← blkT_mulVec A (d.1ᵀ *ᵥ y) k, Matrix.mulVec_mulVec, ← Matrix.transpose_mul]
+  rfl
+
+/-- **the old frame and the lifted label name the same subspace of the address space.** -/
+theorem insub_old_new (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) (y : Space (LB B H)) :
+    InSub (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q) y ↔
+      InSub (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q) y := by
+  rw [insub_conj, insub_coordPerm]
+  have hU := h (fun i => (d.1ᵀ *ᵥ y) (Sum.inl i))
+  constructor
+  · intro hk
+    refine ⟨hU.mpr ((insub_coordPerm A s _).mpr (fun i hi => ?_)), fun b hb => ?_⟩
+    · have h1 := hk (Sum.inl i) (fun hm => hi (Finset.inl_mem_disjSum.mp hm))
+      rw [dot_cols] at h1
+      exact h1
+    · have h1 := hk (Sum.inr b) (fun hm => hb (Finset.inr_mem_disjSum.mp hm))
+      rw [dot_cols] at h1
+      exact h1
+  · rintro ⟨h1, h2⟩ k hk
+    rw [dot_cols]
+    cases k with
+    | inl i =>
+      exact (insub_coordPerm A s _).mp (hU.mp h1) i
+        (fun hm => hk (Finset.inl_mem_disjSum.mpr hm))
+    | inr b => exact h2 b (fun hm => hk (Finset.inr_mem_disjSum.mpr hm))
+
+/-- old frame of a coordinate subspace → representative of any label naming it: FREE. -/
+theorem old_to_new (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) :
+    GReach (PhiB d q (A.mat s)) ((BXMap.ofConj d.1 d.2 (Orth.orth' d) q).Φ U) (fun _ => 0) := by
+  rw [PhiB_eq]
+  obtain ⟨N, hN, e⟩ := repChange (LB B H) _ _ _ _ (insub_old_new d q A s U h)
+  have a : GReach (frame (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))) (JB s q))
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_old_to_core _ _).reach
+  have b : GReach
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (core (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q)) (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_of_free hN e).reach
+  exact (a.trans b).cast (fun φ => by simp [rcost])
+
+/-- the same, backwards. -/
+theorem new_to_old (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) :
+    GReach ((BXMap.ofConj d.1 d.2 (Orth.orth' d) q).Φ U) (PhiB d q (A.mat s)) (fun _ => 0) := by
+  rw [PhiB_eq]
+  obtain ⟨N, hN, e⟩ := repChange (LB B H) _ _ _ _
+    (fun y => (insub_old_new d q A s U h y).symm)
+  have a : GReach (core (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q))
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_of_free hN e).reach
+  have b : GReach
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (frame (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_core_to_old _ _).reach
+  exact (a.trans b).cast (fun φ => by simp [rcost])
+
+/-- **The window of a stage of the bridged geometry.** -/
+def gwinB (hB : 1 ≤ Fintype.card B) (hH : 1 ≤ Fintype.card H) (d : Orth (LB B H))
+    (q : Finset (B × H)) : GWin H (LB B H) where
+  Xm := fmapB hB hH d q
+  X := BXMap.ofConj d.1 d.2 (Orth.orth' d) q
+  big := by
+    rw [card_LB]
+    have := Nat.mul_le_mul_right (Fintype.card H) (show 2 ≤ Fintype.card B + 1 by omega)
+    omega
+  toNew := fun A s U h => old_to_new d q A s U h
+  toOld := fun A s U h => new_to_old d q A s U h
+
+@[simp] lemma gwinB_Xm (hB : 1 ≤ Fintype.card B) (hH : 1 ≤ Fintype.card H) (d : Orth (LB B H))
+    (q : Finset (B × H)) : (gwinB hB hH d q).Xm = fmapB hB hH d q := rfl
+
+end
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.insub_old_new
+#print axioms OAI.PowerSaving.GX.old_to_new
+#print axioms OAI.PowerSaving.GX.new_to_old
+#print axioms OAI.PowerSaving.GX.gwinB
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean
new file mode 100644
index 0000000000..d7ecfebcea
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean
@@ -0,0 +1,33 @@
+import Work.GCert.Scalar.Main
+import Work.GCert.Data.P193ScalOK
+import Work.GCert.Data.B2Gp193
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `P193`: THE CLOSED THEOREMS
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`wht_B2Gp193_of_ids` (label half, price, unit list, rate fact, gx-chain's end theorem) applied to the scalar half
+`GXD.P193.scalOK : GS.ScalOK GXD.P193.raw` (kernel checks `scal<i>_ok`, `ychk_ok`; soundness: gx-scalar).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - 74745/10^8))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `P193`.** -/
+theorem wht_main_B2Gp193 :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 74745/(10:ℝ)^8) W :=
+  wht_B2Gp193_of_ids GXD.P193.scalOK.hv GXD.P193.scalOK.hAi GXD.P193.scalOK.hBi GXD.P193.scalOK.hx GXD.P193.scalOK.hy GXD.P193.scalOK.hid
+
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - 7474547/10^10))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `P193`.** -/
+theorem wht_main_B2Gp193x :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W :=
+  wht_B2Gp193x_of_ids GXD.P193.scalOK.hv GXD.P193.scalOK.hAi GXD.P193.scalOK.hBi GXD.P193.scalOK.hx GXD.P193.scalOK.hy GXD.P193.scalOK.hid
+
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_main_B2Gp193
+#print axioms OAI.PowerSaving.WHT.wht_main_B2Gp193x
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean
new file mode 100644
index 0000000000..c6cbac38e3
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean
@@ -0,0 +1,97 @@
+import Work.GCert.Scalar.Roles
+import Work.GCert.Labels.Main
+
+/-!
+# (key: gx-data) Glue between the scalar half (gx-scalar) and the label half (gx-labels)
+
+For ANY `c : GXD.Raw` (nothing is evaluated here):
+
+* `roles`   gx-scalar's numbering `GS.emb` / `GS.unemb` is gx-labels' `GLab.Roles`;
+* `scalOf`  gx-chain's record `GX.Scal (Fin v) (Fin R) (Fin ret.length)` from the FIVE scalar
+            identities of the matrices `GS.MA`, `GS.MAi`, `GS.MB`, `GS.MBi`, `GS.Jrm`, `GS.Ccm`;
+* `scalOf_MA .. scalOf_MBi`  its gate matrices are the ordered products of the adds of `c`, in
+            the form asked by `GLab.Valid.lab` (`GLab.mic GS.toCoef`);
+* `reg`, `reg_slot`, `reg_mem`  copy `k` reads the retained register `(c.ret.getD k (0,0)).1`.
+
+So a generated instance needs from the scalar side exactly `hAi hBi hx hy hid` (see
+`wht_<Inst>_of_ids` in `Work/GCert/Data/<Inst>.lean`).  No `sorry`.
+-/
+
+namespace GXD
+open SSC OAI.PowerSaving OAI.PowerSaving.CR Matrix
+
+/-- the numbering of the roles: `x_t = t`, `y_t = v + t`, slot `q = 2 v + q` -/
+theorem roles (c : Raw) (hv : 0 < c.v) : GLab.Roles c.v c.R (GS.emb c) (GS.unemb c hv) where
+  hun := GS.unemb_emb hv
+  hin := GS.emb_unemb hv
+  hlt := fun q => by
+    rcases q with (t | S) | q
+    · have := t.isLt; show t.val < 2 * c.v + c.R; omega
+    · have := S.isLt; show c.v + S.val < 2 * c.v + c.R; omega
+    · have := q.isLt; show 2 * c.v + q.val < 2 * c.v + c.R; omega
+  eX := fun _ => rfl
+  eY := fun _ => rfl
+  eS := fun _ => rfl
+
+/-- **the scalar half as gx-chain's record**, from the five scalar identities -/
+noncomputable def scalOf (c : Raw) (hv : 0 < c.v)
+    (hAi : GS.MAi c hv * GS.MA c hv = 1) (hBi : GS.MBi c hv * GS.MB c hv = 1)
+    (hx : ∀ (t : Fin c.v) (j : GS.Rl c), (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      (lX t) j = if lX t = j then 1 else 0)
+    (hy : ∀ (i : GS.Rl c) (t : Fin c.v), (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      i (lY t) = if i = lY t then 1 else 0)
+    (hid : ∀ S t : Fin c.v, (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      (lY S) (lX t) = if S = t then 1 else 0) :
+    GX.Scal (Fin c.v) (Fin c.R) (Fin c.ret.length) where
+  Cc := GS.Ccm c
+  Jr := GS.Jrm c
+  MA := GS.MA c hv
+  MAi := GS.MAi c hv
+  MB := GS.MB c hv
+  MBi := GS.MBi c hv
+  hAi := hAi
+  hBi := hBi
+  hx := hx
+  hy := hy
+  hid := hid
+
+section
+variable (c : Raw) (hv : 0 < c.v) (hAi) (hBi) (hx) (hy) (hid)
+
+theorem scalOf_MA : (scalOf c hv hAi hBi hx hy hid).MA
+    = matP (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesA.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MAi : (scalOf c hv hAi hBi hx hy hid).MAi
+    = matPinv (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesA.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MB : (scalOf c hv hAi hBi hx hy hid).MB
+    = matP (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesB.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MBi : (scalOf c hv hAi hBi hx hy hid).MBi
+    = matPinv (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesB.flatMap Gate.adds)) := rfl
+
+end
+
+/-- the register read by copy `k` (the slot of the retained total `k`) -/
+def reg (c : Raw) (k : Fin c.ret.length) : Nat := (c.ret.getD k.val (0, 0)).1
+
+theorem reg_slot (c : Raw) (hv : 0 < c.v) (hAi) (hBi) (hx) (hy) (hid) (k : Fin c.ret.length)
+    (q : Fin c.R) (h : (scalOf c hv hAi hBi hx hy hid).Cc k q ≠ 0) :
+    reg c k = 2 * c.v + q.val := by
+  have h' : (if 2 * c.v + q.val = (c.ret.getD k.val (0, 0)).1 then (1:ℚ) else 0) ≠ 0 := h
+  by_cases e : 2 * c.v + q.val = (c.ret.getD k.val (0, 0)).1
+  · exact e.symm
+  · rw [if_neg e] at h'; exact absurd rfl h'
+
+theorem reg_mem (c : Raw) (k : Fin c.ret.length) : reg c k ∈ c.ret.map Prod.fst := by
+  unfold reg
+  rw [List.getD_eq_getElem _ _ k.isLt]
+  exact List.mem_map.mpr ⟨_, List.getElem_mem k.isLt, rfl⟩
+
+end GXD
+
+#print axioms GXD.roles
+#print axioms GXD.scalOf
+#print axioms GXD.scalOf_MA
+#print axioms GXD.reg_slot
+#print axioms GXD.reg_mem
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean
new file mode 100644
index 0000000000..9b9925ce26
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean
@@ -0,0 +1,55 @@
+import Work.BridgeGeom.B2
+import Work.FoldRate.Group
+import Work.GCert.Data.RateB2Gp193
+import Work.GCert.Data.RateB2Gp193x
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `P193`, h = 22: the unit price is the price of the block list
+
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.  Arithmetic only (no certificate is imported).
+
+One unit: `W = 14692` live roles (`4 v + R`, `v = 1320`, `R = 9412`), label dimension `m = 110`, deficit `D = 3080`.
+`invPrice φ` = the price of the blocks of ONE invocation (the kernel-counted list `GXD.P193.hist`, by rank);
+`unitPrice φ = 5 * invPrice φ + v * BG.bankPrice h φ = listCost φ BlockAccounting.blocksB2Gp193` (`unit_cost`).
+Whole-block `1 - 74745/10^8` (fails at 74746), ten decimals `1 - 7474547/10^10` (fails at 7474550).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace BridgeRate
+namespace B2Gp193
+open Finset Binary Matrix RAM CB FoldRate
+noncomputable section
+
+/-- price of the blocks of ONE invocation of `P193` (all roles and scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+
+/-- price of ONE unit of the bridged word B_2 -/
+def unitPrice (φ : ℕ → ℝ) : ℝ := 5 * invPrice φ + ((1320:ℕ):ℝ) * BG.bankPrice 22 φ
+
+/-- **The unit price is the price of the unit block list.** -/
+theorem unit_cost (φ : ℕ → ℝ) : unitPrice φ = listCost φ BlockAccounting.blocksB2Gp193 := by
+  unfold unitPrice invPrice
+  simp only [BG.bankPrice, listCost, BlockAccounting.blocksB2Gp193, List.map_cons, List.map_nil,
+    List.sum_cons, List.sum_nil]
+  norm_num [bcost]
+  try ring
+
+theorem blocks_x : BlockAccounting.blocksB2Gp193 = BlockAccounting.blocksB2Gp193x := rfl
+
+theorem unit_cost_x (φ : ℕ → ℝ) : unitPrice φ = listCost φ BlockAccounting.blocksB2Gp193x := by
+  rw [unit_cost, blocks_x]
+
+/-- one unit stands for `W * m - D` unit moves -/
+theorem unit_tally : unitPrice (fun r => (r:ℝ)) = ((14692:ℕ):ℝ) * ((110:ℕ):ℝ) - ((3080:ℕ):ℝ) := by
+  rw [unit_cost]
+  exact BlockAccounting.blocksB2Gp193_tally
+
+end
+end B2Gp193
+end BridgeRate
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BridgeRate.B2Gp193.unit_cost
+#print axioms OAI.PowerSaving.BridgeRate.B2Gp193.unit_tally
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean
new file mode 100644
index 0000000000..3c3250279e
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean
@@ -0,0 +1,81 @@
+import Work.GCert.Labels.Main
+import Work.GCert.Data.P193Price
+import Work.GCert.Data.Gen.P193Tab0
+import Work.GCert.Data.Gen.P193Tab1
+import Work.GCert.Data.Gen.P193Tab2
+import Work.GCert.Data.Gen.P193Tab3
+import Work.GCert.Data.Gen.P193Seg0
+import Work.GCert.Data.Gen.P193Seg1
+import Work.GCert.Data.Gen.P193Seg2
+import Work.GCert.Data.Gen.P193Seg3
+import Work.GCert.Data.Gen.P193Seg4
+import Work.GCert.Data.Gen.P193SegF
+import Work.GCert.Data.Gen.P193End
+/-! # (key: gx-data) gcert/1 certificate `P193` (h = 22): THE LABEL HALF and its price
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+`v = 1320` ports, `R = 9412` slots, 22 scratch copies of rank 20, copy cost `cst = 440`, `N = 262944` unit moves.
+* `aux : GLab.Aux`, `valid : GLab.Valid raw aux`: frame table (`tab<i>_ok` composed by `tabK_node`), the replays of phase A
+  and phase B (`seg<i>_ok` composed by `Run.append`), the final climbs (`segF_ok`, `fin_ok`), the ends (`end_ok`);
+* `lab_cost`, `lab_price`: for ANY scalar half `S` the label half `valid.lab S ..` costs
+  `rcost rA + card C * bcost 20 + rcost rB + rcost rF` = `invPrice φ` = 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+  (`Gen.P193Hist`, `P193Price`) when there are 22 copies. -/
+set_option maxRecDepth 100000
+namespace GXD.P193
+open GXD OAI.PowerSaving OAI.PowerSaving.CB
+theorem raw_h : raw.h = 22 := rfl
+theorem raw_v : raw.v = 1320 := rfl
+theorem raw_R : raw.R = 9412 := rfl
+/-- what the label checks read next to `raw` -/
+noncomputable def aux : GLab.Aux := ⟨par, st0, st2, st5, st6, fins, rA, rB, rF⟩
+theorem fin_ok : GLab.noAdds fins = true := by decide +kernel
+theorem cen_ok : (raw.ret.map Prod.fst).all (fun r => Nat.beq (GLab.cdim (par.tab.get (st2.get r))) 20) = true := by
+  decide +kernel
+theorem tab_ok : GLab.tabK par.h par.tab = true := (GLab.tabK_node _ _ _ (GLab.tabK_node _ _ _ tab0_ok tab1_ok) (GLab.tabK_node _ _ _ tab2_ok tab3_ok))
+theorem gatesA_eq : raw.gatesA = seg0 ++ (seg1) := by
+  show List.flatten [seg0, seg1] = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase A, composed from its kernel-checked segments -/
+theorem runA : GLab.Run par st0 raw.gatesA st2 rA := by
+  rw [gatesA_eq]
+  exact GLab.Run.append (GLab.Run.of_seg seg0_ok) (GLab.Run.of_seg seg1_ok)
+theorem gatesB_eq : raw.gatesB = seg2 ++ (seg3 ++ (seg4)) := by
+  show List.flatten [seg2, seg3, seg4] = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase B, composed from its kernel-checked segments -/
+theorem runB : GLab.Run par st2 raw.gatesB st5 rB := by
+  rw [gatesB_eq]
+  exact GLab.Run.append (GLab.Run.of_seg seg2_ok) (GLab.Run.append (GLab.Run.of_seg seg3_ok) (GLab.Run.of_seg seg4_ok))
+/-- **the kernel-checked label facts** of the certificate -/
+theorem valid : GLab.Valid raw aux where
+  hn := rfl
+  tab := tab_ok
+  runA := runA
+  runB := runB
+  runF := GLab.Run.of_seg segF_ok
+  fin := fin_ok
+  ends := end_ok
+theorem cen_dim (r : Nat) (hr : r ∈ raw.ret.map Prod.fst) : GLab.cdim (par.tab.get (st2.get r)) = 20 :=
+  Nat.eq_of_beq_eq_true (List.all_eq_true.mp cen_ok r hr)
+/-- price of the label half over ANY scalar half -/
+theorem lab_cost {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (φ : ℕ → ℝ) :
+    (valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cost φ
+      = rcost φ rA + (Fintype.card C : ℝ) * bcost φ 20 + rcost φ rB + rcost φ rF := by
+  obtain ⟨h1, h2, h3, h4⟩ := valid.lab_ranks S Ro cf hMA hMAi hMB hMBi reg hCc hreg
+  have h5 : ∀ k, bcost φ (((valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cen k).dim) = bcost φ 20 :=
+    fun k => by rw [h4 k]; exact congrArg (bcost φ) (cen_dim _ (hreg k))
+  rw [GX.Lab.cost, h1, h2, h3, Finset.sum_congr rfl (fun k _ => h5 k), Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
+  rfl
+/-- **the label half costs one invocation price** (`invPrice`, by rank, from the kernel counts) -/
+theorem lab_price {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (hC : Fintype.card C = 22) (φ : ℕ → ℝ) :
+    (valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cost φ = invPrice φ := by
+  rw [lab_cost S Ro cf hMA hMAi hMB hMBi reg hCc hreg φ, hC, ← inv_cost φ]
+  norm_num [bcost]
+end GXD.P193
+#print axioms GXD.P193.valid
+#print axioms GXD.P193.lab_price
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean
new file mode 100644
index 0000000000..eeed011d64
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean
@@ -0,0 +1,54 @@
+import Work.GCert.Data.Price
+import Work.GCert.Data.Gen.P193Hist
+
+/-!
+# (key: gx-data) gcert/1 certificate `P193` (h = 22): the price of one invocation
+
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+`rA_cost`, `rB_cost`, `rF_cost`: the price of the block rank lists of phase A, phase B and the final climbs
+(lists `GXD.P193.rA / rB / rF`, counted by the kernel in `Gen.P193Hist`);
+`inv_cost`: with the 22 scratch copies (22 * φ 20) the blocks of ONE invocation cost
+`invPrice φ` = 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20;  `inv_moves`: they stand for `R h + 2 v (h - 1) + cst = 262944` unit moves.
+-/
+
+namespace GXD.P193
+open GXD OAI.PowerSaving.CB
+
+/-- price of the blocks of phase A, from the kernel counts -/
+theorem rA_cost (φ : ℕ → ℝ) : rcost φ rA = 9900 * φ 1 + 500 * φ 2 + 2402 * φ 3 + 82 * φ 4 + 242 * φ 5 + 175 * φ 6 + 88 * φ 7 + 68 * φ 8 + 110 * φ 9 + 132 * φ 10 + 10 * φ 11 + 67 * φ 12 + 3 * φ 13 + 19 * φ 15 := by
+  rw [GXD.rcost_wsumK φ rA 19 rankBoundA]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankA0_ok, rankA1_ok, rankA2_ok, rankA3_ok, rankA4_ok, rankA5_ok, rankA6_ok, rankA7_ok, rankA8_ok, rankA9_ok, rankA10_ok, rankA11_ok, rankA12_ok, rankA13_ok, rankA14_ok, rankA15_ok, rankA16_ok, rankA17_ok, rankA18_ok, rankA19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of phase B, from the kernel counts -/
+theorem rB_cost (φ : ℕ → ℝ) : rcost φ rB = 16638 * φ 1 + 10380 * φ 2 + 4111 * φ 3 + 3476 * φ 4 + 1531 * φ 5 + 1137 * φ 6 + 531 * φ 7 + 1346 * φ 8 + 293 * φ 9 + 629 * φ 10 + 343 * φ 11 + 1067 * φ 12 + 123 * φ 13 + 712 * φ 14 + 1860 * φ 15 + 81 * φ 16 + 39 * φ 17 + 2640 * φ 18 := by
+  rw [GXD.rcost_wsumK φ rB 19 rankBoundB]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankB0_ok, rankB1_ok, rankB2_ok, rankB3_ok, rankB4_ok, rankB5_ok, rankB6_ok, rankB7_ok, rankB8_ok, rankB9_ok, rankB10_ok, rankB11_ok, rankB12_ok, rankB13_ok, rankB14_ok, rankB15_ok, rankB16_ok, rankB17_ok, rankB18_ok, rankB19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of the final climbs, from the kernel counts -/
+theorem rF_cost (φ : ℕ → ℝ) : rcost φ rF = 2640 * φ 1 + 1518 * φ 2 + 3410 * φ 3 + 651 * φ 4 + 177 * φ 5 + 293 * φ 6 + 87 * φ 7 + 117 * φ 8 + 26 * φ 9 + 169 * φ 10 + 1 * φ 11 + 63 * φ 12 + 1 * φ 13 + 30 * φ 14 + 7 * φ 16 + 42 * φ 17 + 13 * φ 18 + 167 * φ 19 := by
+  rw [GXD.rcost_wsumK φ rF 19 rankBoundF]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankF0_ok, rankF1_ok, rankF2_ok, rankF3_ok, rankF4_ok, rankF5_ok, rankF6_ok, rankF7_ok, rankF8_ok, rankF9_ok, rankF10_ok, rankF11_ok, rankF12_ok, rankF13_ok, rankF14_ok, rankF15_ok, rankF16_ok, rankF17_ok, rankF18_ok, rankF19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of ONE invocation (x roles, y roles, slots, scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+
+/-- **Price of ONE invocation** in the shape of `GX.Lab.cost`: phase A, the scratch copies, phase B, final climbs. -/
+theorem inv_cost (φ : ℕ → ℝ) : rcost φ rA + (22 * φ 20) + rcost φ rB + rcost φ rF = invPrice φ := by
+  rw [rA_cost, rB_cost, rF_cost]
+  unfold invPrice
+  ring
+
+theorem inv_moves : invPrice (fun r => (r:ℝ)) = 9412 * 22 + 2 * 1320 * (22 - 1) + 440 := by
+  unfold invPrice
+  norm_num
+
+theorem inv_count : invPrice (fun _ => (1:ℝ)) = 70169 := by
+  unfold invPrice
+  norm_num
+
+end GXD.P193
+#print axioms GXD.P193.inv_cost
+#print axioms GXD.P193.inv_moves
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean
new file mode 100644
index 0000000000..3539192ac1
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean
@@ -0,0 +1,17 @@
+import Work.GCert.Scalar.Main
+import Work.GCert.Data.Gen.P193Scal0
+import Work.GCert.Data.Gen.P193Scal1
+import Work.GCert.Data.Gen.P193YChk
+/-! # (key: gx-data) gcert/1 certificate `P193` (h = 22): THE SCALAR HALF `scalOK : GS.ScalOK raw`
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+Kernel checks `scal<i>_ok` (2 source batches) and `ychk_ok`. -/
+namespace GXD.P193
+open GXD
+theorem scalOK : GS.ScalOK raw where
+  hv := by decide
+  hs := fun t ht =>
+    if h0 : t < 660 then ⟨0, 660, Nat.zero_le t, h0, GS.XRun.of_check scal0_ok⟩ else
+    ⟨660, 660, Nat.le_of_not_lt h0, Nat.lt_of_lt_of_le ht (by decide), GS.XRun.of_check scal1_ok⟩
+  hyc := fun t ht => ⟨0, 1320, Nat.zero_le t, Nat.lt_of_lt_of_le ht (by decide), GS.YRun.of_check ychk_ok⟩
+end GXD.P193
+#print axioms GXD.P193.scalOK
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean
new file mode 100644
index 0000000000..df563cde73
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean
@@ -0,0 +1,327 @@
+import Work.BlockAccounting.Moment
+import Work.BlockAccounting.Sharp
+import Work.FoldRate.RankTools
+
+/-!
+# (key: gx-data) Rate lemmas for one unit of the bridged word B_2 with the gcert/1 circuit `P193` (h = 22)
+
+GENERATED by checks/wht26/gx-data/py/gxrate.py with the text generators of checks/wht9/bridge-rate/py
+(used read-only).  No `sorry`.  Arithmetic only.
+
+One unit: `W = 14692` live roles, label dimension `m = 110`, deficit `D = 3080`.
+
+* `blocksB2Gp193x`            the block list (rank, count) of ONE unit;
+* `fold_B2Gp193x`             whole-block fact at `1 - 7474547/10^10`, fill parameter `s = 40` (slack 2.37e-12);
+* `fold_B2Gp193x_sharp`       `W ≤ moment` at `1 - 7474550/10^10`: fails for every table (excess 1.40e-10);
+* `foldRank_B2Gp193x`         per-rank fact at `1 - 4058344/10^10`, `s = 40` (slack 1.10e-07);
+* `foldRank_B2Gp193x_sharp`   per-rank: fails for every table at `1 - 4058349/10^10`.
+
+That a Lean word has `G` times this list as its block histogram is NOT proved here.
+-/
+
+set_option maxRecDepth 4000
+
+namespace OAI.PowerSaving.BlockAccounting
+open Finset
+
+/-- Block list `(rank, count)` of ONE unit of the bridged five-stage word B_2 with the gcert/1 circuit `P193` (h = 22, m = 110): five invocations (ALL blocks of one invocation: x roles, y roles, slots, scratch copies; the kernel-counted list `GXD.P193.hist`), and for each of the v = 1320 ports the idle climbs of its two twins (2 blocks each of rank h-1, 2h-2, 2h+2, 4); R = 9412 slots shared by the five stages. -/
+def blocksB2Gp193x : List (ℕ × ℕ) := [(1, 145890), (2, 61990), (3, 49615), (4, 23685), (5, 9750), (6, 8025), (7, 3530), (8, 7655), (9, 2145), (10, 4650), (11, 1770), (12, 5985), (13, 635), (14, 3710), (15, 9395), (16, 440), (17, 405), (18, 13265), (19, 835), (20, 110), (21, 2640), (42, 2640), (46, 2640)]
+
+/-- total rank of one unit (= number of unit moves it stands for): `W * m - D` -/
+theorem blocksB2Gp193x_rank : (blocksB2Gp193x.map fun b => b.1 * b.2).sum = 14692 * 110 - 3080 := by
+  norm_num [blocksB2Gp193x]
+
+/-- the same as a price: the unit list at the price list `r ↦ r` (shape of `hPid` in `RAM.engine_program_group_perRank`) -/
+theorem blocksB2Gp193x_tally : (blocksB2Gp193x.map fun b => (b.2:ℝ) * ((b.1:ℕ):ℝ)).sum = ((14692:ℕ):ℝ) * ((110:ℕ):ℝ) - ((3080:ℕ):ℝ) := by
+  norm_num [blocksB2Gp193x]
+
+theorem blocksB2Gp193x_count : (blocksB2Gp193x.map fun b => b.2).sum = 361405 := by
+  norm_num [blocksB2Gp193x]
+
+theorem blocksB2Gp193x_proper : ∀ b ∈ blocksB2Gp193x, 1 ≤ b.1 ∧ b.1 < 110 := by
+  decide
+
+/-- **whole-block fact** of `blocksB2Gp193x` at exponent `1 - 7474547/10^10`, fill parameter `s = 40`: the hypothesis `hnum` of `RAM.engine_program_group_list` (u = 110, W = 14692).  Relative slack of the rational certificate: 2.37e-12. -/
+theorem fold_B2Gp193x :
+    ((2:ℝ)^40 - 1) * moment 110 (1 - 7474547/(10:ℝ)^10) blocksB2Gp193x
+      + ((14692:ℕ):ℝ) * (T 110 (1 - 7474547/(10:ℝ)^10) (110 - 1) 1 + T 110 (1 - 7474547/(10:ℝ)^10) 1 1)
+      < (2:ℝ)^40 * ((14692:ℕ):ℝ) := by
+  have hsum : moment 110 (1 - 7474547/(10:ℝ)^10) blocksB2Gp193x
+      = T 110 (1 - 7474547/(10:ℝ)^10) 1 145890 + (T 110 (1 - 7474547/(10:ℝ)^10) 2 61990 + (T 110 (1 - 7474547/(10:ℝ)^10) 3 49615 + (T 110 (1 - 7474547/(10:ℝ)^10) 4 23685 + (T 110 (1 - 7474547/(10:ℝ)^10) 5 9750 + (T 110 (1 - 7474547/(10:ℝ)^10) 6 8025 + (T 110 (1 - 7474547/(10:ℝ)^10) 7 3530 + (T 110 (1 - 7474547/(10:ℝ)^10) 8 7655 + (T 110 (1 - 7474547/(10:ℝ)^10) 9 2145 + (T 110 (1 - 7474547/(10:ℝ)^10) 10 4650 + (T 110 (1 - 7474547/(10:ℝ)^10) 11 1770 + (T 110 (1 - 7474547/(10:ℝ)^10) 12 5985 + (T 110 (1 - 7474547/(10:ℝ)^10) 13 635 + (T 110 (1 - 7474547/(10:ℝ)^10) 14 3710 + (T 110 (1 - 7474547/(10:ℝ)^10) 15 9395 + (T 110 (1 - 7474547/(10:ℝ)^10) 16 440 + (T 110 (1 - 7474547/(10:ℝ)^10) 17 405 + (T 110 (1 - 7474547/(10:ℝ)^10) 18 13265 + (T 110 (1 - 7474547/(10:ℝ)^10) 19 835 + (T 110 (1 - 7474547/(10:ℝ)^10) 20 110 + (T 110 (1 - 7474547/(10:ℝ)^10) 21 2640 + (T 110 (1 - 7474547/(10:ℝ)^10) 42 2640 + (T 110 (1 - 7474547/(10:ℝ)^10) 46 2640 + 0)))))))))))))))))))))) := rfl
+  have b0 : T 110 (1 - 7474547/(10:ℝ)^10) 1 145890 ≤ ((16636758090767:ℝ)/12500000000) :=
+    term_le 110 1 145890 (7474547/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b1 : T 110 (1 - 7474547/(10:ℝ)^10) 2 61990 ≤ ((22609438945563:ℝ)/20000000000) :=
+    term_le 110 2 61990 (7474547/(10:ℝ)^10) ((2003666592617:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 26 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b2 : T 110 (1 - 7474547/(10:ℝ)^10) 3 49615 ≤ ((135678423202471:ℝ)/100000000000) :=
+    term_le 110 3 49615 (7474547/(10:ℝ)^10) ((1800934038563:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 24 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b3 : T 110 (1 - 7474547/(10:ℝ)^10) 4 23685 ≤ ((43170446048157:ℝ)/50000000000) :=
+    term_le 110 4 23685 (7474547/(10:ℝ)^10) ((1657093002337:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 24 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b4 : T 110 (1 - 7474547/(10:ℝ)^10) 5 9750 ≤ ((44420693582197:ℝ)/100000000000) :=
+    term_le 110 5 9750 (7474547/(10:ℝ)^10) ((38638030667:ℝ)/12500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 23 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b5 : T 110 (1 - 7474547/(10:ℝ)^10) 6 8025 ≤ ((43867998737293:ℝ)/100000000000) :=
+    term_le 110 6 8025 (7474547/(10:ℝ)^10) ((1454360448283:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 22 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b6 : T 110 (1 - 7474547/(10:ℝ)^10) 7 3530 ≤ ((2250993477097:ℝ)/10000000000) :=
+    term_le 110 7 3530 (7474547/(10:ℝ)^10) ((2754570216739:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 22 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b7 : T 110 (1 - 7474547/(10:ℝ)^10) 8 7655 ≤ ((55781903078171:ℝ)/100000000000) :=
+    term_le 110 8 7655 (7474547/(10:ℝ)^10) ((1310519412057:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b8 : T 110 (1 - 7474547/(10:ℝ)^10) 9 2145 ≤ ((17582868029823:ℝ)/100000000000) :=
+    term_le 110 9 2145 (7474547/(10:ℝ)^10) ((1251627894229:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b9 : T 110 (1 - 7474547/(10:ℝ)^10) 10 4650 ≤ ((10587140349809:ℝ)/25000000000) :=
+    term_le 110 10 4650 (7474547/(10:ℝ)^10) ((2997369091:ℝ)/1250000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b10 : T 110 (1 - 7474547/(10:ℝ)^10) 11 1770 ≤ ((17730489316207:ℝ)/100000000000) :=
+    term_le 110 11 1770 (7474547/(10:ℝ)^10) ((575646273249:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b11 : T 110 (1 - 7474547/(10:ℝ)^10) 12 5985 ≤ ((65399123107589:ℝ)/100000000000) :=
+    term_le 110 12 5985 (7474547/(10:ℝ)^10) ((1107786858003:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b12 : T 110 (1 - 7474547/(10:ℝ)^10) 13 635 ≤ ((3758266936203:ℝ)/50000000000) :=
+    term_le 110 13 635 (7474547/(10:ℝ)^10) ((533882752083:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b13 : T 110 (1 - 7474547/(10:ℝ)^10) 14 3710 ≤ ((47290992642379:ℝ)/100000000000) :=
+    term_le 110 14 3710 (7474547/(10:ℝ)^10) ((2061423036179:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b14 : T 110 (1 - 7474547/(10:ℝ)^10) 15 9395 ≤ ((128304571925681:ℝ)/100000000000) :=
+    term_le 110 15 9395 (7474547/(10:ℝ)^10) ((498107541173:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b15 : T 110 (1 - 7474547/(10:ℝ)^10) 16 440 ≤ ((6409229123791:ℝ)/100000000000) :=
+    term_le 110 16 440 (7474547/(10:ℝ)^10) ((963945821777:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b16 : T 110 (1 - 7474547/(10:ℝ)^10) 17 405 ≤ ((1253566561349:ℝ)/20000000000) :=
+    term_le 110 17 405 (7474547/(10:ℝ)^10) ((933633510869:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b17 : T 110 (1 - 7474547/(10:ℝ)^10) 18 13265 ≤ ((217357516651669:ℝ)/100000000000) :=
+    term_le 110 18 13265 (7474547/(10:ℝ)^10) ((905054303949:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b18 : T 110 (1 - 7474547/(10:ℝ)^10) 19 835 ≤ ((14441670418763:ℝ)/100000000000) :=
+    term_le 110 19 835 (7474547/(10:ℝ)^10) ((1756041386627:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b19 : T 110 (1 - 7474547/(10:ℝ)^10) 20 110 ≤ ((2002550068509:ℝ)/100000000000) :=
+    term_le 110 20 110 (7474547/(10:ℝ)^10) ((21309351153:ℝ)/12500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b20 : T 110 (1 - 7474547/(10:ℝ)^10) 21 2640 ≤ ((25231210703361:ℝ)/50000000000) :=
+    term_le 110 21 2640 (7474547/(10:ℝ)^10) ((165595792807:ℝ)/100000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b21 : T 110 (1 - 7474547/(10:ℝ)^10) 42 2640 ≤ ((100872567578631:ℝ)/100000000000) :=
+    term_le 110 42 2640 (7474547/(10:ℝ)^10) ((962810747511:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 15 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b22 : T 110 (1 - 7474547/(10:ℝ)^10) 46 2640 ≤ ((22094393345401:ℝ)/20000000000) :=
+    term_le 110 46 2640 (7474547/(10:ℝ)^10) ((174367793861:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 14 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b23 : T 110 (1 - 7474547/(10:ℝ)^10) 109 1 ≤ ((198183171:ℝ)/200000000) :=
+    term_le 110 109 1 (7474547/(10:ℝ)^10) ((1826496713:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 5 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b24 : T 110 (1 - 7474547/(10:ℝ)^10) 1 1 ≤ ((456145263:ℝ)/50000000000) :=
+    term_le 110 1 1 (7474547/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have e1 : ((2:ℝ)^40 - 1) = 1099511627775 := by norm_num
+  have e2 : (2:ℝ)^40 = 1099511627776 := by norm_num
+  have e3 : ((14692:ℕ):ℝ) = 14692 := by norm_num
+  have e4 : T 110 (1 - 7474547/(10:ℝ)^10) (110 - 1) 1 = T 110 (1 - 7474547/(10:ℝ)^10) 109 1 := rfl
+  rw [e1, e2, e3, e4, hsum]
+  linarith
+
+/-- **sharpness**: at exponent `1 - 7474550/10^10` the moment of one unit is at least its number of live roles `14692`, so the moment criterion fails for EVERY table made of copies of the unit and idle roles (`FoldRate.block_fails`).  Relative excess of the rational certificate: 1.40e-10. -/
+theorem fold_B2Gp193x_sharp : ((14692:ℕ):ℝ) ≤ moment 110 (1 - 7474550/(10:ℝ)^10) blocksB2Gp193x := by
+  have hsum : moment 110 (1 - 7474550/(10:ℝ)^10) blocksB2Gp193x
+      = T 110 (1 - 7474550/(10:ℝ)^10) 1 145890 + (T 110 (1 - 7474550/(10:ℝ)^10) 2 61990 + (T 110 (1 - 7474550/(10:ℝ)^10) 3 49615 + (T 110 (1 - 7474550/(10:ℝ)^10) 4 23685 + (T 110 (1 - 7474550/(10:ℝ)^10) 5 9750 + (T 110 (1 - 7474550/(10:ℝ)^10) 6 8025 + (T 110 (1 - 7474550/(10:ℝ)^10) 7 3530 + (T 110 (1 - 7474550/(10:ℝ)^10) 8 7655 + (T 110 (1 - 7474550/(10:ℝ)^10) 9 2145 + (T 110 (1 - 7474550/(10:ℝ)^10) 10 4650 + (T 110 (1 - 7474550/(10:ℝ)^10) 11 1770 + (T 110 (1 - 7474550/(10:ℝ)^10) 12 5985 + (T 110 (1 - 7474550/(10:ℝ)^10) 13 635 + (T 110 (1 - 7474550/(10:ℝ)^10) 14 3710 + (T 110 (1 - 7474550/(10:ℝ)^10) 15 9395 + (T 110 (1 - 7474550/(10:ℝ)^10) 16 440 + (T 110 (1 - 7474550/(10:ℝ)^10) 17 405 + (T 110 (1 - 7474550/(10:ℝ)^10) 18 13265 + (T 110 (1 - 7474550/(10:ℝ)^10) 19 835 + (T 110 (1 - 7474550/(10:ℝ)^10) 20 110 + (T 110 (1 - 7474550/(10:ℝ)^10) 21 2640 + (T 110 (1 - 7474550/(10:ℝ)^10) 42 2640 + (T 110 (1 - 7474550/(10:ℝ)^10) 46 2640 + 0)))))))))))))))))))))) := rfl
+  have c0 : ((665470322971:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 1 145890 :=
+    term_ge 110 1 145890 (7474550/(10:ℝ)^10) ((4700480365791:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c1 : ((565235973477:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 2 61990 :=
+    term_ge 110 2 61990 (7474550/(10:ℝ)^10) ((4007333185231:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c2 : ((1356784232023:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 3 49615 :=
+    term_ge 110 3 49615 (7474550/(10:ℝ)^10) ((3601868077123:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c3 : ((431704460547:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 4 23685 :=
+    term_ge 110 4 23685 (7474550/(10:ℝ)^10) ((3314186004671:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c4 : ((44420693593:ℝ)/100000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 5 9750 :=
+    term_ge 110 5 9750 (7474550/(10:ℝ)^10) ((3091042453357:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c5 : ((87735997501:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 6 8025 :=
+    term_ge 110 6 8025 (7474550/(10:ℝ)^10) ((2908720896563:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c6 : ((112549673893:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 7 3530 :=
+    term_ge 110 7 3530 (7474550/(10:ℝ)^10) ((86080319273:ℝ)/31250000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c7 : ((557819030987:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 8 7655 :=
+    term_ge 110 8 7655 (7474550/(10:ℝ)^10) ((2621038824111:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c8 : ((87914340183:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 9 2145 :=
+    term_ge 110 9 2145 (7474550/(10:ℝ)^10) ((500651157691:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c9 : ((423485614161:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 10 4650 :=
+    term_ge 110 10 4650 (7474550/(10:ℝ)^10) ((2397895272797:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c10 : ((88652446617:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 11 1770 :=
+    term_ge 110 11 1770 (7474550/(10:ℝ)^10) ((2302585092993:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c11 : ((130798246269:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 12 5985 :=
+    term_ge 110 12 5985 (7474550/(10:ℝ)^10) ((2215573716003:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c12 : ((15033067751:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 13 635 :=
+    term_ge 110 13 635 (7474550/(10:ℝ)^10) ((2135531008329:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c13 : ((23645496331:ℝ)/50000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 14 3710 :=
+    term_ge 110 14 3710 (7474550/(10:ℝ)^10) ((128838939761:ℝ)/62500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c14 : ((320761429947:ℝ)/250000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 15 9395 :=
+    term_ge 110 15 9395 (7474550/(10:ℝ)^10) ((1992430164689:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 12 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c15 : ((1001442051:ℝ)/15625000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 16 440 :=
+    term_ge 110 16 440 (7474550/(10:ℝ)^10) ((1927891643551:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c16 : ((62678328093:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 17 405 :=
+    term_ge 110 17 405 (7474550/(10:ℝ)^10) ((373453404347:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c17 : ((1086787583699:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 18 13265 :=
+    term_ge 110 18 13265 (7474550/(10:ℝ)^10) ((362021721579:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c18 : ((28883340849:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 19 835 :=
+    term_ge 110 19 835 (7474550/(10:ℝ)^10) ((13719073333:ℝ)/7812500000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c19 : ((20025500693:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 20 110 :=
+    term_ge 110 20 110 (7474550/(10:ℝ)^10) ((1704748092237:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c20 : ((63078026783:ℝ)/125000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 21 2640 :=
+    term_ge 110 21 2640 (7474550/(10:ℝ)^10) ((1655957928067:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c21 : ((126090709507:ℝ)/125000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 42 2640 :=
+    term_ge 110 42 2640 (7474550/(10:ℝ)^10) ((240702686877:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 1 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c22 : ((552359833771:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 46 2640 :=
+    term_ge 110 46 2640 (7474550/(10:ℝ)^10) ((435919484651:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 1 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have e3 : ((14692:ℕ):ℝ) = 14692 := by norm_num
+  rw [e3, hsum]
+  linarith
+
+/-- **per-rank fact** at exponent `1 - 4058344/10^10`, fill parameter `s = 40`: the hypothesis `hnum` of `RAM.engine_program_group_perRank` (u = 110, W = 14692, D = 3080).  Relative slack: 1.10e-07. -/
+theorem foldRank_B2Gp193x :
+    (2:ℝ)^40 * ((14692:ℕ):ℝ) * (((110:ℕ):ℝ) - ((110:ℕ):ℝ)^(1 - 4058344/(10:ℝ)^10)) < ((2:ℝ)^40 - 1) * ((3080:ℕ):ℝ) :=
+  FoldRate.rank_fact3 110 14692 3080 40 (4058344/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) (by norm_num) (by norm_num) (by norm_num)
+    (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+      (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+    (by norm_num) (by norm_num)
+
+/-- **per-rank sharpness**: at exponent `1 - 4058349/10^10` the deficit of one unit is at most `W (m - m^z)`, so the per-rank inequality fails for EVERY table made of copies of the unit and idle roles (`FoldRate.rank_fails`). -/
+theorem foldRank_B2Gp193x_sharp :
+    ((3080:ℕ):ℝ) ≤ ((14692:ℕ):ℝ) * (((110:ℕ):ℝ) - ((110:ℕ):ℝ)^(1 - 4058349/(10:ℝ)^10)) :=
+  FoldRate.rank_fact_sharp 110 14692 3080 (4058349/(10:ℝ)^10) ((4700480365791:ℝ)/1000000000000) (by norm_num) (by norm_num) (by norm_num)
+    (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+      (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+    (by norm_num) (by norm_num)
+
+end OAI.PowerSaving.BlockAccounting
+
+#print axioms OAI.PowerSaving.BlockAccounting.fold_B2Gp193x
+#print axioms OAI.PowerSaving.BlockAccounting.fold_B2Gp193x_sharp
+#print axioms OAI.PowerSaving.BlockAccounting.foldRank_B2Gp193x
+#print axioms OAI.PowerSaving.BlockAccounting.foldRank_B2Gp193x_sharp
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean
new file mode 100644
index 0000000000..499fa67e88
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean
@@ -0,0 +1,93 @@
+/-!
+# (key: gx-data) Raw Lean form of a `gcert/1` file (EXTENDED-CERT-SPEC section 1)
+
+Core Lean only (no Mathlib): the generated data modules import nothing else, so they elaborate
+cheaply.  Field order and meaning are those of the JSON; `pairs` and `cuts` are DERIVED by the
+generator (`checks/wht26/gx-data/py/gxgen.py`) and must be tested by the label check.
+
+Registers: `x_t = t`, `y_t = v + t`, slot `k = 2 v + k`.  Vectors are bit masks.
+-/
+
+namespace GXD
+
+/-- the rational `(-1)^neg * num / den` (`den > 0`) -/
+structure Co where
+  neg : Bool
+  num : Nat
+  den : Nat
+  deriving DecidableEq, Repr
+
+/-- a gate: every register named (extras too) first moves to `frame`; then the adds happen in order -/
+inductive Gate where
+  /-- `tgt += co * src` for each `(tgt, co)` -/
+  | out (frame src : Nat) (tgts : List (Nat × Co)) (extra : List Nat)
+  /-- `tgt += co * src` for each `(src, co)` -/
+  | inn (frame tgt : Nat) (srcs : List (Nat × Co))
+  deriving Repr
+
+/-- the scatter `y_t += sum over k of coef(t, k) * total k` -/
+inductive Scat where
+  /-- star rule: `inside` if coordinate `k` is in port `t`, else `outside` -/
+  | star (inside outside : Co)
+  /-- explicit rows: row `t` = `[(total k, coef)]` -/
+  | table (rows : List (List (Nat × Co)))
+  deriving Repr
+
+/-- a `gcert/1` file -/
+structure Raw where
+  h : Nat
+  v : Nat
+  R : Nat
+  N : Nat
+  cst : Nat
+  /-- `v` masks: the unit vectors of the ports -/
+  ports : List Nat
+  /-- CHUNKED frame table (`flatten` = the table); an entry is a reduced echelon basis, leading bits descending -/
+  frames : List (List (List Nat))
+  /-- frame id per register at the start -/
+  start : List Nat
+  /-- frame id per register at the end -/
+  final : List Nat
+  /-- position `k` = retained total `k`: (slot REGISTER, frame id) -/
+  ret : List (Nat × Nat)
+  scat : Scat
+  /-- CHUNKED gates before the scatter -/
+  A : List (List Gate)
+  /-- CHUNKED gates after the scatter -/
+  B : List (List Gate)
+  /-- CHUNKED, derived: the distinct climbs `(a, b)`, `a ≠ b`, in order of first use -/
+  pairs : List (List (Nat × Nat))
+  /-- derived: replay cut points `(gates of A ++ B before the cut, frame id per register there)` -/
+  cuts : List (Nat × List Nat)
+  /-- slots that start off the zero frame `(slot REGISTER, frame id)` (rule 2); EMPTY on the path -/
+  ext : List (Nat × Nat)
+  /-- derived (questions.md Q1): per port `h` masks, the first is the port, pairwise dots = delta
+  (an orthonormal basis of `F_2^h` through the port) -/
+  obase : List (List Nat)
+
+/-- registers of a gate, in the order they are moved -/
+def Gate.regs : Gate → List Nat
+  | .out _ s ts ex => s :: (ts.map Prod.fst ++ ex)
+  | .inn _ t ss => t :: ss.map Prod.fst
+
+/-- frame of a gate -/
+def Gate.frame : Gate → Nat
+  | .out f _ _ _ => f
+  | .inn f _ _ => f
+
+/-- single adds `(tgt, src, co)` of a gate, in order -/
+def Gate.adds : Gate → List (Nat × Nat × Co)
+  | .out _ s ts _ => ts.map fun p => (p.1, s, p.2)
+  | .inn _ t ss => ss.map fun p => (t, p.1, p.2)
+
+/-- the frame table -/
+def Raw.frameTab (c : Raw) : List (List Nat) := c.frames.flatten
+
+/-- all gates of phase A / phase B -/
+def Raw.gatesA (c : Raw) : List Gate := c.A.flatten
+def Raw.gatesB (c : Raw) : List Gate := c.B.flatten
+
+/-- number of registers -/
+def Raw.nreg (c : Raw) : Nat := 2 * c.v + c.R
+
+end GXD
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean
new file mode 100644
index 0000000000..0392e1f05b
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean
@@ -0,0 +1,38 @@
+import Work.GCert.Data.B2Gp193Main
+
+/-!
+Comparator solution `Work.GCert.Data.SolutionB2Gp193x` (not part of github.com/openai/math).
+
+The whole proof is in `Work.GCert.Data.B2Gp193Main` (and its imports), which ends with
+
+    theorem wht_main_B2Gp193x :
+        ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W
+
+This module adds nothing mathematical: it defines `WHT.WHTTimeBoundsAt` with the text of the
+challenge (the same definition as `BlockWHT.WHTTimeBoundsAt` of `Work.Block.WHT`) and restates
+the theorem under the name the challenge uses.  Its proof is that single term.
+`WHTProgram`, `wht`, `whtInKind`, `whtOutKind` come from `WHTCheck.Solution`.
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open Filter Asymptotics
+
+/-- `W = O(2^k (k+1)^β)` and `W = o(2^k k)` (`WHTTimeBounds` is the case `β = 1 - 2/10^11`). -/
+def WHTTimeBoundsAt (β : ℝ) (W : ℕ → ℕ) : Prop :=
+  let W' := fun k : ℕ => (W k : ℝ)
+  W' =O[atTop] (fun k : ℕ => (2:ℝ)^k * ((k:ℝ)+1)^β) ∧
+  W' =o[atTop] (fun k : ℕ => (2:ℝ)^k * (k:ℝ))
+
+/-- **Walsh-Hadamard transform with the improved exponent**: the statement `WHTGoal` of
+`WHTCheck/Challenge.lean` with `1 - 2/10^11` replaced by `1 - 7474547/10^10`. -/
+theorem wht_main_block_B2Gp193x :
+    ∃ solve W, WHTProgram solve W ∧ WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W :=
+  wht_main_B2Gp193x
+
+end WHT
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.WHT.wht_main_block_B2Gp193x
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean
new file mode 100644
index 0000000000..24e261ad08
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean
@@ -0,0 +1,183 @@
+import Work.GFrame.Engine.Letters
+
+/-!
+# GFrame engine, part 2: the free adapter letters in the RAM (agent key: eng-ram)
+
+One free adapter on the array of one role is ONE linear pass, no recursive call:
+
+* `Gear.permuted`     the address of `x ↦ G.π x` (columnwise), O(1) per entry with the XOR table
+                      (as `Gear.shifted`, through `Gear.body_additive` of `Work/Block/Address.lean`);
+* `Gear.phase_row`    the `f`-bit row `(z·x_j + c)_j` of an entry, O(1);
+* `GRig`              a rig together with the table of `lum` over `Bits f` (`i^popcount`);
+* `Rig.perm_cost`, `GRig.phase_cost`   the two letters, work = length of the role table.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.GF
+open Binary Matrix Finset
+noncomputable section
+section
+variable {α : Type*} [Fintype α] [DecidableEq α]
+
+/-- An address permutation acts on an array with `f` columns by moving the address. -/
+lemma act_perm (G : APerm α) (f : ℕ) (x : Sky α f → ℂ) (j : Sky α f) :
+    matAct f (permMat G) x j = x (fun k => G.π (j k)) := by
+  change ∑ i, digitProd (fun _ : Fin f => permMat G) j i * x i = _
+  have h (i : Sky α f) : digitProd (fun _ : Fin f => permMat G) j i =
+      if (fun k => G.π (j k)) = i then 1 else 0 :=
+    prod_delta (κ:=fun _ : Fin f => Space α) _ _
+  simp_rw [h]
+  simp [ite_mul]
+
+/-- A diagonal phase acts by the scalar `lum` of the row of phase bits. -/
+lemma act_phase (z : Space α) (c : F) (f : ℕ) (x : Sky α f → ℂ) (j : Sky α f) :
+    matAct f (phaseMat z c) x j = lum (fun k : Fin f => dot z (j k) + c) * x j := by
+  unfold matAct phaseMat
+  rw [digitProd_diagonal, Matrix.mulVec_diagonal]
+  rfl
+
+end
+end
+end PowerSaving.GF
+
+namespace PowerSaving.RAM
+open Binary Ty Finset GF
+noncomputable section
+universe U V
+variable {ι : Type U}
+
+namespace Gear
+variable {m : Bool} {B f : ι → ℕ} {s t : Ty} {x : ι → T s}
+variable (g : Gear m B f s x)
+include g
+variable {α : Type*} [Fintype α] [DecidableEq α] (X : Layout α) (r : ℕ)
+
+/-- Address moved by an additive bijection (across the `f` columns). -/
+lemma permuted (G : APerm α) (v : ∀ i, Grid α r (f i))
+    (h : Knows m B s x (fun i => (book X r (f i)).loc (v i))) :
+    Knows m B s x (fun i => (book X r (f i)).loc ((v i).1,
+      fun j => G.π ((v i).2 j))) := by
+  obtain ⟨hg, hh⟩ := g.grid_fetch X r (v:=v) h
+  let K (i : ι) : Grid α r (f i) := ((v i).1, fun j => G.π ((v i).2 j))
+  apply g.grid_combine X r (v:=K) hg (g.body_set X (fun i => (K i).2) _)
+  intro a
+  exact g.body_additive X (fun y => G.π y a) (fun p q => by rw [G.add]; rfl)
+    (fun i => (v i).2) hh
+
+/-- The row of phase bits `(z·x_j + c)_j` of an address. -/
+lemma phase_row (z : Space α) (c : F) (v : ∀ i, Grid α r (f i))
+    (h : Knows m B s x (fun i => (book X r (f i)).loc (v i))) :
+    Knows m B s x (fun i => (bits (f i)).loc (fun l : Fin (f i) => dot z ((v i).2 l) + c)) := by
+  obtain ⟨_, hh⟩ := g.grid_fetch X r (v:=v) h
+  have hv := g.body_additive X (fun y => dot z y) (fun p q => dot_add_right z p q)
+    (fun i => (v i).2) hh
+  rcases bit_cases c with hc|hc
+  · refine hv.cong (fun _ => rfl) (fun i => ?_)
+    simp [hc]
+  · let q i : Bits (f i) × Bits (f i) := (fun l => dot z ((v i).2 l), fun _ => 1)
+    have hf : Knows m B s x (fun i => (bits (f i)).loc (q i).2) :=
+      (g.power.minus (Can.wc 1) g.bound).cong (fun _ => rfl) (fun i => by
+        change 2^f i-1=(bits _).loc (fun _ => 1)
+        rw [← bits_lit]
+        simp)
+    refine (g.addr_xor q hv hf).cong (fun _ => rfl) (fun i => ?_)
+    apply congr_arg (bits (f i)).loc
+    ext k; simp [q,hc]
+
+end Gear
+
+/-- A rig together with the table of `lum` over `Bits f` (the fourth roots `i^popcount`). -/
+structure GRig {α ρ : Type*} (m : Bool) (B f : ι → ℕ) (s : Ty) (x : ι → T s)
+    (cl : Paint) (X : Layout α) (R : Layout ρ) (r : ℕ) (v : ∀ i, Grain α ρ r (f i)) : Prop where
+  rig : Rig m B f s x cl X R r v
+  lumT : Has m B s (a sc) x fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)
+
+section
+variable {α ρ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+variable {m : Bool} {B f : ι → ℕ} {s t : Ty} {x : ι → T s}
+    {cl : Paint} {X : Layout α} {R : Layout ρ} {r : ℕ} {v : ∀ i, Grain α ρ r (f i)}
+
+omit [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ] in
+lemma GRig.gather (h : GRig m B f s x cl X R r v) {κ : Type V} (j : κ → ι) (y : κ → T t)
+    (g : Has m (fun k => B (j k)) t s y (fun k => x (j k))) :
+    GRig m (fun k => B (j k)) (fun k => f (j k)) t y cl X R r (fun k => v (j k)) :=
+  ⟨h.rig.gather j y g, g.then_do (h.lumT.reindex j)⟩
+
+lemma Rig.ferry_perm (h : Rig m B f s x cl X R r v) (l : ρ) (G : APerm α)
+    (q : ∀ i, Beach α ρ r (f i))
+    (g : Knows m B s x fun i => (fleet X R r (f i)).loc (q i)) :
+    Has m B s (c cl) x fun i => ferryM r (f i) l (permMat G) (v i) (q i) := by
+  obtain ⟨hl,hk⟩ := h.addrs q g
+  have hb := h.read q hl hk
+  let t i : Beach α ρ r (f i) := ((q i).1,(q i).2.1,fun j => G.π ((q i).2.2 j))
+  have hh := h.read t hl (h.gear.permuted X r G _ hk)
+  apply Can.cases_code (q:=fun i => (q i).1) R hl
+  intro p
+  by_cases he : p=l
+  · refine (hh.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have hql : (q i.val).1 = l := i.property.trans he
+    change v i.val ((q i.val).1,(q i.val).2.1,fun j => G.π ((q i.val).2.2 j)) = _
+    simp only [ferryM, roleAct, hql, if_true, act_perm]
+  · refine (hb.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have H : (q i.val).1≠l := fun hh => he (i.property.symm.trans hh)
+    simp only [ferryM, roleAct, H, ite_false, Prod.mk.eta]
+
+/-- **Free address permutation**: one pass over the role table. -/
+lemma Rig.perm_cost (h : Rig m B f s x cl X R r v) (l : ρ) (G : APerm α) :
+    Can m B s (a (c cl)) x
+      (fun i => (fleet X R r (f i)).tape (ferryM r (f i) l (permMat G) (v i)))
+      (fun i => (fleet X R r (f i)).n) := by
+  refine h.chart _ ?_
+  let S := Σ i, Beach α ρ r (f i)
+  have hg := h.gather (fun d : S => d.1)
+    (fun d => ((x d.1, (fleet X R r (f d.1)).loc d.2):T (p s w))) (t:=p s w) Can.first
+  exact hg.ferry_perm l G (fun d => d.2) Can.second
+
+lemma GRig.ferry_phase (h : GRig m B f s x cl X R r v) (l : ρ) (z : Space α) (c' : F)
+    (q : ∀ i, Beach α ρ r (f i))
+    (g : Knows m B s x fun i => (fleet X R r (f i)).loc (q i)) :
+    Has m B s (c cl) x fun i => ferryM r (f i) l (phaseMat z c') (v i) (q i) := by
+  obtain ⟨hl,hk⟩ := h.rig.addrs q g
+  have hb := h.rig.read q hl hk
+  have hrow := h.rig.gear.phase_row X r z c' (fun i => (q i).2) hk
+  have hs : Has m B s sc x
+      (fun i => lum (fun k : Fin (f i) => dot z ((q i).2.2 k) + c')) :=
+    Can.fetch (t:=sc) (L:=fun i => bits (f i)) (v:=fun i (y : Bits (f i)) => lum y)
+      (i:=fun i => (fun k : Fin (f i) => dot z ((q i).2.2 k) + c')) h.lumT hrow
+  have hh := hs.mul hb
+  apply Can.cases_code (q:=fun i => (q i).1) R hl
+  intro p
+  by_cases he : p=l
+  · refine (hh.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have hql : (q i.val).1 = l := i.property.trans he
+    change lum (fun k : Fin (f i.val) => dot z ((q i.val).2.2 k) + c') *
+      v i.val ((q i.val).1,(q i.val).2.1,(q i.val).2.2) = _
+    simp only [ferryM, roleAct, hql, if_true, act_phase]
+  · refine (hb.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have H : (q i.val).1≠l := fun hh => he (i.property.symm.trans hh)
+    simp only [ferryM, roleAct, H, ite_false, Prod.mk.eta]
+
+/-- **Free diagonal phase**: one pass over the role table (one table look-up per entry). -/
+lemma GRig.phase_cost (h : GRig m B f s x cl X R r v) (l : ρ) (z : Space α) (c' : F) :
+    Can m B s (a (c cl)) x
+      (fun i => (fleet X R r (f i)).tape (ferryM r (f i) l (phaseMat z c') (v i)))
+      (fun i => (fleet X R r (f i)).n) := by
+  refine h.rig.chart _ ?_
+  let S := Σ i, Beach α ρ r (f i)
+  have hg := h.gather (fun d : S => d.1)
+    (fun d => ((x d.1, (fleet X R r (f d.1)).loc d.2):T (p s w))) (t:=p s w) Can.first
+  exact hg.ferry_phase l z c' (fun d => d.2) Can.second
+
+end
+end
+end PowerSaving.RAM
+end OAI
+
+#print axioms OAI.PowerSaving.RAM.Rig.perm_cost
+#print axioms OAI.PowerSaving.RAM.GRig.phase_cost
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean
new file mode 100644
index 0000000000..2eca6e713b
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean
@@ -0,0 +1,199 @@
+import Work.Block.Bridge
+
+/-!
+# GFrame engine, part 1: the generalised word language (agent key: eng-ram)
+
+Letters = the letters of `BWord` (`localM`, `shift`, `block`) plus TWO FREE ADAPTER letters on
+one role:
+
+* `perm l G`      address permutation by an additive bijection `G` of the label space
+                  (matrix `permMat G`, `(permMat G) x y = 1` iff `G.π x = y`);
+* `phase l z c`   the diagonal phase `i^[z·x + c]` IN THE STANDARD BASIS
+                  (matrix `phaseMat z c = diagonal (fun x => tint (dot z x + c))`).
+
+Products of `phaseMat` are exactly the diagonal matrices `i^Q(x)`, `Q` a `ℤ/4`-valued quadratic
+form plus a constant; with the old free letter `shift` the free letters generate every affine
+address permutation times such a phase.  A "twisted block" is NOT a primitive letter: it is the
+word `free adapters ++ [block] ++ free adapters` (see `Free.lean`, `gstep_of_factor`).
+
+The semantics is `gwalk` (no unit-move word behind it: the new letters are not Walsh-diagonal).
+Old words embed by `GWord.ofB`, and `gwalk f (ofB w) = walk f w.flat`.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.GF
+open Binary Matrix Finset
+noncomputable section
+
+/-- An additive bijection of the label space. -/
+structure APerm (α : Type*) where
+  π : Space α ≃ Space α
+  add : ∀ x y, π (x + y) = π x + π y
+
+section Mats
+variable {α : Type*} [Fintype α] [DecidableEq α]
+
+/-- Permutation matrix of an additive bijection: `(permMat G *ᵥ v) x = v (G.π x)`. -/
+def permMat (G : APerm α) : CMat α := fun x y => if G.π x = y then 1 else 0
+
+/-- Elementary diagonal phase in the standard basis: `i^[z·x + c]`. -/
+def phaseMat (z : Space α) (c : F) : CMat α := Matrix.diagonal fun x => tint (dot z x + c)
+
+end Mats
+
+/-- Letters of the generalised word language. -/
+inductive GMove (α ρ : Type*)
+  | old (mv : BMove α ρ)
+  | perm (l : ρ) (G : APerm α)
+  | phase (l : ρ) (z : Space α) (c : F)
+
+abbrev GWord (α ρ : Type*) := List (GMove α ρ)
+
+namespace GMove
+variable {α ρ : Type*}
+
+/-- The letter of `BWord` with the same price (free adapters ↦ a free letter). -/
+def shadow : GMove α ρ → BMove α ρ
+  | .old mv => mv
+  | .perm _ _ => .localM 0
+  | .phase _ _ _ => .localM 0
+
+/-- Rank paid by a letter (`none` = free). -/
+def rk? (mv : GMove α ρ) : Option ℕ := mv.shadow.rk?
+def costR (φ : ℕ → ℝ) (mv : GMove α ρ) : ℝ := mv.shadow.costR φ
+def Proper (u : ℕ) (mv : GMove α ρ) : Prop := mv.shadow.Proper u
+
+@[simp] lemma costR_perm (φ : ℕ → ℝ) (l : ρ) (G : APerm α) :
+    (GMove.perm l G : GMove α ρ).costR φ = 0 := rfl
+@[simp] lemma costR_phase (φ : ℕ → ℝ) (l : ρ) (z : Space α) (c : F) :
+    (GMove.phase l z c : GMove α ρ).costR φ = 0 := rfl
+@[simp] lemma costR_old (φ : ℕ → ℝ) (mv : BMove α ρ) : (GMove.old mv).costR φ = mv.costR φ := rfl
+lemma proper_perm (u : ℕ) (l : ρ) (G : APerm α) : (GMove.perm l G : GMove α ρ).Proper u :=
+  trivial
+lemma proper_phase (u : ℕ) (l : ρ) (z : Space α) (c : F) :
+    (GMove.phase l z c : GMove α ρ).Proper u := trivial
+@[simp] lemma proper_old (u : ℕ) (mv : BMove α ρ) : (GMove.old mv).Proper u ↔ mv.Proper u :=
+  Iff.rfl
+
+end GMove
+
+namespace GWord
+variable {α ρ : Type*}
+
+def shadow (w : GWord α ρ) : BWord α ρ := w.map GMove.shadow
+def costR (φ : ℕ → ℝ) (w : GWord α ρ) : ℝ := (w.map (GMove.costR φ)).sum
+def Proper (u : ℕ) (w : GWord α ρ) : Prop := ∀ mv ∈ w, mv.Proper u
+def hist (w : GWord α ρ) (r : ℕ) : ℕ := w.shadow.hist r
+/-- Natural-number cost when a block of rank `rk` costs `g rk`. -/
+def cost (g : ℕ → ℕ) (w : GWord α ρ) : ℕ := w.shadow.cost g
+/-- An old block word as a generalised word. -/
+def ofB (w : BWord α ρ) : GWord α ρ := w.map GMove.old
+
+@[simp] lemma shadow_nil : shadow ([] : GWord α ρ) = [] := rfl
+@[simp] lemma shadow_cons (mv : GMove α ρ) (w : GWord α ρ) :
+    shadow (mv :: w) = mv.shadow :: shadow w := rfl
+@[simp] lemma shadow_ofB (w : BWord α ρ) : shadow (ofB w) = w := by
+  simp [shadow, ofB, List.map_map, Function.comp_def, GMove.shadow]
+
+lemma costR_shadow (φ : ℕ → ℝ) (w : GWord α ρ) : costR φ w = BWord.costR φ w.shadow := by
+  unfold costR BWord.costR shadow
+  rw [List.map_map]
+  rfl
+@[simp] lemma costR_nil (φ : ℕ → ℝ) : costR φ ([] : GWord α ρ) = 0 := rfl
+lemma costR_cons (φ : ℕ → ℝ) (mv : GMove α ρ) (w : GWord α ρ) :
+    costR φ (mv :: w) = mv.costR φ + costR φ w := by simp [costR]
+lemma costR_append (φ : ℕ → ℝ) (w w' : GWord α ρ) :
+    costR φ (w ++ w') = costR φ w + costR φ w' := by simp [costR]
+lemma costR_ofB (φ : ℕ → ℝ) (w : BWord α ρ) : costR φ (ofB w) = BWord.costR φ w := by
+  rw [costR_shadow, shadow_ofB]
+@[simp] lemma cost_nil (g : ℕ → ℕ) : cost g ([] : GWord α ρ) = 0 := rfl
+lemma cost_cons (g : ℕ → ℕ) (mv : GMove α ρ) (w : GWord α ρ) :
+    cost g (mv :: w) = mv.shadow.cost g + cost g w := BWord.cost_cons g _ _
+
+lemma Proper.shadow {u : ℕ} {w : GWord α ρ} (h : Proper u w) : BWord.Proper u w.shadow := by
+  intro mv hmv
+  obtain ⟨g, hg, rfl⟩ := List.mem_map.mp hmv
+  exact h g hg
+lemma Proper.tail {u : ℕ} {mv : GMove α ρ} {w : GWord α ρ} (h : Proper u (mv :: w)) :
+    Proper u w := fun x hx => h x (List.mem_cons_of_mem _ hx)
+lemma Proper.head {u : ℕ} {mv : GMove α ρ} {w : GWord α ρ} (h : Proper u (mv :: w)) :
+    mv.Proper u := h mv List.mem_cons_self
+lemma Proper.append {u : ℕ} {w w' : GWord α ρ} (h : Proper u w) (h' : Proper u w') :
+    Proper u (w ++ w') := by
+  intro mv hmv
+  rcases List.mem_append.mp hmv with h1|h1
+  · exact h mv h1
+  · exact h' mv h1
+lemma proper_nil (u : ℕ) : Proper u ([] : GWord α ρ) := fun _ h => by simp at h
+lemma proper_ofB {u : ℕ} {w : BWord α ρ} (h : w.Proper u) : Proper u (ofB w) := by
+  intro mv hmv
+  obtain ⟨g, hg, rfl⟩ := List.mem_map.mp hmv
+  exact h g hg
+
+lemma costR_eq_sum (u : ℕ) (φ : ℕ → ℝ) (w : GWord α ρ) (hw : Proper u w) :
+    costR φ w = ∑ r : Fin u, (w.hist r:ℝ) * φ r := by
+  rw [costR_shadow]; exact BWord.costR_eq_sum u φ _ hw.shadow
+lemma cost_eq_sum (u : ℕ) (g : ℕ → ℕ) (w : GWord α ρ) (hw : Proper u w) :
+    cost g w = ∑ r : Fin u, hist w r * g r := BWord.cost_eq_sum u g _ hw.shadow
+lemma hist_zero (u : ℕ) (w : GWord α ρ) (hw : Proper u w) : hist w 0 = 0 :=
+  BWord.hist_zero u _ hw.shadow
+lemma hist_large (u : ℕ) (w : GWord α ρ) (hw : Proper u w) (r : ℕ) (hr : u ≤ r) :
+    hist w r = 0 := BWord.hist_large u _ hw.shadow r hr
+
+end GWord
+
+section Sem
+variable {α ρ σ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+
+/-- The action of one letter. -/
+def GMove.act (f : ℕ) : GMove α ρ → Data α ρ f → Data α ρ f
+  | .old mv => mv.act f
+  | .perm l G => roleAct f l (permMat G)
+  | .phase l z c => roleAct f l (phaseMat z c)
+
+/-- **Semantics of a generalised word.** -/
+def gwalk (f : ℕ) (w : GWord α ρ) (x : Data α ρ f) : Data α ρ f :=
+  w.foldl (fun y mv => mv.act f y) x
+
+@[simp] lemma gwalk_nil (f : ℕ) (x : Data α ρ f) : gwalk f ([] : GWord α ρ) x = x := rfl
+lemma gwalk_cons (f : ℕ) (mv : GMove α ρ) (w : GWord α ρ) (x : Data α ρ f) :
+    gwalk f (mv :: w) x = gwalk f w (mv.act f x) := rfl
+lemma gwalk_append (f : ℕ) (p q : GWord α ρ) (x : Data α ρ f) :
+    gwalk f (p ++ q) x = gwalk f q (gwalk f p x) := by simp [gwalk]
+
+/-- Old words keep their meaning. -/
+lemma gwalk_ofB (f : ℕ) (w : BWord α ρ) (x : Data α ρ f) :
+    gwalk f (GWord.ofB w) x = walk f w.flat x := by
+  induction w generalizing x with
+  | nil => rfl
+  | cons mv w ih =>
+    rw [walk_flat_cons, ← ih]
+    rfl
+
+/-- The scratch certificate for the generalised language (cf. `RAM.LiveKernel`). -/
+def GLiveKernel (e : σ → ρ) (w : GWord α ρ) : Prop :=
+  ∀ (f : ℕ) (v : Data α ρ f), (∀ s, (∀ l, e l ≠ s) → v s = 0) →
+    ∀ l, gwalk f w v (e l) = matAct f (kernel α) (v (e l))
+
+/-- Every old certificate is a generalised certificate. -/
+theorem GLiveKernel.ofB {e : σ → ρ} {w : BWord α ρ} (h : RAM.LiveKernel e w.flat) :
+    GLiveKernel e (GWord.ofB w) := by
+  intro f v hv l
+  rw [gwalk_ofB]
+  exact h f v hv l
+
+/-- One role goes from matrix `M` to `N` by a generalised word (cf. `XStep`). -/
+def GStep (l : ρ) (M N : CMat α) (c : (ℕ → ℝ) → ℝ) : Prop :=
+  ∃ (w : GWord α ρ) (U : CMat α), w.Proper (Fintype.card α) ∧ (∀ φ, w.costR φ = c φ) ∧
+    U * M = N ∧ ∀ (f : ℕ) (x : Data α ρ f), gwalk f w x = roleAct f l U x
+
+end Sem
+end
+end PowerSaving.GF
+end OAI
+
+#print axioms OAI.PowerSaving.GF.gwalk_ofB
+#print axioms OAI.PowerSaving.GF.GLiveKernel.ofB
+#print axioms OAI.PowerSaving.GF.GWord.costR_eq_sum
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean
new file mode 100644
index 0000000000..6bd7cfa0c3
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean
@@ -0,0 +1,163 @@
+import Work.GFrame.Engine.Sweep
+import WHTCheck.Solution
+
+/-!
+# GFrame engine, part 4: one level of the recursion for generalised words (agent key: eng-ram)
+
+Copy of `amplifyB` (`Work/Block/Recursion.lean`) with two changes:
+
+* the word is a `GWord` with certificate `GLiveKernel e w` (semantics `gwalk`);
+* after the XOR table the level also builds the table of `lum` over `Bits f`
+  (`WHT.lum_tables`, doubling construction, `O(2^f)` work), which the free diagonal phases
+  read; it is part of the environment of the sweep (`GRig`).
+
+Cost: the same `2^k` linear term and the same recursive calls as `amplifyB`.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.RAM
+open Binary Matrix Ty Finset GF
+noncomputable section
+
+section
+universe U
+variable {α ρ σ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+  [Fintype σ] [DecidableEq σ]
+variable {ι : Type U} {m : Bool}
+    {k f : ι → ℕ} {cl : Paint} {b : Bank (hatch cl) ι}
+    {v : ∀ i, Sim σ (k i)→ℂ}
+
+/-- **One level of the recursion for a generalised word** (replaces `amplifyB`). -/
+lemma gamplify (m : Bool) (b : Bank (hatch cl) ι) (v : ∀ i, Sim σ (k i) → ℂ)
+    (X : Layout α) (R : Layout ρ) (Q : Layout σ) (e : σ → ρ) (he : Function.Injective e)
+    (r : ℕ) (hr : 3 ≤ X.n) (hq : ∀ i, X.n*f i+r=k i) (hd : r < X.n) (hQ : 0<Q.n)
+    (n τ : ℕ → ι → ℕ)
+    (hc : ∀ rk, 1 ≤ rk → rk < X.n → ∀ i, n rk i*(sim Q (rk * f i)).n=2^k i)
+    (hk : ∀ rk, 1 ≤ rk → rk < X.n → Contract cl b (fun i => rk * f i) (τ rk) Q)
+    (hB : Small b.B (fun i => 2^k i))
+    (w : GWord α ρ) (hw : GLiveKernel e w) (hP : w.Proper X.n) :
+    Able m b (simIn cl) (bundle cl) (fun i => loaded cl Q (k i) (v i))
+      (fun i => (sim Q (k i)).tape (whole (k i) (v i)))
+      (fun i => 2^k i) (fun i => w.cost (fun rk => n rk i * τ rk i)) := by
+  let W i := 2^k i
+  let s := simIn cl
+  let eQ (i : ι) := ebb X r (f i) (k i) (hq i) (v i)
+  let zQ (i : ι) : Grain α σ r (f i) :=
+    fun j => chords r (f i) (fun l => eQ i (j.1,l)) j.2
+  let Z (i : ι) : Grain α ρ r (f i) := crossAct r (f i) (embM e) (zQ i)
+  let O (i : ι) : Grain α σ r (f i) :=
+    crossAct r (f i) (extM e) (gcoast r (f i) w (Z i))
+  let szQ i := (fleet X Q r (f i)).n
+  let szR i := (fleet X R r (f i)).n
+  have hszQ : Dom W szQ := by
+    refine ⟨Q.n+1, fun i => ?_⟩
+    unfold W szQ fleet
+    rw [Layout.pair_len, book_len,hq]
+    simp only [mul_add,add_mul,mul_one,one_mul]
+    gcongr <;> simp
+  have hszR : Dom W szR := by
+    refine ⟨R.n+1, fun i => ?_⟩
+    unfold W szR fleet
+    rw [Layout.pair_len, book_len,hq]
+    simp only [mul_add,add_mul,mul_one,one_mul]
+    gcongr <;> simp
+  have hn (i : ι) : 0 < W i := pow_pos (by decide) _
+  have hf (i) : f i ≤ k i := by
+    have g := hq i
+    have h := Nat.le_mul_of_pos_left (f i) (show 0 < X.n by omega)
+    omega
+  have hy (i) : k i ≤ W i := Nat.lt_two_pow_self.le
+  have sd := hB.mono hy
+  have sq := sd.mono hf
+  let p2 i := 2^f i
+  have hm : Small b.B p2 :=
+    hB.mono (fun i => Nat.pow_le_pow_right (by omega) (hf i))
+  have hcube (i) : p2 i ^ 3 ≤ W i := by
+    unfold p2 W
+    rw [← pow_mul]
+    apply Nat.pow_le_pow_right (by omega)
+    have hh : 3*f i ≤ X.n*f i := Nat.mul_le_mul_right _ hr
+    have hg := hq i
+    rw [mul_comm]
+    omega
+  let env (i : ι) := loaded cl Q (k i) (v i)
+  -- construct fields (f,p2)
+  have hmf : Can m b.B s Ty.w env f W := by
+    have ht : Can m b.B s Ty.w env k W := Can.first
+    refine (ht.dvdW (Can.wc X.n) sd).cong (fun _ => rfl) ?_
+    intro i
+    rw [← hq,mul_comm X.n]
+    exact Layout.div_join hd
+  have hmp : Can m b.B s (Ty.p Ty.w Ty.w) env (fun i => (f i,p2 i)) W :=
+    hmf.pair (hmf.wTwo sq hm (Dom.of_le (fun i => (hf i).trans (hy i))))
+  let T1 := Ty.p s (Ty.p Ty.w Ty.w)
+  let Y (i : ι) : T T1 := (env i,f i,p2 i)
+  have hmx : Can m b.B T1 (Ty.a Ty.w) Y (fun i => xorTab (f i)) W :=
+    (Can.xor_prepare (m:=m) (f:=f) (B:=b.B) (s:=T1) (x:=Y)
+      (Can.fst Can.second) (Can.snd Can.second) sq hm).mono hcube
+  let T2 := Ty.p T1 (Ty.a Ty.w)
+  let Y' (i : ι) : T T2 := (Y i,xorTab (f i))
+  -- NEW: the table of `lum` over `Bits f`
+  have hE2 : Has m b.B T2 s Y' env := Can.fst Can.first
+  have hml : Can m b.B T2 (Ty.a sc) Y'
+      (fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)) W :=
+    (WHT.lum_tables (k:=f) (Can.fst (Can.snd Can.first)) sq hm hE2.snd.fst).1.mono
+      (fun i => Nat.pow_le_pow_right (by omega) (hf i))
+  let T2' := Ty.p T2 (Ty.a sc)
+  let Y'' (i : ι) : T T2' := (Y' i,(bits (f i)).tape (fun y : Bits (f i) => lum y))
+  -- the input, read as a table on the slots
+  have hG0 : Rig m b.B f T2 Y' cl X Q r eQ := by
+    refine ⟨⟨?_,?_,Can.second,hm⟩,?_,?_⟩
+    · exact Can.snd (Can.snd Can.first)
+    · exact Can.fst (Can.snd Can.first)
+    · exact hE2.snd.fst
+    · exact hE2.snd.snd.cong (fun _ => rfl) (fun i => (ebb_eq ..).symm)
+  have hG : Rig m b.B f T2' Y'' cl X Q r eQ := hG0.gather id Y'' (t:=T2') Can.first
+  -- leftover bits, still on the slots
+  have HH : Can m b.B T2' (bundle cl) Y'' (fun i => (fleet X Q r (f i)).tape (zQ i)) W :=
+    hG.dots_cost.weaken hszQ
+  let T3 := Ty.p T2' (bundle cl)
+  let A (i) : T T3 := (Y'' i,(fleet X Q r (f i)).tape (zQ i))
+  have Hg := hG.gather id A (t:=T3) Can.first
+  have G : Rig m b.B f T3 A cl X Q r zQ := ⟨Hg.gear,Hg.imag,Can.second⟩
+  -- embed the slots into the table of roles; scratch roles are created as zero
+  have HE : Can m b.B T3 (bundle cl) A (fun i => (fleet X R r (f i)).tape (Z i)) W :=
+    (G.cross_point R (embM e)).weaken hszR
+  let T4 := Ty.p T3 (bundle cl)
+  let A4 (i) : T T4 := (A i,(fleet X R r (f i)).tape (Z i))
+  have Hg4 := G.gather id A4 (t:=T4) Can.first
+  have hL4 : Has m b.B T4 (Ty.a sc) A4
+      (fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)) :=
+    Can.snd (Can.fst Can.first)
+  have G4 : GRig m b.B f T4 A4 cl X R r Z := ⟨⟨Hg4.gear,Hg4.imag,Can.second⟩,hL4⟩
+  -- the GENERALISED word on the table of roles
+  have Hy := G4.gsweep n τ Q hQ hk
+    (fun rk h1 h2 i => by rw [book_len,hq]; exact hc rk h1 h2 i) w hP
+  -- extract the slots; scratch roles are dropped
+  let T5 := Ty.p T4 (bundle cl)
+  let A5 (i) : T T5 := (A4 i,(fleet X R r (f i)).tape (gcoast r (f i) w (Z i)))
+  have Hg5 := G4.rig.gather id A5 (t:=T5) Can.first
+  have G5 : Rig m b.B f T5 A5 cl X R r (fun i => gcoast r (f i) w (Z i)) :=
+    ⟨Hg5.gear,Hg5.imag,Can.second⟩
+  have HX : Can m b.B T5 (bundle cl) A5 (fun i => (fleet X Q r (f i)).tape (O i)) W :=
+    (G5.cross_point Q (extM e)).weaken hszQ
+  have heq (i) : O i = ebb X r (f i) (k i) (hq i) (whole (k i) (v i)) :=
+    gamplifies X r (f i) (k i) (hq i) e he w hw (v i)
+  have ha (i) : (fleet X Q r (f i)).tape (O i) =
+      (sim Q (k i)).tape (whole (k i) (v i)) := by
+    rw [heq]; exact ebb_eq ..
+  have Ho := ((Hy.weaken hszR (fun _ => le_rfl)).save_keep
+    (Able.of_can (b:=b) HX)).cong (fun _ => rfl) ha
+  have Hx := (Able.of_can (b:=b) hmp).save_keep
+    ((Able.of_can (b:=b) hmx).save_keep ((Able.of_can (b:=b) hml).save_keep
+      ((Able.of_can (b:=b) HH).save_keep ((Able.of_can (b:=b) HE).save_keep Ho))))
+  simpa only [Nat.zero_add,Nat.add_zero] using Hx
+
+end
+end
+end PowerSaving.RAM
+end OAI
+
+#print axioms OAI.PowerSaving.RAM.gamplify
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md
new file mode 100644
index 0000000000..e28b355d0a
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md
@@ -0,0 +1,64 @@
+# tools/gx/ and tools/certificate/gcert1-p11-pr193.json.gz: where they come from
+
+Everything in this directory is Python 3 (standard library only). No Lean is run by these scripts.
+"The outside repository" means github.com/CrocSwap/integer-mult-bounds (Apache-2.0, `LICENSE` and `NOTICE`
+of that repository; `NOTICE`: "A sharper exponent for integer multiplication, Copyright 2026 Douglas Colkitt").
+
+## The scripts (this project)
+
+| file | what it is |
+|---|---|
+| `gxcore.py` | loads a certificate of format gcert/1, brings it to normal form, and is a Python mirror of both Lean checks (labels and scalars); cut points and label data for the generator |
+| `gxunit.py` | split plan of the kernel evaluations, the unit of the word, expected exponents |
+| `gxbind.py` | the texts of the generated Lean modules (check, histogram, price, certificate and final modules) |
+| `gxgen.py` | certificate -> Lean data modules and one module per kernel evaluation |
+| `gxrate.py` | rate lemmas, unit price list, final theorem modules, comparator challenge / solution / configuration |
+| `gxdry.py`, `gxmut.py` | dry run (mirror, sizes, plan, exponents); mutants that the mirror must reject |
+| `gxconv.py` | converts the earlier format gcert/0 to gcert/1 when a step scales its target (the in-place pair step of #193) |
+| `gsmirror.py` | a second, separately written Python mirror of the scalar check `GS.scalCheck` / `GS.yCheck`; `gxbind.py` calls it for the check parameters |
+| `gx.py`, `gxrun.py` | the reference checker of the format (`gx.check1`: labels and exact scalar identity) and its command line |
+| `gxpaths.py`, `regen_check.py`, `refcheck.py` | written for this repository: relative paths; regenerate and compare; `gx.check1` on a gcert/1 file |
+
+The scripts are the working copies with path edits only (absolute paths of the author's machine replaced through
+`gxpaths.py`; templates read from `tools/gen/templates/`; `foldlib.py` / `foldgen.py` taken from `tools/gen/`).
+The sentences "Generated by checks/..." that the generators print into Lean files name the scripts by their
+working paths; they are kept so that the generated modules come out byte for byte.
+No script of the outside repository is included, imported or executed.
+
+## The certificate `tools/certificate/gcert1-p11-pr193.json.gz`
+
+sha256 of the file: `15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633`
+(gzip stores a time stamp; sha256 of the uncompressed JSON: `c64d2a95431c3cf24452de7391cce780bd71521da44ce23923ebb235f6c7962c`).
+
+It is ONE explicit program (numbered registers, every addition, every frame) for the helper circuit at
+h = 22: 1,320 ports, 9,412 slots, 262,944 unit moves. **The design of that circuit is not this project's.** It is the
+"paired-cube" circuit of the outside repository as of pull request #193 (which builds on #191, #184, #168 and #144).
+The outside repository publishes the design as generator scripts, frozen data files and a ledger; it has no file
+of this kind. This file was produced by this project's own code, which
+
+1. loaded the following files of the outside repository **as data** (JSON; nothing was executed):
+   - at pull request #168, commit `4a3c769e5c5430e7114c4d3e099ff34664677f17`:
+     `references/paired-cube/sources/local_L1.json`,
+     `references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json`,
+     `references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json`,
+     `references/paired-cube/sources/qmod_climb3u_best.json` (the local modules),
+     `references/paired-cube/selected-module/matching-arcs.json` (carrier arcs),
+     `references/paired-cube/physical/frames.json` (moved frames);
+   - at pull request #193, commit `187e1010ac8b259af8e9b5166f68b64bc27b4b47`:
+     `research/source-assisted-v4/data/physical-pairs.json` (the hand-over pairs);
+2. rebuilt the circuit from them step by step, following the algorithms of the outside scripts (read as text),
+   and checked the result exactly (every published count reproduced; the scalar identity as an identity of
+   linear maps with arbitrary contents of the helper registers);
+3. converted it to gcert/1 with `gxconv.py` (tested by `gx.check1`).
+
+Step 1 and step 2 (the rebuild scripts and the outside inputs they read) are NOT part of this repository;
+the inputs can be fetched from the outside repository at the two commits above.
+What this repository proves about the file does not depend on how it was made: the Lean kernel checks the
+generated modules (labels, scalar identity, price), and `regen_check.py` shows that those modules are exactly
+what `gxgen.py` / `gxrate.py` produce from this file.
+
+## Check it yourself
+
+    python3 tools/gx/regen_check.py                       # regenerates the Lean modules and compares
+    python3 tools/gx/gxdry.py tools/certificate/gcert1-p11-pr193.json.gz      # Python mirror of both checks
+    python3 tools/gx/refcheck.py                          # the reference checker gx.check1 on the certificate
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py
new file mode 100644
index 0000000000..fcb625619c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py
@@ -0,0 +1,438 @@
+"""gxbind.py: THE BINDING of the generator to the Lean terms of gx-scalar / gx-labels /
+gx-chain.  Everything that names somebody else's definition is in this file (tables SCAL, LAB, CHAIN)."""
+import os, re, subprocess
+import gxpaths
+ROOT = gxpaths.OUT
+GSM = gxpaths.HERE + '/gsmirror.py'
+
+# gx-scalar (gcert-interface.md, SCALAR v1): GS.scalCheck c p lo n, GS.yCheck c p lo n, p : GS.SPar = <d, sw, ux, us, uy>
+SCAL = dict(imports=['Work.GCert.Scalar.Seg'], scal='GS.scalCheck raw ⟨%(d)d, %(sw)d, %(ux)d, %(us)d, %(uy)d⟩ %(lo)d %(n)d',
+            ychk='GS.yCheck raw ⟨%(d)d, %(sw)d, %(ux)d, %(us)d, %(uy)d⟩ 0 %(v)d')
+# gx-labels (gcert-interface.md LABELS v1 + questions.md N1): namespace GLab; frame = code, table and states = SSC.Trie,
+# GLab.Par = <h, n, d, K, tab>.  `end` = GLab.endK of Labels/EndDef.lean (questions.md N2; no obaseK: Q1 closed).
+LAB = dict(imports=['Work.GCert.Labels.Def'], end_imports=['Work.GCert.Labels.EndDef'], par='⟨%(h)d, %(n)d, %(d)d, %(K)d, tab⟩', ns='GLab',
+           tab='GLab.tabK %(h)d %(sub)s', seg='GLab.segK par %(gs)s st%(i)d st%(j)d %(rs)s',
+           end='GLab.endK par %(v)d ports (raw.ret.map Prod.fst) st0 st%(a)d st%(f)d', noadds='GLab.noAdds fins')
+# gx-chain (CHAIN v1): GX.wht_of_halves; the terms below are PLACEHOLDERS until Labels/Main and Scalar/Main compile
+CHAIN = dict(imports=['Work.GCert.Chain.End', 'Work.GCert.Labels.Main'], scal='(GS.ScalOK.scal GXD.%(c)s.scalOK)',
+             lab='(GXD.%(c)s.valid.lab GXD.%(c)s.scalOK)', lab_cost='GXD.%(c)s.lab_cost')
+
+
+def code(h, basis):
+    """gx-labels' code of a reduced echelon basis: dim + 2^8 M + 2^(8+h) P (M = pivot mask, vector of pivot p at digit p)"""
+    M = P = 0
+    for b in basis:
+        p = b.bit_length() - 1
+        M |= 1 << p
+        P |= b << (h * p)
+    return len(basis) + (M << 8) + (P << (8 + h))
+
+
+MOD = '''import %(imports)s
+/-! Kernel check (%(doc)s) of the gcert/1 certificate `GXD.%(name)s.raw`.  Source: %(src)s.
+Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/
+set_option maxRecDepth 100000
+namespace GXD.%(name)s
+open GXD
+theorem %(thm)s : %(stmt)s := by decide +kernel
+end GXD.%(name)s
+#print axioms GXD.%(name)s.%(thm)s
+'''
+
+
+def spar(D, path):
+    """scalar parameters: from gx-scalar's mirror when it exists, else from my own replay (sw is then a GUESS)"""
+    import gxcore as gc
+    n, d = 2 * D['v'] + D['R'], 0
+    while (1 << d) < n:
+        d += 1
+    dg = gc.digits(D)
+    S = dict(d=d, sw=16, ux=dg['x'][0], us=dg['s'][0], uy=dg['y'][0], source='gx-data replay; sw = 16 is a GUESS', digits=dg)
+    if os.path.exists(GSM):
+        try:
+            o = subprocess.run(['python3', '-B', GSM, path], capture_output=True, text=True, timeout=1800).stdout
+            m = re.search(r'SPar[^\d]*(\d+)[, ]+(\d+)[, ]+(\d+)[, ]+(\d+)[, ]+(\d+)', o)
+            if m:
+                S.update(zip(('d', 'sw', 'ux', 'us', 'uy'), map(int, m.groups())), source='gsmirror.py')
+        except Exception as e:
+            S['source'] += ' (gsmirror.py failed: %r)' % (e,)
+    return S
+
+
+def write_checks(D, M, name, src, out, L, S, plan):
+    base = out[len(ROOT):].replace('/', '.')
+    raw = '%s.Gen.%s' % (base, name)
+    h, v, n = D['h'], D['v'], 2 * D['v'] + D['R']
+    res = []
+
+    def mod(suffix, imports, thm, stmt, doc):
+        m = '%s.Gen.%s%s' % (base, name, suffix)
+        open('%s/Gen/%s%s.lean' % (out, name, suffix), 'w').write(MOD % dict(
+            imports='\nimport '.join(imports), doc=doc, name=name, src=src, thm=thm, stmt=stmt))
+        res.append((m, thm, stmt))
+    for i, (lo, hi) in enumerate(M['scal']['batches']):
+        mod('Scal%d' % i, SCAL['imports'] + [raw], 'scal%d_ok' % i, SCAL['scal'] % dict(S, lo=lo, n=hi - lo) + ' = true',
+            'scalar identity E3 E5 for the sources %d .. %d' % (lo, hi - 1))
+    mod('YChk', SCAL['imports'] + [raw], 'ychk_ok', SCAL['ychk'] % dict(S, v=v) + ' = true', 'the y -> y adds, E4')
+    par = '%s.Gen.%sPar' % (base, name)
+    open('%s/Gen/%sPar.lean' % (out, name), 'w').write(
+        'import %s\nimport %s\n/-! Parameters `GLab.Par` of the label check of `GXD.%s.raw` (h, registers, trie depth, K, frame table).\n'
+        'Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/\nnamespace GXD.%s\nopen GXD\n'
+        'noncomputable def par : GLab.Par := %s\nend GXD.%s\n'
+        % (LAB['imports'][0], raw, name, name, LAB['par'] % dict(h=h, n=n, d=L['d'], K=L['K']), name))
+    paths = [format(i, '0%db' % L['ts']) for i in range(1 << L['ts'])] if L['ts'] else ['']
+    for i, pth in enumerate(paths):
+        mod('Tab%d' % i, LAB['imports'] + [raw], 'tab%d_ok' % i,
+            LAB['tab'] % dict(h=h, sub='tab_n' + pth if pth else 'tab') + ' = true',
+            'E0: subtrie %d of %d of the frame table (codes of reduced echelon bases)' % (i, len(paths)))
+    for i in range(L['nseg']):
+        mod('Seg%d' % i, [par], 'seg%d_ok' % i,
+            LAB['seg'] % dict(gs='seg%d' % i, i=i, j=i + 1, rs='rs%d' % i) + ' = true',
+            'E1: replay of the gates %d .. %d (phase %s) and their block ranks' % (
+                M['cuts'][i], M['cuts'][i + 1] - 1, 'A' if i < L['nsegA'] else 'B'))
+    mod('SegF', [par], 'segF_ok', LAB['seg'] % dict(gs='fins', i=L['nseg'], j=L['nseg'] + 1, rs='rF') + ' = true',
+        'E1: the final climbs and their block ranks')
+    if LAB['end']:
+        mod('End', LAB['end_imports'] + [par], 'end_ok', LAB['end'] % dict(v=v, a=L['nsegA'], f=L['nseg'] + 1) + ' = true',
+            'E1 E2: frames at the start, at the scatter, at the end')
+    return res
+
+
+def nest(xs):
+    return ' ++ ('.join(xs) + ')' * (len(xs) - 1) if xs else '[]'
+
+
+def write_hist(D, M, name, src, out, L):
+    """kernel counts of the block ranks on the EXPLICIT rank lists rA, rB, rF (no replay)"""
+    base = out[len(ROOT):].replace('/', '.')
+    h, rs = D['h'], M['lab']['rs']
+    ph = {'A': sum(rs[:L['nsegA']], []), 'B': sum(rs[L['nsegA']:], []), 'F': M['lab']['rF']}
+    top = max(max(x) if x else 0 for x in ph.values())
+    cop = [M['dim'][f] for _, f in D['ret']]
+    tot = {r: sum(x.count(r) for x in ph.values()) + cop.count(r) for r in range(1, max(top, max(cop)) + 1)}
+    assert {r: c for r, c in tot.items() if c} == M['hist'], 'histogram of the rank lists differs from the mirror'
+    lines = ['/-- block ranks of phase A / phase B, in order (the lists of the replay segments) -/',
+             'noncomputable def rA : List Nat := ' + nest(['rs%d' % i for i in range(L['nsegA'])]),
+             'noncomputable def rB : List Nat := ' + nest(['rs%d' % i for i in range(L['nsegA'], L['nseg'])])]
+    names = []
+    for X, lst in sorted(ph.items()):
+        l = 'r' + X
+        lines.append('theorem rankBound%s : wsumK (SSC.wGt %d) %s 0 = 0 := by decide +kernel' % (X, top, l))
+        lines += ['theorem rank%s%d_ok : wsumK (SSC.wEq %d) %s 0 = %d := by decide +kernel' % (X, r, r, l, lst.count(r))
+                  for r in range(top + 1)]
+        names += ['rankBound' + X] + ['rank%s%d_ok' % (X, r) for r in range(top + 1)]
+    txt = ('import Work.GCert.Data.Count\nimport %s.Gen.%s\n' % (base, name) +
+           '/-! Kernel count of the BLOCK RANKS of the gcert/1 certificate `GXD.%s.raw` (h = %d) on the explicit rank lists\n'
+           '`rA`, `rB`, `rF` (phase A, phase B, final climbs): `wsumK (SSC.wEq r) l 0` blocks of rank `r`, none above %d\n'
+           '(`GXD.sum_of_wsumK` turns a count into `(l.map wt).sum` = `SSC.wsum wt l`).\n'
+           'The %d scratch copies (ranks %s) are not in these lists.  Whole invocation, by rank: %s.\n'
+           'Source: %s.  Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/\n'
+           'set_option maxRecDepth 100000\nnamespace GXD.%s\nopen GXD\n' % (
+               name, h, top, len(cop), sorted(set(cop)), M['hist'], src, name) + '\n'.join(lines) +
+           '\nend GXD.%s\n' % name + '\n'.join('#print axioms GXD.%s.%s' % (name, x) for x in names[:2]) + '\n')
+    open('%s/Gen/%sHist.lean' % (out, name), 'w').write(txt)
+    return '%s.Gen.%sHist' % (base, name)
+
+
+def write_price(D, M, name, src, out, L):
+    """Mathlib module: the price of the rank lists rA, rB, rF from the kernel counts, and of one whole invocation"""
+    base = out[len(ROOT):].replace('/', '.')
+    rs = M['lab']['rs']
+    ph = {'A': sum(rs[:L['nsegA']], []), 'B': sum(rs[L['nsegA']:], []), 'F': M['lab']['rF']}
+    top = max(max(x) if x else 0 for x in ph.values())
+    cop = [M['dim'][f] for _, f in D['ret']]
+    tm = lambda cnt: ' + '.join('%d * φ %d' % (n, r) for r, n in sorted(cnt.items()) if n) or '0'
+    thms = ''
+    for X in 'ABF':
+        cnt = {r: ph[X].count(r) for r in range(1, top + 1)}
+        thms += '''
+/-- price of the blocks of %s, from the kernel counts -/
+theorem r%s_cost (φ : ℕ → ℝ) : rcost φ r%s = %s := by
+  rw [GXD.rcost_wsumK φ r%s %d rankBound%s]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, %s]
+  norm_num [bcost]
+''' % ({'A': 'phase A', 'B': 'phase B', 'F': 'the final climbs'}[X], X, X, tm(cnt), X, top, X,
+       ', '.join('rank%s%d_ok' % (X, r) for r in range(top + 1)))
+    copies = tm({r: cop.count(r) for r in set(cop)})
+    txt = '''import Work.GCert.Data.Price
+import %(base)s.Gen.%(name)sHist
+
+/-!
+# (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): the price of one invocation
+
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+`rA_cost`, `rB_cost`, `rF_cost`: the price of the block rank lists of phase A, phase B and the final climbs
+(lists `GXD.%(name)s.rA / rB / rF`, counted by the kernel in `Gen.%(name)sHist`);
+`inv_cost`: with the %(nc)d scratch copies (%(copies)s) the blocks of ONE invocation cost
+`invPrice φ` = %(terms)s;  `inv_moves`: they stand for `R h + 2 v (h - 1) + cst = %(N)d` unit moves.
+-/
+
+namespace GXD.%(name)s
+open GXD OAI.PowerSaving.CB
+%(thms)s
+/-- price of the blocks of ONE invocation (x roles, y roles, slots, scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := %(terms)s
+
+/-- **Price of ONE invocation** in the shape of `GX.Lab.cost`: phase A, the scratch copies, phase B, final climbs. -/
+theorem inv_cost (φ : ℕ → ℝ) : rcost φ rA + (%(copies)s) + rcost φ rB + rcost φ rF = invPrice φ := by
+  rw [rA_cost, rB_cost, rF_cost]
+  unfold invPrice
+  ring
+
+theorem inv_moves : invPrice (fun r => (r:ℝ)) = %(R)d * %(h)d + 2 * %(v)d * (%(h)d - 1) + %(cst)d := by
+  unfold invPrice
+  norm_num
+
+theorem inv_count : invPrice (fun _ => (1:ℝ)) = %(count)d := by
+  unfold invPrice
+  norm_num
+
+end GXD.%(name)s
+#print axioms GXD.%(name)s.inv_cost
+#print axioms GXD.%(name)s.inv_moves
+''' % dict(base=base, name=name, h=D['h'], src=src, nc=len(cop), copies=copies, terms=tm(M['hist']), N=D['N'], thms=thms,
+           R=D['R'], v=D['v'], cst=D['cst'], count=sum(M['hist'].values()))
+    open('%s/%sPrice.lean' % (out, name), 'w').write(txt)
+    return '%s.%sPrice' % (base, name)
+
+
+def write_cert(D, M, name, src, out, chk, L):
+    """<Name>Cert: THE LABEL HALF (aux, valid : GLab.Valid raw aux, lab_cost, lab_price) -- compiles without the scalar half;
+    <Name>ScalOK: the scalar half `scalOK : GS.ScalOK raw` (needs Work/GCert/Scalar/Main)."""
+    base = out[len(ROOT):].replace('/', '.')
+    bs = M['scal']['batches']
+    hs = ''
+    for i, (lo, hi) in enumerate(bs):
+        lo_pf = 'Nat.zero_le t' if i == 0 else 'Nat.le_of_not_lt h%d' % (i - 1)
+        if i + 1 < len(bs):
+            hs += '    if h%d : t < %d then ⟨%d, %d, %s, h%d, GS.XRun.of_check scal%d_ok⟩ else\n' % (i, hi, lo, hi - lo, lo_pf, i, i)
+        else:
+            hs += '    ⟨%d, %d, %s, Nat.lt_of_lt_of_le ht (by decide), GS.XRun.of_check scal%d_ok⟩' % (lo, hi - lo, lo_pf, i)
+    terms = ' + '.join('%d * φ %d' % (n, r) for r, n in M['hist'].items())
+    info = dict(base=base, name=name, h=D['h'], src=src, v=D['v'], R=D['R'], nc=len(D['ret']), cst=D['cst'], N=D['N'],
+                nb=len(bs), terms=terms, hs=hs)
+    txt = '''import Work.GCert.Scalar.Main
+import %(imps)s
+/-! # (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): THE SCALAR HALF `scalOK : GS.ScalOK raw`
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+Kernel checks `scal<i>_ok` (%(nb)d source batches) and `ychk_ok`. -/
+namespace GXD.%(name)s
+open GXD
+theorem scalOK : GS.ScalOK raw where
+  hv := by decide
+  hs := fun t ht =>
+%(hs)s
+  hyc := fun t ht => ⟨0, %(v)d, Nat.zero_le t, Nat.lt_of_lt_of_le ht (by decide), GS.YRun.of_check ychk_ok⟩
+end GXD.%(name)s
+#print axioms GXD.%(name)s.scalOK
+''' % dict(info, imps='\nimport '.join(c[0] for c in chk if 'Scal' in c[0] or 'YChk' in c[0]))
+    open('%s/%sScalOK.lean' % (out, name), 'w').write(txt)
+    # ---- the label half
+    nA, ns, ts = L['nsegA'], L['nseg'], L['ts']
+    cop = sorted(set(M['dim'][f] for _, f in D['ret']))
+    assert len(cop) == 1, 'scratch copies of several ranks %s: lab_cost of gxbind.py assumes one' % cop
+
+    def tabpf(path):
+        if len(path) == ts:
+            return 'tab%d_ok' % (int(path, 2) if path else 0)
+        return '(GLab.tabK_node _ _ _ %s %s)' % (tabpf(path + '0'), tabpf(path + '1'))
+
+    def runpf(a, b):
+        return 'GLab.Run.of_seg seg%d_ok' % a if a + 1 == b else 'GLab.Run.append (GLab.Run.of_seg seg%d_ok) (%s)' % (a, runpf(a + 1, b))
+
+    def run(X, a, b):
+        segs = ['seg%d' % i for i in range(a, b)]
+        return '''theorem gates%(X)s_eq : raw.gates%(X)s = %(cat)s := by
+  show List.flatten %(lst)s = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase %(X)s, composed from its kernel-checked segments -/
+theorem run%(X)s : GLab.Run par st%(a)d raw.gates%(X)s st%(b)d r%(X)s := by
+  rw [gates%(X)s_eq]
+  exact %(pf)s
+''' % dict(X=X, cat=nest(segs), lst=ll_(segs), a=a, b=b, pf=runpf(a, b))
+    lab = 'valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg'
+    txt = '''import Work.GCert.Labels.Main
+import %(base)s.%(name)sPrice
+import %(imps)s
+/-! # (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): THE LABEL HALF and its price
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+`v = %(v)d` ports, `R = %(R)d` slots, %(nc)d scratch copies of rank %(c)d, copy cost `cst = %(cst)d`, `N = %(N)d` unit moves.
+* `aux : GLab.Aux`, `valid : GLab.Valid raw aux`: frame table (`tab<i>_ok` composed by `tabK_node`), the replays of phase A
+  and phase B (`seg<i>_ok` composed by `Run.append`), the final climbs (`segF_ok`, `fin_ok`), the ends (`end_ok`);
+* `lab_cost`, `lab_price`: for ANY scalar half `S` the label half `valid.lab S ..` costs
+  `rcost rA + card C * bcost %(c)d + rcost rB + rcost rF` = `invPrice φ` = %(terms)s
+  (`Gen.%(name)sHist`, `%(name)sPrice`) when there are %(nc)d copies. -/
+set_option maxRecDepth 100000
+namespace GXD.%(name)s
+open GXD OAI.PowerSaving OAI.PowerSaving.CB
+theorem raw_h : raw.h = %(h)d := rfl
+theorem raw_v : raw.v = %(v)d := rfl
+theorem raw_R : raw.R = %(R)d := rfl
+/-- what the label checks read next to `raw` -/
+noncomputable def aux : GLab.Aux := ⟨par, st0, st%(a)d, st%(n)d, st%(f)d, fins, rA, rB, rF⟩
+theorem fin_ok : GLab.noAdds fins = true := by decide +kernel
+theorem cen_ok : (raw.ret.map Prod.fst).all (fun r => Nat.beq (GLab.cdim (par.tab.get (st%(a)d.get r))) %(c)d) = true := by
+  decide +kernel
+theorem tab_ok : GLab.tabK par.h par.tab = true := %(tabpf)s
+%(runA)s%(runB)s/-- **the kernel-checked label facts** of the certificate -/
+theorem valid : GLab.Valid raw aux where
+  hn := rfl
+  tab := tab_ok
+  runA := runA
+  runB := runB
+  runF := GLab.Run.of_seg segF_ok
+  fin := fin_ok
+  ends := end_ok
+theorem cen_dim (r : Nat) (hr : r ∈ raw.ret.map Prod.fst) : GLab.cdim (par.tab.get (st%(a)d.get r)) = %(c)d :=
+  Nat.eq_of_beq_eq_true (List.all_eq_true.mp cen_ok r hr)
+/-- price of the label half over ANY scalar half -/
+theorem lab_cost {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (φ : ℕ → ℝ) :
+    (%(lab)s).cost φ
+      = rcost φ rA + (Fintype.card C : ℝ) * bcost φ %(c)d + rcost φ rB + rcost φ rF := by
+  obtain ⟨h1, h2, h3, h4⟩ := valid.lab_ranks S Ro cf hMA hMAi hMB hMBi reg hCc hreg
+  have h5 : ∀ k, bcost φ (((%(lab)s).cen k).dim) = bcost φ %(c)d :=
+    fun k => by rw [h4 k]; exact congrArg (bcost φ) (cen_dim _ (hreg k))
+  rw [GX.Lab.cost, h1, h2, h3, Finset.sum_congr rfl (fun k _ => h5 k), Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
+  rfl
+/-- **the label half costs one invocation price** (`invPrice`, by rank, from the kernel counts) -/
+theorem lab_price {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (hC : Fintype.card C = %(nc)d) (φ : ℕ → ℝ) :
+    (%(lab)s).cost φ = invPrice φ := by
+  rw [lab_cost S Ro cf hMA hMAi hMB hMBi reg hCc hreg φ, hC, ← inv_cost φ]
+  norm_num [bcost]
+end GXD.%(name)s
+#print axioms GXD.%(name)s.valid
+#print axioms GXD.%(name)s.lab_price
+''' % dict(info, imps='\nimport '.join(c[0] for c in chk if 'Scal' not in c[0] and 'YChk' not in c[0]), c=cop[0], a=nA, n=ns,
+           f=ns + 1, tabpf=tabpf(''), runA=run('A', 0, nA), runB=run('B', nA, ns), lab=lab)
+    open('%s/%sCert.lean' % (out, name), 'w').write(txt)
+    return ['%s.%sCert' % (base, name), '%s.%sScalOK' % (base, name)]
+
+
+def ll_(xs):
+    return '[' + ', '.join(xs) + ']'
+
+
+def final_module(name, cname, d, dx, g, out):
+    """<Inst>.lean: the final theorems OVER ANY SCALAR HALF (compiles as soon as <C>Cert does): label half, price,
+    unit list, rate fact and gx-chain's `GX.wht_of_halves` are all closed; what is left is `S : GX.Scal` with its
+    gate matrices = the ordered products of the adds of `raw` (gx-scalar)."""
+    h, v, R, W, m, nc = g['h'], g['v'], g['R'], d['W'], d['m'], g['nc']
+    X = 'GXD.%s' % cname
+    args = 'S Ro cf hMA hMAi hMB hMBi reg hCc hreg'
+
+    def thm(nm, rate, A, B, s, ux):
+        return f'''
+/-- **Walsh-Hadamard transform, whole-block recursion on the bridged word B_2 with the gcert/1 circuit `{cname}`**,
+over any scalar half of `{X}.raw`: the statement `WHTGoal` of `WHTCheck/Challenge.lean` with `1 - 2/10^11`
+replaced by `1 - {A}/10^{B}`. -/
+theorem {nm} (Ro : GLab.Roles {X}.raw.v {X}.raw.R emb un)
+    (hMA : S.MA = SSC.matP un (GLab.mic cf ({X}.raw.gatesA.flatMap GXD.Gate.adds)))
+    (hMAi : S.MAi = SSC.matPinv un (GLab.mic cf ({X}.raw.gatesA.flatMap GXD.Gate.adds)))
+    (hMB : S.MB = SSC.matP un (GLab.mic cf ({X}.raw.gatesB.flatMap GXD.Gate.adds)))
+    (hMBi : S.MBi = SSC.matPinv un (GLab.mic cf ({X}.raw.gatesB.flatMap GXD.Gate.adds)))
+    (reg : C → Nat) (hCc : ∀ k (q : Fin {X}.raw.R), S.Cc k q ≠ 0 → reg k = 2 * {X}.raw.v + q.val)
+    (hreg : ∀ k, reg k ∈ {X}.raw.ret.map Prod.fst) (hC : Fintype.card C = {nc}) :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  GX.wht_of_halves S ({X}.valid.lab {args})
+    (by rw [Fintype.card_fin]; decide) {m} {W} (by rw [Fintype.card_fin]; rfl)
+    (by rw [Fintype.card_fin, Fintype.card_fin]; rfl) (by norm_num) BlockAccounting.blocks{rate}
+    (fun φ => by
+      rw [{X}.lab_price {args} hC φ, Fintype.card_fin, Fintype.card_fin]
+      exact BridgeRate.{name}.unit_cost{ux} φ)
+    {s} (1 - {A}/(10:ℝ)^{B}) (by norm_num) (by norm_num) BlockAccounting.fold_{rate}
+
+/-- the same from the FIVE scalar identities of gx-scalar's matrices of `{X}.raw` (`Work/GCert/Data/Glue.lean`) -/
+theorem {nm.replace('_of_scal', '_of_ids')} (hv : 0 < {X}.raw.v)
+    (hAi : GS.MAi {X}.raw hv * GS.MA {X}.raw hv = 1) (hBi : GS.MBi {X}.raw hv * GS.MB {X}.raw hv = 1)
+    (hx : ∀ (t : Fin {X}.raw.v) (j : GS.Rl {X}.raw), (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) (CR.lX t) j = if CR.lX t = j then 1 else 0)
+    (hy : ∀ (i : GS.Rl {X}.raw) (t : Fin {X}.raw.v), (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) i (CR.lY t) = if i = CR.lY t then 1 else 0)
+    (hid : ∀ S t : Fin {X}.raw.v, (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) (CR.lY S) (CR.lX t) = if S = t then 1 else 0) :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  {nm} (GXD.scalOf {X}.raw hv hAi hBi hx hy hid) GS.toCoef (GXD.roles {X}.raw hv)
+    (GXD.scalOf_MA _ hv hAi hBi hx hy hid) (GXD.scalOf_MAi _ hv hAi hBi hx hy hid)
+    (GXD.scalOf_MB _ hv hAi hBi hx hy hid) (GXD.scalOf_MBi _ hv hAi hBi hx hy hid)
+    (GXD.reg {X}.raw) (GXD.reg_slot {X}.raw hv hAi hBi hx hy hid) (GXD.reg_mem {X}.raw)
+    (by rw [Fintype.card_fin]; decide)
+'''
+    txt = f'''import Work.GCert.Chain.End
+import Work.GCert.Data.Glue
+import Work.GCert.Data.{cname}Cert
+import Work.GCert.Data.Inst{name}
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `{cname}` (h = {h}, m = {m}): final theorems over a scalar half
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`GX.wht_of_halves` (gx-chain) on the label half `{X}.valid` (kernel checks of `Work/GCert/Data/Gen/{cname}*`), its
+price `{X}.lab_price`, the unit list `BlockAccounting.blocks{name}` (`W = {W}` live roles) and the rate facts
+`fold_{name}` (`1 - {d['A']}/10^{d['B']}`), `fold_{name}x` (`1 - {dx['A']}/10^{dx['B']}`).
+The ONLY hypothesis left is the scalar half: `S : GX.Scal (Fin {v}) (Fin {R}) C` whose gate matrices are the ordered
+products of the adds of `raw` (`hMA .. hMBi`), with `{nc}` copies read from the retained registers (`reg`, `hCc`, `hreg`, `hC`);
+`wht_{name}_of_ids`, `wht_{name}x_of_ids`: the same from the five identities `hAi hBi hx hy hid` of gx-scalar's matrices
+`GS.MA GS.MAi GS.MB GS.MBi GS.Jrm GS.Ccm` of `raw` (the fields of the planned `GS.ScalOK`).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+
+variable {{C : Type}} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin {X}.raw.v) (Fin {X}.raw.R) C)
+  {{emb : CR.L3 (Fin {X}.raw.v) (Fin {X}.raw.R) → Nat}} {{un : Nat → CR.L3 (Fin {X}.raw.v) (Fin {X}.raw.R)}}
+  (cf : GXD.Co → SSC.Coef)
+''' + thm('wht_' + name + '_of_scal', name, d['A'], d['B'], d['s'], '') + thm('wht_' + name + 'x_of_scal', name + 'x', dx['A'], dx['B'], dx['s'], '_x') + f'''
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_{name}_of_scal
+#print axioms OAI.PowerSaving.WHT.wht_{name}x_of_scal
+#print axioms OAI.PowerSaving.WHT.wht_{name}_of_ids
+#print axioms OAI.PowerSaving.WHT.wht_{name}x_of_ids
+'''
+    open(out + '%s.lean' % name, 'w').write(txt)
+
+
+def main_module(name, cname, d, dx, out):
+    """<Inst>Main.lean: the CLOSED theorems (what the comparator solution cites).  WRITTEN against gx-scalar's planned
+    `GS.ScalOK` (fields / theorems hv hAi hBi hx hy hid, SCALAR v2); compiles when Work/GCert/Scalar/Main.lean exists."""
+    K = 'GXD.%s.scalOK' % cname
+
+    def thm(sfx, A, B):
+        return f'''
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - {A}/10^{B}))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `{cname}`.** -/
+theorem wht_main_{name}{sfx} :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  wht_{name}{sfx}_of_ids {K}.hv {K}.hAi {K}.hBi {K}.hx {K}.hy {K}.hid
+'''
+    txt = f'''import Work.GCert.Scalar.Main
+import Work.GCert.Data.{cname}ScalOK
+import Work.GCert.Data.{name}
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `{cname}`: THE CLOSED THEOREMS
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`wht_{name}_of_ids` (label half, price, unit list, rate fact, gx-chain's end theorem) applied to the scalar half
+`{K} : GS.ScalOK GXD.{cname}.raw` (kernel checks `scal<i>_ok`, `ychk_ok`; soundness: gx-scalar).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+''' + thm('', d['A'], d['B']) + thm('x', dx['A'], dx['B']) + f'''
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_main_{name}
+#print axioms OAI.PowerSaving.WHT.wht_main_{name}x
+'''
+    open(out + '%sMain.lean' % name, 'w').write(txt)
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py
new file mode 100644
index 0000000000..49ebb65973
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py
@@ -0,0 +1,131 @@
+"""gxconv.py: gcert/0 -> gcert/1 for files whose in-place pair op SCALES its target
+(`op dest ctrl ca cb`: dest := ca dest + cb ctrl with ca not in {1}; #193 has ca = -2), questions.md D2.
+COPY of `convert` of gx.py with ONE change: a scaling is not a gate, it changes the
+UNIT in which the register is stored.  wanted(r) = lam[r] * stored(r), lam = 1 at the start;
+    op dest ctrl ca cb :  lam[dest] *= ca ;  stored(dest) += (cb lam[ctrl] / lam[dest]) stored(ctrl)
+    any other add t += k s :  stored(t) += (k lam[s] / lam[t]) stored(s)
+    scatter y_t += coef(t, k) total_k :  coefficient coef(t, k) * lam[slot of total k]   (a TABLE if some lam != 1)
+Only slots may be scaled (tested: lam = 1 on every x and y register, always), so the x / y rows and columns of
+the product (E5: hx, hy, hid) are those of the unscaled circuit; frames, blocks and N are untouched.
+The result is tested by the reference checker `gx.check1` (labels and scalars) before it is written.
+
+usage: gxconv.py <gcert0.json[.gz]> out=<gcert1.json[.gz]> [noext]
+"""
+import sys, time
+from fractions import Fraction as Fr
+import gxpaths
+import gx
+import gxrun
+need = gx.need
+
+
+def convert(c0):
+    need(c0["format"] == "gcert/0", "input is not gcert/0")
+    v, h, R = c0["v"], c0["h"], c0["R"]
+    ev = c0["events"]
+    cen = [n for n, e in enumerate(ev) if e[0] == "centre"]
+    need(cen == list(range(cen[0], cen[0] + len(cen))), "centres are not contiguous: no single scatter cut")
+    A, B, ret = [], [], []
+    neg, openq, lam, nsc = set(), {}, {}, 0
+    L = lambda r: lam.get(r, Fr(1))
+
+    def co(t, s, a, b=1):                       # stored coefficient of the wanted add t += (a/b) s
+        w = Fr(a, b) * L(s) / L(t)
+        return [w.numerator, w.denominator]
+
+    def o(f, s, tg, ex=()):
+        return ["out", f, s, [[t] + co(t, s, a, b) for t, a, b in tg], list(ex)]
+
+    def i(f, t, sr):
+        return ["in", f, t, [[s] + co(t, s, a, b) for s, a, b in sr]]
+    scat_lam = None
+    for n, e in enumerate(ev):
+        k = e[0]
+        out = A if n < cen[0] else B
+        if k in ("read0", "undo", "uninj"):
+            continue
+        if k == "inj":
+            need(e[2] not in neg, "inj reads a negated x register")
+            out.append(o(e[3], e[2], [[e[1], 1, 1]]))
+        elif k == "op":
+            if e[3] != 1:
+                need(e[3] != 0 and e[1] >= 2 * v, "op scales a register that is not a slot (or by 0)")
+                lam[e[1]] = L(e[1]) * e[3]
+                nsc += 1
+            out.append(o(e[5], e[2], [[e[1], e[4], 1]]))
+        elif k == "centre":
+            ret.append([e[2], e[1], e[3]])
+            if scat_lam is None:
+                scat_lam = dict(lam)
+        elif k == "gread":
+            hit = set(t for t, _, _ in e[3])
+            out.append(o(e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], [v + t for t in e[4] if t not in hit]))
+        elif k == "rread":
+            out.append(o(e[2], e[1], [[v + t, a, b] for t, a, b in e[3]]))
+        elif k == "ysh":
+            out.append(o(e[4], e[2], [[e[1], e[3], 1]]))
+        elif k == "yw":
+            out.append(o(e[4], e[2], [[e[1], e[3][0], e[3][1]]]))
+        elif k == "kd":
+            out.append(o(e[3], e[2], [[e[1], -1 if e[2] in neg else 1, 1]]))
+        elif k == "ktr":
+            q = tuple(e[1])
+            need(e[2] == gx.KJ, "ktr matrix is not 1 - J/2")
+            x1, rest = q[0], list(q[1:])
+            if q not in openq:
+                out.append(i(e[3], x1, [[r, 1, 1] for r in rest]))
+                out.append(o(e[3], x1, [[r, -1, 2] for r in rest]))
+                out.append(i(e[3], x1, [[r, 1, 1] for r in rest]))
+                openq[q] = n
+                neg.add(x1)
+            else:
+                out.append(i(e[3], x1, [[r, -1, 1] for r in rest]))
+                out.append(o(e[3], x1, [[r, 1, 2] for r in rest]))
+                out.append(i(e[3], x1, [[r, -1, 1] for r in rest]))
+                del openq[q]
+                neg.discard(x1)
+        else:
+            raise AssertionError("unknown event kind %r" % k)
+        need(all(r >= 2 * v for r, x in lam.items() if x != 1), "an x or y register is scaled")
+    need(not openq and not neg, "a K block is not closed")
+    ret = sorted(ret)
+    need([z[0] for z in ret] == list(range(len(ret))), "retained totals are not 0 .. n-1")
+    sin, sout = Fr(*c0["scat"]["inside"]), Fr(*c0["scat"]["outside"])
+    sl = [(scat_lam or {}).get(z[1], Fr(1)) for z in ret]
+    if all(x == 1 for x in sl):
+        scat = dict(inside=c0["scat"]["inside"], outside=c0["scat"]["outside"])
+    else:
+        need(len(ret) == h, "star rule with a number of totals other than h")
+        scat = dict(table=[[[kk, (w * sl[kk]).numerator, (w * sl[kk]).denominator]
+                            for kk in range(h) for w in [sin if c0["ports"][t] >> kk & 1 else sout]] for t in range(v)])
+    ext = sorted([z[3], z[1]] for z in c0["gauge"] if z[5])
+    c1 = dict(format="gcert/1", derived_from=c0["name"] + " (gcert/0; %d scalings as units, gxconv.py)" % nsc, p=c0["p"],
+              h=h, v=v, R=R, cst=c0["cst"], N=c0["N"], ports=c0["ports"], frames=c0["frames"], start=c0["start"],
+              final=c0["final"], ext=ext, ret=ret, scat=scat, A=A, B=B, blocks=c0["blocks"])
+    return c1, nsc, sorted(set(str(x) for x in lam.values())), sum(1 for x in sl if x != 1)
+
+
+if __name__ == "__main__":
+    t0 = time.time()
+    opt = dict(a.split("=", 1) for a in sys.argv[2:] if "=" in a)
+    c0 = gxrun.load(sys.argv[1])
+    c1, nsc, lams, nsl = convert(c0)
+    c1["two_hosts"] = sorted(2 * c0["v"] + i for i, hs in enumerate(c0["hosts"]) if len(hs) > 1)
+    if "noext" in sys.argv and c1["ext"]:        # as gxrun.py: exterior gauges become first blocks
+        for r, f in c1["ext"]:
+            d = str(len(c1["frames"][f]))
+            c1["start"][r] = 0
+            c1["blocks"]["s"][d] = c1["blocks"]["s"].get(d, 0) + 1
+            c1["N"] += int(d)
+        c1["blocks"]["s"] = {k: c1["blocks"]["s"][k] for k in sorted(c1["blocks"]["s"], key=int)}
+        c1["derived_from"] += ", exterior gauges turned into first blocks"
+        c1["ext"] = []
+    st = {}
+    gx.check1(c1, scalar=True, stats=st)
+    print("ACCEPTED by gx.check1: %s h=%d v=%d R=%d N=%d gates A=%d B=%d ext=%d; scalings %d, final units %s, scaled totals %d, "
+          "scatter %s, stats %s (%.1fs)" % (c0["name"], c1["h"], c1["v"], c1["R"], c1["N"], len(c1["A"]), len(c1["B"]),
+                                           len(c1["ext"]), nsc, lams, nsl, "table" if "table" in c1["scat"] else "star", st,
+                                           time.time() - t0))
+    if "out" in opt:
+        gxrun.dump(c1, opt["out"])
+        print("written", opt["out"])
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py
new file mode 100644
index 0000000000..3e3f0a3076
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py
@@ -0,0 +1,375 @@
+"""gxcore.py: gcert/1 JSON -> normal data D, PYTHON MIRROR of the two Lean checks
+(label side: E0 frames, E1 pairs, E1/E2/E6 replay in segments; scalar side: E3 kinds, E4 bracket, E5 replay
+in source batches, E7), derived data (distinct climbs, cut states, block histogram) and kernel sizes.
+Own code; the reference is gx.py (check1), not imported.  Python 3, standard library only."""
+import json, gzip
+from collections import Counter
+from math import gcd
+
+
+class Reject(Exception):
+    pass
+
+
+def need(c, msg):
+    if not c:
+        raise Reject(msg)
+
+
+def load(path):
+    c = json.load(gzip.open(path, "rt") if path.endswith(".gz") else open(path))
+    need(c.get("format") == "gcert/1", "E0: format is not gcert/1")
+    return c
+
+
+def co(num, den):
+    need(den > 0, "E0: denominator")
+    return (num < 0, abs(num), den)
+
+
+def normal(c):
+    """the Lean-facing data: gates as tuples, coefficients (neg, num, den), ret by total"""
+    def gate(g):
+        if g[0] == "out":
+            return ("out", g[1], g[2], [(t, co(a, b)) for t, a, b in g[3]], list(g[4]))
+        need(g[0] == "in", "E0: unknown gate kind %r" % (g[0],))
+        return ("in", g[1], g[2], [(s, co(a, b)) for s, a, b in g[3]])
+    ret = sorted(c["ret"])
+    need([k for k, _, _ in ret] == list(range(len(ret))), "E2: retained totals numbered 0..")
+    sc = c["scat"]
+    scat = ("table", [[(k, co(a, b)) for k, a, b in row] for row in sc["table"]]) if "table" in sc else \
+        ("star", co(*sc["inside"]), co(*sc["outside"]))
+    return dict(h=c["h"], v=c["v"], R=c["R"], N=c["N"], cst=c["cst"], ports=list(c["ports"]),
+                frames=[list(f) for f in c["frames"]], start=list(c["start"]), final=list(c["final"]),
+                ext=[tuple(e) for e in c.get("ext", [])], ret=[(s, f) for _, s, f in ret], scat=scat,
+                A=[gate(g) for g in c["A"]], B=[gate(g) for g in c["B"]],
+                blocks={k: {int(r): n for r, n in c["blocks"][k].items()} for k in "xysc"})
+
+
+def regs(g):
+    return [g[2]] + [t for t, _ in g[3]] + (g[4] if g[0] == "out" else [])
+
+
+def adds(g):
+    """single adds (tgt, src, coef) in order"""
+    return [(t, g[2], k) for t, k in g[3]] if g[0] == "out" else [(g[2], s, k) for s, k in g[3]]
+
+
+def reduce(u, basis):
+    for b in basis:
+        if u >> (b.bit_length() - 1) & 1:
+            u ^= b
+    return u
+
+
+def echelon_ok(f):
+    piv = [b.bit_length() - 1 for b in f]
+    if any(b == 0 for b in f) or any(piv[i] <= piv[i + 1] for i in range(len(piv) - 1)):
+        return False
+    return all(not (b >> p & 1) for i, b in enumerate(f) for j, p in enumerate(piv) if i != j)
+
+
+def par(x):
+    return bin(x).count("1") & 1
+
+
+def cls(D, r):
+    return "x" if r < D["v"] else "y" if r < 2 * D["v"] else "s"
+
+
+# ---- label side ------------------------------------------------------------------------------------------
+def chk_frames(D):
+    """E0: ports; frame table reduced echelon, no repeats, zero first, full second"""
+    h, v, fr = D["h"], D["v"], D["frames"]
+    p = D["ports"]
+    need(len(p) == v == len(set(p)) and all(par(q) and 0 < q < 1 << h for q in p), "E0: ports")
+    need(len(fr) >= 2 and fr[0] == [] and fr[1] == [1 << i for i in range(h - 1, -1, -1)], "E0: frames 0 and 1")
+    need(all(echelon_ok(f) and all(b < 1 << h for b in f) for f in fr), "E0: frame table not reduced echelon")
+    need(len(set(map(tuple, fr))) == len(fr), "E0: frame table has repeats")
+    return [len(f) for f in fr]
+
+
+def derive(D):
+    """distinct climbs in order of first use (NOT a check: plain replay of the frame ids)"""
+    cur, seen, pairs = list(D["start"]), set(), []
+
+    def go(r, f):
+        o = cur[r]
+        if o != f:
+            if (o, f) not in seen:
+                seen.add((o, f))
+                pairs.append((o, f))
+            cur[r] = f
+    for g in D["A"] + D["B"]:
+        for r in regs(g):
+            go(r, g[1])
+    for r, f in enumerate(D["final"]):
+        go(r, f)
+    return pairs
+
+
+def chk_pairs(D, dim, pairs):
+    """E1, level 2: every listed pair is a nested pair of the table; returns the mask-operation count"""
+    fr, n, work = D["frames"], len(D["frames"]), 0
+    for a, b in pairs:
+        need(a < n and b < n and dim[a] < dim[b], "E1: pair (%d, %d) does not climb" % (a, b))
+        need(all(reduce(u, fr[b]) == 0 for u in fr[a]), "E1: pair (%d, %d) is not nested" % (a, b))
+        work += dim[a] * dim[b]
+    return work
+
+
+def cut_points(D, gmax, wmax=210000):
+    """replay segments: each phase (A, B) is cut into k pieces of equal gate count, k = the least number with at
+    most `gmax` gates AND at most `wmax` work per piece on average (work = sum over gates of the dimension of the
+    gate's frame; measured at h = 22: about 1 ms of kernel time per unit, NOTES.md).
+    Cut points = gate counts in A ++ B (always 0, |A| and the end)."""
+    nA, nB = len(D["A"]), len(D["B"])
+    cuts = [0]
+    for off, gs in ((0, D["A"]), (nA, D["B"])):
+        n = len(gs)
+        k = max(1, -(-n // gmax), -(-sum(len(D["frames"][g[1]]) for g in gs) // wmax))
+        cuts += [off + (n * i) // k for i in range(1, k + 1)]
+    return sorted(set(cuts))
+
+
+def label_data(D, dim, cuts):
+    """for gx-labels (gcert-interface.md LABELS v1): ordered block ranks per replay segment, the final climbs as
+    gates without adds (same final frame, at most 32 registers, only registers that still climb), their ranks,
+    the largest number of registers named by one gate.  Plain replay (the mirror has accepted the file)."""
+    cur, G = list(D["start"]), D["A"] + D["B"]
+    rs, most = [], 0
+    for a, b in zip(cuts, cuts[1:]):
+        r = []
+        for g in G[a:b]:
+            most = max(most, len(regs(g)))
+            for x in regs(g):
+                if cur[x] != g[1]:
+                    r.append(dim[g[1]] - dim[cur[x]])
+                    cur[x] = g[1]
+        rs.append(r)
+    by = {}
+    for x, f in enumerate(D["final"]):
+        if cur[x] != f:
+            by.setdefault(f, []).append(x)
+    fins, rF = [], []
+    for f in sorted(by):
+        for i in range(0, len(by[f]), 32):
+            xs = by[f][i:i + 32]
+            fins.append(("out", f, xs[0], [], xs[1:]))
+            rF += [dim[f] - dim[cur[x]] for x in xs]
+    return dict(rs=rs, fins=fins, rF=rF, most=max(most, 32 if fins else 0))
+
+
+def chk_replay(D, dim, pairs, cuts):
+    """E1 (labels), E2 (scatter cut), E6 (price), in the segments given by `cuts`.
+    Returns (states at the cuts, histogram by class, visits per segment)."""
+    h, v, R, fr = D["h"], D["v"], D["R"], D["frames"]
+    n = 2 * v + R
+    start, final, ext = D["start"], D["final"], dict(D["ext"])
+    need(len(start) == len(final) == n, "E0: start / final")
+    for t in range(v):
+        need(fr[start[t]] == [D["ports"][t]] and final[t] == 1, "E1: x start / final")
+        f = fr[final[v + t]]
+        need(start[v + t] == 0 and len(f) == h - 1 and all(par(u & D["ports"][t]) == 0 for u in f), "E1: y start / final")
+    for r in range(2 * v, n):
+        need(start[r] == ext.get(r, 0) and final[r] == 1, "E1: slot start / final")
+    ok = set(pairs)
+    need(len(ok) == len(pairs), "E1: pair list has repeats")
+    cur = list(start)
+    H = {k: Counter() for k in "xysc"}
+
+    def climb(r, f, where):
+        o = cur[r]
+        if o != f:
+            need((o, f) in ok, "E1: climb (%d, %d) is not a tested pair (%s, register %d)" % (o, f, where, r))
+            H[cls(D, r)][dim[f] - dim[o]] += 1
+            seg[dim[f] - dim[o]] += 1
+            cur[r] = f
+    seg, segs = Counter(), []
+    G, nA = D["A"] + D["B"], len(D["A"])
+    states, visits = [], []
+    need(cuts[0] == 0 and cuts[-1] == len(G) and cuts == sorted(cuts), "cut points")
+    for a, b in zip(cuts, cuts[1:]):
+        states.append(list(cur))
+        vs = 0
+        for i in range(a, b):
+            if i == nA:
+                scatter_cut(D, cur, dim, H, seg)
+            g = G[i]
+            rs = regs(g)
+            need(all(0 <= r < n for r in rs) and len(set(rs)) == len(rs), "E3: registers of gate %d" % i)
+            need(i >= nA or all(r < v or r >= 2 * v for r in rs), "E2: y role named in phase A (gate %d)" % i)
+            vs += len(rs)
+            for r in rs:
+                climb(r, g[1], "gate %d" % i)
+        visits.append(vs)
+        if b < len(G):
+            segs.append(seg)
+            seg = Counter()
+    if nA == len(G):
+        scatter_cut(D, cur, dim, H, seg)
+    states.append(list(cur))
+    for r in range(n):
+        climb(r, final[r], "final")
+    segs.append(seg)
+    Hb = {k: dict(sorted(w.items())) for k, w in H.items()}
+    need(Hb == D["blocks"], "E6: block histogram differs from `blocks`")
+    N = sum(r * c for w in H.values() for r, c in w.items())
+    need(N == D["N"] and N + sum(dim[f] for f in ext.values()) == R * h + 2 * v * (h - 1) + D["cst"], "E6: N")
+    need(sum(r * c for r, c in H["c"].items()) == D["cst"], "E6: cst")
+    return states, Hb, visits, [[w[r] for r in range(h + 1)] for w in segs]
+
+
+def scatter_cut(D, cur, dim, H, seg):
+    v = D["v"]
+    if D["scat"][0] == "table":
+        need(len(D["scat"][1]) == v and all(k < len(D["ret"]) for row in D["scat"][1] for k, _ in row), "E2: scatter table")
+    else:
+        need(len(D["ret"]) == D["h"], "E2: one retained total per coordinate (star rule)")
+    for s, f in D["ret"]:
+        need(s >= 2 * v and cur[s] == f, "E2: retained slot %d is not at its frame" % s)
+        H["c"][dim[f]] += 1
+        seg[dim[f]] += 1
+    need(all(cur[v + t] == 0 for t in range(v)), "E2: a y role left frame 0 before the scatter")
+
+
+# ---- scalar side -----------------------------------------------------------------------------------------
+SC = 6            # all scalar entries are kept as integers in units of 1/6
+KINDS = {("x", "s"), ("s", "s"), ("s", "y"), ("x", "y"), ("x", "x"), ("y", "y")}
+
+
+def chk_shape(D):
+    """E3 kinds, E4 bracket"""
+    ysum, piv, ytg = Counter(), set(), set()
+    for ph in "AB":
+        for i, g in enumerate(D[ph]):
+            for t, s, (ng, a, b) in adds(g):
+                kd = (cls(D, s), cls(D, t))
+                need(kd in KINDS and t != s, "E3: gate kind %s -> %s (gate %s%d)" % (kd + (ph, i)))
+                need(ph == "B" or kd in {("x", "s"), ("s", "s")}, "E3: bank gate before the scatter (gate A%d)" % i)
+                if kd == ("y", "y"):
+                    need(SC % b == 0, "E4: denominator beyond sixths")
+                    ysum[s, t] += (-a if ng else a) * (SC // b)
+                    piv.add(s)
+                    ytg.add(t)
+    need(not (piv & ytg), "E4: a pivot is the target of a gate reading y")
+    need(all(x == 0 for x in ysum.values()), "E4: y-reads of a (pivot, target) pair do not cancel")
+    return len(ysum)
+
+
+def scat_row(D, t):
+    sc = D["scat"]
+    if sc[0] == "table":
+        return sc[1][t]
+    return [(k, sc[1] if D["ports"][t] >> k & 1 else sc[2]) for k in range(D["h"])]
+
+
+
+def replay(D, init, count=None):
+    """exact replay through A, scatter, B of sparse vectors with entries in sixths; `init` = register -> {key: 6}"""
+    v = D["v"]
+    reg = [dict(init.get(r, ())) for r in range(2 * v + D["R"])]
+
+    def axpy(t, src, k):
+        ng, a, b = k
+        d = reg[t]
+        for key, u in src.items():
+            w = u * a
+            need(w % b == 0, "E5: an entry needs a denominator beyond sixths (register %d)" % t)
+            w = w // b
+            w = d.get(key, 0) + (-w if ng else w)
+            if count is not None:
+                count[key] += 1
+            if w:
+                d[key] = w
+            else:
+                d.pop(key, None)
+
+    def run(gates):
+        for g in gates:
+            if g[0] == "out":
+                src = dict(reg[g[2]])
+                for t, k in g[3]:
+                    axpy(t, src, k)
+            else:
+                for s, k in g[3]:
+                    axpy(g[2], reg[s], k)
+    run(D["A"])
+    afterA = sum(len(d) for d in reg)
+    tot = [dict(reg[s]) for s, _ in D["ret"]]
+    for t in range(v):
+        for k, cf in scat_row(D, t):
+            if tot[k]:
+                axpy(v + t, tot[k], cf)
+    run(D["B"])
+    return reg, afterA
+
+
+def chk_scalar(D, batches=1):
+    """E5 (+ E7 when `ext` is non-empty).  Returns stats: denominators and largest numerators per class in the
+    units of the spec (x halves, y sixths, slots integers), updates per source batch, entries after A."""
+    v = D["v"]
+    count = Counter()
+    reg, afterA = replay(D, {t: {t: SC} for t in range(v)}, count)
+    need(all(reg[t] == {t: SC} for t in range(v)), "E5: an x role is not restored (X3)")
+    need(all(reg[v + t] == {t: SC} for t in range(v)), "E5: a target does not receive exactly its source (hid)")
+    if D["ext"]:
+        rg, _ = replay(D, {r: {r: SC} for r, _ in D["ext"]})
+        need(all(not rg[v + t] for t in range(v)), "E7: the dirt of an exterior-gauged slot reaches a y role")
+    step = -(-v // batches)
+    per = [sum(count[k] for k in range(lo, min(lo + step, v))) for lo in range(0, v, step)]
+    return dict(updates=sum(count.values()), per_batch=per, afterA=afterA,
+                batches=[(lo, min(lo + step, v)) for lo in range(0, v, step)])
+
+
+def digits(D):
+    """largest |entry| met and denominators per class, by a second replay that watches every write (slow path
+    kept separate from the check): returns {class: (lcm of denominators, largest |numerator| in units 1/den)}"""
+    v = D["v"]
+    den = {"x": 1, "y": 1, "s": 1}
+    mx = {"x": 0, "y": 0, "s": 0}
+    reg = [({r: SC} if r < v else {}) for r in range(2 * v + D["R"])]
+
+    def axpy(t, src, k):
+        ng, a, b = k
+        d, kk = reg[t], cls(D, t)
+        for key, u in src.items():
+            w = d.get(key, 0) + (-(u * a // b) if ng else u * a // b)
+            if w:
+                d[key] = w
+                q = SC // gcd(w, SC)
+                if den[kk] % q:
+                    den[kk] = den[kk] * q // gcd(den[kk], q)
+                if abs(w) > mx[kk]:
+                    mx[kk] = abs(w)
+            else:
+                d.pop(key, None)
+    for g in D["A"]:
+        for t, s, k in adds(g):
+            axpy(t, reg[s], k)
+    tot = [dict(reg[s]) for s, _ in D["ret"]]
+    for t in range(v):
+        for k, cf in scat_row(D, t):
+            axpy(v + t, tot[k], cf)
+    for g in D["B"]:
+        for t, s, k in adds(g):
+            axpy(t, reg[s], k)
+    return {k: (den[k], mx[k] * den[k] // SC if (mx[k] * den[k]) % SC == 0 else "%d/6" % mx[k]) for k in "xys"}
+
+
+def mirror(D, gmax=12000, batches=1, pairs=None, cuts=None):
+    """both checks; returns everything the generator and the dry run need"""
+    dim = chk_frames(D)
+    pairs = derive(D) if pairs is None else pairs
+    work = chk_pairs(D, dim, pairs)
+    cuts = cut_points(D, gmax) if cuts is None else cuts
+    states, H, visits, segH = chk_replay(D, dim, pairs, cuts)
+    ysh = chk_shape(D)
+    S = chk_scalar(D, batches)
+    hist = Counter()
+    for k in "xysc":
+        for r, n in H[k].items():
+            hist[r] += n
+    return dict(dim=dim, pairs=pairs, pair_work=work, cuts=cuts, states=states, H=H, visits=visits, ysh=ysh,
+                scal=S, hist=dict(sorted(hist.items())), segH=segH,
+                lab=label_data(D, dim, cuts))
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/math_check.py b/research/gen4-retiming-entrances-target/vendor/pr276/math_check.py
new file mode 100644
index 0000000000..e3453703bc
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/math_check.py
@@ -0,0 +1,57 @@
+"""Source-bound banked five-stage moments and all47outerconstraints.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+Uses PR234 five-stage architecture and complex baseline, the gen4 helper and
+PR197-derived actual five-stage entrance banks. Inputs must be live verifier outputs.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import importlib.util
+HERE=Path(__file__).resolve().parent
+
+def load(name):
+ p=HERE/(name+'.py');s=importlib.util.spec_from_file_location('banked527_'+name,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+
+def serial(x):
+ if isinstance(x,Q):return str(x)
+ if isinstance(x,dict):return {str(k):serial(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return list(map(serial,x))
+ return x
+
+def hist(x):return Counter({int(k):v for k,v in x.items()if v})
+
+def run(raw,complex_histogram,banks,global_result):
+ cost=load('moment');other=load('base_two_moment');outer=load('outer')
+ assert raw['source_aliases']==0 and raw['physical_R']==16410 and raw['h']==24 and raw['v']==1760
+ H=hist(raw['five_stage_profile']['histogram']);assert H==hist(global_result['paid_histogram'])
+ assert global_result['paid_rank_mass']==sum(k*n for k,n in H.items())==2809600
+ gauges=hist(raw['auxiliary_entrance_rank_histogram']);assert gauges=={20:2200,21:266}
+ assert banks['assignments']==4923000 and banks['gen4_roles']==16410 and banks['physical_replicas']==60
+ assert banks['literal_stock']==1283035 and banks['banks_total']==860635 and banks['charts']==370
+ for a,n in gauges.items():assert H.pop(5*a)==n
+ assert len(H)>0 and min(H.values())>0 and max(H)==50
+ literal={k:n*60 for k,n in H.items()};literal_mass=sum(k*n for k,n in literal.items());literal_W=banks['literal_stock']
+ assert 120*literal_W-literal_mass==60*4400
+ # Divide the literal profile by5 to an integer normalization. The executed
+ # realization is still60replicas, and finite accounting uses its literalstock.
+ assert literal_W%5==0 and all(n%5==0 for n in literal.values())
+ normalized={k:n//5 for k,n in literal.items()};W=literal_W//5;m=120;mass=sum(k*n for k,n in normalized.items())
+ bp=dict(m=m,W=W,histogram=normalized,calls=sum(normalized.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(normalized),normalization=12,physical_replicas=60,literal_stock=literal_W,literal_children=sum(literal.values()),literal_rank_mass=literal_mass)
+ root=cost.certify(normalized,m,W,True);c=Q(int(Q(root['lower'])*10**18),10**18);bm=cost.moment(normalized,m,W,c,True);nextbm=cost.moment(normalized,m,W,c+Q(1,10**18),True);assert bm[1]<1<nextbm[0]
+ fallback=32*m*m*sum(normalized.values())
+ _,upper=other.moment(m,W,list(normalized.items()),c);_,bad=other.moment(m,W,[(1,fallback)],c)
+ lower,_=other.moment(m,W,list(normalized.items()),c+Q(1,10**18));badlower,_=other.moment(m,W,[(1,fallback)],c+Q(1,10**18));assert upper+Q(1,10**16)*bad<1<lower+Q(1,10**16)*badlower
+ CH=hist(complex_histogram);assert sum(CH.values())==361405 and sum(k*n for k,n in CH.items())==1613040
+ cp=dict(m=110,W=14692,histogram=dict(CH),calls=sum(CH.values()),rank_mass=sum(k*n for k,n in CH.items()),deficit=3080,maxchild=max(CH));b=Q(747454944651775,10**18);cm=cost.moment(dict(CH),110,14692,b,False);assert cm[1]<1
+ chain=[Q(384599,10**10)]
+ for _ in range(3):
+  a=(1-c)*c+c*chain[-1];assert chain[-1]<a<c<1-a;chain.append(a)
+ bit=chain[-1];eta=Q(1,10**12);beta=Q(1,10**9);assert bit<(1-beta)*b
+ bridge=dict(proof='PROOF.md',representation='Exact powers with source-bound finite overcharges',semantic=dict(G=dict(base=2,exponent=30000),E=dict(base=2,exponent=100000),B_upper=dict(base=2,exponent=100001),C0=dict(base=2,exponent=210000),C1=1,strict_literal_gap=1,induction_gap_lower=1),rows=dict(coefficient=20161,degree=10**6,suffix_slope=4*10**6,degree_gap=Q(10**6)-Q(51*20161,25)))
+ assert bridge['rows']['degree_gap']>0
+ q=bit*(1-2*eta);minimum=(1-eta)*q/(1+q);ticks=minimum*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+ assembly=outer.assembly(bit,b,bridge,k,eta=eta,beta=beta);assert len(assembly['strict_constraints'])==47 and len(assembly['margins'])==7 and min(assembly['strict_constraints'].values())>0
+ try:outer.assembly(bit,b,bridge,k+Q(1,10**18),eta=eta,beta=beta)
+ except AssertionError:pass
+ else:raise AssertionError('Adjacentkappaadmitted')
+ return serial(dict(status='PASS_BANKED_FIVE_STAGE_GEN4_EXACT_MOMENTS_AND_OUTER47',mathematics=dict(bit_profile=bp,complex_profile=cp,bit_coarse=c,complex_coarse=b,bit_moment_interval=bm,complex_moment_interval=cm,next_bit_grid_excluded=nextbm,independent_base_two_pass=True,ordinary_bootstrap_chain=chain,finite_bridge=bridge,assembly=assembly,kappa=k,kappa_decimal=cost.decimal(k),kappa_scientific=format(float(k),'.15e'),binding='bit'),adjacent_grid_point_rejected=True))
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/moment.py b/research/gen4-retiming-entrances-target/vendor/pr276/moment.py
new file mode 100644
index 0000000000..1e43aaeaca
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/moment.py
@@ -0,0 +1,114 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v=1760,h=24):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell==4400
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=24,copy_rank=22,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m120 admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    result['source_owned_gauges_not_banked']={19:3,2:26,4:2}
+    print(json.dumps(result,indent=2))
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR210-coordinated-crossover-NOTICE b/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR210-coordinated-crossover-NOTICE
new file mode 100644
index 0000000000..d08cb66ac7
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR210-coordinated-crossover-NOTICE
@@ -0,0 +1,431 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
+
+Fourth finite bootstrap refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+This arithmetic refinement builds on PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf
+level. The 302 frame overrides, completed banks, scalar words and upstream
+assistance disclosures are inherited, not newly attributed to this work.
+The Apache-2.0 license and all preceding notices remain applicable.
+
+PR211 plateau frame refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The additional seven equal-frame component moves build directly on Rohan
+Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347,
+prepared with Anthropic Claude assistance. Its original notice is preserved
+byte-for-byte in search/PR211-NOTICE. The offline certificate package and
+independent stage-private bank admission derive from Dugongue's PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices,
+licenses, source pins and all upstream AI disclosures remain applicable.
+
+The final refinement also includes seeded bidirectional cascade search after
+the seven initial component moves. Exact canonical subspace comparison
+records 274 changed operations beyond PR211. Search, integration and replay
+were prepared with substantial OpenAI Codex assistance.
+
+Shared rank-18 gauges and two donor substitutions (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The new actual gauge/read chronology, gauged-donor handoff, shared target
+transitions, rank6 residual banks and donor substitutions extend the same
+PR200/PR211 word and PR207/PR197 completed-bank framework. All original
+licenses, notices, authorship and upstream AI disclosures remain in force.
+
+Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR230-NOTICE b/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR230-NOTICE
new file mode 100644
index 0000000000..bc1cfc52a1
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR230-NOTICE
@@ -0,0 +1,441 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
+
+Fourth finite bootstrap refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+This arithmetic refinement builds on PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf
+level. The 302 frame overrides, completed banks, scalar words and upstream
+assistance disclosures are inherited, not newly attributed to this work.
+The Apache-2.0 license and all preceding notices remain applicable.
+
+PR211 plateau frame refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The additional seven equal-frame component moves build directly on Rohan
+Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347,
+prepared with Anthropic Claude assistance. Its original notice is preserved
+byte-for-byte in search/PR211-NOTICE. The offline certificate package and
+independent stage-private bank admission derive from Dugongue's PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices,
+licenses, source pins and all upstream AI disclosures remain applicable.
+
+The final refinement also includes seeded bidirectional cascade search after
+the seven initial component moves. Exact canonical subspace comparison
+records 274 changed operations beyond PR211. Search, integration and replay
+were prepared with substantial OpenAI Codex assistance.
+
+Shared rank-18 gauges and two donor substitutions (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The new actual gauge/read chronology, gauged-donor handoff, shared target
+transitions, rank6 residual banks and donor substitutions extend the same
+PR200/PR211 word and PR207/PR197 completed-bank framework. All original
+licenses, notices, authorship and upstream AI disclosures remain in force.
+
+Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable.
+
+Equal-frame plateau refinement on PR210's 471-source word (2026-10-10)
+Prepared by sennemmi with substantial OpenAI Codex assistance. The deterministic
+frame search, 19 operation retimings, exact price update and repository
+integration extend eumemic's PR210 head
+df95878d11190518e45ef9717c9ee05011f88ace. They do not claim the inherited
+source word, shared gauges, completed banks or upstream proof framework.
+All PR200, PR197, PR202/193, PR207, PR211, PR216 and PR210 attributions,
+licenses and AI disclosures remain in force; the repository's Apache-2.0
+license is unchanged.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR230-PROVENANCE.json b/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR230-PROVENANCE.json
new file mode 100644
index 0000000000..ff39579387
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/notices/PR230-PROVENANCE.json
@@ -0,0 +1,27 @@
+{
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/230",
+  "author": "sennemmi",
+  "assistance": "Substantial OpenAI Codex assistance, as disclosed by the original contributor.",
+  "imported_head": "fee4c05b91d4cdebc0b9d8cbb266a98069928a9a",
+  "scope": "Nineteen operation-frame changes inherited from the independently verified492-source composition and replayed with493sourcealiases,82equal-response groups,seven integer-response groups andfour signed echelon groups. Original search,result,framewitness andnotice remain byte-preserved.",
+  "original_files": {
+    "NOTICE": "7dfbad087ee49b74fd5075d517eaa263c5dd3d4fbd4c69bfba34ee1cb55e837f",
+    "joint-plateau-result-prdf958.json": "cd5731260af0daa62952c3b82debdb26cfb79e62a5c615688d8ccac6f7a95fcc",
+    "joint-plateau-search-prdf958.py": "80f3f9e8ba1972b911b701a4de4f811d6d25c9b4c0bc6282d640c2f44caafd0d",
+    "opframe-bases.json": "387ae1b5e69004426d094f4947b29c532d60fdf31f727f5e8830468278fe0f92"
+  },
+  "final_frame_sha256": "9a2bba5c72aebc9ee4f21e59b10ce810b2da98a1fa1748fbc44c50a080e584ff",
+  "raw_child_delta": {
+    "1": -27,
+    "2": -36,
+    "3": 51,
+    "4": -30,
+    "7": 30,
+    "8": -15,
+    "9": -15,
+    "10": 24,
+    "11": -24,
+    "12": 30,
+    "15": -15
+  }
+}
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/notices/README.md b/research/gen4-retiming-entrances-target/vendor/pr276/notices/README.md
new file mode 100644
index 0000000000..7af7caa733
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/notices/README.md
@@ -0,0 +1,15 @@
+# Retained upstream notices
+
+These notices are retained verbatim from eumemic's source527 package. They carry the contributor credits and
+AI-assistance disclosures for the package machinery reused here: the scalar program, emitters, parity fusion,
+census, banks, and the moment, prime and finite checks.
+
+| File | Origin |
+| --- | --- |
+| `source527-loader-NOTICE.md` | source527's source loader |
+| `PR230-NOTICE`, `PR230-PROVENANCE.json` | sennemmi's PR230 operation-frame witnesses, including the PR211 and PR216/207 lineage |
+| `base-bit-PR200-PR202-NOTICE` | Chafik Boukhalfa's PR200/PR202 base bit package |
+| `PR210-coordinated-crossover-NOTICE` | eumemic's PR210 coordinated-crossover package |
+
+The source471/source527 helper data they describe is not used by the gen4 word. The notices are kept for the
+inherited code and attribution.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/notices/base-bit-PR200-PR202-NOTICE b/research/gen4-retiming-entrances-target/vendor/pr276/notices/base-bit-PR200-PR202-NOTICE
new file mode 100644
index 0000000000..ba5ea80dd7
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/notices/base-bit-PR200-PR202-NOTICE
@@ -0,0 +1,399 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/notices/source527-loader-NOTICE.md b/research/gen4-retiming-entrances-target/vendor/pr276/notices/source527-loader-NOTICE.md
new file mode 100644
index 0000000000..47090d6e93
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/notices/source527-loader-NOTICE.md
@@ -0,0 +1,11 @@
+# Attribution
+
+This focused preparation adapter is distributed under Apache-2.0. It preserves the original source files, headers and notices in the supplied source roots.
+
+- eumemic: the current PR210 operation frames, joint gauges, donor assignments, source borrowing and retimed source471 schedule at df95878d11190518e45ef9717c9ee05011f88ace; original OpenAI Codex assistance disclosure retained.
+- Chafik Boukhalfa (chafreaky): the PR200 physical bit construction and terminal interfaces, carried by the consumed PR202 base at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, eumemic, Douglas Colkitt, OpenAI, and preceding contributors retain the attribution and assistance disclosures recorded in the supplied original notices.
+
+The new contribution here is the explicit public-root binding, source-derived terminal records, exact semantic comparison and independent raw-path recount. It does not claim authorship of the inherited helper, frames, compiler or theorem interfaces, nor review or endorsement by the named contributors.
+
+Assisted with ChatGPT.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/outer.py b/research/gen4-retiming-entrances-target/vendor/pr276/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/parity_transform.py b/research/gen4-retiming-entrances-target/vendor/pr276/parity_transform.py
new file mode 100644
index 0000000000..30528550be
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/parity_transform.py
@@ -0,0 +1,143 @@
+"""F2 payload identity elision and exact nested address-MOVE fusion.
+The inherited signed source decoder is retained as producer evidence.
+All odd-prime address projectors and routes remain unchanged.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time
+if not __debug__:raise SystemExit('assertions required')
+
+def transform(records):
+    out = array('i')
+    pending = {}
+    chains = []
+    removed = Counter()
+    hist = Counter()
+    merged = 0
+    maxchain = 0
+    uses = Counter()
+
+    def flush(a):
+        nonlocal merged, maxchain
+        if a in pending:
+            old, new, rank, count, first, last = pending.pop(a)
+            if rank:
+                hist[rank] += 1
+            out.extend((0, a, old, new, rank, 0))
+            merged += count - 1
+            maxchain = max(maxchain, count)
+            if count > 1:
+                chains.append(dict(stream=a, old=old, new=new, rank=rank, moves=count, first=first, last=last))
+    for index in range(0, len(records), 6):
+        op, a, b, c, f, z = records[index:index + 6]
+        if op == 1 and c % 2 == 0:
+            removed[c] += 1
+            continue
+        if op == 0:
+            assert z == 0
+            if a in pending:
+                old, prev, rank, count, first, last = pending[a]
+                assert prev == b, ('disconnected movechain', a, prev, b)
+                pending[a] = (old, c, rank + f, count + 1, first, index // 6)
+            else:
+                pending[a] = (b, c, f, 1, index // 6, index // 6)
+            continue
+        assert op in (1, 2, 3)
+        flush(a)
+        flush(b)
+        if op == 1:
+            uses[a] += 1
+            uses[b] += 1
+        elif op == 2:
+            hist[z] += 1
+            uses[a] += 1
+            uses[b] += 1
+        out.extend((op, a, b, c, f, z))
+    for a in sorted(pending):
+        flush(a)
+    return (out, dict(removed_even_adds=dict(removed), removed_even_add_count=sum(removed.values()), merged_move_count=merged, max_chain=maxchain, fused_chains=len(chains), paid_histogram=dict(sorted(hist.items())), paid_calls=sum(hist.values()), paid_rank_mass=sum((r * n for r, n in hist.items())), surviving_additions=sum((out[k] == 1 for k in range(0, len(out), 6))), output_records=len(out) // 6, unused_streams=[i for i in range(19930) if not uses[i]], stream_use_counts=dict(uses)), chains)
+
+def run(producer,output_dir=None):
+    begun=time.monotonic();W,C=producer['W'],producer['C'];v=W.v;n=19930;assert n==2*v+len(producer['context']['regs'])
+    old=producer['records'];out,stats,chains=transform(old);oldmeta=producer['physical']
+    assert stats['removed_even_add_count']==1510656 and stats['surviving_additions']==626360
+    assert stats['paid_rank_mass']==425742 and stats['merged_move_count']==0
+    initial=producer['initial_state'];ZERO,FULL=producer['ZERO'],producer['FULL']
+    # Independent required-frame census: ignore all original MOVE instructions.
+    # Use only surviving gate operands, copy sources and mathematical endpoints.
+    needs={i:[] for i in initial};copies=Counter();copy=None
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==1 and c%2:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert copy is not None
+        elif op==2:
+            assert copy is None;copy=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert copy==(a,b,c);copy=None
+    assert copy is None and copies=={22:24}
+    final={i:FULL for i in initial}
+    for t in range(v):final[v+t]=W.register(W.module.kernel([C.cov[t]],W.h)[0])
+    census=Counter(copies);per_role={};pairs=set()
+    for i,oldf in initial.items():
+        H=Counter()
+        for f in needs[i]+[final[i]]:
+            assert C.sub(oldf,f);rank=C.dimf[f]-C.dimf[oldf]
+            if rank:H[rank]+=1
+            pairs.add((oldf,f));oldf=f
+        per_role[i]=H;census.update(H)
+    assert census==Counter({int(r):c for r,c in stats['paid_histogram'].items()})
+    # Read back the actual annihilator rows as a separate reflected ledger.
+    # A(new) annihilating B(old) states new^perp <= old^perp exactly.
+    reflected_pairs=0;endpoint_frames={f for pair in pairs for f in pair};nondeg_bases=set()
+    for f in endpoint_frames:
+        assert len(C.B[f])==C.dimf[f] and len(C.A[f])+C.dimf[f]==24
+        key=tuple(map(tuple,C.B[f]))
+        if key not in nondeg_bases:
+            assert C.nondeg(f),'singular required endpoint frame'
+            nondeg_bases.add(key)
+    for oldf,newf in sorted(pairs):
+        assert len(C.A[newf])<=len(C.A[oldf])
+        assert all(W.module.dot(a,b)==0 for a in C.A[newf]for b in C.B[oldf])
+        reflected_pairs+=1
+    # Validate the actual transformed instruction stream against its own frames.
+    state=dict(initial);copy=None;used=set(initial.values());hist=Counter();cat=Counter();coeff=Counter();centers=[];count=0
+    scalar=hashlib.sha256();tagged=hashlib.sha256();category_names=oldmeta['category_names']
+    def event(d,row):d.update(json.dumps(row,separators=(',',':')).encode());d.update(b'\n')
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c) and C.dimf[c]-C.dimf[b]==f
+            # Complement reflection reverses containment and preserves the gap.
+            assert (24-C.dimf[b])-(24-C.dimf[c])==f
+            state[a]=c;used.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert c%2 and state[a]==state[b]==f and a!=b
+            kind=category_names[z];source=copy['source']if b==n else b
+            event(scalar,[a,source,c]);event(tagged,[a,b,c,f,kind]);count+=1;cat[kind]+=1;coeff[abs(c)]+=1;used.add(f)
+        elif op==2:
+            assert copy is None and b==n and state[a]==c and f==ZERO and z==22
+            state[b]=f;hist[z]+=1;copy=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and copy is not None and (a,b,c)==(copy['source'],copy['temporary'],copy['frame']) and state[b]==f==ZERO
+            copy.update(after_event=count,scatter_reads=count-copy['first_event']);assert copy['scatter_reads']==220
+            centers.append(copy);copy=None;del state[b]
+    assert copy is None and state==final and hist==census
+    assert count==626360 and coeff=={1:624600,3:1760} and len(centers)==24
+    delta=Counter(hist);delta.subtract(Counter({int(r):c for r,c in oldmeta['paid_histogram'].items()}));delta={r:c for r,c in delta.items()if c}
+    assert delta=={}
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for i,H in per_role.items():(sourceH if i<v else targetH if i<2*v else internalH).update(H)
+    receipt=dict(status='PASS_FRESH_PARITY_FUSION_AND_INDEPENDENT_REQUIRED_FRAME_CENSUS',removed_even_add_count=stats['removed_even_add_count'],remaining_payload_additions=count,merged_moves=stats['merged_move_count'],chains=chains,local_histogram_delta=delta,both_reflected_ledgers=True,unchanged_all_input_output_frames=True,unique_required_frame_pairs=len(pairs),explicit_reflected_annihilator_pairs=reflected_pairs,nondegenerate_endpoint_bases=len(nondeg_bases),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),producer_scalar_sha256=oldmeta['scalar_projection_sha256'],producer_tagged_sha256=oldmeta['tagged_scalar_sha256'],transform_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest())
+    meta=dict(oldmeta);meta.update(status='PASS_PHYSICAL_GEN4_PARITY_FUSED_EXACT_FRAME_AND_SCALAR_PROJECTION',scalar_projection_sha256=scalar.hexdigest(),tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-24,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=hashlib.sha256(json.dumps(C.B[f],separators=(',',':')).encode()).hexdigest())for f in sorted(used)],parity_transform=receipt,producer_physical_emitter_sha256=oldmeta['physical_emitter_sha256'],physical_emitter_sha256=receipt['transform_sha256'])
+    result=dict(producer);result.update(records=out,physical=meta,result=meta,producer_physical=oldmeta,parity_census=receipt)
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True)
+        (p/'records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/'physical.json').write_text(json.dumps(meta,indent=2)+'\n')
+        (p/'parity.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print('PASS parity fusion',count,'ADDs',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/portable_bit.py b/research/gen4-retiming-entrances-target/vendor/pr276/portable_bit.py
new file mode 100644
index 0000000000..9d0355827f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/portable_bit.py
@@ -0,0 +1,55 @@
+"""Fresh gen4 local physical and complete five-stage global lowering (source527 integration, rebound).
+
+Inherited source-bound PR234 lowering, integrated with source527 using
+substantial OpenAI Codex assistance. Cover expansion is phase-major.
+"""
+from pathlib import Path
+import hashlib,importlib.util,sys,time,json
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+
+def load(name,path):
+ spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m
+
+def phase_major_templates(lower):
+ """Expand all cover classes for each yielded phase before advancing."""
+ for stage in range(5):
+  yield('helper',stage,lambda s=stage:lower.iter_stage(s))
+  if stage in(1,2,4):
+   i={1:0,2:1,4:2}[stage]
+   yield('idle',i,lambda i=i:lower.iter_idle(i))
+   yield('bridge',i,lambda i=i:lower.iter_bridges(i))
+ yield('completion',0,lower.iter_completions)
+ yield('terminal_exchange',0,lower.iter_exchanges)
+
+def run(prepared_context=None,raw=None,output_dir=None,run_geometry=True,package_root=None):
+ begun=time.monotonic();package=Path(package_root or HERE).resolve()
+ if prepared_context is None:prepared_context=load('portable527_prepare',package/'prepare.py').prepare()
+ if raw is None:raw=load('portable527_raw_ledger',package/'raw_ledger.py').run(prepared_context)
+ physical_module=load('portable527_physical',package/'code/physical527.py');global_module=load('portable527_global',package/'code/global_lowering.py')
+ context=dict(prepared_context);source=context['SOURCE_TEXT']
+ producer_output=Path(output_dir)/'producer-bit' if output_dir is not None else None
+ producer=physical_module.run(context,source,output_dir=producer_output)
+ physical_run=load('portable527_parity',package/'parity_transform.py').run(producer,output_dir=output_dir)
+ raw=load('portable527_parity_raw',package/'raw_ledger.py').rebind_parity(raw,physical_run['parity_census'])
+ physical=physical_run['physical'];physical['source_head']=raw['source_head']
+ assert physical['source_heads']==raw['source_aliases']and physical['independent_dirty_registers']==raw['physical_R']
+ assert physical['paid_histogram']=={int(k):v for k,v in raw['one_stage_helper_histogram_including_copies'].items()}
+ assert physical['initial_independent_entrances']=={int(k):v for k,v in raw['auxiliary_entrance_rank_histogram'].items()}
+ lower=global_module.Lowerer(physical_run['records'],physical_run);global_result=global_module.verify(lower,raw)
+ assert global_result['paid_histogram']=={int(k):v for k,v in raw['five_stage_profile']['histogram'].items()}
+ global_result.update(source_head=raw['source_head'],scalar_projection_sha256=physical['scalar_projection_sha256'],local_tagged_sha256=physical['tagged_scalar_sha256'],weighted_stage_additions=global_result['opcode_counts'][global_module.ADD],bridge_additions=global_result['opcode_counts'][global_module.BRIDGE],total_weighted_additions=global_result['opcode_counts'][global_module.ADD]+global_result['opcode_counts'][global_module.BRIDGE],m=global_module.M,global_live=global_module.LIVE,external_work_family=global_module.WORK)
+ phases=[(name,index)for name,index,method in phase_major_templates(lower)]
+ assert phases==[('helper',0),('helper',1),('idle',0),('bridge',0),('helper',2),('idle',1),('bridge',1),('helper',3),('helper',4),('idle',2),('bridge',2),('completion',0),('terminal_exchange',0)]
+ geometry=None
+ if run_geometry:geometry=load('portable527_geometry',package/'code/geometry527.py').run(context,global_module)
+ result=dict(context=context,W=context['W'],C=context['C'],records=physical_run['records'],lower=lower,raw=raw,physical=physical,global_result=global_result,geometry=geometry,phase_major_schedule=phases,scalar_observer_result=physical_run['scalar_result'],seconds=time.monotonic()-begun)
+ if output_dir is not None:
+  out=Path(output_dir);out.mkdir(parents=True,exist_ok=True)
+  for name in('physical','global_result','geometry','raw'):
+   if result[name]is not None:(out/(name+'.json')).write_text(json.dumps(result[name],indent=2)+'\n')
+ return result
+
+def summary(result):
+ return dict(status='PASS_PORTABLE_GEN4_FRESH_PHYSICAL_GLOBAL_AND_GEOMETRY',source_head=result['raw']['source_head'],local_record_count=len(result['records'])//6,scalar_projection_sha256=result['physical']['scalar_projection_sha256'],physical_tagged_sha256=result['physical']['tagged_scalar_sha256'],global_result=result['global_result'],geometry=result['geometry'],phase_major_schedule=result['phase_major_schedule'],seconds=result['seconds'])
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/portable_complex.py b/research/gen4-retiming-entrances-target/vendor/pr276/portable_complex.py
new file mode 100644
index 0000000000..c068be3e1c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/portable_complex.py
@@ -0,0 +1,151 @@
+#!/usr/bin/env python3
+"""Fresh complex label, scalar, splice and finite-guard checks from primary inputs.
+No saved PASS receipts, workstation paths, network or Lean rebuild are required.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha256
+from math import prod
+from pathlib import Path
+import gzip, importlib.util, json, sys
+sys.dont_write_bytecode = True
+
+PIN='f010392c923279e3dd59ef3aa5fedad23affc5fd'
+CHRONOLOGY=['stage0','stage1','climbA','bridgeA','stage2','climbB','bridgeB','stage3','stage4','final_climbs','bridgeC','terminal_shifts','signed_exchange']
+
+def need(ok, why):
+    if not ok: raise ValueError(why)
+
+def module(root, name):
+    spec=importlib.util.spec_from_file_location('portable_'+name,root/'code'/(name+'.py'))
+    result=importlib.util.module_from_spec(spec);spec.loader.exec_module(result)
+    return result
+
+def finite_guard(m, b, basis):
+    p=m['parameters'];l=m['ledger'];dim=p['m'];R=p['R'];h=p['h'];W=p['W_live']
+    need((dim,R,h,W)==(110,9412,22,14692),'complex family changed')
+    scalar=max(b[o]['totals']['real_component_primitive_steps'] for o in ['forward','backward'])
+    macros=max(b[o]['totals']['scalar_macros'] for o in ['forward','backward'])
+    scalar5=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps']
+    physical=W+R+h+1
+    adapters=8*(macros+m['checks']['invocation_calls']+p['invocation_live']+h)+32*dim
+    outside=8*(l['idle_calls']+6*p['v']+physical)+32*dim
+    compiler=64*(dim+1)**3
+    local=scalar+adapters*compiler
+    pervertex=scalar5+12*p['v']+(5*adapters+outside)*compiler+64*physical
+    group=(1<<(dim-1+(dim//2-1)**2))*prod((1<<(2*i))-1 for i in range(1,dim//2))
+    live_stock=group*W;physical_stock=group*physical;s=group*l['rank_mass']
+    K=group*pervertex+64;router=compiler*(K+1)*(physical_stock+1)**2
+    G,E,C0=1<<30000,1<<100000,1<<210000;B=s+E
+    literal=2*G*physical_stock**2+8*s+4*physical_stock+4+32*dim
+    need(local==213063694563472 and local<1<<48 and K<1<<6050,'fresh local/global bill')
+    need((group.bit_length(),live_stock.bit_length(),physical_stock.bit_length(),s.bit_length())==(5995,6009,6010,6016),'fresh cover/work stock')
+    need(router<G and literal<E and B<1<<100001,'fresh router/literal guard')
+    need(2*B*(dim-l['max_child'])-s-E==127*B,'completed-child induction')
+    need(32*dim*B*B<C0 and 2*B+18<C0 and 2*l['max_child']<dim,'semantic and half-shrink guard')
+    row=live_stock.bit_length()+9909+252;rowphysical=physical_stock.bit_length()+9909+252
+    need(row<=rowphysical<20161,'external rows')
+    gap=Q(10**6)-Q(51,25)*20161;need(gap>0,'row reserve gap')
+    need(2*(dim*(dim-1)+3*dim+dim+3*dim*(dim-1)//2+dim+1)+2*dim<compiler,'explicit quadratic-phase lowering')
+    for e in range(1,100001):need((e-1).bit_length()+1<=2*e,'grid-depth endpoint')
+    def validate(c):
+        need(c['physical']==c['live']+R+h+1,'missing work stock')
+        need(dim*c['live']-l['rank_mass']==l['deficit'],'wrong live normalization')
+        need(c['copy_calls']==5*h,'missing center child')
+        need(c['denominators']==[1,2,3,6],'unrecorded denominator')
+        need(physical_stock<1<<c['stock_exponent'],'false stock bound')
+    original=dict(physical=physical,live=W,copy_calls=5*h,denominators=[1,2,3,6],stock_exponent=6010)
+    validate(original);controls={}
+    for name,key,value in [('missing_tableau','physical',physical-R),('scratch_in_live','live',physical),('dropped_center','copy_calls',5*h-1),('unrecorded_divisor','denominators',[1,2,3,5,6]),('stale_stock_bound','stock_exponent',5208)]:
+        bad=dict(original);bad[key]=value
+        try:validate(bad)
+        except ValueError:controls[name]=True
+        else:raise ValueError('finite guard mutation accepted: '+name)
+    return dict(status='PASS_FRESH_EXACT_COMPLEX_GUARD',m=dim,live_per_vertex=W,physical_per_vertex=physical,
+        coefficient_denominators=[1,2,3,6],semantic_C1=1,complete_local_group_upper=local,
+        complete_local_group_bits=local.bit_length(),global_logical_groups_bits=K.bit_length(),
+        simple_global_logical_bound_exponent=6050,router_bits=router.bit_length(),G_exponent=30000,
+        literal_charge_bits=literal.bit_length(),E_exponent=100000,required_C0_bits=(32*dim*B*B).bit_length(),
+        C0_exponent=210000,induction_gap_multiple_of_B=127,group_bits=group.bit_length(),
+        live_stock_bits=live_stock.bit_length(),physical_stock_bits=physical_stock.bit_length(),
+        rank_mass_bits=s.bit_length(),live_row_coefficient=row,physical_row_overcharge_coefficient=rowphysical,
+        retained_row_coefficient=20161,retained_row_gap=str(gap),controls=controls,
+        binary_basis_count_tests=basis.gl_count_test(),
+        odd_denominator_grid='2^(-P)3^(-G(D+1)); no return rounding')
+
+def run(package_root=None, progress=lambda text:None):
+    root=Path(package_root).resolve() if package_root else Path(__file__).resolve().parent
+    labels=module(root,'complex_labels');scalar=module(root,'complex_scalars')
+    splice=module(root,'complex_splice');basis=module(root,'complex_basis')
+    pinpath=root/'inputs/complex/source-pins.json'
+    if not pinpath.is_file():pinpath=root/'inputs/complex-source-pins.json'
+    pins=json.loads(pinpath.read_text());verified={};by_upstream={}
+    for relative,spec in pins['files'].items():
+        path=root/relative;got=sha256(path.read_bytes()).hexdigest()
+        need(got==spec['sha256'],'primary proof input changed: '+relative)
+        verified[relative]=got;by_upstream[spec['upstream']]=(path,spec)
+    cp=pins['certificate'];z=(root/cp['path']).read_bytes()
+    need(sha256(z).hexdigest()==cp['compressed_sha256'],'compressed certificate binding')
+    raw=gzip.decompress(z);need(sha256(raw).hexdigest()==cp['uncompressed_sha256'],'expanded certificate binding')
+    verified[cp['path']]=sha256(z).hexdigest();c=json.loads(raw)
+    progress('Checking every complex source label and paid child.')
+    checks=labels.replay_label_counts(c)
+    H=Counter({int(k):5*n for k,n in checks['invocation_histogram'].items()})
+    v,R,h=c['v'],c['R'],c['h'];dim=5*h;W=4*v+R
+    for rank in [2*h-2,h-1,2*h+2,4]:H[rank]+=2*v
+    ledger=dict(histogram={str(k):n for k,n in sorted(H.items())},calls=sum(H.values()),
+        rank_mass=sum(k*n for k,n in H.items()),max_child=max(H),deficit=dim*W-sum(k*n for k,n in H.items()),
+        copy_calls=5*h,idle_calls=8*v)
+    need((ledger['calls'],ledger['rank_mass'],ledger['deficit'],ledger['max_child'])==(361405,1613040,3080,46),'fresh five-stage ledger')
+    source_path,source_spec=by_upstream['Work/GCert/Chain/NetDef.lean'];lines=source_path.read_text().splitlines();refs={}
+    for name in ['x01','y01','x12','y12','x23','y23','x34','y34','sfin','term']:
+        indices=[i for i,line in enumerate(lines) if name+' :' in line];need(indices,'missing exact matrix field '+name)
+        i=indices[-1] if name=='sfin' else indices[0]
+        text=' '.join(x.strip() for x in lines[i:i+(2 if name=='sfin' else 1)])
+        refs[name]=dict(source='Work/GCert/Chain/NetDef.lean',anchor=name+' :',line=i+1,declaration_line=text,
+            url='https://github.com/jacobalansussman/wht-power-saving-lean/blob/'+PIN+'/Work/GCert/Chain/NetDef.lean#L'+str(i+1))
+    m=dict(source_pin=PIN,parameters=dict(h=h,m=dim,v=v,R=R,W_live=W,invocation_live=2*v+R),
+        ledger=ledger,checks=checks,chronology=CHRONOLOGY,source_frame_equalities=refs)
+    progress('Deriving both complex scalar words and temporary lifetimes.')
+    A=scalar.flat(c['A']);B=scalar.flat(c['B']);b={};life={}
+    for orientation in ['forward','backward']:
+        b[orientation]=scalar.bill(scalar.inv_schedule(orientation,A,B,c))
+        life[orientation]=scalar.lifecycle(scalar.inv_schedule(orientation,A,B,c))
+    need((b['forward']['totals']['real_component_primitive_steps'],b['backward']['totals']['real_component_primitive_steps'])==(1492984,1549456),'fresh scalar expansion')
+    b['scratch_lifecycle_checks']=life;b['template_tests']=scalar.toy_checks()
+    b['five_invocation_scalar_primitives_per_vertex']=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps']
+    b['scratch']=dict(live_roles=W,physical_roles_per_cover=W+R+h+1,additional_recursive_calls=0,extra_external_row_coordinate=False)
+    progress('Merging scalar events, exact frames and all final climbs.')
+    programs={};controls=[]
+    for orientation in ['forward','backward']:
+        events=list(splice.emit(c,orientation));programs[orientation]=splice.validate(events,c,orientation,m,b)
+        controls.extend(splice.controls(events,c,orientation,m,b))
+    g=splice.global_contract(m);splice.validate_global(g,m)
+    mutations=[('wrong_helper_owner',lambda x:x['stage_recipe'][1].__setitem__('helper_owner','s1^(-1)(d)')),
+        ('rank_only_frame',lambda x:x['exact_frame_bindings']['x23'].__setitem__('declaration_line','same rank only')),
+        ('scratch_alias',lambda x:x['scratch_namespace'].__setitem__('centers',[14691,14713])),
+        ('wrong_live_normalization',lambda x:x.__setitem__('recursive_volume_denominator',24127)),
+        ('free_RAM',lambda x:x.__setitem__('primitive_policy','free_RAM')),
+        ('missing_tableau',lambda x:x.__setitem__('physical',14715))]
+    for name,fn in mutations:
+        bad=deepcopy(g);fn(bad)
+        try:splice.validate_global(bad,m)
+        except ValueError as error:controls.append(dict(name=name,rejected=True,reason=str(error)))
+        else:raise ValueError('global mutation accepted: '+name)
+    progress('Recomputing complex cover, router, precision and row inequalities.')
+    precision=finite_guard(m,b,basis)
+    need(labels.scalar_word([(1,0,1),(0,1,-1),(0,2,1),(3,1,-1),(1,0,1),(3,1,1),(0,2,-1),(2,3,-1),(3,2,1),(1,3,-1),(2,0,1)])==[[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]],'global scalar signed exchange')
+    return dict(status='PASS_FRESH_COMPLEX_LABEL_SCALAR_SPLICE_PRECISION',five_stage_histogram=ledger['histogram'],
+        label_checks=checks,ledger=ledger,scalar_bill=b,
+        splice=dict(program=programs,global_contract=g,controls=controls,source_pin=PIN,certificate_sha256=cp['compressed_sha256']),
+        precision_guard=precision,input_pins=verified,
+        inherited_theorem_dependencies=[
+            'Pinned hAi,hBi,hx,hy,hid establish the full scalar identity; this is not a fresh Lean or full scalar-column replay.',
+            'Pinned Lab.inv dirty lifting, exact gwinB/G0..G4 geometry, owner bijections and NetCert composition are inherited source theorems.',
+            'Retained general Clifford synthesis, compact complete-stream tape primitives, common-grid precision and complete-row proofs remain analytic dependencies.',
+            'The finite operational recipe is regenerated and checked; no astronomical cover enumeration or universal tape-machine execution is claimed.'])
+
+if __name__=='__main__':
+    result=run(progress=lambda text:print(text,file=sys.stderr))
+    print(json.dumps(result,indent=2))
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/prepare.py b/research/gen4-retiming-entrances-target/vendor/pr276/prepare.py
new file mode 100644
index 0000000000..952bd727b4
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/prepare.py
@@ -0,0 +1,63 @@
+"""Clean gen4 preparation: the arc-aware local-design paired-cube bit word with its physical layer.
+
+The bit word (gen4bit/selected/bit) is admitted by PR200's unmodified physical-word classes
+(gen4bit/bit/word.py, base_word.py) over PR168-v4's unmodified exact checker. The context exposes
+the interface of the retained source527 scalar program (scalar/word.py, byte-identical); every
+source527-specific selection (source loans, aggregation/rank/echelon groups, fresh and paired
+source reads, terminal sinks, early mixes, retimed prefixes) is empty for this word.
+No payload execution occurs here.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from types import SimpleNamespace
+import hashlib,importlib.util,json,sys
+sys.dont_write_bytecode=True
+HERE=Path(__file__).resolve().parent
+WORD_SHA='e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42'
+
+def prepare():
+ G=HERE/'gen4bit'
+ spec=importlib.util.spec_from_file_location('gen4_pr200_physical_word',G/'bit/word.py');module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+ W=module.Candidate();C=W.C
+ # Exact decoder/geometry of the virtual graph, and every changed operation frame and alias handoff.
+ C.decoder();C.geometry();W.exact_frames()
+ W.changed_frames=[i for i,(a,b)in enumerate(zip(W.original_opframe,W.opframe))if a!=b]
+ W.endframe={r:W.opframe[ii[-1]]for r,ii in W.role_ops.items()}
+ assert W.R==17904 and len(W.pairs)==1494 and len(W.gauge)==3960 and W.v==1760 and W.h==24 and len(W.changed_frames)==1802
+ assert all(0<=W.readtime[s]<=W.first[s]for s in W.gauge)
+ assert all(W.last[d]<W.readtime[b]and C.sub(W.endframe[d],W.gauge[b]['frame'])for b,d in W.pairs)
+ assert all(not(set(W.gauge)&set(W.ops[i][:2]))for i in W.phase1)
+ # The centre prefix is exactly phase one, executed in its listed order.
+ schedule=dict(events=[dict(kind='gate',op=i)for i in W.phase1],center_prefix_events=list(range(len(W.phase1))),deferred_ops=[],new_phase1=list(W.phase1),new_untouched_roles=[])
+ selection=[];gauge_selection=[];new_gauge_selection=[];extra_selection=[];new_phase_roles=set()
+ borrow={};by_source={};omitted=set();early={};gauge_borrow={}
+ kpair={e['passive']:e for e in W.k['entries']};assert len(kpair)==880
+ adj=[{}for _ in range(W.R)]
+ for r,s in zip(W.g['roots'],W.w['rootroles']):
+  for t in r['targets']:adj[s][t]=adj[s].get(t,0)+1
+ for i in reversed(W.phase1+W.rest):
+  a,b,_=W.ops[i]
+  for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c
+ assert adj==W.adjoint()
+ assert all(set(adj[s])==set(z['targets'])for s,z in W.gauge.items()),'gauge targets are exact response supports'
+ terminal=[];removed=set();deletedroots=set();bywrite={};afterwrite={}
+ regs=sorted(set(W.phys.values())-set(borrow)-removed);idx={r:2*W.v+j for j,r in enumerate(regs)}
+ assert len(regs)==W.R-len(W.pairs)==16410
+ at=defaultdict(list)
+ for b in W.order:at[W.readtime[b]].append(b)
+ deliveries=defaultdict(list)
+ for e in W.k['entries']:deliveries[e['deliver_after_root']].append(e)
+ m=SimpleNamespace(W=W,C=C,schedule=schedule,selection=selection,gauge_selection=gauge_selection,new_gauge_selection=new_gauge_selection,
+  extra_selection=extra_selection,new_phase_roles=new_phase_roles,borrow=borrow,by_source=by_source,omitted=omitted,early=early,
+  gauge_borrow=gauge_borrow,kpair=kpair,adj=adj,terminal=terminal,removed=removed,deletedroots=deletedroots,bywrite=bywrite,
+  afterwrite=afterwrite,regs=regs,idx=idx,at=at,deliveries=deliveries,deferred=[],
+  agg=[],role_groups={},target_group={},read_frames={},extra_byrole={},rankgroups=[],rankowner={},echelon=[],eowner={},
+  fresh={},pair_byalias={},pair_bydirty={},pair_selection=[],zero=W.register([]),source_head='gen4')
+ # Names the retained scalar program reads from its preparation namespace.
+ m.Counter,m.defaultdict,m.json,m.sys,m.hashlib,m.Path=Counter,defaultdict,json,sys,hashlib,Path
+ m.SOURCE_TEXT=(HERE/'scalar/word.py').read_text()
+ assert hashlib.sha256(m.SOURCE_TEXT.encode()).hexdigest()==WORD_SHA
+ m.input_pins={str(p.relative_to(HERE)):hashlib.sha256(p.read_bytes()).hexdigest()for p in sorted(G.rglob('*'))if p.is_file()}
+ m.portable_source_pins=dict(m.input_pins)
+ return dict(m.__dict__)
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/prime_check.py b/research/gen4-retiming-entrances-target/vendor/pr276/prime_check.py
new file mode 100644
index 0000000000..a7151e2807
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/prime_check.py
@@ -0,0 +1,67 @@
+"""Recompute exact determinants for every physically consumed gen4 basis.
+Based on PR234's prime coverage check; substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from pathlib import Path
+import hashlib,importlib.util,json,time
+HERE=Path(__file__).resolve().parent
+
+def basis_hash(basis):return hashlib.sha256(json.dumps(basis,separators=(',',':')).encode()).hexdigest()
+
+def validate_record(row,dimension,determinant,allowed_primes):
+    assert type(row['dimension'])is int and type(row['determinant'])is int and type(row['residual'])is int,'exact integer witness fields'
+    assert row['dimension']==dimension and row['determinant']==determinant!=0,'exact determinant mismatch or singular basis'
+    assert 0<row['residual']<2**80,'retained prime lower bound'
+    product=row['residual']
+    for prime,exponent in row['factors'].items():
+        p=int(prime);assert p in allowed_primes and type(exponent)is int and exponent>0,'factor shape';product*=p**exponent
+    assert product==abs(determinant),'factor identity'
+
+def run(context,physical,progress=lambda text:None):
+    started=time.monotonic();w,c=context['W'],context['C']
+    p=HERE/'prime_witnesses.py';spec=importlib.util.spec_from_file_location('source527_exact_prime_validator',p);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+    required=set(w.opframe)|set(w.w['source_frame'])|set(w.w['root_frame'])|{w.w['full_frame'],w.register([])}
+    required.update(g['frame']for g in w.gauge.values())
+    for e in w.k['entries']:required.update((e['mix_frame'],e['deliver_frame']))
+    for t in range(w.v):required.add(w.register(w.module.kernel([c.cov[t]],w.h)[0]))
+    required.update(g['frame']for g in context['agg']+context['rankgroups']+context['echelon'])
+    required.update(r['mix_frame']for r in context['pair_selection'])
+    used=set();groups={}
+    for row in physical['used_frames']:
+        f=row['frame_id'];assert f not in used;used.add(f)
+        h=basis_hash(c.B[f]);assert h==row['basis_sha256'] and len(c.B[f])==c.dimf[f]==row['dimension'],'fresh physical basis identity'
+        groups.setdefault(h,f)
+    assert {basis_hash(c.B[f])for f in required}<=set(groups),'base and added transform coverage'
+    determinants={};largest=0;prime_factors=set();witnesses={}
+    for j,(h,f)in enumerate(sorted(groups.items())):
+        B=c.B[f];s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[k]for k,y in enumerate(B)]for i,x in enumerate(B)]
+        det=module.det(gram);powers,residual=module.factor_witness(det)
+        row=dict(dimension=len(B),determinant=det,residual=residual,factors={p:e for p,e in powers.items()if e})
+        validate_record(row,len(B),det,module.PRIMES);prime_factors.update(map(int,row['factors']));witnesses[h]=row
+        determinants[h]=det;largest=max(largest,abs(det).bit_length())
+        if j and j%5000==0:progress('Validated '+str(j)+' exact basis determinants')
+    ranks=Counter();bundle_bases=set()
+    for role,g in w.gauge.items():
+        if role in w.donor or role in context['borrow']:continue
+        a=g['dim'];h=basis_hash(c.B[g['frame']]);d=determinants[h]
+        assert 0<5*a<120 and d!=0;ranks[a]+=1;bundle_bases.add(h)
+        assert abs(d**5)==abs(d)**5
+    assert ranks=={20:2200,21:266}and len(bundle_bases)==370
+    assert 2*120**3*10**16<2**80
+    from copy import deepcopy
+    controls=[]
+    def reject(name,call):
+        try:call()
+        except AssertionError:controls.append(name)
+        else:raise AssertionError('invalid witness accepted: '+name)
+    first=next(iter(groups));row=witnesses[first];det=determinants[first]
+    missing=dict(witnesses);missing.pop(first)
+    def coverage(actual,wanted):assert set(actual)==set(wanted),'complete current basis coverage'
+    reject('missing current basis',lambda:coverage(groups,missing))
+    changed=deepcopy(row);changed['determinant']=det+1;reject('incorrect determinant',lambda:validate_record(changed,row['dimension'],det,module.PRIMES))
+    changed_factor=deepcopy(row);changed_factor['residual']+=1;reject('incorrect factor identity',lambda:validate_record(changed_factor,row['dimension'],det,module.PRIMES))
+    singular=deepcopy(row);singular['determinant']=0;reject('singular basis',lambda:validate_record(singular,row['dimension'],module.det([[1,2],[1,2]]),module.PRIMES))
+    huge=deepcopy(row);huge['residual']=2**80;reject('residual at prime lower bound',lambda:validate_record(huge,row['dimension'],det,module.PRIMES))
+    noninteger=deepcopy(row);noninteger['residual']=float(row['residual']);reject('noninteger residual',lambda:validate_record(noninteger,row['dimension'],det,module.PRIMES))
+    return dict(status='PASS_FRESH_ALL_ACTUAL_GEN4_BASIS_DETERMINANTS_AND_FIVEFOLD_BUNDLES',unique_bases=len(groups),current_frame_ids=len(used),basis_inventory_sha256=hashlib.sha256(json.dumps(sorted(groups),separators=(',',':')).encode()).hexdigest(),maximum_determinant_bits=largest,prime_factors=sorted(prime_factors),all_remaining_factors_below_2_power_80=True,independent_entrances=sum(ranks.values()),bundled_unique_bases=len(bundle_bases),entrance_rank_counts=dict(ranks),controls=controls,physical_inventory_bound=True,seconds=time.monotonic()-started,scope='Every actual physical basis of the gen4 word is freshly evaluated over exact integers; all source, gauge, operation, root, partner-mix, delivery and cap frames are covered. Five disjoint copies inherit nondegeneracy; compiler and prime supply remain theorem dependencies.')
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/prime_witnesses.py b/research/gen4-retiming-entrances-target/vendor/pr276/prime_witnesses.py
new file mode 100644
index 0000000000..7f16d93030
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/prime_witnesses.py
@@ -0,0 +1,99 @@
+"""Exact finite prime exclusions for the selected new rational bit frames.
+
+For integer basis B and G=I-J/9, det(9 B G B^t) is a nonzero integer.
+Excluding its prime divisors and 2,3,5 makes the reduced frame nondegenerate
+over every odd local ring Z/q^w. Projector denominators divide this determinant
+times fixed powers of 3. Retained frames retain their old exclusion witnesses.
+The selected q is an arbitrarily large fixed prime chosen after this finite
+set; this is not verification at a preselected numeric q.
+"""
+from pathlib import Path
+import argparse,gzip,hashlib,json,sys
+
+HERE=Path(__file__).resolve().parent
+
+def det(A):
+    A=[list(r) for r in A];n=len(A)
+    if not n:return 1
+    sign=1;previous=1
+    for k in range(n-1):
+        pivot=next((i for i in range(k,n) if A[i][k]),None)
+        if pivot is None:return 0
+        if pivot!=k:A[k],A[pivot]=A[pivot],A[k];sign=-sign
+        p=A[k][k]
+        for i in range(k+1,n):
+            for j in range(k+1,n):
+                v=A[i][j]*p-A[i][k]*A[k][j]
+                assert v%previous==0
+                A[i][j]=v//previous
+            A[i][k]=0
+        previous=p
+    return sign*A[-1][-1]
+
+PRIMES=(2,3,5,7,11,13,17,19,23,29,31)
+
+def factor_witness(determinant):
+    assert type(determinant) is int and determinant != 0
+    residual=abs(determinant);powers={}
+    for prime in PRIMES:
+        power=0
+        while residual%prime==0:residual//=prime;power+=1
+        powers[str(prime)]=power
+    validate_factor(determinant,powers,residual)
+    return powers,residual
+
+def validate_factor(determinant,powers,residual):
+    assert type(determinant) is int and determinant != 0
+    assert set(powers)==set(map(str,PRIMES))
+    assert all(type(x) is int and x>=0 for x in powers.values())
+    assert type(residual) is int and 0<residual<2**80
+    reconstructed=residual
+    for p in PRIMES:reconstructed*=p**powers[str(p)]
+    assert reconstructed==abs(determinant)
+
+def certificate(word=None):
+    if word is None:
+        from word import Candidate
+        word=Candidate()
+    C=word.C;h=word.h
+    used=set(word.opframe)|set(word.w['source_frame'])|set(word.w['root_frame'])|{word.w['full_frame']}
+    used.update(z['frame'] for z in word.w['gauges'])
+    for e in word.k['entries']:used.update((e['mix_frame'],e['deliver_frame']))
+    groups={}
+    for frame in sorted(used):
+        B=C.B[frame]
+        key=json.dumps(B,separators=(',',':'));groups.setdefault(key,[]).append(frame)
+    records=[]
+    for key,frames in sorted(groups.items()):
+        B=json.loads(key);s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[j] for j,y in enumerate(B)] for i,x in enumerate(B)]
+        determinant=det(gram);powers,residual=factor_witness(determinant)
+        records.append(dict(basis_sha256=hashlib.sha256(key.encode()).hexdigest(),
+            frame_ids=frames,dimension=len(B),cleared_gram_determinant=determinant,
+            small_prime_powers=powers,remaining_factor=residual,gram_denominator_power_of_9=len(B)))
+    controls=[];zeros={str(p):0 for p in PRIMES}
+    for name,args in (('zero determinant',(0,zeros,1)),('incorrect factor identity',(15,zeros,1)),
+        ('residual above retained prime lower bound',(2**80+7,zeros,2**80+7))):
+        try:validate_factor(*args)
+        except AssertionError:controls.append(name)
+        else:raise ValueError('Invalid prime witness accepted: '+name)
+    return dict(status='PASS exact prime witnesses for every used physical frame',h=h,
+        source_commit='4a3c769e5c5430e7114c4d3e099ff34664677f17',
+        input_sha256={str(p.relative_to(HERE.parents[2])):hashlib.sha256(p.read_bytes()).hexdigest() for p in word.input_paths},
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),
+        stripped_primes=list(PRIMES),frame_witnesses=records,unique_used_bases=len(records),
+        total_used_frames=len(used),total_operation_frames=len(word.changed_frames),
+        maximum_determinant_bits=max(abs(z['cleared_gram_determinant']).bit_length() for z in records),
+        all_remaining_factors_below_retained_prime_lower_bound=True,adverse_controls=controls,
+        rule='Every q>2^80 avoids every nonzero used-frame determinant, so the original prime range is unchanged.',
+        scope='Exact integer cleared-Gram factors for all physical frames including every changed operation, gauge, source, root, partner-mix, delivery and ambient frame. Uniform split-rank and fallback arguments remain the retained local-ring interface.')
+
+def main():
+    assert not sys.flags.optimize
+    ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args()
+    record=certificate();target=HERE/'prime-witnesses.json.gz'
+    if args.write:target.write_bytes(gzip.compress((json.dumps(record,sort_keys=True,separators=(',',':'))+'\n').encode(),mtime=0))
+    else:assert record==json.loads(gzip.decompress(target.read_bytes())),'Exact prime witnesses changed'
+    print(json.dumps({k:v for k,v in record.items() if k!='frame_witnesses'}))
+
+if __name__=='__main__':main()
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md b/research/gen4-retiming-entrances-target/vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md
new file mode 100644
index 0000000000..42a585d742
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md
@@ -0,0 +1,126 @@
+# Portable five-stage BIT finite bill
+
+The executable `finite_check.run` accepts the freshly reconstructed source
+ledger, physical tags, independently checked scalar projection, exact current
+basis-prime result, exact moment calculation and optional global lowering
+result. It reads no saved execution receipt. Source expectations are checked
+against those computed objects, not substituted for them. The complete
+package runner is responsible for generating its inputs before this call.
+
+## Quantifiers and inherited primitive hypotheses
+
+Fix this candidate and an eligible odd prime q>2^80 before the input widths
+n,w are chosen. All represented determinant and route exclusions lie in
+{2,3,5,7}. The primitive constant C may depend on q, the fixed source recipe,
+the finite bootstrap level and the retained primitive implementations. It
+does not depend on n,w, ancestor values or unrelated spectator widths except
+through logical volume V.
+
+The three byte-pinned public sources supplied here are
+`three-stage-cover-bit.tex`, `three-stage-cover-rows.tex`, and
+`copied-centers-lemma.tex`. Their exact-tape, completed ordinary-leaf and
+complete-stream hypotheses are retained. All high matrix fibers are batched;
+prefix descriptor preparation has fixed polynomial cost in w and is paid
+over the complete q^w target fiber. Unrelated spectators use ripple counters.
+Fresh child role fields never enter the ancestor weight descriptor. Finite
+low-type tables, initialization and sequential scans are charged in C.
+There is no unit-cost random-access oracle or new numerical Turing-machine
+constant requirement.
+
+## Actual finite recipe
+
+Let m=120, W=23,683, E=495,304, v=1,760, R=16,643, d=m^2 and
+J=20v+10R+4v=208,670. The last 4v=7,040 families pay the explicit final
+complete-stream exchange; they are not equal-frame payload shears.
+
+The check derives from the fresh word 12,858,690 weighted additions or
+21,787,770 unit additions, including all six bridge families. Its
+cancellation-free prefix lift is
+64*37,623^3*9,430,154^2=303,094,329,841,208,644,962,256,113,408<2^98.
+No old defining-integer endpoint is imposed on the F2 supplier.
+
+The actual rational 48-dimensional route is reconstructed, eliminated and
+inversely replayed: 195 additions, 44 swaps and 27 scalings, with denominator
+set {1,2,3,6}. A missing addition fails reconstruction. Coordinate
+permutations and embedding give the other ports and stages.
+
+Per route, pay at most 23,707*|GL_120(F_q)| low-role transpositions and
+16*(d+1)^2 high affine factors. Per good edge, pay at most 8m^2+8 elementary
+normalizer wrappers. The same compiler pays all exterior completions.
+There are 120 copied-center episodes. Their recursive rank-22 calls and
+their scalar reads are already included in E and the scalar count; their
+copy/erase and parking passes are separately paid by the complete-stream
+primitive, using one additional work stream.
+
+For a bad edge with N=2m=240, the exact inherited Gaussian fallback uses at
+most 6N(N-1)+3N+6(N-1)=346,314<32m^2=460,800 children. Keep the entire
+larger allowance in the moment. Coefficient preparation uses only unit
+pivot inversions. Allocate 128N^3 ring operations per edge per low class:
+four 8N^3 elimination/inversion allocations and sixteen 2N^3 matrix products
+give 64N^3; the remaining 64N^3 pays extraction, copying, generic tests,
+factor output and the bad-branch elimination. Matrix bit costs and descriptor
+arithmetic are paid by the inherited primitive theorem. Invertibility testing
+of each candidate low matrix additionally gets 16m^3 operations.
+
+Overcharging every finite recipe item over every low matrix gives
+
+    B(q) <= [unit+J*16(d+1)^2+J*(W+24)+E*(8m^2+8)
+             +E*128(2m)^3+16m^3+120+E+1]*q^14400
+         = 1,568,901,757,016,837*q^14400 < q^14401.
+
+These are explicit ring/recipe counts, not single-step machine costs. All
+fixed-tape, table, setup and selector constants stay in C_primitive, giving
+the normalized toll C*n+C*w^(1-a_old) after increasing one finite C.
+No recursive child is absorbed into this nonrecursive constant.
+
+## Weighted induction and rows
+
+Set c=704197288590873/10^18 and tau=1-c. Exact interval recomputation,
+adding the entire 10^-16*32m^2 fallback envelope per edge, proves
+
+    1-mu_tau > 774/10^21,
+    1-mu_1 = 107421874442783/69383789062500000 > 0.
+
+For the retained recurrence
+T(n,w)<=sum_r c_r*T(r*floor(n/120),w)+C*n+C*w^(1-a_old),
+take A=C*(1+1/(1-mu_1)+1/(1-mu_tau)). Induction bounds T by
+A*(n+n^tau*w^(1-a_old)): the linear and stopped gaps separately pay the
+two tolls; the leaves follow A>=C. Floors only decrease the child sizes.
+
+The maximum ratio is 5/6, so four levels halve. The depth bound
+4*ceil(log2(max(2,n))) changes stock, not the one-level moment. Paying all
+24 temporary roles gives per-level log_q stock below 14400w+1. Add the
+inherited old-leaf reserve. The new contribution is at most
+57,604w*ceil(log2(max(2,n))). Borrow and restore these complete high digits;
+successive residuals and the two-call ordinary wrapper reuse the reserve.
+One outer row padding factor is below two; binary-radix padding costs less
+than q^2 in logical volume. The temporary roles never enter the denominator W.
+
+## Finite ordinary bootstrap and cutoff
+
+Starting with completed ordinary a0=384599/10^10, set beta=c and repeat
+a_(j+1)=(1-c)c+c*a_j exactly three times. The finite result is
+
+    a3=704197288358392787581160456097840009769165126434639147437106139267359/10^72.
+
+At each stage, the paid exponents are 1-c, 1-a_(j+1), c with a logarithm,
+and c(1-a_j). The exact positive gaps are c-a_(j+1),
+1-a_(j+1)-c, 1-a_(j+1)-c(1-a_j), and 1-c (for row fitting).
+
+Choose a finite integer C>=1 dominating that stage's already fixed primitive,
+recurrence, wrapper, row, setup, padding and previous ordinary constants.
+Let delta be the minimum positive gap and
+
+    L=ceil(max(1,36/delta^2,2*(4+ceil(log2 C))/delta)), e0=2^L.
+
+For e>=e0, C(1+log2 e)e^(-delta)<=1/16. Indeed for t=log2 e,
+log2(1+t)<=3sqrt(t)<=delta*t/2 and log2 C+4<=delta*t/2.
+Thus every lower-order toll is covered and the borrowed high part fits.
+Below e0 use the previously completed ordinary algorithm. A finite next
+constant is C_large+C_old*2^(L*(a_(j+1)-a_j)). This choice is sequential,
+not circular, and uniform in the input and complete spectators.
+
+This proves the finite-accounting and ordinary-bootstrap step at the same
+conditional theorem level as the retained public baseline. It does not claim
+an independent proof of those inherited primitives, a measured universal
+machine constant, or execution at every input width.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/INTEGRATED_PROOF.md b/research/gen4-retiming-entrances-target/vendor/pr276/proof/INTEGRATED_PROOF.md
new file mode 100644
index 0000000000..c624da6c5c
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/INTEGRATED_PROOF.md
@@ -0,0 +1,87 @@
+# Source-bound five-stage compositional candidate
+
+9 October 2026. This is an isolated research admission branch. Its executable checks immutable finite receipts and recomputes exact scalar moments, a finite ordinary bootstrap, and all 47 balanced outer inequalities. It additionally binds fresh public-source bit preparation, raw-ledger construction, and the complete globally lowered physical event stream. It does not repeat the exhaustive F2 column proof, run the Lean kernel or universal tape machine, or claim Mac qualification or publication.
+
+## 1. Meaning of admission here
+
+The branch is an explicit conjunction of constructive source theorems and finite source-bound evidence. It does not replace any proof with a numerical root or infer source correctness from a PASS string. The new family names are `new5stageF2` and `baseline5stageComplex`; the old dimension-72 entry point and written bounds are kept byte-identical. The branch has no general-purpose dimension override.
+
+The executable's semantic guards reject a wrong source, omitted copied centers, a rank-only complex frame contract, a work/live denominator substitution, omitted final climbs, incorrect reverse-copy lowering, and a one-level bit-halving substitution. The source lock identifies the exact evidence, code, and primary proof files consumed. The more detailed emitted-program verifiers exercise local chronology and addresses, beyond these top-level schema controls.
+
+## 2. Raw source471 provenance
+
+The saved raw helper ledger pins an older screen.py. The older screen bytes are unavailable; no byte-delta assertion is made. The rebind verifier reruns the current exact geometry/ledger construction with all writes suppressed and a hash-verified cached certificate in place of its redundant network fetch. Every semantic field, all 471 source paths, and all 1,760 target paths agree. The saved ledger is not rewritten.
+
+The apparent target-prefix duplication is resolved by the actual chronology: screen.py removes the two latest loan prefixes for its predecessor positive controls; raw_ledger.py puts those two prefixes back. There are exactly eight restored target reads. Current-source dependency hashes and the canonical semantic-payload digest make this equivalence independently inspectable. The sole historical pin exception is specifically this screen.py field and is allowed only with the exact rebind witness.
+
+## 3. Local bit helper and global lowering
+
+The source is PR210 df95878d11190518e45ef9717c9ee05011f88ace. The independently recorded local scalar word has 2,569,626 weighted events. Its projection is fixed by SHA256 e74e43692685ad5f716b41b363acb8b443c2c90096634a55f0e3728980713944. Both literal forward and signed inverse pass all 20,163 F2 columns, including arbitrary targets and 16,643 independent dirty helpers. The 471 borrowed sources are source aliases, never extra independent dirty coordinates.
+
+The tagged physical word has digest 614f19da4288021cd5c10a575ec7759c069962a6030bf30edb047573ed76edf6 and realizes the telescope Dout M Din^-1. Its input frames are X:Pq, Y:0, Z:sigma and output frames X:H, Y:H-Pq, Z:H. Thus a completed invocation has no data/helper cross blocks and each independent helper residual is D_(H-sigma). This is a full arbitrary-input operator identity, not just zero-dirt testing.
+
+The five-stage compiler maps every local live index through the stage owner injection, maps every local temporary to external family 23,683, and applies the stage's data or helper cover bijection. The active source/target pairs are (X1,Y1), (Y1,X1), (X1,Y1), (Y2,X2), (X2,Y2). The unused pair stays parked. A data route is right multiplication by the exact rational rho_i,S; a helper route is the whole-block exchange tau_i. Both are bijections of the eligible GL cover. They are charged address movements, not dense payload arithmetic.
+
+Cover expansion is strictly phase-major: complete every cover class in stage i before starting the next routed stage or boundary phase. The same rule applies separately to idle, bridge, completion and terminal-exchange phases. Running all five stages for one class before proceeding to another class would be incorrect because rho and tau refer to other classes. The callable stage and boundary iterators specify the phases; a flattened one-class-per-phase template is not a class-major execution schedule. The admission contract rejects that alternative loop ordering.
+
+For backward stages the compiler reverses the complete local event order, negates scalar coefficients, and replaces local P by H-P. A copied-center block is lowered afresh: copy the original at H-U, transform the copy to H, perform reverse signed scatter, and erase it. It is forbidden to invert an erased temporary. Every original center also retains its complementary live climb. Copy/live index injectivity is checked for all stage orientations.
+
+The global lowering artifact must emit bridges, idle children, independent gauge completions, and the final signed bank exchange. That exchange is an explicitly paid complete-stream role permutation, not a same-frame shear. A stage-descriptor string alone does not meet this obligation.
+
+## 4. Rational five-window geometry and prime eligibility
+
+Take H=Q^24, G=I-J/9 and a triple line q*. Its projector has denominator 6; coordinate permutations supply the port isometries. The two-block involution rho_i,S fixes the two port lines and exchanges their complementary spaces. With Q_i the direct sum of the first i copied complements, the frame is D_[g rho_i,S(P direct_sum Q_i)rho_i,S^-1 g^-1]. The four elementary two-block projector identities imply all eight bank boundary equalities. Rational complements are I-P.
+
+The exact rational partial swap is D_P=[[I-P,P],[P,I-P]]. It is involutory. Every same-frame scalar gate telescopes exactly, all idle transitions are nested actual projectors, and D_I D_Pq=D_(I-Pq) gives the terminal all-data address endpoint after the scalar exchange. No Pauli or Fourier phase claim is imported from the complex compiler into this bit proof.
+
+For each independent physical helper, the five routed residuals occupy different H_i. Their supported projectors have pairwise zero products. Their product is D_(I-sum_i sigma_i), so one paid child D_(sum_i sigma_i) completes D_I. This is one correction for each helper, not a packing of unrelated dirty rows. The 2,279 independent entrances have ranks {12:18,13:48,18:13,20:2200}; the 31 source-owned gauge entrances receive no extra completion.
+
+All 26,750 used physical frame IDs (26,380 distinct bases) have exact determinant witnesses. Their factors lie in {2,3,5,7}; the 231 distinct gauge-bundle bases use {2,3,5}. Window-map denominators also use {2,3,5}. Hence every retained q>2^80 preserves these ranks. General GL charts use gPg^-1, not a recomputed Euclidean orthogonal projection.
+
+The weighted generic normalizer allows every proper rank, including 60,65,90,100 in dimension120. Its cleared pivot-polynomial degree is at most m r(r+1)/2 < m^3. Thus the bad fraction is at most2m^3/q<10^-16. Each bad edge retains the full invertible local-ring residual and is paid 32m^2=460,800 rank-one fallback children. No field elimination at nonunit pivots is substituted.
+
+## 5. Exact bit ledger and ordinary finite recurrence
+
+One invocation has 95,789 positive-rank children and rank mass435,846. Its24 rank22 center copies are included once, as are each original center's live climbs. With H this histogram,
+
+n5 = 5H + 3520(delta4+delta23+delta46+delta50)
+     +18delta60+48delta65+13delta90+2200delta100.
+
+Thus m=120, W=23,683, calls495,304, mass2,837,560, deficit4,400. Work streams do not enlarge the live moment denominator. Five invocations retain all120 rank22 centers.
+
+The counted finite-bit adapter pays the literal scalar word, six bridge families, weighted good-edge wrappers, bad-class residuals, copy/read/erase, class routing, selector arithmetic, and fixed-tape movement. Its retained primitive theorem fixes the eligible prime and finite source recipe before varying width, so its finite constant may depend on that prime and recipe. It cannot depend on width, ancestor payload values or unrelated spectators except through complete volume. This is the correct quantifier order; an invented numerical Turing-machine constant is unnecessary.
+
+The largest child ratio is5/6. Three levels do not halve and four do: (5/6)^4=625/1296<1/2. The same one-level weighted moment induction remains valid; the factor4 is used only in depth/descriptor/borrowed-row bounds. Even paying24 simultaneous temporaries gives physical stock23,707 per GL cover vertex and log_q Wphysical(w)<14400w+1. The resulting internal log_q row charge is at most4ceil(log2(max(2,n)))(14400w+1), plus the old-leaf reserve. High digits are borrowed and restored internally; this is not a new external q-adic group factor.
+
+The defining-integer lift need not equal the older supplier's decoder endpoint. A safe cancellation-free prefix bound is64*37623^3*9430154^2<2^98. It uses neither signed integer restoration nor commutation between stage-dependent decoder channels. F2 payload exactness does not require complex floating precision.
+
+Let c=704197288590873/10^18. The freshly enclosed full bit moment, including all bad fallback charges, has a strictly positive gap. Start from the retained completed ordinary leaf a0=384599/10^10. Three finite levels with atom exponent beta=c give
+
+a_(j+1)=(1-c)c+c a_j,
+a3=.000704197288358392787581160456097840009769165126434639147437106139267359.
+
+At every level a_j<a_(j+1)<c<1-a_(j+1). The actual finite-cutoff witness binds the positive moment and lower-order toll gaps to the new finite recipe. This is not an infinite limiting bootstrap or a packed-profile substitution.
+
+## 6. Complex source, complete splice and finite guard
+
+The complex source is f010392c923279e3dd59ef3aa5fedad23affc5fd. The published gcert/1 gzip and expanded JSON identities are checked directly. Its pinned scalar identities and GBridge2 matrix equalities are reused as source theorems, including phases; no same-rank substitute or changed-185 helper is admitted.
+
+The source-defined old-response and cleanup maps are realized by filtered, reversed and transposed literal helper words. Their scalar projections are checked against complete schedule hashes. Old-response uses a9,412-stream temporary tableau, cleared before all recursive children. The coefficient work stream is also cleared after use. The emitted label/scalar splice preserves13,798 phaseA transitions,46,937 phaseB transitions, and9,412 final climbs, totaling70,147 live transitions. It retains22 center children. Final climbs occur after B, followed by exact final-frame adapters and then cleanup.
+
+The five-stage source theorem supplies all ten exact matrix fields x01/y01 through x34/y34, sfin and term, the actual cover owner bijections, all idle banks and final signed exchange. The complete finite compiler uses the retained two-rank-zero-factor construction around each exact recursive C^r child. Rank-zero phase/permutation operations are charged selected-bit and complete-stream tape primitives, not free RAM lookups.
+
+The exact scalar primitive counts are1,492,984 forward and1,549,456 backward, totaling7,577,864 for three forward plus two backward invocations. All361,405 recursive children, including110 rank20 centers, remain charged. The profile has m110, W14692, mass1,613,040, deficit3,080 and maxchild46.
+
+Physical work stock is24,127|O(110,2)|, with6010 bits; live recursion stock has6009 bits. The proved local operation bill is below2^48 and the complete fixed-program bound below2^6050. Router and literal guards fit G=2^30000 and E=2^100000. Coefficients use only denominators1,2,3,6, so the exact common grid2^-P 3^-G(D+1) introduces no return rounding. Completed child semantics give C1=1, induction gap127B, and C0=2^210000>32mB^2. The complex half-shrink requirement is preserved:2*46<110.
+
+The physical row overcharge16,171 remains below20,161. Degree1,000,000 and suffix slope4,000,000 retain exact row gap23,971,789/25. These constants come from the changed stock and counted program, not from simply replacing72 by110 in the old guard.
+
+## 7. Fresh outer47 arithmetic and completion boundary
+
+Use complex saving747454944651775/10^18, strictly inside its freshly re-enclosed moment. The bit saving is the exact finite a3 above. Both moment gaps exceed7.7e-19. With eta=10^-12 and stopping fraction10^-9, the unchanged retained balanced assembly produces47 positive strict constraints and7 margins.
+
+The isolated candidate is kappa=703701743496697/10^18, or.000703701743496697. The minimum outer margin exceeds it by approximately7.3899e-19. This arithmetic value exceeds the retained frontier. Exact rational gaps, rather than printed decimals, are the evidence.
+
+The certificate remains a receipt-bound compositional research candidate with explicit source-theorem dependencies. The clean loader consumes 22 pinned public files and agrees in 23 exact semantic components with the audited context. Its fresh raw ledger and complete five-stage histogram agree; an empty-directory extraction passes all 10 focused tests. The clean-root global emitter regenerates all 12,858,690 weighted additions, 495,304 paid children, 120 fresh copies and erasures, 2,279 helper completions, and 3,520 final pair exchanges. Source-bound global lowering, exact h24 geometry, clean-loader qualification, and finite closure supplements are all mandatory before the entry point emits its PASS certificate.
+
+These fresh computations do not pretend that the inherited exhaustive F2 columns, exact determinant archive, or complex source theorems were independently reproved. Full portable packaging and Mac qualification remain separate delivery checks. The pinned comparison frontier is df95878's .000694782719690783; the subsequently reported public head31f4ccc1c16c538749845f9244b24747f1cf93dd claims .000695191451687307, which is a separate comparator pending independent validation and is not substituted into this source freeze.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/PARITY-CONTRACT.md b/research/gen4-retiming-entrances-target/vendor/pr276/proof/PARITY-CONTRACT.md
new file mode 100644
index 0000000000..fad6150b1f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/PARITY-CONTRACT.md
@@ -0,0 +1,45 @@
+# Parity-even payload gate removal: inherited contract audit
+
+Conclusion: removing an even-coefficient pointwise payload ADD is valid for the bit supplier. The odd-prime address arithmetic remains unchanged. A new paid profile still requires the actual filtered word and full frame schedule; this conclusion alone does not certify a new kappa value.
+
+## Primary source evidence
+
+The bundled, unmodified primary section [`primary/03-motifs.tex`](primary/03-motifs.tex) states the following. Its exact source, attribution, and file hashes are recorded in [`primary/PROVENANCE.md`](primary/PROVENANCE.md).
+
+* Line50: in the bit construction scalars lie in F2.
+* Lines149–177: replace a scalar by an array in R^Omega, with R the scalar ring of the network. Common R-linear frames give the exact operator `D_out S_Omega D_in^-1`.
+* Around line223: the scalar domain need not equal the label field. Bit labels are rational subspaces even though the payload scalars are binary.
+* Lines483–493: rational-address frames are F2-linear permutations of array entries; the bit network uses pointwise XOR gates.
+
+The byte-pinned [`copied-centers-lemma.tex`](copied-centers-lemma.tex) in this package opens with its scalar restoration identity explicitly over F2. Its copy contract preserves the complete role stream, controls and spectators; each copy's frame change and erasure remain paid.
+
+The retained PR234 [`INTEGRATED_PROOF.md`](INTEGRATED_PROOF.md), line56, explicitly says: "The defining-integer lift need not equal the older supplier's decoder endpoint" and the majorant "uses neither signed integer restoration nor commutation between stage-dependent decoder channels." The package's signed integer decoder checks are stronger supplier evidence; the inherited bit interface does not impose their particular integer endpoint on a newly synthesized F2-equivalent word.
+
+The retained weighted bit theorem, [`three-stage-cover-bit.tex`](three-stage-cover-bit.tex), uses the odd-prime local ring Z/q^w for address fields and weighted address interchanges. Its rational projectors, unit-pivot tests, route matrices and fallback coefficients are address geometry. They are not the F2 payload ADD coefficients.
+
+## Operator proof
+
+Fix the finite complete address set Omega and let one stream be a vector in F2^Omega. A payload gate is `x_a <- x_a + (c mod2) x_b`. For even c this is the identity on every input, including arbitrary correlated dirty streams and spectators. Removing any number of these identity gates leaves the complete scalar operator S_Omega unchanged. Negative odd coefficients and coefficient3 also reduce to1, though the simplest experimental witness can retain their original signed integer representatives.
+
+Retain each original input/output frame and every remaining gate's original common frame. The common-frame identity then gives the same `D_out S_Omega D_in^-1` for the filtered word. In particular, every independent helper still has its required partial-swap residual and the existing completed-bank proof still applies. No integer identity of the new lift is needed to conclude this F2 operator identity.
+
+## Safe frame compression
+
+Deleting an ADD removes its operand-frame alignment requirement. For a given stream, collect successive MOVE operations between surviving uses. A use includes any surviving ADD, COPY read/write, ERASE or required phase/endpoint boundary. No use may be crossed merely because another stream is idle.
+
+Suppose the original local frames form a nested chain U0 <= U1 <= ... <= Uk. Their exact address changes telescope to `D_Uk D_U0^-1`. Their orthogonal increments are disjoint commuting projectors, so this is one allowed residual of rank dim(Uk)-dim(U0). In the reflected orientation the chain is the reversed complementary chain; the same endpoint difference and rank follow exactly. The ambient stage background cancels. Rebuild both ledgers from the actual surviving uses and actual basis inclusions; do not infer this from summed ranks alone.
+
+Keep every physical input/output family and its endpoint, all stage boundaries, all data routes/bridges, and every copied-center lifetime. For source527 the120 center copies in the five-stage construction have odd scatter coefficients, so parity filtering does not itself remove those episodes. The shared work stream cannot be used before COPY or after ERASE. A COPY is a barrier even if its original register has no intervening ADD.
+
+## Required finite admission
+
+1. Filter actual emitted ADD records by the literal coefficient modulo2; retain all odd-coefficient records in their original order. Check all20107 formal F2 source, target and dirty columns against the admitted shear. The expected local event counts before any further resynthesis are1,783,196 removed and786,621 retained.
+2. Generate the actual complemented inverse schedule, with fresh reverse copies as before, and verify every formal F2 column again. Do not reverse an erasure.
+3. Compute cancellation-free prefix bounds for the new literal signed forward/inverse projections. Recompute the five-stage bound and finite bill. Failure to reproduce the previous integer decoder is not itself a contract failure; a missing F2 dirty restoration is.
+4. Regenerate exact monotone forward/reflected physical paths and the complete paid histogram. Every fused residual's actual endpoints must be checked. Keep all remaining recursive children, copied-center calls, fallback allowance, data idle edges and stock.
+5. Rebind the completed banks and final global address lowering to the new word and tags. Their actual rational address projectors, odd-q routes and normalizers must not be reduced modulo2.
+6. Rerun actual basis/prime coverage, finite ordinary-leaf assembly, both rational moment engines and all47 outer inequalities before claiming a result.
+
+For simple monotone MOVE fusion the paid rank mass and physical stock remain unchanged; combining positive increments can improve the concave moment while reducing the number of children. Any different deficit or stock must be explained by a separate exact endpoint change. The displayed bound is still conditional on the retained all-size compiler, selectors, common ancestor charts, restored rows, routing, prime and analytic interfaces.
+
+Prepared with OpenAI Codex assistance. This audit is independent of the physical parity-filter/fusion implementation owned by the complex research lane.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/README.md b/research/gen4-retiming-entrances-target/vendor/pr276/proof/README.md
new file mode 100644
index 0000000000..19751671be
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/README.md
@@ -0,0 +1,8 @@
+# Retained proof documents
+
+The `.tex` files are byte-pinned theorem sources. `finite_check.py` checks their hashes and phrases.
+
+`INTEGRATED_PROOF.md`, `FINITE_BIT_ACCOUNTING.md` and `PARITY-CONTRACT.md` are retained verbatim from the
+PR234 and source527 packages. Their arguments apply to this package unchanged. Their numerical instances,
+such as R, W, stock, bills and digests, describe the earlier source471 and source527 helpers, not gen4.
+The gen4 values are recomputed by `verify.py` and stated in `../PROOF.md` and `../BANK-PROOF.md`.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/copied-centers-lemma.tex b/research/gen4-retiming-entrances-target/vendor/pr276/proof/copied-centers-lemma.tex
new file mode 100644
index 0000000000..8933aaf508
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/copied-centers-lemma.tex
@@ -0,0 +1,103 @@
+\subsection{Scalar, frame and temporary-stream contracts}
+The retained source-copy, reversible mixer and scatter maps satisfy
+$JLV=I$. Over $\mathbb F_2$ the chronological word
+\[
+ L,\ J,\ L^{-1},\ V,\ L,\ J,\ L^{-1},\ V
+\]
+adds the input to the target and restores every arbitrary auxiliary.
+Over Gaussian dyadics use its corresponding old-value subtraction and
+new-value addition. A designated retained output has a distinct terminal
+output-use carrier: a matching may feed that carrier, but cannot merge
+two designated terminals or append a later middle-producer consumer.
+Its remaining uses before cleanup are its scatter reads, all of which
+leave its scalar value unchanged.
+
+Within one tensor invocation suppress the fixed future line and put
+\[
+ D_0=B\otimes F_h,\quad D_1=A\otimes F_h,\quad
+ A=B\mathbin{\perp}P,\quad D_U=D_0\mathbin{\perp}(P\otimes U),
+\]
+where $P$ and the suppressed future factor are one-dimensional and
+$U$ is a nondegenerate retained-center space of dimension $r$.
+Thus a local change of rank $d$ has ambient rank $d$.
+Write $\mathcal F_Q$ for the address frame: it is the rational partial
+swap $D_Q$ in the bit construction, and the binary phase $C_Q$ in the
+complex construction. Changing a copy from frame $Q_1$ to $Q_2$ means
+applying $\mathcal F_{Q_2}\mathcal F_{Q_1}^{-1}$ to its physical stream.
+Orthogonal backgrounds cancel in this quotient.
+
+Copies use Paureel's retained copy/transform/read/discard interface
+\cite{paureel,pr29}. A copy has precisely the original complete role
+stream, including all control and spectator ranges, and volume $V/W$.
+It is processed while inactive original streams are parked on the fixed
+depth-first stack tapes. Copying, pointwise reads and erasure are linear
+in that stream's volume. Sequential processing needs one additional
+fixed work stream, not an independently varying row coordinate.
+
+\begin{lemma}[Copied retained-center schedule]
+In either invocation orientation a designated retained center's
+physical rank profile can be changed from $z^r+z^h$ to
+$z^r+z^{h-r}$, with the same scalar action, original role endpoints,
+and arbitrary-scratch restoration. The rank-$r$ transform on the copy
+is included in the recursive call list.
+\end{lemma}
+\begin{proof}
+In the forward orientation the original center has scalar value $w$
+at frame $D_U$ after the middle mixer. Its old sequence was
+$D_U\to D_0\to D_1$: scatter at $D_0$, then cleanup at $D_1$,
+with ranks $r,h$.
+Keep the original at $D_U$, copy its physical stream, and transform
+only the copy to $D_0$, paying rank $r$. Supply every scatter read
+from that transformed copy while its data targets remain at their
+unchanged common frame $D_0$, then erase the temporary. The reads
+are exactly those of $w$ in the old schedule. Since they do not change
+$w$, move the original directly from $D_U$ to $D_1$ before its first
+cleanup incidence; this costs $h-r$. Every subsequent original gate
+therefore receives the same scalar value at its required frame.
+
+In the reverse complementary orientation the old sequence was
+$D_0\to D_1\to D_{U^\perp}$, with ranks $h,r$ and scatter at $D_1$.
+After the preceding all-$D_0$ operations, advance the original directly
+to $D_{U^\perp}=D_0\mathbin{\perp}(P\otimes U^\perp)$, paying
+$h-r$. Copy it and transform the copy to $D_1$, paying $r$.
+Use that copy for all early scatter reads, then erase it. The original
+already has the exact frame and unchanged scalar value required by the
+following inverse mixer. Terminal output-use separation ensures no
+intervening producer consumer has been bypassed.
+
+For partial swaps either direction of the rank-$r$ change is the same
+involution. For complex phases the forward copy uses $C_U^{-1}$,
+the direct original growth uses $C_{U^\perp}$, and the reverse copy
+uses $C_FC_{U^\perp}^{-1}=C_U$. These are the same charged ranks,
+implemented by the retained forward/inverse residual interface.
+All tensor backgrounds cancel as stated. Every original scalar
+incidence, final source-copy cancellation and auxiliary source/sink
+operator is unchanged. Thus the scalar identity and all endpoints
+remain exact on arbitrary initial auxiliary values.
+\end{proof}
+
+For the selected centers $r=h-1$, and there are $h$ distinct retained
+output uses per invocation. Their old histogram has rank mass
+$hR_h+2\ell_h$, where $\ell_h=h(h-1)$. The new histogram is exactly
+\[
+ H'_{h,1}=H_{h,1}+h,\qquad H'_{h,h}=H_{h,h}-h,
+ \qquad H'_{h,r}=H_{h,r}\quad(r\ne1,h),
+\]
+and hence $\sum_r rH'_{h,r}=hR_h+\ell_h$.
+Every old rank-$(h-1)$ residual remains as a paid transform of a copy;
+its projector and ordinary bit pivot profile are unchanged. Only the
+full-rank original transition becomes the rank-one complement.
+The physical role count $R_h$ is unchanged.
+
+For two factors, put $N=v_av_b$, $B_a=v_bR_a$, $B_b=v_aR_b$,
+$W=2N+B_a+B_b$ and $L=v_b\ell_a+v_a\ell_b$.
+All exterior, data-front and endpoint-correction calls remain in place.
+The resulting complete rank mass is
+\[
+ s=Wm-N+L,\qquad Wm-s=N-L.
+\]
+This follows by subtracting exactly $L$ from the retained two-stage
+physical mass $Wm-N+2L$. The $N$ rank-one endpoint-copy calls are
+separate and remain fully charged. Because center copies retain the
+same complete role-volume fraction $1/W$, the existing complete-row,
+integer-width remainder and fixed-tape recurrence proofs apply.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/03-motifs.tex b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/03-motifs.tex
new file mode 100644
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+\section{Two finite networks with a rank saving}
+\label{sec:finite-networks}
+
+We construct two fixed linear networks that exchange two banks of values
+while restoring every auxiliary value.  When the values are replaced by
+arrays, a common representation on all wires at a gate lets that gate act
+pointwise without disturbing the representation.  We explain this invariant
+before constructing the subspace labels that make changes of representation
+cheap.  The first network uses bit values and rational subspaces; the second
+uses Gaussian dyadic values and binary subspaces.  The scalar domain specifies
+the values combined at a gate, while the subspace labels are used to construct operators
+on each wire's address-indexed array.
+
+Put
+\[
+ h=100,\qquad v=\binom h3=161700,\qquad
+ N=v^3=4227952113000000,\qquad m=h^3=1000000.
+\]
+Let $\mathcal T$ be the set of three-element subsets of $[h]$.
+There are two data banks $X_a,Y_a$, indexed by
+$a=(a_1,a_2,a_3)\in\mathcal T^3$.
+A wire carries one scalar.  A gate is a fixed linear map on a specified
+set of wires; untouched wires retain their values.  The vertices on a
+wire are its source, the gates that touch it in time order, and its sink;
+its edges join consecutive vertices.  We call the name of a wire its
+\emph{role}, so that we can distinguish a fixed place in the network
+from the value currently carried there.
+
+\subsection{Scalar operations and restored auxiliary values}
+
+There are three stages.  At stage $j$, fix the other two coordinates and
+operate on the $v$ values in each bank obtained by varying coordinate $j$.  Thus
+there are $v^2$ separate invocations at each stage.
+Each such invocation has its own auxiliary wires, distinct from all
+other invocations, including those in other stages.  There are
+\[
+ I=3v^2=78440670000
+\]
+invocations.  In a forward invocation, write $x_T$ for the data used as
+controls and $y_S$ for the data to be updated; $S,T\in\mathcal T$ are
+their varying $j$th coordinates.  These are the logical source and
+target banks of the invocation.  For each ordered pair $(S,T)$ that is
+neighboring under the rule below, there is an auxiliary wire $A_{ST}$.
+There are also central wires $C_i$, $i\in[h]$, and in the second
+construction a wire $C_\ast$.  We call all these auxiliary wires
+\emph{scratch wires}; their initial values may be arbitrary.
+
+The following maps specify the construction.
+\begin{itemize}
+\item In the bit construction, scalars lie in $\mathbb F_2$, and
+$S,T$ are neighbors when $|S\cap T|=1$.
+The copy map adds $x_T$ to $A_{ST}$ for each neighbor pair.
+The side injection adds $\sum_{T:\,|S\cap T|=1}A_{ST}$ to $y_S$.
+The gather adds $\sum_{T\ni i}x_T$ to $C_i$, and the scatter adds
+$\sum_{i\in S}C_i$ to $y_S$.
+\item In the complex construction, scalars lie in
+$\mathbb Z[i,1/2]$, and neighbors are distinct triples with even
+intersection.  Copy is unchanged.  Side injection adds
+\[
+ -\sum_{T\text{ neighboring }S}\frac{|S\cap T|-1}{2}A_{ST}
+\]
+to $y_S$.  Gather adds $\sum_{T\ni i}x_T$ to $C_i$ and
+$\sum_Tx_T$ to $C_\ast$.  Scatter adds
+$(\sum_{i\in S}C_i-C_\ast)/2$ to $y_S$.
+\end{itemize}
+Each update leaves its control wires unchanged.  The first two rows of
+the following schedule remove the effect of the old scratch values;
+the next four introduce the source values and add their effect to the
+target; the last two restore the scratch values.
+This cancellation of arbitrary initial scratch values is a linear
+instance of the restoration construction for transparent computation in
+Buhrman, Cleve, Kouck\'y, Loff and Speelman~\cite[Section~3]{BuhrmanCleveKouckyLoffSpeelman2014}.
+The forward schedule is
+\begin{equation}
+\begin{array}{c|l|l}
+\text{row}&\text{operation}&\text{gate grouping}\\ \hline
+0&\text{subtract side injection}&\text{one gate per target}\\
+1&\text{subtract scatter}&\text{one gate on targets and center}\\
+2&\text{copy}&\text{one gate per source}\\
+3&\text{gather}&\text{one gate on sources and center}\\
+4&\text{scatter}&\text{one gate on targets and center}\\
+5&\text{side injection}&\text{one gate per target}\\
+6&\text{undo gather}&\text{one gate on sources and center}\\
+7&\text{undo copy}&\text{one gate per source}.
+\end{array}
+\label{eq:motif-schedule}
+\end{equation}
+
+\begin{lemma}\label{lem:scalar-motifs}
+For arbitrary initial values of its auxiliary wires, a forward
+invocation changes $y_S$ to $y_S+x_S$ and leaves every other value
+unchanged.  Performing a forward invocation from $X$ to $Y$ at stage 1,
+the inverse forward schedule from $Y$ to $X$ at stage 2, and a forward
+invocation from $X$ to $Y$ at stage 3 sends
+\[
+ (X_a,Y_a)\longmapsto(-Y_a,X_a)
+\]
+and restores every auxiliary value.  In the bit construction this is the
+permutation exchanging $X_a$ and $Y_a$.
+\end{lemma}
+
+\begin{proof}
+Write $\mathcal V$ for copy, $\mathcal G$ for gather,
+$\mathcal J$ for side injection and $\mathcal R$ for scatter.
+If the initial side and central vectors are $a,c$, the first two rows
+subtract $\mathcal J a+\mathcal R c$ from $y$.  Rows 2 and 3 change
+them to $a+\mathcal Vx,c+\mathcal Gx$.  Rows 4 and 5 therefore add
+$\mathcal R(c+\mathcal Gx)+\mathcal J(a+\mathcal Vx)$.
+Rows 6 and 7 restore $c,a$.  The net target change is
+$(\mathcal J\mathcal V+\mathcal R\mathcal G)x$, independently of
+$a,c$.
+
+In the bit case, the central coefficient from $x_T$ to $y_S$ is
+$|S\cap T|\bmod2$.  The side contribution cancels exactly the
+intersection-one cases; distinct triples with intersection zero or two
+already have coefficient zero, and the self coefficient is one.
+In the complex case, the central coefficient is $(|S\cap T|-1)/2$.
+The side cancels it for distinct triples with intersection zero or two;
+intersection one contributes zero, and the self coefficient is one.
+Thus both net maps are $y\gets y+x$.
+
+The inverse schedule with logical source $Y$ and target $X$ effects
+$X\gets X-Y$.  Starting from $(x,y)$, the three stages give
+$(x,y+x)$, then $(-y,y+x)$, then $(-y,x)$.
+Each invocation restores its own auxiliary wires.
+\end{proof}
+
+A fixed triple has
+\[
+ z_{\rm b}=3\binom{97}{2}=13968,\qquad
+ z_{\rm c}=\binom{97}{3}+3\cdot97=147731
+\]
+neighbors in the two constructions, respectively.  The second count
+separates intersection zero and intersection two.  Ordered pairs must
+be counted: there are $vz$ side wires in each invocation, not $vz/2$.
+With $c_{\rm b}=100$ and $c_{\rm c}=101$ central wires per invocation,
+the total wire counts are
+\begin{align}
+ W_{\rm b}&=2N+I(vz_{\rm b}+c_{\rm b})
+          =177176569091445000000,\label{eq:bit-wire-count}\\
+ W_{\rm c}&=2N+I(vz_{\rm c}+c_{\rm c})
+          =1873807244643542670000.\label{eq:complex-wire-count}
+\end{align}
+All these numbers are fixed, independently of any eventual input length.
+
+\subsection{From scalar values to arrays}
+
+We record the representation principle before choosing the labels.  Let
+$R$ be the scalar ring of either network and let $\Omega$ be a finite address
+set common to all wires.  Replace each scalar by an array in $R^\Omega$, and
+apply each scalar gate pointwise at every address.  Write $\mathsf S_\Omega$
+for the resulting network on the vector of wire arrays.
+
+At each source, gate and sink $v$, assign an invertible $R$-linear operator
+$D_v$ on $R^\Omega$, called its \emph{frame}.  A frame acts on the values
+indexed by addresses within one wire's array and may mix them; a gate instead
+combines wire values at each fixed address.  All incoming and outgoing
+incidences of one gate use the same $D_v$.  On an edge from $u$ to $v$, apply
+$D_vD_u^{-1}$ to that wire's array.  Define the operators on all input and
+output roles by
+\[
+ D_{\rm in}=\bigoplus_w D_{\mathrm{source}(w)},\qquad
+ D_{\rm out}=\bigoplus_w D_{\mathrm{sink}(w)}.
+\]
+For a supplied physical input $f$, define its logical interpretation to be
+$g=D_{\rm in}^{-1}f$; this definition requires no physical preprocessing.
+At a vertex $v$, the invariant is that the stored array equals $D_v$ applied
+to the logical array there.  It holds at the sources by definition.  On an
+edge whose logical array is $\varphi$, the edge operator changes $D_u\varphi$
+to $D_v\varphi$.  At a gate with logical input arrays $\varphi_j$,
+$R$-linearity gives
+$\sum_j c_jD_v\varphi_j=D_v(\sum_j c_j\varphi_j)$ for each output combination, with
+$c_j\in R$.  Thus the common frame commutes with the pointwise gate, and
+the invariant continues to the sinks.  The implemented operator is therefore
+\begin{equation}
+ D_{\rm out}\,\mathsf S_\Omega\,D_{\rm in}^{-1}.
+ \label{eq:common-frame-identity}
+\end{equation}
+In particular, if the scalar network is a signed role permutation that
+sends input role $w$ to output role $\rho(w)$ with scalar sign
+$\varepsilon_w$, that route applies
+$\varepsilon_wD_{\mathrm{sink}(\rho(w))}
+D_{\mathrm{source}(w)}^{-1}$ to its input array.  All roles, including
+the auxiliary roles, enter this identity.  Once the scalar routing is fixed,
+the endpoint frames determine the array operator on each route; the
+intermediate frames can then be chosen to make each edge change inexpensive.
+
+Figure~\ref{fig:frame-compatibility} summarizes this invariant.
+\begin{figure}[ht]
+\centering
+\input{figures/proof-map.tex}
+\caption{An edge changes the representation of one role's logical array
+$g_w$. At the next gate $G$, all $t$ input arrays have the common frame
+$D_v$, so the pointwise linear gate commutes with that frame. The same
+$D_v$ acts on each output component.}
+\label{fig:frame-compatibility}
+\end{figure}
+
+\subsection{Subspaces attached to the gates}
+
+The scalar network already has the required signed exchange. We now
+choose its intermediate labels to make the changes of frame inexpensive.
+A label is a nondegenerate subspace of a fixed bilinear space. On every
+edge one label will contain the other. For such an edge, the
+\emph{orthogonal residual} is the orthogonal complement of the smaller label inside
+the larger one; its dimension is the absolute change in label dimension.
+The saving will come from keeping the total dimension lost on decreasing
+edges small relative to $N$.
+
+For the bit network, let $F=\mathbb Q^h$ with bilinear form
+\[
+ \langle x,y\rangle=x^{\mathsf T}(I-J/9)y,
+\]
+where $J$ is the all-one matrix.  This form has eigenvalues $1$ and
+$1-h/9=-91/9$, so it is nondegenerate.  For a triple $T$ let $t_T$ be
+its indicator vector.  Then
+\[
+ \langle t_S,t_T\rangle=|S\cap T|-1,
+ \qquad \langle t_T,t_T\rangle=2.
+\]
+For the complex network, take instead $F=\mathbb F_2^h$ with the
+ordinary dot product; here $t_T\cdot t_T=1$.
+Thus every triple line is nondegenerate, and neighboring triple lines
+are orthogonal, in the label field belonging to either construction.
+The scalar domain need not equal the label field.
+These degree-one intersection formulas specialize the construction
+described by Alon~\cite[Section~3, remark after Theorem~1.1]{Alon1998}
+to the prime $2$, with the ground-set size changed to $h=100$.
+
+The ambient label space is $\mathcal F=F^{\otimes3}$ with its tensor
+bilinear form.  It has dimension $m$ and is nondegenerate.  Write
+\[
+ u_a=t_{a_1}\otimes t_{a_2}\otimes t_{a_3},\qquad U_a=\langle u_a\rangle.
+\]
+The prescribed terminal labels are
+\[
+\begin{array}{c|cc}
+\text{role}&\text{source label}&\text{sink label}\\ \hline
+X_a&U_a&\mathcal F\\
+Y_a&0&U_a^\perp\\
+\text{each scratch role}&0&\mathcal F.
+\end{array}
+\]
+Write $W$ for the wire count in the construction under consideration.
+The source dimensions sum to $N$ and the sink dimensions to $Wm-N$.
+Thus the signed dimension changes will sum to $Wm-2N$, because the
+contributions at gates cancel. If decreasing edges lose a total
+dimension $L$, the sum of absolute changes is $Wm-2N+2L$.
+We will obtain $L<N/2$. The rational interface below will require
+an additional $N$ source ranks, so this inequality will leave a strict
+saving in both constructions.
+
+At stage $j$, fix an invocation.  Put
+\[
+ A=F^{\otimes(j-1)},\qquad
+ P=\langle t_{a_1}\otimes\cdots\otimes t_{a_{j-1}}\rangle,
+ \qquad B=P^\perp\subset A.
+\]
+An empty tensor product is the one-dimensional ground field; thus
+$B=0$ at stage 1.  Let
+$Q=\langle t_{a_{j+1}}\otimes\cdots\otimes t_{a_3}\rangle
+\subset F^{\otimes(3-j)}$, again using the empty tensor product at
+stage 3.  Since $P$ is nondegenerate,
+$A=B\mathbin{\perp}P$.  
+We prescribe the following transition for each data wire in the stage,
+where $t$ is the indicator of that wire's $j$th triple:
+\[
+\begin{array}{c|c|c}
+ &\text{incoming label}&\text{outgoing label}\\ \hline
+ X&A\otimes\langle t\rangle\otimes Q&(A\otimes F)\otimes Q\\
+ Y&B\otimes\langle t\rangle\otimes Q&
+ \bigl((B\otimes F)\mathbin{\perp}(P\otimes t^\perp)\bigr)\otimes Q.
+\end{array}
+\]
+The outgoing $Y$ label can also be written
+$(P\otimes\langle t\rangle)^\perp_{A\otimes F}\otimes Q$.
+These transitions expose one tensor factor at each stage. To see that
+they fit together, for $j<3$ write
+$Q=\langle t_{a_{j+1}}\rangle\otimes Q'$. The next stage has
+\[
+ A'=A\otimes F,\qquad
+ P'=P\otimes\langle t\rangle,\qquad
+ B'=(P')^\perp_{A'}
+    =(B\otimes F)\mathbin{\perp}(P\otimes t^\perp).
+\]
+Thus the prescribed outgoing labels are
+$A'\otimes\langle t_{a_{j+1}}\rangle\otimes Q'$ on $X$ and
+$B'\otimes\langle t_{a_{j+1}}\rangle\otimes Q'$ on $Y$, exactly
+the next incoming labels. At stage 1 they start at $U_a$ on $X_a$
+and zero on $Y_a$; at stage 3 they end at $\mathcal F$ on $X_a$
+and $U_a^\perp$ on $Y_a$, as prescribed at the terminals.
+
+The gate labels are organized by the decomposition
+\[
+ A\otimes F=(B\otimes F)\mathbin{\perp}(P\otimes F),
+\]
+with the common summand $B\otimes F$ and the remaining summand
+$P\otimes F$ of dimension $h$. Suppress the one-dimensional factor
+$Q$ for the moment. On a side wire joining neighboring physical triples
+with indicators $t_X,t_Y$, the common component grows to $B\otimes F$,
+while the remaining component passes through
+\[
+ P\otimes\langle t_X\rangle
+ \ \subset\ P\otimes t_Y^\perp
+ \ \subset\ P\otimes F.
+\]
+The first inclusion is possible because $t_X\perp t_Y$.
+For the central gates we assign $A\otimes F$ on the physical $X$
+bank and $B\otimes F$ on the physical $Y$ bank. A central wire
+returns once from the former label to the latter, losing exactly
+$P\otimes F$. The gate order below confines all decreases to this
+return, while the other edges realize the prescribed stage transitions.
+
+Number the successive times in an invocation by
+$r=0,\ldots,7$. At stages 1 and 3, time $r$ uses row $r$ of the scalar
+schedule~\eqref{eq:motif-schedule}. At stage 2 it uses the inverse of
+row $7-r$, with the logical banks exchanged. In either case the gates
+touch the physical wires in the order
+\[
+ Y\text{-side},\quad Y\text{-center},\quad X\text{-side},\quad
+ X\text{-center},\quad Y\text{-center},\quad Y\text{-side},\quad
+ X\text{-center},\quad X\text{-side}.
+\]
+A side wire still joins neighboring physical triples in stage 2 because
+the neighbor relation is symmetric. The following table assigns the
+common gate labels. It suppresses the tensor factor $Q$; for a gate
+indexed by a physical bank triple, $t$ denotes that triple's indicator.
+
+\begin{equation}
+\begin{array}{c|l|l}
+\text{time}&\text{physical wires}&\text{common gate label}\\ \hline
+0&Y,\ \text{its side wires}&B\otimes\langle t\rangle\\
+1&Y,\ \text{all center wires}&B\otimes F\\
+2&X,\ \text{its side wires}&(B\otimes F)\mathbin{\perp}(P\otimes\langle t\rangle)\\
+3&X,\ \text{all center wires}&A\otimes F\\
+4&Y,\ \text{all center wires}&B\otimes F\\
+5&Y,\ \text{its side wires}&(B\otimes F)\mathbin{\perp}(P\otimes t^\perp)\\
+6&X,\ \text{all center wires}&A\otimes F\\
+7&X,\ \text{its side wires}&A\otimes F.
+\end{array}
+\label{eq:motif-labels}
+\end{equation}
+All labels are tensored by $Q$ and viewed as subspaces of $\mathcal F$.
+Every displayed summand is nondegenerate.
+
+All scratch sources have label zero and all scratch sinks have label
+$\mathcal F$, as prescribed above. The next lemma verifies the stage
+boundaries and all intervening edge changes, including these scratch
+edges.
+
+\begin{lemma}\label{lem:motif-residuals}
+Every edge joins comparable nondegenerate labels.  The only decreasing
+edges are the central-wire edges from time 3 to time 4; their dimension
+loss is $h$.  Consequently, if $c$ is the number of central wires per
+invocation and $W$ the total number of wires, then
+\begin{equation}
+ L=Ich,\qquad
+ \sum_{e}\bigl|\dim U_{\mathrm{head}(e)}-
+                       \dim U_{\mathrm{tail}(e)}\bigr|
+ =Wm-2N+2L.                                      \label{eq:rank-budget-labels}
+\end{equation}
+For the binary label space, every nonzero orthogonal residual of an
+edge has an orthonormal basis.
+\end{lemma}
+
+\begin{proof}
+Write $a=\dim A=h^{j-1}$ and $f=h^{3-j}$.  In the table below,
+$\mathrm{in}$ denotes the preceding vertex on that data wire: its source
+at stage 1, and its last gate in the preceding stage otherwise.  The
+interstage calculation above gives its label.  The table lists the
+orthogonal residual and its dimension for every edge except the final
+data edges to their sinks, whose labels agree and whose residuals are zero.
+Tensor each residual by $Q$, except in the last row.  The symbols $t_X,t_Y$ are
+the indicators of the neighboring physical triples joined by a side wire.
+\[
+\begin{array}{l|l|r}
+\text{wire and edge}&\text{orthogonal residual}&\text{dimension}\\ \hline
+X:\ \mathrm{in}\to2&B\otimes t_X^\perp&(a-1)(h-1)\\
+X:\ 2\to3&P\otimes t_X^\perp&h-1\\
+X:\ 3\to6,\ 6\to7&0&0\\
+Y:\ \mathrm{in}\to0&0&0\\
+Y:\ 0\to1&B\otimes t_Y^\perp&(a-1)(h-1)\\
+Y:\ 1\to4&0&0\\
+Y:\ 4\to5&P\otimes t_Y^\perp&h-1\\
+\mathrm{center}:\ \mathrm{source}\to1&B\otimes F&(a-1)h\\
+\mathrm{center}:\ 1\to3&P\otimes F&h\\
+\mathrm{center}:\ 3\to4&P\otimes F&h\\
+\mathrm{center}:\ 4\to6&P\otimes F&h\\
+\mathrm{side}:\ \mathrm{source}\to0&B\otimes\langle t_Y\rangle&a-1\\
+\mathrm{side}:\ 0\to2&(B\otimes t_Y^\perp)\mathbin{\perp}(P\otimes\langle t_X\rangle)
+ &(a-1)(h-1)+1\\
+\mathrm{side}:\ 2\to5&P\otimes\langle t_X,t_Y\rangle^\perp&h-2\\
+\mathrm{side}:\ 5\to7&P\otimes\langle t_Y\rangle&1\\
+\mathrm{scratch}:\ \mathrm{last}\to\mathrm{sink}
+ &(A\otimes F)\otimes Q^\perp&ah(f-1).
+\end{array}
+\]
+The last gate on a central wire is at time 6, and the last gate on a side
+wire is at time 7.  Both have label $(A\otimes F)\otimes Q$.  Enlarging it
+to $\mathcal F$ at the sink gives the last residual in the table, with
+$Q^\perp$ taken in the entire future tensor space.
+The side edge $2\to5$ uses the neighbor relation
+essentially.  Since $t_X\perp t_Y$, we have
+$\langle t_X\rangle\subset t_Y^\perp$.  Hence its two labels satisfy
+\[
+ (B\otimes F)\mathbin{\perp}(P\otimes\langle t_X\rangle)
+ \ \subset\
+ (B\otimes F)\mathbin{\perp}(P\otimes t_Y^\perp).
+\]
+The complement of $\langle t_X\rangle$ inside $t_Y^\perp$ is
+$\langle t_X,t_Y\rangle^\perp$, of dimension $h-2$; tensoring by
+$P$ and then by $Q$ gives the residual in the table.  The other entries
+follow directly by splitting $A=B\mathbin{\perp}P$ and
+$F=\langle t\rangle\mathbin{\perp}t^\perp$.
+Label dimension is nondecreasing along every edge except center $3\to4$, which removes
+$P\otimes F\otimes Q$.  The table includes the interstage edges through
+$\mathrm{in}$, and the initial and final data labels match their terminals,
+so no other dimension changes occur.
+
+The signed sum of dimension changes telescopes at every gate: each
+touched wire has one incoming and one outgoing incidence with the same
+gate label.  The sum of source dimensions is $N$, while the sum of
+sink dimensions is $Wm-N$.  The signed increase is therefore $Wm-2N$.
+There are $Ic$ decreasing edges, each of loss $h$; replacing signed
+changes by absolute changes adds $2L$.
+
+Now work over $\mathbb F_2$.  A nondegenerate symmetric bilinear space
+is nonalternating precisely when it contains a vector of norm one.
+The lines $P,Q$ have such vectors.  If $B\ne0$, a coordinate unit
+outside the support of the earlier tensor vector belongs to $B$:
+that support has size $3^{j-1}<h^{j-1}$ when $j>1$.
+The same argument gives a unit vector in $Q^\perp$ when it is nonzero.
+A triple complement, and the complement of two neighboring triple
+lines, contain coordinate units outside supports of sizes at most
+three and six, respectively.  Full tensor spaces contain coordinate
+units as well.  In each nonzero tensor summand, tensoring these chosen
+norm-one vectors gives a norm-one vector; placing it in that orthogonal
+summand gives one in the whole residual.  Each residual is nondegenerate
+by the decompositions above.  Thus every nonzero residual is nonalternating.
+
+For completeness, every nondegenerate nonalternating binary symmetric
+space has an orthonormal basis.  Split off unit lines until the
+remaining space is alternating.  A nonzero nondegenerate alternating
+space splits into planes with bases $a,b$ satisfying
+$a\cdot a=b\cdot b=0$, $a\cdot b=1$; this follows by choosing a
+nonzero $a$, choosing $b$ with $a\cdot b=1$, and taking the orthogonal
+complement of their nondegenerate plane.  Retain one unit vector $w$
+from the lines already split off.  A plane orthogonal to $w$ can be
+absorbed into that line: the three vectors
+\[
+ w+a,\qquad w+b,\qquad w+a+b
+\]
+are independent, pairwise orthogonal, and have norm one.
+Use one of these new unit vectors in place of $w$ for the next plane;
+the remaining planes are still orthogonal to it.  Repeating this
+operation absorbs every alternating plane.
+\end{proof}
+
+The loss ratios have the exact values
+\[
+ \frac{L_{\rm b}}{N}=\frac{100}{539},\qquad
+ \frac{L_{\rm c}}{N}=\frac{101}{539}.
+\]
+In particular, both are smaller than $1/2$.  We now turn the dimension
+count into the two interfaces needed later.
+
+\subsection{The rational matrix interface}
+
+For a nondegenerate rational subspace $U\subset\mathcal F$, write
+$P_U$ for the projection onto $U$ along $U^\perp$.  Assign $P_U$ to
+each gate or sink with label $U$.  Assign the source matrix $-P_{U_a}$
+to $X_a$ and zero to every other source.
+These are fixed rational $m\times m$ matrices; write $M_v$ for the matrix
+at vertex $v$.  Define
+$\rho(X_a)=Y_a$, $\rho(Y_a)=X_a$, and let $\rho$ fix every auxiliary
+wire.
+
+In the tape application, two address chunks are written as vectors $H,D$
+of $m$ fields.  For a matrix $M$, the frame $\Phi_M$ moves the array entry
+at $(H,D)$ to $(H+MD,D)$, leaving the other address fields unchanged.
+The fields use a radix coprime to the fixed denominators, and addition is
+modulo their common range.  Hence $\Phi_M$ is an invertible
+$\mathbb F_2$-linear permutation of array entries, and
+$\Phi_{M'}\Phi_M=\Phi_{M'+M}$.  Using $D_v=\Phi_{M_v}$
+in \eqref{eq:common-frame-identity}, the endpoint matrix difference on each
+routed role is exactly the shear applied to that role.  The following identity
+makes it the same shear $H\gets H+D$ on every role;
+Section~\ref{sec:tape-interchange} turns that shear into a field interchange
+and implements an edge change with one smaller interchange per unit of its
+rational rank.
+
+\begin{proposition}\label{prop:bit-motif-interface}
+The bit network has $W_{\rm b}$ wires, uses only pointwise XOR gates,
+and sends its input vector to the permutation $\rho$ of that vector.
+Its rational matrices are common to all incidences of a gate and obey
+\[
+ M_{\mathrm{sink}(\rho(w))}-M_{\mathrm{source}(w)}=I_m
+ \quad\text{for every input role }w.
+\]
+The sum of the rational ranks of all edge differences is
+\begin{align}
+ s_{\rm b}
+ &=\sum_{e}\operatorname{rank}_{\mathbb Q}
+      (M_{\mathrm{head}(e)}-M_{\mathrm{tail}(e)})\\
+ &=W_{\rm b}m-N+2L_{\rm b}
+  =177176569088785861287000000<W_{\rm b}m.
+\end{align}
+\end{proposition}
+
+\begin{proof}
+Lemma~\ref{lem:scalar-motifs} gives the scalar permutation, including
+all auxiliary roles.  For $U\subset V$ nondegenerate,
+$P_V-P_U$ is the identity on $V\cap U^\perp$ and zero on its
+orthogonal complement.  Its rank is $\dim V-\dim U$; reversing the
+edge negates the matrix without changing its rank.
+The only exceptions are the $N$ negative source projections.
+At stage 1, $B=0$, and the first gate on $X_a$ has label exactly $U_a$.
+Its first edge matrix is therefore $2P_{U_a}$, of rational rank one,
+where the corresponding dimension change was zero.
+Lemma~\ref{lem:motif-residuals} consequently gives the stated rank sum.
+Its deficit from $W_{\rm b}m$ is $N-2L_{\rm b}>0$.
+
+For an input $X_a$ the endpoint difference is
+$P_{U_a^\perp}-(-P_{U_a})=I_m$.  Every other role has zero source
+matrix and identity sink matrix.  This proves the interface.
+\end{proof}
+
+\subsection{The binary phase interface}
+
+Use the complex scalar network and binary labels.  For a binary vector
+$x$, let $\operatorname{wt}(x)$ denote its integer Hamming weight, and
+write $[b]\in\{0,1\}$ for the integer representative of $b\in\mathbb F_2$.
+For a label $U$, let
+\[
+ q_U(x)=\operatorname{wt}(P_Ux)\pmod4.
+\]
+The projection here is over $\mathbb F_2$.
+Let
+\[
+ H=\frac1{\sqrt2}\begin{pmatrix}1&1\\1&-1\end{pmatrix},\quad
+ C=H\begin{pmatrix}1&0\\0&i\end{pmatrix}H
+   =aI+bX,\qquad a=\frac{1+i}{2},\quad b=\frac{1-i}{2},
+\]
+where $X$ interchanges the two coordinates.  On functions of
+$x\in\mathbb F_2^m$ define
+\[
+ \mathcal C_U=H^{\otimes m}\operatorname{diag}_x(i^{q_U(x)})H^{\otimes m}.
+\]
+The use of $H$ in this definition is an identity of matrices.  Each entry
+of $\mathcal C_U$ and its inverse is a Gaussian integer divided by $2^m$,
+so both preserve arrays over $\mathbb Z[i,1/2]$.  The kernels implemented
+below have Gaussian dyadic coefficients.
+
+To apply the scalar network to these functions, replace the scalar on
+each wire $w$ by an array
+$f_w:\mathbb F_2^m\to\mathbb Z[i,1/2]$.  At each address, a gate
+applies its scalar linear map to the values on the wires it touches.
+The frame in \eqref{eq:common-frame-identity} is $D_v=\mathcal C_U$ at a
+vertex with label $U$.  On an edge from label $U$ to label $V$, apply
+$\mathcal C_V\mathcal C_U^{-1}$ to that wire's array.
+All frames are diagonalized by the same matrix $H^{\otimes m}$.
+For an integer $k\ge1$, an address for $k$ columns is
+$(x^{(1)},\ldots,x^{(k)})\in(\mathbb F_2^m)^k$; every frame and edge
+operator is then the tensor product of its one-column version over
+these $k$ coordinates.  Each scalar gate is still applied once at each
+joint address, to the vector of values on the roles it touches.
+
+\begin{proposition}\label{prop:complex-motif-interface}
+For each edge of the complex network, write $U,V$ for its tail and
+head labels.  Its phase-frame difference
+$\mathcal C_V\mathcal C_U^{-1}$ is a product of one translation
+kernel $aI+bX_v$, or its inverse, per vector in an orthonormal basis
+of the edge residual.  Here $(X_vf)(x)=f(x+v)$.
+The sum of these basis lengths is
+\[
+ s_{\rm c}=W_{\rm c}m-2N+2L_{\rm c}
+ =1873807244636671267308000000<W_{\rm c}m.
+\]
+After source and sink diagonal corrections, and undoing the signed
+bank exchange, telescoping these phase frames gives $C^{\otimes m}$
+on every role, including auxiliary roles.  The same assertion holds
+on any positive number of columns by taking tensor products over columns.
+\end{proposition}
+
+\begin{proof}
+For binary vectors $z,w$,
+\[
+ \operatorname{wt}(z+w)
+ =\operatorname{wt}(z)+\operatorname{wt}(w)
+       -2|\operatorname{supp}(z)\cap\operatorname{supp}(w)|.
+\]
+If $z\cdot w=0$, the intersection cardinality is even, so weight is
+additive modulo four.  If $V=U\mathbin{\perp}E$ and $\mathcal B$
+is an orthonormal basis of $E$, it follows that
+\[
+ q_V(x)-q_U(x)=\sum_{v\in\mathcal B}
+                 \operatorname{wt}(v)[v\cdot x]\pmod4.
+\]
+For a decreasing edge the right side is negated.
+Each $v$ has norm one, so $\operatorname{wt}(v)$ is odd.  Its
+coefficient in the phase, including the sign for the edge direction,
+is therefore some $\varepsilon\in\{1,-1\}$ modulo four.  The function
+$i^{\varepsilon[v\cdot x]}$ equals
+\[
+ \frac{1+i^\varepsilon}{2}
+ +\frac{1-i^\varepsilon}{2}(-1)^{v\cdot x}.
+\]
+The identity $H\operatorname{diag}(1,-1)H=X$, tensored over the
+coordinates in $\operatorname{supp}(v)$, sends the diagonal character
+$(-1)^{v\cdot x}$ to translation $X_v$.  The displayed phase therefore
+becomes $aI+bX_v$ or its inverse.  The nonzero residuals have such
+bases by Lemma~\ref{lem:motif-residuals}; for a zero residual use the
+empty basis.  The same lemma gives the count $s_{\rm c}$.
+The deficit is $2N-2L_{\rm c}>0$.
+
+For an edge $e$, write $\mathcal B_e$ for its residual basis and
+$K_{e,v}$ for the forward or inverse translation kernel associated
+with $v\in\mathcal B_e$.  Taking tensor products preserves their
+product, so on $k$ columns
+\[
+ \bigl(\mathcal C_V\mathcal C_U^{-1}\bigr)^{\otimes k}
+ =\prod_{v\in\mathcal B_e}K_{e,v}^{\otimes k}.
+\]
+Thus each residual vector contributes one factor acting on all $k$
+columns, and there are $s_{\rm c}$ such factors over the network.
+
+Let $\rho$ denote the underlying permutation of the complex roles: it
+exchanges $X_a,Y_a$ and fixes each scratch role.
+By Lemma~\ref{lem:scalar-motifs}, the pointwise scalar network sends an input array at
+$X_a$ to $Y_a$ with sign $+1$, an input at $Y_a$ to $X_a$ with sign
+$-1$, and each scratch input to its own output with sign $+1$.
+Applying \eqref{eq:common-frame-identity} with $D_v=\mathcal C_{U_v}$,
+where $U_v$ is the label at vertex $v$, shows that an input role $w$ reaches
+output role $\rho(w)$ with that sign and with operator
+$\mathcal C_{U_{\mathrm{sink}(\rho(w))}}
+ \mathcal C_{U_{\mathrm{source}(w)}}^{-1}$.
+For $k$ columns, use $D_v=\mathcal C_{U_v}^{\otimes k}$ on the joint
+address set in the same identity.  The route operator is then the $k$th
+tensor power of the displayed address operator, multiplied by its scalar
+route sign once.
+The zero label has frame $I$, while the full label has frame
+$C^{\otimes m}$ because $q_{\mathcal F}(x)=\operatorname{wt}(x)$.
+Every pair except $X_a\to Y_a$ has these zero and full labels.
+For the remaining pair, write $u=u_a$.  Its binary norm is one and
+its weight is $3^3=27$.  Orthogonal weight additivity yields
+\begin{align*}
+ q_{U_a^\perp}(x)-q_{U_a}(x)
+ &=\operatorname{wt}(x)-2\operatorname{wt}(u)[u\cdot x]\\
+ &=\operatorname{wt}(x)+2[u\cdot x]\pmod4.
+\end{align*}
+Since $2[u\cdot x]\equiv2\sum_{j\in\operatorname{supp}(u)}x_j
+\pmod4$, the operator on $X_a\to Y_a$ is the tensor of $C^{-1}$ on the
+27 coordinates of $\operatorname{supp}(u)$ and $C$ elsewhere.
+Put $Z=\operatorname{diag}(1,-1)$.  Direct multiplication gives
+\[
+ C=iZC^{-1}Z,\qquad C^{-1}=-iZCZ.
+\]
+For $k$ columns, let $Z_{a,k}$ be the tensor product of $Z$ on
+those 27 coordinates in every column and the identity elsewhere.
+Apply $Z_{a,k}$ before the network at $X_a$, and apply
+$i^{27k}Z_{a,k}$ after the network at $Y_a$; the latter scalar is
+applied once to the whole role.  There are $27k$ inverse factors, so
+the identity $C=iZC^{-1}Z$ turns each of them into $C$.  The operator
+on this pair is therefore $C^{\otimes mk}$ as well.
+Only the physical $X$ outputs still carry the minus sign of the
+scalar exchange.  Negate those outputs and send output role $\rho(w)$
+back to role $w$.  Every role, including every scratch role, now has
+the required forward tensor product.
+\end{proof}
+
+\subsection{Explicit rational bounds for the two recurrences}
+
+The relative rank deficits are
+\[
+ \eta_{\rm b}=\frac{W_{\rm b}m-s_{\rm b}}{W_{\rm b}m}
+       =\frac{339}{22587335000000},\qquad
+ \eta_{\rm c}=\frac{W_{\rm c}m-s_{\rm c}}{W_{\rm c}m}
+       =\frac{73}{19906842167500}.
+\]
+For both recurrences we may use the fixed rational exponent
+\begin{equation}
+ \tau=\sigma=1-2^{-50}.
+ \label{eq:explicit-motif-exponents}
+\end{equation}
+Both exact deficits displayed above are greater than $20\cdot2^{-50}$.
+Since $m<2^{20}$ and $\log 2<1$, we have $\log m<20$, whence
+\[
+ m^{1-2^{-50}}
+ =m\exp(-2^{-50}\log m)
+ >m(1-20\cdot2^{-50})>m(1-\eta)
+\]
+for either $\eta=\eta_{\rm b}$ or $\eta=\eta_{\rm c}$.
+Consequently
+\[
+ \frac{s_{\rm b}}{W_{\rm b}}<m^\tau,
+ \qquad \frac{s_{\rm c}}{W_{\rm c}}<m^\sigma,
+ \qquad 0<\tau=\sigma<1.
+\]
+Here $\sigma$ is a rational upper bound for the logarithmic exponent
+of the complex recurrence.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/LICENSE b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
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+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/PROVENANCE.md b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/PROVENANCE.md
new file mode 100644
index 0000000000..bebdb72910
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/PROVENANCE.md
@@ -0,0 +1,23 @@
+# Primary bit-scalar and common-frame contract
+
+The three unmodified source files in this directory are carried by Henry Grant / hcg890's PR234 snapshot:
+
+- Repository: https://github.com/hcg890/integer-mult-bounds
+- PR: https://github.com/CrocSwap/integer-mult-bounds/pull/234
+- Exact snapshot commit: `af3fe331ca60c936229e060681ffccbc1c208678`
+- Primary section path in that snapshot: `upstream/build/sections/03-motifs.tex`
+- Accompanying source paths: `upstream/README.md` and `upstream/LICENSE`
+
+The accompanying README identifies the primary work as **OpenAI, Integer multiplication below n log n, September 23, 2026** and records its original citation and publication link. It is retained as `UPSTREAM-README.md`. This is attribution to the primary source; the snapshot commit above belongs to the carrying repository and is not asserted to be an original OpenAI commit. These credits do not imply review or endorsement of this contribution.
+
+The accompanying Apache-2.0 license is retained without modification as `LICENSE`. These files have not been edited, excerpted, or reformatted. The exact content hashes are:
+
+| Bundled file | SHA256 |
+| --- | --- |
+| `03-motifs.tex` | `ed76761194988a01af77ead0ea6469cb5dcd29690ab985a0b5a4006b0f2b69bb` |
+| `UPSTREAM-README.md` | `8d1ceff898a4e0e681679f91c4def485820be9e99f04e4861f2ce601a364723e` |
+| `LICENSE` | `c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4` |
+
+`03-motifs.tex` supplies the bit scalar ring at line50, the common-frame identity at lines149–177, the distinction between scalar and label fields at line225, and the rational-address bit frame contract at lines483–493. It is bundled as theorem evidence, not as a standalone compilable document. The accompanying [`../PARITY-CONTRACT.md`](../PARITY-CONTRACT.md) proves the parity-filter adaptation and records the finite verification obligations. No theorem dependency in that parity argument requires a machine-local path.
+
+This provenance note and the parity contract were prepared with substantial OpenAI Codex assistance. Original source authorship and assistance disclosures remain separate from that disclosure.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/UPSTREAM-README.md b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/UPSTREAM-README.md
new file mode 100644
index 0000000000..c8cb3c3857
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/primary/UPSTREAM-README.md
@@ -0,0 +1,17 @@
+# [Integer multiplication below n log n](paper.pdf)
+
+**Author:** OpenAI
+
+**Date:** September 23, 2026
+
+## Citation
+
+```bibtex
+@misc{OAI:Integer-multiplication-below-n-log-n-September-23-2026,
+  author = {{OpenAI}},
+  title = {{Integer multiplication below $n\log n$}},
+  howpublished = {OpenAI Math Release preprint
+                  \href{https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf}{OAI:Integer-multiplication-below-n-log-n-September-23-2026}},
+  year = {2026}
+}
+```
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/three-stage-cover-bit.tex b/research/gen4-retiming-entrances-target/vendor/pr276/proof/three-stage-cover-bit.tex
new file mode 100644
index 0000000000..f05225d21f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/three-stage-cover-bit.tex
@@ -0,0 +1,264 @@
+\subsection{Atom contract and common endpoint}
+Fix an odd prime $q$, chosen below, and put $R_w=\mathbb Z/q^w\mathbb Z$.
+An atom is a complete consecutive $w$-digit address field. Write $C_n$ for
+reversal of the $n$ atom positions, without reversing digits inside an atom.
+The recursive contract is the involution
+\[
+ F_A(H,D)=(AC_nD,C_nA^{-1}H),
+\]
+where $A$ is a diagonal array of units on the head atoms. Its entries may
+depend on exposed ancestor row fields and the atom index, but not on the
+fresh role fields of this invocation or on the head/data values. Only the
+polynomial-time descriptors generated by the construction are required;
+no constant-cost oracle for arbitrary functions of a prefix is assumed.
+Every call preserves all complete spectator fields and restores its row
+coordinate. The original unweighted call has $A=I$.
+
+For a split idempotent $P$ on the head coordinates set
+\[
+ D_P=\begin{pmatrix}I-P&PC_n\\C_nP&I-C_nPC_n\end{pmatrix},
+ \qquad F=D_I.
+\]
+These are involutions, and $D_P-I$ has split rank $\operatorname{rank}P$.
+Nested commuting-projector identities are polynomial identities and require
+no symmetry of $P$. For $n=mf$ and $G=g\otimes I_f$ define
+\[
+ Q_g=\operatorname{diag}(G,C_nGC_n).
+\]
+Then $Q_gF=FQ_g$ and $Q_gD_PQ_g^{-1}=D_{GPG^{-1}}$.
+Consequently conjugating every base frame by any $g\in\operatorname{GL}_m(R_w)$
+leaves the same full physical endpoint $F$.
+
+Put $Q_A=\operatorname{diag}(A,I)$. Conjugate the entire completed scalar
+word by $Q_A$. Scalar gates mix roles having the same address map, so they
+commute with $Q_A$. A current role routing also commutes with $Q_A$, since
+it changes only fresh fields. Thus only address residuals change, and the
+completed endpoint is $Q_AFQ_A^{-1}=F_A$. More explicitly, when a port
+changes charts from $g$ to $gR_s$, its local label changes from $M$ to
+$R_s^{-1}MR_s$, and
+\[
+ (gR_s)(R_s^{-1}MR_s)(gR_s)^{-1}=gMg^{-1}.
+\]
+This routing is a change of row/chart, not an uncharged dense address map.
+The adapted chart $Q_AQ_gQ_A^{-1}$ commutes with $F_A$. None of these
+conjugations is executed as an extra normalization pass.
+
+\subsection{Explicit rational three-stage geometry}
+Use the retained PR97 local producer with
+\[
+ h=23,\qquad v=1771,\qquad R_{\rm loc}=28866,\qquad \ell=506.
+\]
+Its physical projector ranks and scalar word are unchanged. On
+$\mathcal A=\mathbb Q^{23}$ take the form $H_0=(I-J/9)/2$.
+For a triple $S$ let $q_S=\chi_S$; then $q_S^tH_0q_S=1$.
+Fix $q_0=\chi_{\{1,2,3\}}$ and $K=q_0^\perp$. A rational basis is
+\[
+ k_i=e_i-(e_i^tH_0q_0)q_0,\qquad 2\le i\le23.
+\]
+Projection along $q_0$ is injective on the span of $e_2,\ldots,e_{23}$,
+since $q_0$ has nonzero first coordinate. Thus this is indeed a basis.
+Let $\mathcal B,\mathcal C$ be orthogonal copies of $K$ and put
+$\mathcal E=\mathcal A\perp\mathcal B\perp\mathcal C$, of dimension $m=67$.
+
+Choose a coordinate permutation $\pi_S$ taking $\{1,2,3\}$ to $S$.
+It preserves $H_0$. The rational isometry $R_{12,S}$ fixes $q_S$ and
+$\mathcal C$, and exchanges $\pi_Sk_i\in q_S^\perp\subset\mathcal A$
+with $k_i\in\mathcal B$. Define $R_{23,S}$ by exchanging the same vectors
+with their copies in $\mathcal C$, fixing $q_S$ and $\mathcal B$.
+Both maps are involutions. A hyperedge $(g,S)$ uses the invocations
+$gR_{12,S},g,gR_{23,S}$, with active spaces
+\[
+ g(\mathcal B+\mathbb Qq_S),\qquad g\mathcal A,
+ \qquad g(\mathcal C+\mathbb Qq_S).
+\]
+Their projectors commute; their pairwise and common intersection is the
+projector $P_{gq_S}$, and their sum is $I+2P_{gq_S}$.
+This follows from the orthogonal decomposition
+$\mathbb Qq_S\perp q_S^\perp\perp\mathcal B\perp\mathcal C$ before
+conjugation. These are the cumulative-projector three-stage transfer
+identities: the three scalar shears complete the interchange, with zero
+interstage connectors and no rank-one endpoint correction. Each port
+family visits the full cover bijectively, by right multiplication with
+its displayed involution. The physical ledger is therefore three copies
+of the local auxiliary, data and center histograms, and three copies of
+the exterior histogram $m-\text{nullity}$.
+
+\subsection{One weighted child on a generic residue class}
+Work first on one atom column. Let $g$ be its weighted residual involution,
+of split rank $r$ relative to $I$. If the cross block has generic northeast
+rank profile, unit lower row and column elimination, without normalizing
+pivots, gives
+\[
+ Lg_{XY}R=ED_pF_0^t,
+ \quad E=(e_1,\ldots,e_r),\quad
+ F_0=(e_m,\ldots,e_{m-r+1}),
+\]
+with invertible diagonal $D_p$. Conjugate by $\operatorname{diag}(L,R^{-1})$.
+Split rank and the unit pivot minor give a factorization
+\[
+ g-I=\binom EB(A_0,D_pF_0^t),\qquad
+ A_0E+D_pF_0^tB=-2I_r.
+\]
+For clarity, if $g-I=UV$, then $g^2=I$ gives
+$U(VU+2I)V=0$. The unit minor supplies a left inverse of $U$ and a right
+inverse of $V$, proving the identity over the local ring itself.
+Set
+\[
+ K=-(B+F_0D_p^{-1})E^t+F_0D_p^{-1}A_0(I-EE^t),
+ \qquad S=\begin{pmatrix}I&0\\K&I\end{pmatrix}.
+\]
+The identities $KE=-B-F_0D_p^{-1}$ and
+$D_pF_0^tK=A_0+E^t$ give
+\[
+ SgS^{-1}=\begin{pmatrix}
+ I-EE^t&ED_pF_0^t\\F_0D_p^{-1}E^t&I-F_0F_0^t
+ \end{pmatrix}.
+\]
+This is one weighted reversed interchange on the first $r$ head and last
+$r$ tail coordinates. All other factors are unit lower intrabank maps or
+lower cross-bank additive maps. Thus variable diagonal units remain in
+the child's weight array rather than becoming unsupported routing passes.
+
+For $n=mf$, group atoms by coarse coordinate $i$ and column $j$.
+If $L_P,R_P,D_P$ are unweighted normalizers for the current projector and
+$A_j=\operatorname{diag}(A[if+j])$, then
+$L_j=A_jL_PA_j^{-1}$ and $R_j=R_P$ are unit lower normalizers for
+$A_jPC_m$. The child's exact contiguous index rule is
+\[
+ A_{\rm child}[kf+j]=A[i_kf+j]D_P[k].
+\]
+The cross-bank atom pairing is reversed, and $C_r\otimes C_f=C_{rf}$.
+Hence the middle operation is exactly one $rf$-atom call of the same
+contract, with no interleaving or gathering. Its coefficients depend only
+on parent prefix fields, which become ancestor spectators at the child;
+the child's fresh roles come from disjoint unused row stock.
+
+All unit lower adapters require $O(n)$ atom passes. The retained ordered
+affine lemma implements each later-target shear in $O(V)$, including
+prefix-controlled offsets. The generated descriptors have polynomial cost
+in $w$: good-class evaluation follows one ancestral index per level;
+fallback evaluation branches by a constant per level. Since depth is
+$O(\log e)$ and $w=\lceil e^{1/1000}\rceil$, this costs $e^{O(1)}=w^{O(1)}$.
+Stored ancestor data use $O(w\log e)$ bits. The proof of the ordered affine
+lemma still applies with these controls: polynomial preparation per prefix
+is absorbed by the complete $q^w$ target fiber. Unrelated spectator counters
+are incremented by ripple counting rather than read in their entirety.
+
+\subsection{Weighted leaves and a genuine local-ring fallback}
+At one atom write $J_a=\left(\begin{smallmatrix}0&a\\a^{-1}&0\end{smallmatrix}\right)$,
+$U(a)=\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)$ and
+$L(b)=\left(\begin{smallmatrix}1&0\\b&1\end{smallmatrix}\right)$.
+Then
+\[
+ J_a=\operatorname{diag}(1,-1)U(a)L(-a^{-1})U(a),
+ \qquad U(a)=J_1L(a)J_1.
+\]
+Thus a weighted leaf uses four old ordinary atom interchanges, three
+prefix-controlled shifts and one fixed sign. With
+$a_{\rm old}=384599/10^{10}$ it costs $O(Vw^{1-a_{\rm old}})$.
+This constant occurs only at stopped leaves.
+
+A bad residue class cannot be treated by field Bruhat elimination:
+an entry zero modulo $q$ need not vanish modulo $q^w$. Instead Gaussian
+eliminate the full invertible residual of size $N_0=2m$ with unit pivots.
+Each invertible Schur complement has a unit in its next pivot column;
+row swaps and unnormalized additions clear that column. There are at most
+$N_0(N_0-1)$ additions and $N_0$ swaps. Pivot choices are determined by
+the unweighted low residue class: diagonal conjugation scales every
+Schur-complement row and column by units and preserves its zero pattern.
+The final diagonal has product a fixed sign, since the residual has
+determinant $(-1)^r$ and row swaps change only the sign.
+
+A lower addition is a paid additive adapter. An upper addition is
+conjugated into a lower addition by two ordinary coarse-field swaps.
+For a field of $f$ atoms, let $R_{\rm tail}$ reverse the later field.
+Then the ordinary weighted swap is
+\[
+ J_A=R_{\rm tail}F_AR_{\rm tail},\qquad
+ J_A(H,D)=(AD,A^{-1}H).
+\]
+Each $R_{\rm tail}$ is one unweighted reversed call on the first and last
+$\lfloor f/2\rfloor$ atoms, fixing a possible middle atom. Thus $J_A$
+costs at most three children of widths $f,\lfloor f/2\rfloor,
+\lfloor f/2\rfloor$. A paired diagonal scaling is $J_aJ_1$, at most six
+children. The full diagonal is a product of $N_0-1$ such pairs and a fixed
+sign. Across the two banks the reversed pairing already makes the swaps
+and diagonal pairs directly reversed calls; the preceding ordinary bounds
+remain conservative. Reindexing a tail weight by $j\mapsto f-1-j$ changes
+only its descriptor. Charging every addition as upper therefore gives
+\[
+ 6N_0(N_0-1)+3N_0+6(N_0-1)<32m^2.
+\]
+Every child has width at most $f$, hence ratio at most $1/m$. Coefficients
+are computed from constant-sized local-ring matrices and parent weight
+descriptors; only units are inverted. This proves the fallback cost,
+including its actual reversals, rather than assuming nonunit pivots away.
+
+\subsection{Finite covers, batching, and the strict moment}
+Take $q>2^{80}$ avoiding all fixed rational denominators and rank witnesses.
+At atom width $w$ use the finite cover $\operatorname{GL}_m(R_w)$ and its
+right-multiplication edges $g\mapsto gR_s$. Every vertex has the unique chart
+\[
+ g=g_0+qG_1,\quad g_0\in\operatorname{GL}_m(\mathbb F_q),
+ \quad G_1\in(\mathbb Z/q^{w-1}\mathbb Z)^{m^2},
+\]
+using fixed representatives for $g_0$. Right multiplication permutes $g_0$
+and acts affinely on $G_1$, with a carry determined by $g_0$. Its fixed
+dimensional rational linear part factors into fixed scalings, ordered
+shifts and a constant number of old width-$O(w)$ interchanges. Thus each
+fixed port routing costs $O(Vw^{1-a_{\rm old}})$.
+
+Let $W_0=|\operatorname{GL}_m(\mathbb F_q)|(2v+3R_{\rm loc})$.
+The full role count is $W(w)=W_0q^{m^2(w-1)}$. Split preceding rows into
+low role type, high matrix and unused stock. Batch \emph{all} high matrices
+for each low type in one stream. A frame edge is one child on this whole
+batch, of volume $V/W_0$, and routing is executed once per fixed operation
+type. Consequently neither the number of tapes nor the number of child
+programs grows with $w$. High cardinality cancels in the normalized moment,
+but its $m^2(w-1)$ digits are charged in the row reserve.
+
+For each fixed projector require the leading minors of sizes $1$ through
+$r$ to be units. Each cleared minor polynomial in $g_0$ is nonzero:
+similarity to $\operatorname{diag}(I_r,0)$ supplies a witness after the
+fixed rank is preserved modulo $q$. Their total degree is at most $m^3$.
+The polynomial zero bound and conditioning on invertibility (a factor at
+most two) give bad fraction at most $2m^3/q<10^{-16}$ for each edge type.
+No simultaneous union bound over edge types is needed, since their moments
+are averaged separately. Good classes use the whole-rank child; bad
+classes use the full $32m^2$-child fallback just proved.
+
+Let $H_r$ be the three-stage histogram described above and
+$W=2v+3R_{\rm loc}=90140$. The retained ledger gives
+\[
+ \sum_r rH_r=6037356,\qquad Wm-\sum_r rH_r=2024=2v-3\ell,
+ \qquad \max\{r:H_r>0\}=66.
+\]
+For $a=747/2000000$, $\tau=1-a$, and $b=10^{-16}$ the conservative moment is
+\[
+ \mu_\tau\le
+ \sum_r\frac{H_r}{W}(r/m)^\tau+
+ b\frac{32m^2\sum_rH_r}{W}(1/m)^\tau<1.
+\]
+The entire fallback is added; no displaced good contribution is subtracted.
+The exact script \path{scripts/three_stage_cover_network.py} and certificate
+\path{certificates/three-stage-cover-network.json}, from the retained axis
+\path{certificates/three-stage-cover-bit-input.json}, give
+$1-\mu_\tau>6.3397366396\cdot10^{-7}$.
+The certificate uses the 32-term positive atanh logarithm series with its
+geometric tail, $\exp(u)\le1+u+u^2/(2(1-u/3))$, and upward rounding to
+the grid $2^{-120}$. All inputs have $0\le u<3$; these are rational upper
+bounds, not floating-point root estimates. Since every child ratio is at
+most one and $\tau<1$, this same strict bound implies $\mu_1<1$.
+
+With $T(n,w)$ denoting time divided by logical volume, the fixed low-type
+profile $\{c_r\}$, including fallback classes, satisfies
+\[
+ T(n,w)\le\sum_rc_rT(r\lfloor n/m\rfloor,w)+Cn+Cw^{1-a_{\rm old}}
+ \quad(n\ge m),\qquad
+ T(n,w)\le Cw^{1-a_{\rm old}}\quad(n<m).
+\]
+Peeling fewer than $m$ leftover atoms uses the weighted leaf algorithm.
+The constants are independent of $w,n$ and ancestor values. Induction,
+using $\mu_1<1$ for the linear term and $\mu_\tau<1$ for the stopped term,
+gives $T(n,w)=O(n+n^\tau w^{1-a_{\rm old}})$. The maximum proper ratio
+$66/67$ has halving degree $47$, so recursion depth is $O(\log n)$.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/proof/three-stage-cover-rows.tex b/research/gen4-retiming-entrances-target/vendor/pr276/proof/three-stage-cover-rows.tex
new file mode 100644
index 0000000000..590da4b892
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/proof/three-stage-cover-rows.tex
@@ -0,0 +1,95 @@
+\subsection{Internal row reserve and ordinary conversion}
+The finite cover requires a row divisor $W(w)$ at each coarse level.
+All children have ratio at most $66/67$ and depth
+$D(n)\le47\lceil\log_2\max(2,n)\rceil+O(1)$.
+A sufficient common divisor is $W(w)^{D(n)}$ times the inherited old-leaf
+reserve. The old supplier has its retained complete-row contract and
+logarithmic reserve. Therefore a sufficient integer $S(e,w)$ satisfies
+\[
+ \log_qS(e,w)=O(w\log e).
+\]
+Unused stock is divided only into fresh descendant role fields; exposed
+parent low/high fields are spectator prefixes. Their weights cannot depend
+on those fresh roles. Every completed call restores its row coordinate,
+so successive residuals and the outer wrapper reuse one reserve instead
+of multiplying reserves for sequential calls.
+
+The unweighted reversed endpoint $F_n(H,D)=(C_nD,C_nH)$ converts to an
+ordinary interchange by the chronological sequence
+\[
+ D\leftarrow D-H;\quad F_n;\quad D\leftarrow D+H;\quad
+ F_n;\quad D\leftarrow H-D.
+\]
+Indeed the successive values are $(H,D-H)$, $(C_n(D-H),C_nH)$,
+$(C_n(D-H),C_nD)$, $(D,D-H)$, and $(D,H)$.
+The three additive maps cost $O(Vn)$ in the atom model. The two calls
+reuse restored rows; their constant multiplicity is outside the recursion
+and does not multiply its characteristic moment.
+
+\subsection{Borrowing and restoring the stock}
+Set $\beta=1/1000$, $w=\lceil e^\beta\rceil$, and
+$k=\lceil\log_qS(e,w)\rceil=O(w\log e)$, using the depth bound for the
+original width $e$. For sufficiently large $e$, $k<e/2$. Write the two
+original complete radix-$q$ chunks as $H=(H_{\rm hi},H_{\rm body})$ and
+$D=(D_{\rm hi},D_{\rm body})$, both high parts having $k$ digits. The
+physical order, including arbitrary original complete spectators $Z$, is
+\[
+ H_{\rm hi},\ H_{\rm body},\ Z,\ D_{\rm hi},\ D_{\rm body}.
+\]
+The complete $q^k$ range of $H_{\rm hi}$ already precedes both bodies.
+Reinterpret it as a preceding row field; $D_{\rm hi}$ remains an intervening
+spectator. Pad only this row range to $\lceil q^k/S\rceil S$. As $q^k\ge S$,
+the padding factor is less than two.
+
+Execute the completed \emph{ordinary} body wrapper with this row reserve,
+then remove the padding. Each row is restored, so the genuine row range
+is invariant at the completed endpoint. The order of values is now
+\[
+ H_{\rm hi},\ D_{\rm body},\ Z,\ D_{\rm hi},\ H_{\rm body}.
+\]
+One inherited ordinary width-$k$ interchange of the two high parts,
+with the bodies and $Z$ as spectators, gives
+\[
+ D_{\rm hi},\ D_{\rm body},\ Z,\ H_{\rm hi},\ H_{\rm body}.
+\]
+This is precisely the original full-chunk interchange. Its extra cost is
+$O(Vk^{1-a_{\rm old}})\le O(Vw\log e)$, conservatively. No full body is
+moved once per borrowed digit. Padding occurs only in this outer wrapper;
+it contributes one volume constant, not a recursive branching factor.
+The wrapper does not rely on a raw reversed call preserving borrowed high
+positions. Small widths use the retained supplier directly.
+
+\subsection{Uniform saving and return to binary addresses}
+Select atom width from the original $e$. Since $k=o(e)$, the body width
+$e-k$ has the same asymptotic powers as $e$. Apply the ordinary wrapper to
+its complete atom body and the old ordinary supplier to fewer than $w$
+remaining digits. The stopped recurrence and the borrowing cost give
+\[
+ O\!\left(V\left[e^{1-\beta}+
+ e^{(1-\beta)(1-a)+\beta(1-a_{\rm old})}+e^\beta\log e\right]\right).
+\]
+Here $a=747/2000000$ and $a_{\rm old}=384599/10^{10}$. Set
+\[
+ a_{\rm bit}=(1-\beta)a+\beta a_{\rm old}
+ =\frac{3731649599}{10^{13}}=0.0003731649599.
+\]
+The inequalities $\beta>a_{\rm bit}$ and $\beta<1-a_{\rm bit}$ make both
+the atom-adapter and borrowing terms lower order. The remainder cost
+$O(Vw^{1-a_{\rm old}})$ is also covered. Thus the ordinary radix-$q$
+interchange has cost $O(Ve^{1-a_{\rm bit}})$, without an externally supplied
+superpolynomial stock of rows.
+
+For an original binary chunk range $[2^e]$, let
+$t=\lceil e/\log_2q\rceil$ and embed it numerically into $[q^t]$.
+Pad both exchanged ranges while retaining every spectator. The total
+logical-volume increase is below $q^2$. Execute the completed ordinary
+radix-$q$ interchange, then remove the padding. Its endpoint preserves the
+rectangular genuine set $[2^e]\times[2^e]$; intermediate maps may mix genuine
+and padded addresses, which does not affect this endpoint justification.
+As $q$ is fixed and $t=\Theta(e)$, the binary interchange has the same
+saving exponent. All schedules use a fixed number of finite-alphabet
+tapes; low residue tables and port types are fixed independently of $w$.
+
+The conclusion retains the original local-producer, ordered-affine,
+ordinary-leaf and multiplication-framework hypotheses. It adds no free
+unit-scaling, dense chart transformation, or external row-stock primitive.
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/raw_ledger.py b/research/gen4-retiming-entrances-target/vendor/pr276/raw_ledger.py
new file mode 100644
index 0000000000..b55b02fd11
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/raw_ledger.py
@@ -0,0 +1,189 @@
+"""Independent fresh gen4 physical path census, including both reflections.
+Derived from the source527 census (eumemic); constants rebound to the gen4 word.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+No saved receipt, search script, or historical profile is consumed.
+"""
+from collections import Counter,defaultdict
+from types import SimpleNamespace
+
+def run(context):
+ m=SimpleNamespace(**context);W=m.W;C=m.C;chosen=m.pair_selection;fresh=m.fresh;pair_byalias=m.pair_byalias;pair_bydirty=m.pair_bydirty
+ compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ zero=W.register([]);compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ # Exact raw event sequence, with every actual extra source included.
+ events=[]
+ for j,op in enumerate(W.rest):
+  for s in m.at[j]:events.append(dict(kind='gauge',ref=s,frame=W.gauge[s]['frame'],targets=list(m.adj[s])))
+  if op in m.bywrite:events.append(dict(kind='terminalwrite',ref=op,frame=W.opframe[op],targets=[m.bywrite[op]['pivot']]))
+  if op in m.afterwrite:events.append(dict(kind='terminalread',ref=op,frame=m.afterwrite[op]['root_frame'],targets=m.afterwrite[op]['targets']))
+ for s in m.at[len(W.rest)]:events.append(dict(kind='gauge',ref=s,frame=W.gauge[s]['frame'],targets=list(m.adj[s])))
+ endgauge=len(events)
+ for j,r in enumerate(W.g['roots']):
+  if r['kind']=='side'and j not in m.deletedroots:events.append(dict(kind='root',ref=j,frame=W.w['root_frame'][j],targets=r['targets']))
+  for e in m.deliveries[j]:events.append(dict(kind='K',ref=e['passive'],frame=e['deliver_frame'],targets=e['receivers']))
+ for t in range(W.v):events.append(dict(kind='endpoint',ref=t,frame=W.register(W.module.kernel([C.cov[t]],W.h)[0]),targets=[t]))
+ 
+ def histogram(t,path):
+  h=Counter();rev=Counter();assert path[0]==zero and C.dimf[path[-1]]==W.h-1
+  for f in path:assert C.nondeg(f)and all(W.module.dot(C.cov[t],b)==0 for b in C.B[f]),('cap/nondeg',t,f)
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b),('forward inclusion',t,a,b)
+   d=C.dimf[b]-C.dimf[a];assert d>=0
+   if d:h[d]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]),('reflected inclusion',t,a,b)
+   d=len(C.A[b])-len(C.A[a]);assert d>=0
+   if d:rev[d]+=1
+  assert h==rev and sum(k*v for k,v in h.items())==W.h-1
+  return h
+ 
+ def paths(agg,readframes,echelon,rankgroups):
+  rankowner={t:k for k,g in enumerate(rankgroups)for t in g['targets']}
+  out=[[zero]for _ in range(W.v)];owner={t:k for k,g in enumerate(agg)for t in g['targets']};roles=defaultdict(list)
+  for k,g in enumerate(agg):
+   for s in g['roles']:roles[s].append(k)
+  active=set(range(len(agg)));rankactive=set(range(len(rankgroups)));echactive=set(range(len(echelon)));seen=[set()for _ in echelon];restores=[]
+  for j,e in enumerate(events):
+   if j>=endgauge:assert not active and not rankactive and not echactive
+   s=e['ref'];T=set(e['targets'])
+   if e['kind']=='gauge':
+    if s in pair_byalias:continue
+    if s in fresh:
+     for t,c in fresh[s]['transformed_response'].items():
+      if c:out[int(t)].append(W.gauge[s]['frame'])
+     continue
+    skip=set()
+    for k,g in enumerate(echelon):
+     if k not in echactive:continue
+     if s not in g['roles']:
+      if T&set(g['targets']):
+       assert seen[k]==g['roles'];restores.append(dict(group=k,before_role=s,event=j))
+       for t in g['targets']:out[t].append(g['frame'])
+       echactive.remove(k)
+      continue
+     seen[k].add(s);skip.update(g['targets'])
+     for t,a in g['response'].items():
+      if a.get(s,0):out[t].append(W.gauge[s]['frame'])
+    for k in sorted({rankowner[t]for t in T if t in rankowner}):
+     if k in rankactive and s not in rankgroups[k]['roles']:
+      for t in rankgroups[k]['targets']:out[t].append(rankgroups[k]['frame'])
+      rankactive.remove(k)
+    for k in sorted({owner[t]for t in T if t in owner}):
+     if k in active and s not in agg[k]['roles']:
+      for t in agg[k]['targets']:out[t].append(agg[k]['frame'])
+      active.remove(k)
+    for k in roles[s]:
+     assert k in active;g=agg[k];out[g['pivot']].append(readframes[s,k]);skip.update(g['targets'])
+    for t in e['targets']:
+     if t in skip:continue
+     rk=rankowner.get(t)
+     if rk in rankactive and t in rankgroups[rk]['dependent']:continue
+     out[t].append(e['frame'])
+   else:
+    assert not(T&{t for k in active for t in agg[k]['targets']})
+    assert not(T&{t for k in echactive for t in echelon[k]['targets']})
+    for t in e['targets']:out[t].append(e['frame'])
+  H=Counter()
+  for t,p in enumerate(out):H.update(histogram(t,p))
+  return out,H,restores
+ 
+ newpaths,target,restores=paths(m.agg,m.read_frames,m.echelon,m.rankgroups)
+ # Recover raw literal adjoint independently, respecting all omitted copies.
+ adj=[{}for _ in range(W.R)]
+ for root,role in zip(W.g['roots'],W.w['rootroles']):
+  for t in root['targets']:adj[role][t]=adj[role].get(t,0)+1
+ for i in reversed(W.phase1+W.rest):
+  if i in m.omitted:continue
+  a,b,_=W.ops[i]
+  for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c
+ assert adj==m.adj
+ oldused={r[k]for r in m.selection+m.gauge_selection if r['role']not in pair_byalias for k in('source','partner')}
+ assert len({r[k]for r in chosen for k in('source','partner')})==2*len(chosen)==0 and not oldused&{r[k]for r in chosen for k in('source','partner')}
+ for r in chosen:
+  b=r['aliased_role'];response=Counter(adj[b])
+  for a,c in r['retained_dirty_coefficients'].items():
+   for t,v in adj[a].items():response[t]+=c*v
+  assert not any(response.values())
+ # Complete physical source and auxiliary census, including all alias handoffs.
+ recipient={d:b for b,d in W.pairs};roots=defaultdict(list)
+ for j,s in enumerate(W.w['rootroles']):roots[s].append(W.w['root_frame'][j])
+ source_role={s:n for n,s in W.source.items()};plainborrow={r['role']:r for r in m.selection};gauges={r['role']:r for r in m.gauge_selection}
+ assert len(plainborrow)==0 and len(gauges)==0 and len(m.borrow)==0
+ seq={s:[('op',i,W.opframe[i])for i in W.role_ops[s]]+[('root',j,f)for j,f in enumerate(roots[s])]for s in range(W.R)}
+ def physical_path(s):
+  a=list(seq[s])
+  if s in pair_bydirty:a=[('paired-source-injection',s,pair_bydirty[s]['mix_frame'])]+a
+  if s in recipient:
+   b=recipient[s];a+=[('alias',b,W.gauge[b]['frame'])]+seq[b]
+  return a+[('full',s,W.w['full_frame'])]
+ count=0
+ 
+ def census_hist(start,events):
+  nonlocal count
+  count+=1;prev=start;dim=C.dimf[start]if start is not None else 0;out=Counter();chain=[]if start is None else[start]
+  for _,_,f in events:
+   assert C.nondeg(f)and(prev is None or C.sub(prev,f));d=C.dimf[f]-dim;assert d>=0
+   if d:out[d]+=1
+   prev=f;dim=C.dimf[f];chain.append(f)
+  assert dim==24;reflected=Counter()
+  for a,b in zip(reversed(chain),list(reversed(chain))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);d=len(C.A[b])-len(C.A[a]);assert d>=0
+   if d:reflected[d]+=1
+  if start is None:
+   d=24-len(C.A[chain[0]])
+   if d:reflected[d]+=1
+  assert reflected==out
+  return out,chain
+ internal=Counter();sources=Counter();pathrows={};sourcepaths={};dirtypaths={}
+ for s in m.regs:
+  start=W.gauge[s]['frame']if s in W.gauge else W.w['source_frame'][source_role[s]]if s in source_role else None
+  H,chain=census_hist(start,physical_path(s))
+  if s in source_role:H[1]+=1
+  internal.update(H);pathrows['a'+str(s)]=compact(H)
+  if s in pair_bydirty:dirtypaths[str(s)]=[zero]+chain
+ for j,r in enumerate(W.g['roots']):
+  if r['kind']=='center':internal[C.dimf[W.w['root_frame'][j]]]+=1
+ for entry in W.k['entries']:
+  carrier,n=entry['carrier'],entry['passive'];H,chain=census_hist(entry['carrier_chain'][0],[('carrier',j,f)for j,f in enumerate(entry['carrier_chain'][1:])]);sources.update(H)
+  if n not in m.by_source:
+   H,chain=census_hist(entry['passive_chain'][0],[('passive',j,f)for j,f in enumerate(entry['passive_chain'][1:])]);sources.update(H);pathrows['s'+str(n)]=compact(H);continue
+  r=m.by_source[n];s=r['role'];events=physical_path(s)
+  if s in plainborrow:
+   r=plainborrow[s];events=[x for x in events if not(x[0]=='op'and x[1]==r['omit_copy'])];at=next(i for i,x in enumerate(events)if x[0]=='op'and x[1]==r['early']);events.insert(at,('mix',n,entry['mix_frame']))
+  else:
+   assert s in gauges;events=[('mix',n,entry['mix_frame']),('gauge',s,W.gauge[s]['frame'])]+events
+  H,chain=census_hist(W.w['source_frame'][n],events);sources.update(H);pathrows['s'+str(n)]=compact(H)
+  if s in m.extra_byrole:sourcepaths[str(s)]=chain
+ assert count==18170 and len(sourcepaths)==0 and len(dirtypaths)==0 and sum(k*v for k,v in sources.items())==1760*23
+ gauges=Counter(z['dim']for s,z in W.gauge.items()if s not in W.donor and s not in m.borrow)
+ assert gauges=={20:2200,21:266}
+ copies=Counter(C.dimf[W.w['root_frame'][j]]for j,r in enumerate(W.g['roots'])if r['kind']=='center');assert copies=={22:24}
+ withoutcopies=internal.copy();withoutcopies.subtract(copies);assert min(withoutcopies.values())>=0
+ helper=internal+sources+target;h=24;v=1760;R=len(m.regs);M=120;stock=4*v+R
+ assert R==16410 and len(m.borrow)==0
+ assert sum(k*n for k,n in helper.items())==h*R+2*v*(h-1)+sum(k*n for k,n in copies.items())-sum(k*n for k,n in gauges.items())
+ idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)});five=Counter({r:5*n for r,n in helper.items()});five.update(idle)
+ for r,n in gauges.items():five[5*r]+=n
+ mass=sum(k*n for k,n in five.items());assert M*stock-mass==4400
+ raw=dict(schema='gen4-fresh-raw-ledger/1',source_head=context.get('source_head','gen4'),h=h,v=v,physical_R=R,source_aliases=len(m.borrow),terminal_sinks=len(m.terminal),physical_donor_recipient_identifications=len(W.pairs),physical_internal_excluding_center_copies=compact(withoutcopies),paid_center_copy_histogram=compact(copies),physical_source_histogram=compact(sources),physical_target_histogram=compact(target),one_stage_helper_histogram_including_copies=compact(helper),auxiliary_entrance_rank_histogram=compact(gauges),auxiliary_entrance_count=sum(gauges.values()),helper_rank_mass=sum(k*n for k,n in helper.items()),five_stage_profile=dict(m=M,W=stock,histogram=compact(five),idle_histogram=compact(idle),calls=sum(five.values()),rank_mass=mass,deficit=M*stock-mass,maxchild=max(five)),source_aux_paths=count,target_paths=1760,extra_source_paths=len(sourcepaths),paired_dirty_paths=len(dirtypaths),all_reflected_ledgers=True,all_zero_response_relations=True,scope='Fresh complete gen4 raw physical source/internal/target and copied-center ledger. Both reflected chains checked; no saved execution receipt consumed.')
+ assert raw['five_stage_profile']['calls']==487546 and mass==2809600
+ return raw
+
+def rebind_parity(raw,receipt):
+ """Bind the fresh required-use census to the retained producer source ledger."""
+ from copy import deepcopy
+ def hist(x):return Counter({int(r):n for r,n in x.items()if n})
+ assert receipt['status']=='PASS_FRESH_PARITY_FUSION_AND_INDEPENDENT_REQUIRED_FRAME_CENSUS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_all_input_output_frames']
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert source==hist(raw['physical_source_histogram'])
+ assert internal==hist(raw['physical_internal_excluding_center_copies'])+copies
+ delta=target.copy();delta.subtract(hist(raw['physical_target_histogram']));assert {r:n for r,n in delta.items()if n}=={}
+ producer=deepcopy(raw);helper=source+target+internal;five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for a,n in hist(raw['auxiliary_entrance_rank_histogram']).items():five[5*a]+=n
+ assert sum(five.values())==487546 and sum(r*n for r,n in five.items())==2809600
+ raw['schema']='gen4-parity-fused-fresh-raw-ledger/1';raw['producer_ledger']=producer
+ raw['physical_target_histogram']={str(r):n for r,n in sorted(target.items())};raw['one_stage_helper_histogram_including_copies']={str(r):n for r,n in sorted(helper.items())}
+ raw['five_stage_profile'].update(histogram={str(r):n for r,n in sorted(five.items())},calls=sum(five.values()))
+ raw['parity_transform']=receipt;raw['scope']='Fresh gen4 producer ledger plus independently rebuilt actual surviving-use ledger after F2 payload identity elision and same-stream nested MOVE fusion. Both reflected endpoint inclusions checked. No address arithmetic reduced modulo2.'
+ return raw
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/requirements.txt b/research/gen4-retiming-entrances-target/vendor/pr276/requirements.txt
new file mode 100644
index 0000000000..1ca5fd0616
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/requirements.txt
@@ -0,0 +1 @@
+sympy==1.14.0
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/scalar/word.py b/research/gen4-retiming-entrances-target/vendor/pr276/scalar/word.py
new file mode 100644
index 0000000000..95b9affd44
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/scalar/word.py
@@ -0,0 +1,263 @@
+def replay(mode='F2',direction=1,bits=24,mutation=None):
+ major=mode=='bound';binary=mode=='F2';v=W.v
+ unit=(lambda i:1)if major else(lambda i:1<<i)if binary else(lambda i:1<<(bits*i))
+ def add(x,c,y):return x+abs(c)*y if major else x^y if binary and c&1 else x if binary else x+c*y
+ target_frames=[None]*v;target_paths=[[]for _ in range(v)];center_reads=[];target_hist=Counter()
+ aggregation_active=[True]*len(agg);aggregation_read=[set()for _ in agg];aggregation_restores=[];aggregation_pivot_reads=0
+ rank_active=set(range(len(rankgroups)));rank_seen=[set()for _ in rankgroups];rank_restores=[];rank_skipped=0
+ echelon_active=set(range(len(echelon)));echelon_seen=[set()for _ in echelon];echelon_restores=[];echelon_reads=0
+ def target_move(t,f):
+  previous=target_frames[t];assert previous is None or C.sub(previous,f),('actual target chronology',t,previous,f)
+  assert all(W.module.dot(C.cov[t],b)==0 for b in C.B[f]),('actual target cap',t,f)
+  d=C.dimf[f]-(0 if previous is None else C.dimf[previous]);assert d>=0
+  if d:target_hist[d]+=1
+  target_frames[t]=f;target_paths[t].append(f)
+ X0=[unit(i)for i in range(v)];Y0=[unit(v+i)for i in range(v)];Z0={r:unit(idx[r])for r in regs};x=X0[:];y=Y0[:];z=Z0.copy();top=1;done=[]
+ def track(value):
+  nonlocal top
+  if major:top=max(top,value)
+  return value
+ def value(s):
+  s=W.phys[s];return x[borrow[s]]if s in borrow else z[s]
+ def assign(s,val):
+  s=W.phys[s]
+  if s in borrow:x[borrow[s]]=track(val)
+  else:z[s]=track(val)
+ source_paths={role:[W.w['source_frame'][r['source']],r['mix_frame']]for role,r in extra_byrole.items()}
+ pair_dirty_paths={r:[zero]for r in pair_bydirty}
+ def source_move(s,f):
+  role=W.phys[s]
+  if role in pair_dirty_paths:
+   assert C.sub(pair_dirty_paths[role][-1],f),('paired dirty chronology',role,pair_dirty_paths[role][-1],f)
+   pair_dirty_paths[role].append(f)
+  if role not in source_paths:return
+  assert C.sub(source_paths[role][-1],f),('orderedsource chronology',s,role,source_paths[role][-1],f)
+  source_paths[role].append(f)
+ responses=W.adjoint() if mutation=='old_adjoint' else adj
+ def aggregate_restore(k,trigger):
+  if not aggregation_active[k]:return
+  group=agg[k];pivot=group['pivot'];assert aggregation_read[k]==set(group['roles']),('early aggregation inverse',k,trigger,aggregation_read[k])
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_aggregation_inverse' or k!=39:
+   for t in group['targets']:
+    if t!=pivot:y[t]=track(add(y[t],1,y[pivot]))
+  aggregation_active[k]=False;aggregation_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def rank_restore(k,trigger):
+  group=rankgroups[k];assert k in rank_active and rank_seen[k]==group['roles']
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_rank_inverse'or k!=0:
+   for t,cs in group['dependent'].items():
+    for p,c in cs.items():y[t]=track(add(y[t],c,y[p]))
+  rank_active.remove(k);rank_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def echelon_restore(k,trigger):
+  group=echelon[k];assert echelon_seen[k]==group['roles']
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_echelon_inverse'or k!=0:
+   for t,p,c in reversed(group['moves']):y[t]=track(add(y[t],-c,y[p]))
+  echelon_active.remove(k);echelon_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def read(s):
+  nonlocal aggregation_pivot_reads,rank_skipped,echelon_reads
+  if s in pair_byalias:
+   if mutation=='subtract_paired_alias'and s==next(iter(pair_byalias)):
+    for t,c in adj[s].items():y[t]=track(add(y[t],-direction*c,value(s)))
+   return
+  if s in fresh:
+   if mutation=='omit_transformed_source_read'and s==next(iter(fresh)):return
+   for t,c in fresh[s]['transformed_response'].items():
+    t=int(t);source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame']);y[t]=track(add(y[t],-direction*c,value(s)))
+   return
+  echelon_skip=set()
+  if s in W.gauge:
+   for k,group in enumerate(echelon):
+    if k not in echelon_active:continue
+    if s not in group['roles']:
+     if set(responses[s])&set(group['targets']):echelon_restore(k,s)
+     continue
+    echelon_seen[k].add(s);echelon_skip.update(group['targets'])
+    for t,a in group['response'].items():
+     c=a.get(s,0)
+     if not c:continue
+     if mutation=='flip_echelon_sign'and k==0 and c<0:c=-c
+     source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame']);y[t]=track(add(y[t],-direction*c,value(s)));echelon_reads+=1
+  if s in W.gauge:
+   for k in sorted({rankowner[t]for t in responses[s]if t in rankowner}):
+    if k not in rank_active:continue
+    if s not in rankgroups[k]['roles']:rank_restore(k,s)
+    else:rank_seen[k].add(s)
+  if mutation=='omit_gauge_compensation'and s==new_gauge_selection[-1]['role']:return
+  if mutation=='omit_extra_compensation'and s==extra_selection[0]['role']:return
+  grouped=role_groups.get(s,[])
+  for k in sorted({target_group[t]for t in responses[s]if t in target_group}) if s in W.gauge else []:
+   if k not in grouped:aggregate_restore(k,s)
+  skipped=set()
+  for k in grouped:
+   group=agg[k];pivot=group['pivot'];assert aggregation_active[k]
+   assert set(group['targets'])<=set(responses[s])and len({responses[s][t]for t in group['targets']})==1
+   c=responses[s][pivot];source_move(s,read_frames[s,k]);target_move(pivot,read_frames[s,k]);y[pivot]=track(add(y[pivot],-direction*c,value(s)))
+   if mutation=='repeat_aggregation_read'and k==39:
+    t=next(t for t in group['targets']if t!=pivot);target_move(t,read_frames[s,k]);y[t]=track(add(y[t],-direction*c,value(s)))
+   skipped.update(group['targets']);aggregation_read[k].add(s);aggregation_pivot_reads+=1
+  for t,c in responses[s].items():
+   if t in skipped or t in echelon_skip:continue
+   rk=rankowner.get(t)
+   if s in W.gauge and rk in rank_active and t in rankgroups[rk]['dependent']:
+    rank_skipped+=1
+    if mutation!='repeat_rank_read'or rk!=0:continue
+   if s in W.gauge:source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame'])
+   else:assert target_frames[t]is None,'initial correction leaves target atD0'
+   y[t]=track(add(y[t],-direction*c,value(s)))
+ def gate(i,sign):
+  a,b,_=W.ops[i]
+  if sign==1:
+   source_move(a,W.opframe[i]);source_move(b,W.opframe[i])
+  assign(a,add(value(a),sign,value(b)))
+ for s in range(W.R):
+  if s not in W.gauge and s not in borrow and s not in removed:read(s)
+ for n,s in W.source.items():assign(s,add(value(s),1,x[n]))
+ for r in gauge_selection:
+  if mutation=='omit_transformed_source_mix'and r is next(iter(fresh.values())):continue
+  if mutation=='omit_extra_mix'and r is extra_selection[0]:continue
+  if mutation!='omit_gauge_mix' or r is not new_gauge_selection[-1]:x[r['partner']]=track(add(x[r['partner']],1,x[r['source']]))
+ def forward(i):
+  if i not in omitted:gate(i,1);done.append(i)
+ for k in schedule['center_prefix_events']:
+  event=schedule['events'][k];i=event['op']
+  if event['kind']=='early_mix':
+   r=early[i];a,b=r['partner'],r['source']
+   if mutation!='omit_early_mix' or r is not selection[0]:x[a]=track(add(x[a],1,x[b]))
+  else:forward(i)
+ for r,s in zip(W.g['roots'],W.w['rootroles']):
+  if r['kind']=='center':
+   for t in r['targets']:
+    assert all(f is None for f in target_frames),'copied centers scatter before any nonzero target movement'
+    center_reads.append((s,t));y[t]=track(add(y[t],direction,value(s)))
+ for k,group in enumerate(echelon):
+  assert all(target_frames[t]is None for t in group['targets'])
+  if mutation!='omit_echelon_setup'or k!=0:
+   for t,p,c in group['moves']:y[t]=track(add(y[t],c,y[p]))
+ for k,group in enumerate(rankgroups):
+  assert all(target_frames[t]is None for t in group['targets'])
+  if mutation!='omit_rank_setup'or k!=0:
+   for t,cs in group['dependent'].items():
+    for p,c in cs.items():y[t]=track(add(y[t],-c,y[p]))
+ for k,group in enumerate(agg):
+  assert all(target_frames[t]is None for t in group['targets']), 'aggregation setup after all D0 center scatters'
+  if mutation!='omit_aggregation_setup'or k!=39:
+   for t in group['targets']:
+    if t!=group['pivot']:y[t]=track(add(y[t],-1,y[group['pivot']]))
+ for e in terminal:
+  assert all(target_frames[t]is None for t in e['targets']),'terminal setup afterD0center scatter'
+  for t in e['targets']:
+   if t!=e['pivot']:y[t]=track(add(y[t],-1,y[e['pivot']]))
+ # Original dirty compensation happened at D0 before these source injections.
+ for r in pair_selection:
+  b,f=r['aliased_role'],r['mix_frame']
+  for a,c in r['retained_dirty_coefficients'].items():
+   source_move(a,f);source_move(b,f)
+   if mutation=='omit_sparse_anchor'and r is pair_selection[14]and a==next(iter(r['retained_dirty_coefficients'])):continue
+   if mutation=='wrong_sparse_sign'and r is pair_selection[14]and a==next(iter(r['retained_dirty_coefficients'])):c=-c
+   if mutation!='omit_pair_initialization'or r is not pair_selection[0]:assign(a,add(value(a),c,value(b)))
+ for j,i in enumerate(W.rest):
+  for s in at[j]:
+   if mutation!='late_phase1_gauge' or s not in new_phase_roles:read(s)
+  if mutation=='late_phase1_gauge'and j==168:
+   for s in sorted(new_phase_roles):read(s)
+  if i in bywrite:
+   e=bywrite[i];a,b,n=W.ops[i];source_move(b,W.opframe[i]);target_move(e['pivot'],W.opframe[i]);y[e['pivot']]=track(add(y[e['pivot']],direction,value(b)))
+  else:forward(i)
+  if i in afterwrite:
+   e=afterwrite[i]
+   for t in e['targets']:
+    target_move(t,e['root_frame'])
+    if t!=e['pivot']:y[t]=track(add(y[t],1,y[e['pivot']]))
+ for s in at[len(W.rest)]:read(s)
+ assert not any(aggregation_active),'all quotient inverses precede original side/K reads'
+ assert not rank_active,'rank quotient inverses precede side/K reads'
+ assert not echelon_active,'echelon inverses precede side/K reads'
+ for j,(r,s)in enumerate(zip(W.g['roots'],W.w['rootroles'])):
+  if r['kind']=='side' and j not in deletedroots:
+   for k in sorted({target_group[t]for t in r['targets']if t in target_group}):aggregate_restore(k,('root',j))
+   source_move(s,W.w['root_frame'][j])
+   for t in r['targets']:target_move(t,W.w['root_frame'][j]);y[t]=track(add(y[t],direction,value(s)))
+  for e in deliveries[j]:
+   a,b=e['carrier'],e['passive']
+   if b not in by_source:x[a]=track(add(x[a],1,x[b]))
+   for k in sorted({target_group[t]for t in e['receivers']if t in target_group}):aggregate_restore(k,('K',j))
+   for t in e['receivers']:target_move(t,e['deliver_frame']);y[t]=track(add(y[t],direction,x[a]))
+ assert not any(aggregation_active),'all target inverses completed beforecleanup'
+ for e in W.k['entries']:
+  if e['passive']not in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ if mutation=='undo_before_restore':
+  for e in W.k['entries']:
+   if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ for role in source_paths:source_move(role,W.w['full_frame'])
+ for role in pair_dirty_paths:source_move(role,W.w['full_frame'])
+ for i in reversed(done):gate(i,-1)
+ for r in reversed(pair_selection):
+  b=r['aliased_role']
+  for a,c in reversed(list(r['retained_dirty_coefficients'].items())):
+   c=-c
+   if mutation=='wrong_pair_restore_sign'and r is pair_selection[0]:c=-c
+   if mutation!='omit_pair_restoration'or r is not pair_selection[0]:assign(a,add(value(a),c,value(b)))
+ if mutation!='undo_before_restore':
+  for e in W.k['entries']:
+   if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ for n,s in W.source.items():assign(s,add(value(s),-1,x[n]))
+ if binary:want=[Y0[t]^X0[t]for t in range(v)]
+ else:
+  want=Y0[:];cache={}
+  for root in W.g['roots']:
+   n=root['node']
+   if n not in cache:
+    mask=C.sup[n];val=0
+    while mask:low=mask&-mask;mask-=low;val=add(val,1,X0[low.bit_length()-1])
+    cache[n]=val
+   for t in root['targets']:want[t]=add(want[t],direction,cache[n])
+  for e in W.k['entries']:
+   val=add(X0[e['carrier']],1,X0[e['passive']])
+   for t in e['receivers']:want[t]=add(want[t],direction,val)
+ # Finish every local target at its codimension-one cap, then reverse the exact
+ # annihilator stream. All copied-center scatters lie before these movements,
+ # hence atD0 forward and atD1 after the complementary movements reverse.
+ reflected=Counter()
+ for t,chain in enumerate(target_paths):
+  assert chain
+  d=W.h-1-C.dimf[chain[-1]];assert d>=0
+  if d:target_hist[d]+=1
+  previous=[C.cov[t]];dimension=1
+  for f in reversed(chain):
+   assert all(W.module.dot(a,b)==0 for a in previous for b in C.B[f])
+   basis=C.A[f];step=len(basis)-dimension;assert step>=0
+   if step:reflected[step]+=1
+   previous=basis;dimension=len(basis)
+  if W.h>dimension:reflected[W.h-dimension]+=1
+ assert reflected==target_hist
+ assert len(center_reads)==sum(len(r['targets'])for r in W.g['roots']if r['kind']=='center')
+ assert sum(k*n for k,n in target_hist.items())==W.v*(W.h-1)
+ source_histogram=Counter();source_reflected=Counter()
+ for role,path in source_paths.items():
+  assert C.dimf[path[0]]==1 and C.dimf[path[-1]]==W.h
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b)and C.nondeg(a)and C.nondeg(b)
+   step=C.dimf[b]-C.dimf[a]
+   if step:source_histogram[step]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);step=len(C.A[b])-len(C.A[a]);assert step>=0
+   if step:source_reflected[step]+=1
+ assert source_histogram==source_reflected and sum(k*n for k,n in source_histogram.items())==len(source_paths)*(W.h-1)
+ paired_hist=Counter();paired_reflected=Counter()
+ for role,path in pair_dirty_paths.items():
+  assert C.dimf[path[0]]==0 and C.dimf[path[-1]]==W.h
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b)and C.nondeg(a)and C.nondeg(b)
+   d=C.dimf[b]-C.dimf[a]
+   if d:paired_hist[d]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);d=len(C.A[b])-len(C.A[a])
+   if d:paired_reflected[d]+=1
+ assert paired_hist==paired_reflected and sum(k*n for k,n in paired_hist.items())==len(pair_dirty_paths)*W.h
+ if major:return max(top,max(a+b for a,b in zip(y,want)),max(z[r]+Z0[r]for r in regs),max(a+b for a,b in zip(x,X0)))
+ assert y==want,('wrong targets',mode,[t for t in range(v)if y[t]!=want[t]][:10])
+ assert x==X0,('source restoration',mode,[s for s in range(v)if x[s]!=X0[s]][:10])
+ assert z==Z0,('dirty restoration',mode)
+ return dict(mode=mode,direction=direction,formal_columns=2*v+len(regs),sources=v,targets=v,dirty=len(regs),all_targets=True,all_source_and_dirty_restored=True,copied_center_target_reads=len(center_reads),all_forward_centers_at_D0=True,all_reflected_centers_at_D1=True,actual_target_histogram={str(k):n for k,n in sorted(target_hist.items())},actual_reflected_target_histogram={str(k):n for k,n in sorted(reflected.items())},aggregation_groups=len(agg),aggregation_pivot_reads=aggregation_pivot_reads,aggregation_restores=aggregation_restores,actual_extra_source_paths=source_paths,rank_groups=len(rankgroups),rank_targets=len(rankowner),rank_restores=rank_restores,rank_removed_reads=rank_skipped,actual_extra_source_histogram=dict(source_histogram),actual_extra_reflected_source_histogram=dict(source_reflected),echelon_restores=echelon_restores,echelon_reads=echelon_reads,paired_dirty_paths=pair_dirty_paths,paired_dirty_histogram=dict(paired_hist),paired_dirty_reflected_histogram=dict(paired_reflected))
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/scalar_check.py b/research/gen4-retiming-entrances-target/vendor/pr276/scalar_check.py
new file mode 100644
index 0000000000..cd33eefeaa
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/scalar_check.py
@@ -0,0 +1,125 @@
+"""Fresh F2 source proof, independent literal projection/inverse and controls.
+No saved execution receipt is accepted. Uses the actual clean source context
+and freshly emitted local physical records. Assisted with ChatGPT (source527).
+Rebound to the gen4 word: 19930 formal columns; the controls corrupt the actual
+gen4 context (responses, read chronology, alias reads, gates, centres, partner
+deliveries, injections and signs) instead of absent source527 selections.
+Gen4 rebinding and controls by DreamingOfClouds with Anthropic Claude assistance.
+"""
+from collections import Counter,defaultdict
+from copy import copy
+import hashlib,json,time
+
+EXPECTED_EVENT='c0f4da07311f1998e0813b39098da9015969c180fa55d72f281e45cdd50aaba8'
+N=19930;V=1760;EVENTS=626360;COUNTS={1:624600,3:1760}
+
+
+def events(records,reverse=False):
+    center=None
+    for k in (range(len(records)-6,-1,-6) if reverse else range(0,len(records),6)):
+        op,a,b,c,f,z=records[k:k+6]
+        if op==1:
+            if b==N:
+                assert center is not None
+                b=center
+            assert 0<=a<N and 0<=b<N and a!=b
+            yield a,b,-c if reverse else c
+        elif op==(3 if reverse else 2):
+            assert center is None and b==N
+            center=a
+        elif op==(2 if reverse else 3):
+            assert center==a and b==N
+            center=None
+    assert center is None
+
+
+def replay_projection(records,reverse=False,omit_event=None):
+    n=N;v=V
+    columns=[1<<i for i in range(n)];norms=[1]*n
+    wanted=columns[:]
+    for i in range(v):wanted[v+i]^=1<<i
+    largest=1;counts=Counter();digest=hashlib.sha256();count=0
+    for event_index,(a,b,c) in enumerate(events(records,reverse)):
+        if event_index==omit_event:continue
+        if c&1:columns[a]^=columns[b]
+        norms[a]+=abs(c)*norms[b];largest=max(largest,norms[a])
+        counts[abs(c)]+=1
+        digest.update(json.dumps([a,b,c],separators=(',',':')).encode());digest.update(b'\n');count+=1
+    assert columns==wanted,'independent literal all-column endpoint'
+    assert count==EVENTS and counts==COUNTS
+    if not reverse:assert digest.hexdigest()==EXPECTED_EVENT
+    return dict(all_formal_columns=n,all_source_and_dirty_restored=True,
+                arbitrary_target_contents_preserved=True,
+                event_sha256=digest.hexdigest(),weighted_additions=count,
+                coefficient_counts=dict(counts),literal_unit_additions=sum(c*n for c,n in counts.items()),
+                max_intermediate_row_l1=largest,final_source_row_l1=max(norms[:v]),
+                final_target_row_l1=max(norms[v:2*v]),final_dirty_row_l1=max(norms[2*v:]))
+
+
+def mutated_namespaces(context):
+    """Actual-context corruptions; each must make the unchanged scalar program fail."""
+    W=context['W'];adj=context['adj'];at=context['at']
+    recipients={b:d for b,d in W.pairs}
+    plain_gauge=next(s for s in W.order if s not in recipients and adj[s])
+    recipient=next(b for b in W.order if b in recipients and adj[b])
+    dirty=next(s for s in range(W.R) if s not in W.gauge and s in set(W.phys.values()) and adj[s] and s not in context['borrow'])
+    def with_adj(role,row):
+        a=list(adj);a[role]=row;return dict(adj=a)
+    def drop_first(role):
+        t=next(iter(adj[role]));return with_adj(role,{u:c for u,c in adj[role].items() if u!=t})
+    def move_read(role,time):
+        a=defaultdict(list,{k:list(v) for k,v in at.items()})
+        a[W.readtime[role]].remove(role);a[time].append(role);return dict(at=a)
+    def proxy(**changes):
+        P=copy(W);P.__dict__.update(changes);return dict(W=P)
+    yield 'omit_gauge_compensation','F2',drop_first(plain_gauge)
+    yield 'omit_dirty_compensation','F2',drop_first(dirty)
+    yield 'omit_alias_recipient_compensation','F2',drop_first(recipient)
+    t=next(iter(adj[plain_gauge]));other=(t+1)%V
+    while other in adj[plain_gauge]:other=(other+1)%V
+    row=dict(adj[plain_gauge]);row[other]=row.pop(t)
+    yield 'misrouted_gauge_response','F2',with_adj(plain_gauge,row)
+    row=dict(adj[plain_gauge]);row[t]=-row[t]
+    yield 'flipped_gauge_compensation_sign','Z',with_adj(plain_gauge,row)
+    position={i:j for j,i in enumerate(W.rest)}
+    def last_write(d):
+        js=[position[i] for i in W.role_ops[d] if W.ops[i][0]==d and i in position]
+        return max(js) if js else None
+    written=next(b for b in W.order if b in recipients and adj[b] and last_write(recipients[b]) is not None)
+    yield 'alias_read_before_donor_last_write','F2',move_read(written,last_write(recipients[written]))
+    yield 'gauge_read_after_first_use','F2',move_read(plain_gauge,W.first[plain_gauge]+1)
+    gate=next(i for i in W.rest if W.ops[i][0] not in W.gauge)
+    yield 'omitted_gate','F2',dict(omitted={gate})
+    roots=[dict(r) for r in W.g['roots']];j=next(k for k,r in enumerate(roots) if r['kind']=='center');roots[j]['targets']=roots[j]['targets'][1:]
+    yield 'omitted_centre_scatter','F2',proxy(g=dict(W.g,roots=roots))
+    deliveries=defaultdict(list,{k:list(v) for k,v in context['deliveries'].items()});k=next(k for k,v in sorted(deliveries.items()) if v);deliveries[k]=deliveries[k][1:]
+    yield 'omitted_partner_delivery','F2',dict(deliveries=deliveries)
+    source=dict(W.source);source.pop(next(iter(source)))
+    yield 'omitted_source_injection','F2',proxy(source=source)
+
+
+def run(context,records,progress=lambda text:None):
+    import gc
+    started=time.monotonic();ns=dict(context);source=ns['SOURCE_TEXT']
+    assert hashlib.sha256(source.encode()).hexdigest()=='e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42'
+    exec(compile(source,'retained source527 exact scalar word','exec'),ns)
+    progress('Checking all19930 source, target and arbitrary dirty F2 columns')
+    exact=ns['replay']('F2');assert exact['formal_columns']==N and exact['all_targets']and exact['all_source_and_dirty_restored']
+    progress('Checking independent literal physical projection and inverse')
+    forward=replay_projection(records);inverse=replay_projection(records,True)
+    assert forward['max_intermediate_row_l1']==21725 and inverse['max_intermediate_row_l1']==1850360
+    try:replay_projection(records,omit_event=EVENTS-1)
+    except AssertionError:filtered_control='omitted surviving odd payload ADD rejected'
+    else:raise AssertionError('filtered odd payload omission accepted')
+    bound=ns['replay']('bound');bits=8*((bound.bit_length()+2+7)//8);assert 1<<bits>2*bound
+    progress('Checking the signed integer source decoder and dirty restoration')
+    integer=[]
+    for direction in(1,-1):integer.append(ns['replay']('Z',direction,bits));gc.collect()
+    controls={}
+    for name,mode,changes in mutated_namespaces(context):
+        bad=dict(context);bad.update(changes);exec(compile(source,'retained source527 exact scalar word','exec'),bad)
+        try:bad['replay'](mode,bits=bits)
+        except AssertionError as error:controls[name]=dict(rejected=True,reason=str(error)[:200])
+        else:raise AssertionError('invalid gen4 context mutation accepted: '+name)
+    assert len(controls)==11
+    return dict(status='PASS_FRESH_GEN4_PRODUCER_SIGNED_DECODER_AND_PARITY_FUSED_F2_INVERSE_AND_CONTROLS',filtered_control=filtered_control,F2=exact,integer=integer,majorant=dict(residual_bound=bound,packing_bits=bits),forward=forward,inverse=inverse,controls=controls,source_sha256=hashlib.sha256(source.encode()).hexdigest(),seconds=time.monotonic()-started,scope='The retained source527 scalar program, run on the gen4 context, proves the signed defining-integer decoder in both directions and rejects11 actual-context corruptions. The emitted parity-filtered word is independently checked on all19930formal F2columns and literalreverse, with its own cancellation-free signed-lift prefix bounds. Its integer endpoint is not asserted equal to the producer decoder; F2payload identity supplies the bit contract. Odd-prime address arithmetic is unchanged.')
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/verify.py b/research/gen4-retiming-entrances-target/vendor/pr276/verify.py
new file mode 100644
index 0000000000..6b1a5fa662
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/verify.py
@@ -0,0 +1,83 @@
+#!/usr/bin/env python3
+"""Immutable gen4 five-stage banks: regenerate every mandatory finite stage.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import sys
+if not __debug__:raise SystemExit('Assertions required; refusing-O')
+sys.dont_write_bytecode=True
+from pathlib import Path
+from datetime import datetime,timezone
+from fractions import Fraction
+import argparse,hashlib,importlib.util,json,time,traceback
+ROOT=Path(__file__).resolve().parent
+REQUIRED={'virtual','raw','bit','scalar','primes','banks','complex','math','finite'}
+
+def progress(message):print(datetime.now(timezone.utc).strftime('%H:%M:%S UTC')+'  '+message,flush=True)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def serial(x):
+ if isinstance(x,Fraction):return str(x)
+ if isinstance(x,dict):return {str(k):serial(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return list(map(serial,x))
+ return x
+
+def load(name):
+ s=importlib.util.spec_from_file_location('source527_'+name,ROOT/(name+'.py'));m=importlib.util.module_from_spec(s);sys.modules[s.name]=m;s.loader.exec_module(m);return m
+
+def integrity():
+ p=ROOT/'MANIFEST.json';m=json.loads(p.read_text());actual={}
+ for q in ROOT.rglob('*'):
+  assert not q.is_symlink(),'Symlink in package'
+  if q.is_file()and q.name!='MANIFEST.json':actual[q.relative_to(ROOT).as_posix()]=sha(q)
+ # Nested source manifests are also ordinary pinned inputs.
+ for q in ROOT.rglob('MANIFEST.json'):
+  if q!=p:actual[q.relative_to(ROOT).as_posix()]=sha(q)
+ assert actual==m['files'],'Missing, changed or unpinned package/source file'
+ return sha(p),len(actual)
+
+def validate_required(results):
+ assert set(results)==REQUIRED,'Missing mandatory proof stage'
+ assert all(isinstance(results[k],dict)and results[k]for k in REQUIRED)
+
+def controls():
+ out=[];good={k:{'present':True}for k in REQUIRED}
+ for k in sorted(REQUIRED):
+  bad=good.copy();bad.pop(k)
+  try:validate_required(bad)
+  except AssertionError:out.append('omitted '+k+' stage')
+  else:raise AssertionError('Missingstageaccepted')
+ return out
+
+def main():
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--output',type=Path,required=True);args=ap.parse_args()
+ import sympy
+ assert sys.version_info>=(3,11)and sympy.__version__=='1.14.0'
+ digest,count=integrity();output=args.output.resolve();assert not output.is_relative_to(ROOT)and not output.exists(),'Output must be new and outside package';output.mkdir(parents=True)
+ results={};timings={};start=time.monotonic()
+ def save(name,value):(output/name).write_text(json.dumps(serial(value),sort_keys=True,indent=2)+'\n')
+ def stage(name,call):
+  t=time.monotonic();value=call();results[name]=value;timings[name]=time.monotonic()-t;save(name+'.json',value);progress(name+' PASS '+format(timings[name],'.1f')+'s');return value
+ try:
+  progress('Admitting the pinned gen4 physical bit word')
+  stage('virtual',lambda:load('virtual_check').run(output,progress))
+  context=load('prepare').prepare()
+  raw=stage('raw',lambda:load('raw_ledger').run(context))
+  portable=load('portable_bit');bit=portable.run(prepared_context=context,raw=raw,output_dir=output,run_geometry=True,package_root=ROOT);raw=bit['raw'];results['raw']=raw;save('raw.json',raw);results['bit']=portable.summary(bit);timings['bit']=bit['seconds'];save('bit.json',results['bit']);progress('bit physical/global/geometry PASS')
+  scalar=stage('scalar',lambda:load('scalar_check').run(context,bit['records'],progress))
+  primes=stage('primes',lambda:load('prime_check').run(context,bit['physical'],progress))
+  bankresult=stage('banks',lambda:load('bank_check').run(context,bit['global_result'],bit['lower']))
+  banks=bankresult['banks'];banked=bankresult['banked_result']
+  complex_result=stage('complex',lambda:load('portable_complex').run(package_root=ROOT,progress=progress))
+  assert complex_result['precision_guard']['retained_row_coefficient']==20161
+  math=stage('math',lambda:load('math_check').run(raw,complex_result['five_stage_histogram'],banks,bit['global_result']))
+  finite=stage('finite',lambda:load('finite_check').run(raw,bit['physical'],scalar,primes,math,banks,banked,bit['global_result']))
+  assert math['mathematics']['finite_bridge']['rows']['coefficient']==complex_result['precision_guard']['retained_row_coefficient']==finite['row_reserve']['external_complex_coefficient']
+  validate_required(results);assert len(scalar['controls'])==11 and len(primes['controls'])==6
+  assert math['mathematics']['kappa']=='144573965469499/200000000000000000'
+  after,_=integrity();assert after==digest,'Package changed during replay'
+  certificate=dict(schema='gen4-parity-fused-five-stage-banks/1',**math['mathematics'],scope='Conditionalfiniteconstruction; inheritedallsizecompiler,weightedselector,commonancestorchart,restoredrow,routing,prime,recovery,complexsymbolicandanalyticinterfacesremainassumptions.')
+  save('certificate.json',certificate)
+  report=dict(status='PASS_IMMUTABLE_PARITY_FUSED_GEN4_FIVE_STAGE_BANKED_CONSTRUCTION',manifest_sha256=digest,files=count,kappa=math['mathematics']['kappa'],kappa_scientific=math['mathematics']['kappa_scientific'],fresh_stages=sorted(REQUIRED),inputs_unchanged=True,timings=timings,seconds=time.monotonic()-start,negative_controls=controls())
+  save('verification.json',report);print(json.dumps(report),flush=True)
+ except BaseException as exc:
+  save('failure.json',dict(status='FAIL',error=str(exc),completed_stages=sorted(results),timings=timings,traceback=traceback.format_exc()));raise
+if __name__=='__main__':main()
diff --git a/research/gen4-retiming-entrances-target/vendor/pr276/virtual_check.py b/research/gen4-retiming-entrances-target/vendor/pr276/virtual_check.py
new file mode 100644
index 0000000000..8538bd1297
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/vendor/pr276/virtual_check.py
@@ -0,0 +1,63 @@
+"""Retained admissions of the gen4 bit word: PR168-v4 package checker and PR200 physical-word proof.
+
+1. eumemic's unmodified PR168-v4 check_paired_cube_bit.py on the virtual (node-frame, unaliased) word:
+   exact frames, mod-2 decoder with stars and side parts, geometry (source lines, root caps, operand
+   nesting, star spans), role and target chains, partner chronology, G-nondegeneracy, a literal F2
+   dirty-scratch replay and the ledger recount, with its five mutation controls.
+2. Chafik Boukhalfa's unmodified PR200 physical-word classes, run as PR200's bit/prove.py runs them:
+   exact changed operation frames and handoffs, the physical row (phase one = centre closure, actual
+   addition operands, gauge supports, partner chronology, nested physical role and target chains,
+   telescoping deficit), the physical word on every formal column over F2 and the defining integer
+   decoder, and its adverse controls (omitted compensation, missing partner delivery, stale recipient
+   read, zero operation frame).
+Gen4 integration by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+from pathlib import Path
+import gzip,hashlib,importlib.util,json,shutil,time
+HERE=Path(__file__).resolve().parent
+
+def load(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod);return mod
+
+def run(output_dir,progress=lambda text:None):
+    begun=time.monotonic();src=HERE/'gen4bit/selected/bit';d=Path(output_dir)/'virtual-bit';d.mkdir(parents=True)
+    for name in ('graph','kchron','profile'):shutil.copyfile(src/(name+'_p12.json'),d/(name+'_p12.json'))
+    for name in ('word','frames'):(d/(name+'_p12.json')).write_bytes(gzip.decompress((src/(name+'_p12.json.gz')).read_bytes()))
+    p=HERE/'gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py'
+    mod=load('gen4_pr168_v4_checker',p)
+    progress('Running the PR168-v4 package checker on the gen4 virtual word')
+    result=mod.Checker(d,12).run()
+    assert result==dict(frames=26058,roles=17904,W=21424,m=72,deficit=1936,children=293416)
+    controls={}
+    for m in ('broken_mix','outside_cap','below_level','dropped_star','non_nested'):
+        try:mod.Checker(d,12,mutate=m).run()
+        except mod.Fail as error:controls[m]=str(error)
+        else:raise AssertionError('PR168 mutation control accepted: '+m)
+    assert len(controls)==5
+    progress('Running the PR200 physical-word proof on the gen4 physical word')
+    word=load('gen4_pr200_physical_word_admission',HERE/'gen4bit/bit/word.py').Candidate()
+    word.exact_frames();row=word.row()
+    reference=json.loads((src/'profile_p12.json').read_text())
+    assert row['reused_registers']==len(word.pairs)==1494 and row['virtual_R']==reference['R']==17904
+    assert row['R']==16410 and row['W_per_vertex']==19930 and row['deficit_per_vertex']==reference['deficit_per_vertex']==1936 and row['loss']==reference['loss']==528
+    assert row['changed_operation_frames']==1802 and row['selected_roles']==2466 and row['selected_rank_histogram']=={20:2200,21:266}
+    formal=[word.formal(r) for r in (2,0)]
+    assert formal[0]['identity'] and all(f['defining_decoder'] and f['all_dirty_and_source_columns_restored'] and f['formal_variables']==19930 for f in formal)
+    physical_controls=[]
+    for tamper in ('omit_compensation','missing_partner','stale'):
+        try:word.formal(2,tamper)
+        except ValueError:physical_controls.append(tamper)
+        else:raise AssertionError('PR200 adverse word control accepted: '+tamper)
+    i=word.changed_frames[0];old=word.opframe[i];word.opframe[i]=word.register([])
+    try:word.exact_frames()
+    except ValueError:physical_controls.append('zero_operation_frame')
+    else:raise AssertionError('zero operation frame accepted')
+    word.opframe[i]=old
+    assert len(physical_controls)==4
+    row={k:(dict(v) if isinstance(v,dict) else v) for k,v in row.items()}
+    return dict(status='PASS_PR168_V4_VIRTUAL_AND_PR200_PHYSICAL_ADMISSION_OF_GEN4',virtual=result,virtual_controls_rejected=controls,
+        physical_row=row,physical_formal=formal,physical_controls_rejected=physical_controls,
+        checker_sha256=hashlib.sha256(p.read_bytes()).hexdigest(),
+        pr200_classes_sha256={n:hashlib.sha256((HERE/'gen4bit/bit'/n).read_bytes()).hexdigest() for n in ('word.py','base_word.py')},
+        seconds=time.monotonic()-begun,
+        scope='The pinned word is admitted by both retained checkers exactly as PR200 admitted its own word (its terminal-sink and prime steps have no gen4 counterpart here; primes are rechecked by prime_check).')
diff --git a/research/gen4-retiming-entrances-target/verify.py b/research/gen4-retiming-entrances-target/verify.py
new file mode 100644
index 0000000000..81dd26f02f
--- /dev/null
+++ b/research/gen4-retiming-entrances-target/verify.py
@@ -0,0 +1,65 @@
+#!/usr/bin/env python3
+"""Fresh, network-free admission of the composed conditional gen4 construction."""
+import sys
+if not __debug__: raise SystemExit('Assertions required; refusing -O')
+sys.dont_write_bytecode = True
+import argparse, hashlib, json, os, shlex, shutil, subprocess, time
+from pathlib import Path
+ROOT = Path(__file__).resolve().parent
+BASE_MANIFEST = '6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d'
+WORD = '00704c44a562a115454152cff41f1b39ec5491be192b1e792855a8541c3f34ee'
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def integrity():
+    manifest = ROOT/'MANIFEST.json'
+    files = {}
+    for p in ROOT.rglob('*'):
+        assert not p.is_symlink(), 'Symlink in immutable package'
+        if p.is_file() and p != manifest: files[p.relative_to(ROOT).as_posix()] = sha(p)
+    assert files == json.loads(manifest.read_text())['files'], 'Changed, missing or unpinned source'
+    assert sha(ROOT/'vendor/pr276/MANIFEST.json') == BASE_MANIFEST
+    return sha(manifest)
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--output',type=Path,required=True)
+    a=ap.parse_args(); out=a.output.resolve()
+    assert not out.exists() and not out.is_relative_to(ROOT), 'Use a fresh output outside package'
+    import sympy
+    assert sys.version_info >= (3,11) and sympy.__version__ == '1.14.0'
+    digest=integrity(); out.mkdir(parents=True); start=time.monotonic(); stages=[]
+    env=dict(os.environ, PYTHONDONTWRITEBYTECODE='1')
+    def run(name,args):
+        print(name, flush=True); t=time.monotonic()
+        with (out/(name+'.log')).open('w') as log:
+            subprocess.run([str(x) for x in args],check=True,stdout=log,stderr=subprocess.STDOUT,env=env)
+        stages.append({'stage':name,'seconds':time.monotonic()-t})
+    py=[sys.executable,'-B']; code=ROOT/'code'; base=ROOT/'vendor/pr276'
+    try:
+        run('01-baseline',py+[base/'verify.py','--output',out/'baseline'])
+        run('02-export',py+[code/'export.py','--base',base,'--output',out/'export'])
+        run('03-retime',py+[code/'retime.py','--export-dir',out/'export','--output',out/'retimed'])
+        run('04-cleanup',py+[code/'cleanup.py','--source-dir',out/'retimed','--export-dir',out/'export','--output',out/'cleanup'])
+        run('05-entrances',py+[code/'entrances.py','--source-dir',out/'cleanup','--export-dir',out/'export','--output',out/'candidate'])
+        # Exact F2 target-prefix compression (PR268's mechanism, native stage from PR273): 280 disjoint target groups whose
+        # dependent's frame-20 prefix response is the F2 sum of its retained group-mates'; literal dependencies are recomputed
+        # from the actual word and both all-column replays run before anything is emitted. Rewrites candidate/COHORT249-RECORDS.bin
+        # in place (the pre-compression word is kept as COHORT249-PRE-TARGET-RECORDS.bin); every later checker re-reads the word.
+        run('05b-target-prefix',py+[code/'target_prefix.py',out/'export',out/'candidate',ROOT/'data/target-selection.json'])
+        assert sha(out/'candidate/COHORT249-RECORDS.bin') == WORD
+        compiler=shlex.split(os.environ.get('CXX','c++'))
+        for name in ['five-stage-columns','charts']:
+            run('compile-'+name,compiler+['-std=c++17','-O2','-I'+str(ROOT/'vendor'),code/(name+'.cpp'),'-o',out/name])
+        run('06-columns',[out/'five-stage-columns',out/'candidate/COHORT249-RECORDS.bin',out/'candidate/COHORT-FIVE-STAGE-COLUMNS.json','1760','16410'])
+        # The binary and chart output directory must have distinct names.
+        chartdir=out/'chart-audit'; chartdir.mkdir()
+        run('07-charts',[out/'charts',out/'export',out/'candidate',chartdir])
+        run('08-price',py+[code/'price.py',out/'candidate','--base',base,'--output',out/'PRICE.json'])
+        run('09-admission',py+[code/'admit.py',out/'candidate','--export',out/'export','--baseline',out/'baseline','--charts',chartdir/'COMBINED-CHART-AUDIT.json','--price',out/'PRICE.json','--output',out/'admission'])
+        assert integrity()==digest
+        price=json.loads((out/'PRICE.json').read_text())
+        report={'status':'PASS_IMMUTABLE_COMPOSED_GEN4_CONSTRUCTION','manifest_sha256':digest,'word_sha256':WORD,'kappa':price['kappa'],'kappa_decimal':price['kappa_decimal'],'inputs_unchanged':True,'fresh_stages':stages,'seconds':time.monotonic()-start,'scope':'Conditional finite construction. Inherited all-size compiler, common weighted chart, restored rows, selectors, routing, prime supply, precision/recovery, complex symbolic correctness and analytic interfaces remain assumptions. No claim about the latest public comparator is inferred by this offline verifier.'}
+        (out/'VERIFICATION.json').write_text(json.dumps(report,indent=2)+'\n')
+        print('PASS kappa = '+price['kappa_decimal'],flush=True)
+    except BaseException as e:
+        (out/'FAILURE.json').write_text(json.dumps({'status':'FAIL','error':str(e),'completed':stages},indent=2)+'\n')
+        raise
+if __name__=='__main__': main()
diff --git a/research/gen4-retiming-entrances/LICENSE b/research/gen4-retiming-entrances/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gen4-retiming-entrances/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
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+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
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diff --git a/research/gen4-retiming-entrances/MANIFEST.json b/research/gen4-retiming-entrances/MANIFEST.json
new file mode 100644
index 0000000000..3ce7343959
--- /dev/null
+++ b/research/gen4-retiming-entrances/MANIFEST.json
@@ -0,0 +1,138 @@
+{
+  "files": {
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "9d50a15b5445f35cdb4105f50ac19b420d5e9f294e3cfb0dd98b16542a9c9d73",
+    "PROOF.md": "3a8c069f518fa3992840da743ec6f20cbda06387b9817c642a3e9ae88fef0754",
+    "README.md": "47e178dce75a29ff0c5babc4fbd470ddf677a2af2427c79fc30c1911a4bca062",
+    "code/admit.py": "c18a83e907a3faece947a727fab790be1938c6c26f9b738c8e0196439fd3378c",
+    "code/charts.cpp": "40576d17ff335e61c2669f93a096df1b961ab5a3546f85e778670bd2fcc20ac6",
+    "code/cleanup.py": "7cc979a6581c7c8b739cfeaaa54ccc2d85a498342b0aef367b3d61c2250d1494",
+    "code/cleanup_emit.py": "3a3a315291985a45bb62ec39c700d33fa9df422d524fb8583a93735d6a0e5d6c",
+    "code/cleanup_reference.py": "a368d184558c660b07da63fd3727181c69fc48ba493a39c465a7b556e34558da",
+    "code/cleanup_screen.py": "89cfa098e77f043b87c7de0c76bd35f4b33404929de3aa5d9e48d1a6f506aba8",
+    "code/entrances.py": "ea6beed63ef03618042212c0514f39770a76049f5eb3f444eb540b5deca1eadc",
+    "code/export.py": "471256c73bfb1e701917b4d3719f0795170f37b9ea238967af425d0e9621f2c0",
+    "code/five-stage-columns.cpp": "a7432be590e68bac9e48df432c5f22767bce6af1c237499280e4e3bce09e5131",
+    "code/price.py": "78eb95d76c84afd0c9610c81e9ed416aca6d537fbec8b81e0f346e03b4ebd64f",
+    "code/retime.py": "1fde7cf2f03dfb5072f1a75db35161337541de2c2abde608878f344672b2d0c8",
+    "data/EXPECTED.json": "3c5b3056761524fe558255afb7d31c4ccb271d2980258e480a0c0448dbadea5f",
+    "data/entrances60.json": "c79f5a9541fac28b544af01cc278c99aa3d0a7e1574a2404d1abf8b19a1c0f2e",
+    "data/retiming880.json": "6ea6812c02765e222afecf2f1c43aae370ea866a27efcd09f2196e42eda29571",
+    "docs/cleanup-proof.md": "f19cdc93bef81e8926924b61049c12082dcb78c48f98cb7e8eaf879ce37a52ca",
+    "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
+    "vendor/json.hpp": "aaf127c04cb31c406e5b04a63f1ae89369fccde6d8fa7cdda1ed4f32dfc5de63",
+    "vendor/pr276/BANK-PROOF.md": "bbc328e05848a211c981288514380a4ba12fddaed16c9d23328b5764502be411",
+    "vendor/pr276/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/pr276/MANIFEST.json": "6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d",
+    "vendor/pr276/NOTICE.md": "fa439daf29eb87d38cfdcf60c7ff43af7854fdc7e71570ae79b76dd524427f90",
+    "vendor/pr276/PR-STATEMENT.md": "1741f2d9e3c8d61c2ab2a27298b33c3ea8579fc09c00fcbb979186be7b6e6dbd",
+    "vendor/pr276/PROOF.md": "c4adbffdc7181b67ba61db134ca40e6b731e836ca07607d7ce6a76fb7434df9e",
+    "vendor/pr276/README.md": "1741f2d9e3c8d61c2ab2a27298b33c3ea8579fc09c00fcbb979186be7b6e6dbd",
+    "vendor/pr276/UPSTREAM-PR234-NOTICE.md": "ce978c8dfc8a2b36eed7a53014b1a792248b22ef4cee3edd8adab825a571c429",
+    "vendor/pr276/UPSTREAM-PR234-PROOF.md": "c9722b07256758cd3b307dd46689f99984c66e16c3dd934f9c34e551620bfc0f",
+    "vendor/pr276/bank_check.py": "fb25305ddd97e8341bef591e04c6fcd9e8cc06ef9207a340eb883045d43a40ff",
+    "vendor/pr276/bank_template.py": "ca97c34524b409621336c0d4046f26e8da156f4b657c9d94463d8025ddfdbb4a",
+    "vendor/pr276/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "vendor/pr276/code/complex_basis.py": "52d68781eaf6d9decf02446a532a7336fcf15924a9f6781ba0833d038decb9f8",
+    "vendor/pr276/code/complex_labels.py": "ff5d5e914ef1be0f0cc30283a1ee39089b77e4b572f09543e7313d126bd26256",
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+}
diff --git a/research/gen4-retiming-entrances/NOTICE.md b/research/gen4-retiming-entrances/NOTICE.md
new file mode 100644
index 0000000000..40d71f8285
--- /dev/null
+++ b/research/gen4-retiming-entrances/NOTICE.md
@@ -0,0 +1,14 @@
+# Attribution
+
+Prepared for **utcorvusvolat-dotcom** with substantial OpenAI Codex assistance. Apache-2.0. Original prerequisite source, notices, license and AI-assistance disclosures are preserved verbatim in `vendor/pr276`; these credits do not imply review or endorsement.
+
+- DreamingOfClouds and Anthropic Claude: PR276 gen4 physical bit word and its five-stage completed-bank package.
+- Henry Grant (hcg890), PR234, and Jacob Sussman: five-stage architecture and certificate interface.
+- eumemic: paired-cube/source527 scalar and physical machinery, common-delivery-frame retiming in PR244, and PR168 lineage; see inherited notices for full attributions.
+- Evan McKinney (evmckinney9): PR197 completed banks and PR271 cleanup-sandwich identity. `code/cleanup_reference.py` adapts the public PR271 exact sandwich reference; `cleanup_screen.py` and `cleanup_emit.py` apply its argument to gen4.
+- Rohan Arun: PR237 width-120 bank application, PR263 frame descent and concurrent PR279 application of the same 880 retimings to gen4.
+- utcorvusvolat-dotcom: PR270 connected-block scan and selection binding; this package composes the 880 gen4 retimings with 440 shortened endpoints and 60 dirty entrance transports, with regenerated exact admissions.
+- Chafik Boukhalfa (chafreaky), PR200: physical-word classes; icekylinx, PR144: paired-cube framework; Avi Eisenberg (ikeboy), PR193: retained complex supplier.
+- `vendor/json.hpp`: nlohmann JSON, copyright Niels Lohmann, MIT license reproduced in the file header.
+
+No priority or global-optimality claim is made. The complete inherited attribution chains are in `vendor/pr276/NOTICE.md`, its `notices/` directory and its upstream notices.
diff --git a/research/gen4-retiming-entrances/PROOF.md b/research/gen4-retiming-entrances/PROOF.md
new file mode 100644
index 0000000000..7826bfcedb
--- /dev/null
+++ b/research/gen4-retiming-entrances/PROOF.md
@@ -0,0 +1,27 @@
+# Composition argument
+
+The prerequisite is the immutable PR276 package, whose full verifier runs first. Its scalar word, decoder, physical frames, COPY lifetimes, prime guards, completed-bank template, complex supplier and analytic admission supply the unchanged facts. This document only describes the three modifications and their interface costs.
+
+## Common-frame retiming
+
+The 880 frozen pairs partition the 1,760 source roles. Each selected scalar ADD keeps its operands and coefficient and changes only its frame annotation, from rank 2 to an existing common delivery frame of rank 22. Its old frame is contained in the new one. The emitter preserves the complete scalar/COPY/ERASE projection, reconstructs each MOVE from the current role frame and checks every new inclusion exactly against B/A tables. COPY/ERASE source bindings and all endpoints remain fixed.
+
+Per gate, the paid ranks 1,1,20,22 become 21,21,2. The local histogram delta is {1:-1760, 2:880, 20:-880, 21:1760, 22:-880}; its rank mass is zero. Existing operand containment in the old frame implies containment in the enlarged frame. This is the same common-delivery-frame mechanism developed in the source527 lineage and independently applied to gen4 in PR279.
+
+## Early restoration
+
+After the target output has been completed, each of 440 selected helpers has exactly one remaining signed restoration ADD, helper -= donor. No other suffix instruction uses that helper, and its donor is not written between the new and old positions. The two sets of helper/donor roles are disjoint. Consequently each elementary shear commutes through every intervening scalar instruction. The new endpoint is their exact nondegenerate rank-23 join, rather than FULL24; the initial helper rank remains 20. This reduces its residual rank from 4 to 3. The frozen recipe checks these conditions on the actual retimed word, preserving the signed coefficient -1. See `docs/cleanup-proof.md`.
+
+## Dirty entrance transport
+
+Sixty independent zero-entry helpers are unwritten and never copied before the transport cut just after the final copied-center discard. No target is a scalar source (or copied source). Each of their 240 signed initial helper-to-target reads therefore commutes with every intervening instruction; these reads are moved to the cut with their exact coefficients intact. Every selected helper column is also replayed over the integers. MOVE chains are rebuilt, and exact full ranks, ordinary annihilators, nondegenerate Grams and changed connector inclusions are checked.
+
+The new helper entrances have ranks 19 (12 helpers) and 18 (48 helpers); their endpoints remain FULL24. They are disjoint from the 440 early-restored helpers. The residual ranks become 5 and 6. The local histogram delta is {1:48, 2:168, 3:72, 19:-12, 18:192, 20:-120, 21:-120}. Initial rank rises by 1,092 and paid rank mass decreases by the same amount.
+
+## Completed banks and finite admission
+
+At 60 physical replicas in each of five stages, residual helper ranks 3,4,5,6,24 have populations 706,1760,12,48,13884. They tile homogeneous width-120 banks with 40,30,24,20,5 blocks per bank, giving 1059,3520,30,144,166608 banks per stage. All 4,923,000 actual assignments are enumerated; no padding savings are assumed.
+
+The exact chart generator derives its required pairs from the baseline and final raw words, together with every helper whose initial or final frame changes. Each projector difference is checked idempotent, of the claimed rank, and conjugate to its standard diagonal projector. The largest required chart has 208 factors. Retained cost terms give a conservative normalizer 208+119+120=447. The admission recomputes the signed cancellation-free prefix bound on the actual word and the complete finite invoice, including the unchanged complex/row interfaces from the baseline replay.
+
+The final histogram and stock are passed to both pinned rational moment engines. The prime is verified, the full rare-branch fallback remains charged, eight positive-gap ordinary levels are admitted, all 47 strict assembly constraints hold, and the next 10^-27 grid point is rejected at the finite ordinary saving. This gives the stated conditional κ. It does not remove any inherited all-size hypothesis.
diff --git a/research/gen4-retiming-entrances/README.md b/research/gen4-retiming-entrances/README.md
new file mode 100644
index 0000000000..d438ffe6b6
--- /dev/null
+++ b/research/gen4-retiming-entrances/README.md
@@ -0,0 +1,40 @@
+# Gen4 retiming, early restoration and dirty entrances
+
+This package constructs the conditional finite bound
+
+**κ = 724189082265949363570532 / 10^27 = 0.000724189082265949363570532.**
+
+It composes 880 source-pair frame retimings, 440 early helper restorations and 60 transported dirty entrances on the PR276 gen4 word. The signed scalar maps are preserved by the checked commutation identities; all changed geometry, completed banks and finite charges are recomputed on the resulting word.
+
+At the latest comparison during preparation, this is **0.08533948% above PR279** (κ = 0.000723571590007464), and **0.18250242% above PR276** (κ = 0.000722869827347495). PR279 independently posted the same 880 retimings while this package was being prepared. The extra improvement here is the composition with shortened helper endpoints and new dirty entrances. No priority or global optimality is claimed. These are changes to a conditional asymptotic bound, not measured multiplication speedups.
+
+## Reproduce
+
+Python 3.11+, SymPy 1.14.0, a C++17 compiler and Boost headers are required. On Ubuntu:
+
+```sh
+sudo apt-get install g++ libboost-dev
+python3 -m pip install -r research/gen4-retiming-entrances/requirements.txt
+python3 -B research/gen4-retiming-entrances/verify.py --output /tmp/gen4-composed-replay
+```
+
+Use a fresh output directory outside this package. The verifier runs without network access. It freshly verifies the unmodified, vendored PR276 package, regenerates its raw word, applies the three exact recipes, checks every global formal column, generates the changed projector charts, enumerates the bank assignments, reproduces the price and admits the complete finite invoice. Saved PASS files are not inputs to this recipe. Its immutable manifest is checked before and after execution. Assertions are mandatory.
+
+PR276 is pinned to commit `d428ab0462b9dfd3131ab4e89999f0adcd6173dd`, with its original manifest SHA256 `6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d`. The complete 110-file prerequisite package and original licenses/notices are retained in `vendor/pr276`. Later edits to that PR do not alter this dependency.
+
+## Concrete checks and result
+
+- The final word SHA256 is `71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48`.
+- All 23,450 global formal columns pass the five-stage construction, with 120 fresh copies, original-source immutability and six nonzero omitted-bridge controls. The signed changes are separately justified over the integers; the F₂ replay is not used as a substitute for that argument.
+- All 3,784 changed connector/endpoint projector charts, including 500 changed helper endpoints, are recomputed exactly. The largest chart has 208 elementary factors; numerator and denominator maxima are 764 and 351.
+- All 4,923,000 role/replica/stage assignments are enumerated. The inventory has 171,361 banks per stage, 1,279,205 literal stock families and 255,841 normalized stock families. There are 2,400 endpoint columns and 2,400 nonzero omission/repetition control columns.
+- Normalizer 447 = 208 + 119 + 120; selector charge 528,906,962,400; finite primitive coefficient 92,488,203,535,344,001; recomputed signed payload bound 91 bits.
+- Exact fixed-prime proof for q = 2^127 − 1, the full fallback, two rational moment engines, eight ordinary levels, all 47 strict outer inequalities and adjacent-grid rejection.
+
+The normalized paid histogram has 5,808,240 calls, rank mass 30,648,120 and deficit 52,800. The largest child remains 50. Recursive children are charged explicitly and are not included in the finite coefficient.
+
+## Scope
+
+This is a conditional finite construction under the inherited all-size compiler, common weighted chart, restored rows, selectors, routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction interfaces. It does not establish those assumptions, an unconditional multiplication theorem, a new Lean proof or a practical runtime result. The offline verifier proves this pinned construction; the public-frontier comparison is a separate dated observation.
+
+See `PROOF.md`, `docs/cleanup-proof.md`, code-level exact checks, and `NOTICE.md` for the construction and attribution.
diff --git a/research/gen4-retiming-entrances/code/admit.py b/research/gen4-retiming-entrances/code/admit.py
new file mode 100644
index 0000000000..c1c1c82733
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/admit.py
@@ -0,0 +1,293 @@
+#!/usr/bin/env python3
+"""Reconstruct final gen4 banks and finite accounting from the actual word.
+
+The orchestrator must freshly run the immutable baseline, scalar replay and
+exact chart checker before invoking this integration component.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import sys
+if not __debug__:
+    raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+sys.set_int_max_str_digits(0)
+
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import hashlib
+import json
+import price as pricing
+
+
+def read(path):
+    return json.loads(Path(path).read_text())
+
+
+def cutoff(delta, coefficient):
+    assert 0 < delta <= 1 and isinstance(coefficient, int) and coefficient >= 1
+    return max(1, pricing.ceil_fraction(36 / delta**2),
+               pricing.ceil_fraction(2 * (4 + (coefficient - 1).bit_length()) / delta))
+
+
+def signed_bounds(records, n):
+    result = []
+    for reverse in (False, True):
+        norms, largest, open_copy = [1] * (n + 1), 1, False
+        for op, a, b, coefficient, frame, category in (reversed(records) if reverse else records):
+            if op == 1:
+                norms[a] += abs(coefficient) * norms[b]
+                largest = max(largest, norms[a])
+            elif op == (3 if reverse else 2):
+                assert not open_copy and b == n
+                norms[b], open_copy = norms[a], True
+            elif op == (2 if reverse else 3):
+                assert open_copy and b == n
+                norms[b], open_copy = 0, False
+        assert not open_copy
+        result.append(dict(reverse=reverse, bits=largest.bit_length(),
+                           cancellation_free_signed_row_l1_upper=str(largest)))
+    return result
+
+
+def exact_banks(initial, final, frames):
+    families, endpoint_pairs = defaultdict(list), set()
+    for role in range(3520, 19930):
+        before, after = initial[str(role)], final[str(role)]
+        endpoint_pairs.add((before, after))
+        rank = frames[str(after)]["dim"] - frames[str(before)]["dim"]
+        assert 0 < rank <= 24
+        families[rank].append(role)
+    assert {r: len(roles) for r, roles in families.items()} == {
+        24: 13884, 4: 1760, 3: 706, 5: 12, 6: 48
+    }
+    for before, after in endpoint_pairs:
+        for b in frames[str(before)]["B"]:
+            for a in frames[str(after)]["A"]:
+                assert sum(Q(x) * Q(y) for x, y in zip(a, b)) == 0
+    patterns, slots, bank, columns, wrong_columns = [], {}, 0, 0, 0
+    for rank, roles in sorted(families.items()):
+        blocks, count = 120 // rank, 60 * len(roles)
+        assert blocks * rank == 120 and blocks <= 40 and count % blocks == 0
+        patterns.append(dict(width=rank, blocks=blocks, banks_per_stage=count//blocks,
+                             occurrences_per_stage=count))
+        slots[rank] = []
+        for _ in range(count // blocks):
+            slots[rank].extend((bank, j * rank, j + 1) for j in range(blocks))
+            bank += 1
+        for reverse in (False, True):
+            permutation = list(range(240))
+            for j in (reversed(range(blocks)) if reverse else range(blocks)):
+                for a in range(j * rank, (j + 1) * rank):
+                    permutation[a], permutation[120+a] = permutation[120+a], permutation[a]
+            assert permutation == list(range(120, 240)) + list(range(120))
+            columns += 240
+        for omitted in range(blocks):
+            for repetitions in (0, 2):
+                permutation = list(range(240))
+                for j in range(blocks):
+                    for _ in range(repetitions if j == omitted else 1):
+                        for a in range(j * rank, (j + 1) * rank):
+                            permutation[a], permutation[120+a] = permutation[120+a], permutation[a]
+                wrong = sum(permutation[j] != (j + 120) % 240 for j in range(240))
+                assert wrong == 2 * rank
+                wrong_columns += wrong
+    assignments, mass, digest = 0, 0, hashlib.sha256()
+    for stage in range(5):
+        for rank, roles in sorted(families.items()):
+            assert len(slots[rank]) == len(roles) * 60
+            for j, role in enumerate(roles):
+                for replica in range(60):
+                    bank_id, offset, scalar = slots[rank][j * 60 + replica]
+                    assert 1 <= scalar <= 40 and offset + rank <= 120
+                    digest.update(f"{stage},{replica},{role},{bank_id},{offset},{rank},{scalar}\n".encode())
+                    assignments += 1
+                    mass += rank
+    assert assignments == 4923000 and bank == 171361 and mass == 5 * 120 * bank
+    literal_stock = 4 * 1760 * 60 + 5 * bank
+    assert literal_stock == 1279205 and literal_stock % 5 == 0
+    return dict(status="PASS_ACTUAL_ROLE_REPLICA_STAGE_BANK_TILING",
+                actual_role_replica_stage_assignments=assignments,
+                assignment_sha256=digest.hexdigest(), patterns=patterns,
+                residual_role_counts={r: len(roles) for r, roles in families.items()},
+                exact_nested_endpoint_pairs=len(endpoint_pairs), banks_per_stage=bank,
+                covered_rank_mass=mass, literal_stock=literal_stock,
+                normalized_stock=literal_stock//5, max_block_scalar=40,
+                endpoint_columns_checked=columns, omission_repeat_wrong_columns=wrong_columns)
+
+
+def admit(candidate, export, baseline, chart_path, price_path):
+    candidate, export, baseline = map(lambda p: Path(p).resolve(), (candidate, export, baseline))
+    chart_path, price_path = Path(chart_path).resolve(), Path(price_path).resolve()
+    supplied_price = read(price_path)
+    base_package = Path(supplied_price["base_package"]).resolve()
+    price = pricing.compute(candidate, base_package)
+    assert price == supplied_price, "Price must reproduce from the actual candidate word"
+    full = read(baseline / "verification.json")
+    assert full["status"] == "PASS_IMMUTABLE_PARITY_FUSED_GEN4_FIVE_STAGE_BANKED_CONSTRUCTION"
+    assert full["inputs_unchanged"] and full["manifest_sha256"] == pricing.BASE_MANIFEST_SHA256
+    assert set(full["fresh_stages"]) == {"virtual", "raw", "bit", "scalar", "primes", "banks", "complex", "math", "finite"}
+    assert len(full["negative_controls"]) == 9
+    primes = read(baseline / "primes.json")
+    assert primes["all_remaining_factors_below_2_power_80"]
+    native = read(candidate / "COHORT-FIVE-STAGE-COLUMNS.json")
+    assert native["status"] == "PASS_GENERIC_FIVE_STAGE_FORMAL_COLUMNS_AND_COMPUTED_PREFIX"
+    assert native["formal_columns_checked"] == 23450 and native["independent_dirty_registers"] == 16410
+    assert len(native["negative_controls"]) == 6 and all(x["rejected"] for x in native["negative_controls"])
+    assert native["copied_center_original_source_immutable"] and native["fresh_center_copies"] == 120
+    state = read(export / "249-states.json")
+    initial, final = read(candidate / "COHORT249-INITIAL.json"), read(candidate / "COHORT249-FINAL.json")
+    frames = read(export / "frames.json")["frames"]
+    frames.update(read(candidate / "COHORT249-FRAMES.json"))
+    assert set(initial) == set(final) == {str(i) for i in range(19930)}
+    assert all(initial[str(i)] == state["initial"][str(i)] and final[str(i)] == state["final"][str(i)] for i in range(3520))
+    changed_entrances = {i for i in range(3520, 19930) if initial[str(i)] != state["initial"][str(i)]}
+    changed_exits = {i for i in range(3520, 19930) if final[str(i)] != state["final"][str(i)]}
+    assert len(changed_entrances) == 60 and len(changed_exits) == 440 and not changed_entrances & changed_exits
+    assert Counter(frames[str(initial[str(i)])]["dim"] for i in changed_entrances) == {18: 48, 19: 12}
+    assert all(frames[str(state["initial"][str(i)])]["dim"] == 0 and frames[str(final[str(i)])]["dim"] == 24 for i in changed_entrances)
+    assert all(frames[str(initial[str(i)])]["dim"] == 20 and frames[str(final[str(i)])]["dim"] == 23 and frames[str(state["final"][str(i)])]["dim"] == 24 for i in changed_exits)
+    records, local, operations, coefficients = pricing.word_inventory(candidate)
+    old_records = pricing.read_word(export / "COHORT249-RECORDS.bin")
+    assert [x for x in records if x[0] in (2, 3)] == [x for x in old_records if x[0] in (2, 3)]
+    current, open_copy = {int(i): f for i, f in initial.items()}, None
+    for op, a, b, c, frame, category in records:
+        if op == 0:
+            assert current[a] == b and frames[str(c)]["dim"] - frames[str(b)]["dim"] == frame
+            current[a] = c
+        elif op == 1:
+            assert current[a] == current[b] == frame
+            assert a != open_copy
+        elif op == 2:
+            assert open_copy is None and current[a] == c and b == 19930
+            current[b], open_copy = frame, b
+        else:
+            assert open_copy == b and current[a] == c and current[b] == frame
+            del current[b]
+            open_copy = None
+    assert open_copy is None and current == {int(i): f for i, f in final.items()}
+    old_pairs = {(b, c, rank) for op, a, b, c, rank, z in old_records if op == 0 and rank}
+    required_charts = {(b, c, rank) for op, a, b, c, rank, z in records if op == 0 and rank} - old_pairs
+    for role in changed_entrances | changed_exits:
+        before, after = initial[str(role)], final[str(role)]
+        required_charts.add((before, after, frames[str(after)]["dim"] - frames[str(before)]["dim"]))
+    chart = read(chart_path)
+    chart_details_path = chart_path.with_name("COMBINED-CHARTS.json")
+    charts = read(chart_details_path)
+    assert {(c["before"], c["after"], c["rank"]) for c in charts} == required_charts
+    assert len(charts) == len(required_charts) == chart["unique_projectors_checked"] == 3784
+    assert chart["retired_endpoints"] == 500 and chart["all_entries_below_two_to_80"]
+    assert int(chart["max_numerator"]) < 2**80 and int(chart["max_denominator"]) < 2**80
+    assert chart["max_factors"] == max(c["factors"] for c in charts) == 208
+    normalizer = max(186, chart["max_factors"]) + 119 + 120
+    assert normalizer == 447
+    bank = exact_banks(initial, final, frames)
+    stock, normalized_stock = bank["literal_stock"], bank["normalized_stock"]
+    assert normalized_stock == price["stock"] == 255841
+    adds, units, copies = operations[1], sum(c * n for c, n in coefficients.items()), operations[2]
+    assert adds == native["local_scalar_additions"] == 626360 and units == 629880 and copies == 24
+    assert dict(local) == dict(native["local_raw_H"]) == {int(k): n for k, n in price["local_histogram"].items()}
+    bounds = signed_bounds(records, 19930)
+    assert bounds == native["signed_lift_prefix"]
+    forward, backward = (int(row["cancellation_free_signed_row_l1_upper"]) for row in bounds)
+    payload = 64 * forward**3 * backward**2
+    assert payload == int(native["payload_prefix_upper"]) and payload.bit_length() == 91 and payload < 2**104
+    m, replicas, v, helpers = 120, 60, 1760, 16410
+    calls, mass = price["calls"], price["rank_mass"]
+    assert m * normalized_stock - mass == 52800
+    literal_histogram = {int(k): 5 * n for k, n in price["histogram"].items()}
+    children = sum(literal_histogram.values())
+    assert children == 5 * calls and sum(k*n for k, n in literal_histogram.items()) == 5 * mass
+    weighted = replicas * (5 * adds + 6 * v)
+    unit = replicas * (5 * units + 6 * v)
+    routes = replicas * (24 * v + 10 * helpers)
+    dimension, doubled = m*m, 2*m
+    good, high = 8*m*m + 8, 16*(dimension+1)**2
+    selectors = 2 * 5 * replicas * ((stock-1) + helpers * m * normalizer)
+    assert selectors == 528906962400 < 2**40
+    items = dict(unit_scalar_additions=unit, high_affine=routes*high,
+                 low_role_transpositions=routes*(stock+24), good_wrappers=children*good,
+                 matrix_preparation=children*128*doubled**3, invertibility_tests=16*m**3,
+                 copy_erase_episodes=120*replicas, edge_descriptors=children,
+                 bank_selectors=selectors, fixed_unit=1)
+    coefficient = sum(items.values())
+    assert coefficient == 92488203535344001 < 2**80 and stock+24 < 2**80
+    prime, residue = pricing.PRIME, 4
+    for _ in range(125):
+        residue = (residue * residue - 2) % prime
+    assert residue == 0 and all(127 % divisor for divisor in range(2, 12))
+    rho = Q(2*m**3, prime)
+    assert rho == Q(price["rare_density"]) and prime > 2**80
+    cutoffs = []
+    for row in price["ordinary_gaps"]:
+        delta = min(Q(value) for value in row["gaps"].values())
+        exponent = cutoff(delta, coefficient)
+        assert exponent * delta**2 >= 36 and exponent * delta >= 2*(4+(coefficient-1).bit_length())
+        cutoffs.append(dict(level=row["level"], minimum_gap=delta, log2_cutoff=exponent))
+    assert len(cutoffs) == 8
+    rejected = []
+    for name, delta, constant in [("zero cutoff gap", Q(0), coefficient), ("zero coefficient", Q(1, 2), 0)]:
+        try:
+            cutoff(delta, constant)
+        except AssertionError:
+            rejected.append(name)
+        else:
+            raise AssertionError("Invalid finite cutoff admitted")
+    moment_slack = 1 - Q(price["first_engine_interval"][1])
+    linear_slack = 1 - Q(mass, 120*normalized_stock) - rho*Q(32*m*calls, normalized_stock)
+    assert moment_slack > 0 and linear_slack > 0
+    sources = [Path(__file__).resolve(), Path(pricing.__file__).resolve(), Path(__file__).with_name("charts.cpp"),
+               chart_path, chart_details_path, price_path, export / "249-states.json", export / "frames.json",
+               export / "COHORT249-RECORDS.bin"]
+    sources += [candidate/name for name in ("COHORT249-RECORDS.bin", "COHORT249-INITIAL.json", "COHORT249-FINAL.json",
+                                           "COHORT249-FRAMES.json", "COHORT-FIVE-STAGE-COLUMNS.json")]
+    sources += [baseline/name for name in ("verification.json", "finite.json", "banks.json", "scalar.json", "primes.json", "complex.json")]
+    bindings = {str(path.resolve()): pricing.sha(path) for path in sources}
+    bank.update(source_word_sha256=price["source_word_sha256"], selector_charge=selectors,
+                normalizer_factor_bound=normalizer)
+    invoice = dict(
+        status="PASS_SOURCE_BOUND_GEN4_RETIREMENT_ENTRANCE_FIXED_PRIME_FINITE_INVOICE",
+        source_word_sha256=price["source_word_sha256"], source_bindings=bindings,
+        original_package_manifest_sha256=full["manifest_sha256"], price_independently_recomputed=True,
+        fixed_prime=prime, lucas_lehmer_steps=125, lucas_lehmer_residue=residue, rare_density=rho,
+        normalized_stock=normalized_stock, literal_stock=stock, physical_replicas=replicas, stages=5,
+        local_additions=adds, local_unit_expanded_additions=units, local_copy_episodes=copies,
+        global_weighted_additions=weighted, global_unit_expanded_additions=unit,
+        literal_histogram=literal_histogram, literal_positive_rank_children=children,
+        literal_rank_mass=5*mass, literal_deficit=264000, bank_assignments=4923000,
+        bank_selector_charge=selectors, normalizer_factor_bound=normalizer,
+        new_chart_factor_max=chart["max_factors"], primitive_coefficient_items=items,
+        full_counted_primitive_coefficient=coefficient, primitive_coefficient_bits=coefficient.bit_length(),
+        signed_lift_prefix=bounds, payload_prefix_upper=payload, payload_prefix_bits=91,
+        moment_slack=moment_slack, linear_slack=linear_slack, ordinary_levels=8,
+        ordinary_cutoffs=cutoffs, rejected_controls=rejected, all_47_constraints_positive=True,
+        kappa=price["kappa"], kappa_decimal=price["kappa_decimal"], gain_percent=price["gain_percent"],
+        exceeds_PR276_0p1_percent=True,
+        full_constant_rule="C_full dominates the displayed finite coefficient and every retained primitive, wrapper, "
+                           "setup, row, padding and preceding ordinary-level constant. Enlarge each cutoff with "
+                           "ceil(log2(C_full)); no recursive child is absorbed.",
+        scope="Conditional on the pinned PR276 all-size compiler, weighted chart, restored row, selectors, routing, "
+              "prime supply, recovery, complex symbolic and analytic hypotheses. The orchestration must regenerate "
+              "the baseline, actual candidate, scalar replay and exact chart audit."
+    )
+    return pricing.serial(bank), pricing.serial(invoice)
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("candidate", type=Path)
+    parser.add_argument("--export", type=Path, required=True)
+    parser.add_argument("--baseline", type=Path, required=True)
+    parser.add_argument("--charts", type=Path, required=True)
+    parser.add_argument("--price", type=Path, required=True)
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    bank, invoice = admit(args.candidate, args.export, args.baseline, args.charts, args.price)
+    args.output.mkdir(parents=True, exist_ok=True)
+    for name, value in [("BANK-ASSIGNMENT-REPLAY.json", bank), ("FINITE-INVOICE.json", invoice)]:
+        (args.output/name).write_text(json.dumps(value, sort_keys=True, indent=2) + "\n")
+    print("PASS integrated finite admission", invoice["kappa_decimal"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/gen4-retiming-entrances/code/charts.cpp b/research/gen4-retiming-entrances/code/charts.cpp
new file mode 100644
index 0000000000..3b2c4ce776
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/charts.cpp
@@ -0,0 +1,35 @@
+// Exact projector charts derived from the actual candidate and baseline words.
+// Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+#include <algorithm>
+#include <cstddef>
+#include <fstream>
+#include <iostream>
+#include <map>
+#include <set>
+#include <stdexcept>
+#include <string>
+#include <tuple>
+#include <vector>
+#include <json.hpp>
+#include <boost/multiprecision/cpp_int.hpp>
+using namespace std;using J=nlohmann::json;using Q=boost::multiprecision::cpp_rational;using Z=boost::multiprecision::cpp_int;using M=vector<vector<Q>>;
+J ld(string p){ifstream f(p);if(!f)throw runtime_error("missing "+p);J j;f>>j;return j;}
+Q rat(J j){return j.is_string()?Q(j.get<string>()):Q(j.get<long long>());}M eye(int n){M a(n,vector<Q>(n));for(int i=0;i<n;i++)a[i][i]=1;return a;}M tr(M a){M b(a[0].size(),vector<Q>(a.size()));for(int i=0;i<a.size();i++)for(int j=0;j<a[0].size();j++)b[j][i]=a[i][j];return b;}M mul(M a,M b){M c(a.size(),vector<Q>(b[0].size()));for(int i=0;i<a.size();i++)for(int k=0;k<b.size();k++)if(a[i][k]!=0)for(int j=0;j<b[0].size();j++)c[i][j]+=a[i][k]*b[k][j];return c;}
+Z maxnum=1,maxden=1;void admit(Q q){Z n=abs(numerator(q)),d=denominator(q);maxnum=max(maxnum,n);maxden=max(maxden,d);if(n>=(Z(1)<<80)||d>=(Z(1)<<80))throw runtime_error("finite prime guard exceeded");}
+M inverse(M a,int &ops,Q &det){int n=a.size();M b=eye(n);det=1;ops=0;for(int k=0;k<n;k++){int t=k;while(t<n&&a[t][k]==0)t++;if(t==n)throw runtime_error("singular");if(t!=k){swap(a[k],a[t]);swap(b[k],b[t]);det=-det;ops++;}Q p=a[k][k];admit(p);det*=p;if(p!=1){ops++;for(int j=0;j<n;j++){a[k][j]/=p;b[k][j]/=p;admit(a[k][j]);admit(b[k][j]);}}for(int i=0;i<n;i++)if(i!=k&&a[i][k]!=0){ops++;Q c=a[i][k];admit(c);for(int j=0;j<n;j++){a[i][j]-=c*a[k][j];b[i][j]-=c*b[k][j];admit(a[i][j]);admit(b[i][j]);}}}if(a!=eye(n))throw runtime_error("inverse failure");return b;}
+M nullspace(M a){int n=a[0].size(),row=0;vector<int>piv;for(int col=0;col<n&&row<a.size();col++){int t=row;while(t<a.size()&&a[t][col]==0)t++;if(t==a.size())continue;swap(a[row],a[t]);Q p=a[row][col];admit(p);for(auto &q:a[row]){q/=p;admit(q);}for(int i=0;i<a.size();i++)if(i!=row){Q c=a[i][col];for(int j=0;j<n;j++)a[i][j]-=c*a[row][j];}piv.push_back(col);row++;}if(row!=a.size())throw runtime_error("basis rank failure");M out;for(int free=0;free<n;free++)if(find(piv.begin(),piv.end(),free)==piv.end()){vector<Q>v(n);v[free]=1;for(int i=0;i<row;i++)v[piv[i]]=-a[i][free];out.push_back(v);}return out;}
+J mj(M a){J out=J::array();for(auto r:a){J z=J::array();for(Q q:r)z.push_back(q.str());out.push_back(z);}return out;}
+
+M sub(M a,M b){for(int i=0;i<a.size();i++)for(int j=0;j<a[i].size();j++)a[i][j]-=b[i][j];return a;}
+M independent_columns(M a){int m=a.size(),n=a[0].size(),row=0;vector<int> piv;M copy=a;for(int c=0;c<n&&row<m;c++){int k=row;while(k<m&&a[k][c]==0)k++;if(k==m)continue;swap(a[k],a[row]);Q p=a[row][c];for(int j=c;j<n;j++)a[row][j]/=p;for(int i=row+1;i<m;i++){Q b=a[i][c];for(int j=c;j<n;j++)a[i][j]-=b*a[row][j];}piv.push_back(c);row++;}M out(m);for(int i=0;i<m;i++)for(int c:piv)out[i].push_back(copy[i][c]);return out;}
+M kernel_general(M a){int m=a.size(),n=a[0].size(),row=0;vector<int>piv;for(int col=0;col<n&&row<m;col++){int t=row;while(t<m&&a[t][col]==0)t++;if(t==m)continue;swap(a[row],a[t]);Q p=a[row][col];for(auto&q:a[row])q/=p;for(int i=0;i<m;i++)if(i!=row){Q c=a[i][col];for(int j=0;j<n;j++)a[i][j]-=c*a[row][j];}piv.push_back(col);row++;}M out;for(int free=0;free<n;free++)if(find(piv.begin(),piv.end(),free)==piv.end()){vector<Q>v(n);v[free]=1;for(int i=0;i<row;i++)v[piv[i]]=-a[i][free];out.push_back(v);}return out;}
+struct Ev{int op,a,b,c,r,z;};
+int main(int ac,char**av){if(ac!=4)throw runtime_error("usage: charts EXPORT CANDIDATE OUT");string base=av[1],candidate=av[2],output=av[3];J fs=ld(base+"/frames.json")["frames"];J nf=ld(candidate+"/COHORT249-FRAMES.json"),ini=ld(candidate+"/COHORT249-INITIAL.json"),fin=ld(candidate+"/COHORT249-FINAL.json");for(auto it=nf.begin();it!=nf.end();++it)fs[it.key()]=it.value();M G=eye(24);for(auto&r:G)for(auto&q:r)q-=Q(1)/9;map<int,M>projectors;auto proj=[&](int f)->M{if(projectors.count(f))return projectors[f];int d=fs.at(to_string(f))["dim"];if(d==24)return projectors[f]=eye(24);if(!d)return projectors[f]=M(24,vector<Q>(24));M B;for(auto row:fs.at(to_string(f))["B"]){vector<Q>r;for(auto x:row)r.push_back(rat(x));B.push_back(r);}int ops;Q det;M BG=mul(B,G), gram=mul(BG,tr(B)), inv=inverse(gram,ops,det);return projectors[f]=mul(mul(tr(B),inv),BG);};set<tuple<int,int,int>>pairs,oldpairs;int endpoints=0;
+auto events=[&](string path){ifstream f(path,ios::binary);if(!f)throw runtime_error("missing word");f.seekg(0,ios::end);size_t size=f.tellg();f.seekg(0);if(size%sizeof(Ev))throw runtime_error("word shape");vector<Ev>v(size/sizeof(Ev));f.read((char*)v.data(),size);return v;};
+for(auto e:events(base+"/COHORT249-RECORDS.bin"))if(e.op==0&&e.r)oldpairs.insert({e.b,e.c,e.r});
+for(auto e:events(candidate+"/COHORT249-RECORDS.bin"))if(e.op==0&&e.r&&!oldpairs.count({e.b,e.c,e.r}))pairs.insert({e.b,e.c,e.r});
+J oldstate=ld(base+"/249-states.json");int v=oldstate["v"],n=oldstate["n"];
+for(int a=2*v;a<n;a++){string role=to_string(a);int before=ini[role],after=fin[role];if(before!=oldstate["initial"][role].get<int>()||after!=oldstate["final"][role].get<int>()){int rank=fs.at(to_string(after))["dim"].get<int>()-fs.at(to_string(before))["dim"].get<int>();pairs.insert({before,after,rank});endpoints++;}}
+
+int maxops=0,checked=0;J charts=J::array();for(auto[before,after,r]:pairs){M E=sub(proj(after),proj(before));if(mul(E,E)!=E)throw runtime_error("not projector");M C=independent_columns(E);if(C[0].size()!=r)throw runtime_error("rank mismatch");M K=kernel_general(E);if(K.size()!=24-r)throw runtime_error("nullity mismatch");for(int i=0;i<24;i++)for(auto&v:K)C[i].push_back(v[i]);int ops;Q det;M inv=inverse(C,ops,det),want=eye(24);for(int i=r;i<24;i++)want[i][i]=0;if(mul(mul(inv,E),C)!=want||mul(C,inv)!=eye(24))throw runtime_error("chart identity");maxops=max(maxops,ops);charts.push_back({{"before",before},{"after",after},{"rank",r},{"basis",mj(C)},{"inverse",mj(inv)},{"factors",ops},{"determinant",det.str()}});checked++;if(checked%50==0)cout<<"checked "<<checked<<"/"<<pairs.size()<<" maxfactors "<<maxops<<endl;}
+if(maxops>548)throw runtime_error("factor budget exceeded");J receipt={{"status","PASS_EXACT_CHANGED_ENDPOINT_AND_MOVE_CHARTS"},{"retired_endpoints",endpoints},{"unique_projectors_checked",checked},{"max_factors",maxops},{"max_numerator",maxnum.str()},{"max_denominator",maxden.str()},{"all_entries_below_two_to_80",true}};ofstream(output+"/COMBINED-CHART-AUDIT.json")<<receipt.dump(2)<<endl;ofstream(output+"/COMBINED-CHARTS.json")<<charts.dump()<<endl;cout<<receipt.dump(2)<<endl;}
diff --git a/research/gen4-retiming-entrances/code/cleanup.py b/research/gen4-retiming-entrances/code/cleanup.py
new file mode 100644
index 0000000000..263df838b9
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/cleanup.py
@@ -0,0 +1,41 @@
+#!/usr/bin/env python3
+"""Reproduce the fixed440 early-restoration word and its exact checks."""
+import argparse
+import hashlib
+from pathlib import Path
+import subprocess
+import sys
+if not __debug__:
+    raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+
+SOURCE_SHA256 = '2d22a9530f0b04a7a794d15077459234ef52183d6e7a70f813cfa849b79f2ebe'
+OUTPUT_SHA256 = '8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373'
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--source-dir', type=Path, required=True)
+    parser.add_argument('--export-dir', type=Path, required=True)
+    parser.add_argument('--output', type=Path, required=True)
+    args = parser.parse_args()
+    assert digest(args.source_dir / 'COHORT249-RECORDS.bin') == SOURCE_SHA256
+    code = Path(__file__).resolve().parent
+    screen = args.output / 'cleanup-selection'
+    common = ['--source-dir', str(args.source_dir),
+              '--export-dir', str(args.export_dir)]
+    subprocess.run([sys.executable, "-B", str(code / 'cleanup_screen.py'), *common,
+                    '--output-dir', str(screen)], check=True)
+    subprocess.run([sys.executable, "-B", str(code / 'cleanup_emit.py'), *common,
+                    '--screen', str(screen / 'screen.json'),
+                    '--output', str(args.output)], check=True)
+    assert digest(args.output / 'COHORT249-RECORDS.bin') == OUTPUT_SHA256
+    print('PASS fixed440 cleanup word:', OUTPUT_SHA256, flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances/code/cleanup_emit.py b/research/gen4-retiming-entrances/code/cleanup_emit.py
new file mode 100644
index 0000000000..16191acf0c
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/cleanup_emit.py
@@ -0,0 +1,106 @@
+#!/usr/bin/env python3
+import sys
+if not __debug__: raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+import json,hashlib,struct,time,argparse
+from array import array
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+import sympy as sp
+from sympy.polys.matrices import DomainMatrix
+ap=argparse.ArgumentParser();ap.add_argument('--output',type=Path,required=True);ap.add_argument('--source-dir',type=Path,required=True);ap.add_argument('--export-dir',type=Path,required=True);ap.add_argument('--screen',type=Path,required=True);a=ap.parse_args();t=time.time();D=Path(__file__).parent;P=a.source_dir;X=a.export_dir;out=a.output;out.mkdir(parents=True,exist_ok=True)
+def load(p):return json.loads(p.read_text())
+def sha(b):return hashlib.sha256(b).hexdigest()
+screen=load(a.screen);cut=screen['cut'];edits=screen['candidates'][:440];assert len(edits)==440 and len(screen['candidates'])==440;A={e['role']for e in edits};skip={e['incidences'][0][0]for e in edits};assert all(len(e['incidences'])==1 for e in edits)
+base=load(X/'gen4-states.json');n,v=base['n'],base['v'];fs={int(k):r for k,r in load(X/'frames.json')['frames'].items()};extras=load(P/'COHORT249-FRAMES.json');fs.update({int(k):r for k,r in extras.items()});newfs={e['frame']:screen['newframes'][str(e['frame'])]for e in edits};assert not set(newfs).intersection(fs);fs.update(newfs)
+initial={int(k):f for k,f in load(P/'COHORT249-INITIAL.json').items()};final={int(k):f for k,f in load(P/'COHORT249-FINAL.json').items()};final.update({e['role']:e['frame']for e in edits});state=dict(initial)
+q=2**127-1;G=9*sp.eye(24)-sp.ones(24);aud=[]
+for f,z in newfs.items():
+ B=sp.Matrix(z['B']);AA=sp.Matrix(z['A']);d=z['dim'];assert B.shape==(d,24) and AA.shape==(24-d,24);assert AA*B.T==sp.zeros(24-d,d);assert DomainMatrix.from_Matrix(AA).rank()==24-d
+ det=sp.Rational(DomainMatrix.from_Matrix(B*G*B.T).det());assert det and int(det.p)%q and int(det.q)%q
+ aud.append(dict(frame=f,dim=d,cleared_gram_determinant=str(det)))
+print('exact newframes',len(aud),'seconds',time.time()-t,flush=True)
+raw=(P/'COHORT249-RECORDS.bin').read_bytes();old=array('i');old.frombytes(raw)
+# Each moved gate commutes over Z with the entire crossed interval: no other
+# use of its destination and no intervening write to its donor. Thus the exact
+# signed scalar operator and original maximum coefficient bound are retained.
+first_write={}; uses={role:[] for role in A}
+for i in range(cut,len(old)//6):
+ op,dest,src,coef,frame,tag=old[6*i:6*i+6]
+ assert op not in (2,3), 'COPY lifetime crosses cleanup interval'
+ if op==1:
+  first_write.setdefault(dest,i)
+  if dest in uses:uses[dest].append(i)
+  if src in uses:uses[src].append(i)
+for e in edits:
+ idx=e['incidences'][0][0];role=e['role'];donor=e['donors'][0]
+ assert uses[role]==[idx]
+ assert tuple(old[6*idx:6*idx+3])==(1,role,donor)
+ assert first_write.get(donor,len(old)//6)>idx
+new=array('i');cols=[1<<i for i in range(n)]+[0];checked=set();inherited={(old[i+2],old[i+3])for i in range(0,len(old),6)if old[i]==0};basis={f:[[Q(x)for x in row]for row in z['B']]for f,z in fs.items()};ann={f:[[Q(x)for x in row]for row in z['A']]for f,z in fs.items()}
+def move(role,f):
+ before=state[role]
+ if before==f:return
+ if (before,f)not in inherited and (before,f)not in checked:
+  assert all(sum(x*y for x,y in zip(u,w))==0 for u in basis[before]for w in ann[f]),('not nested',role,before,f);checked.add((before,f))
+ rank=fs[f]['dim']-fs[before]['dim'];assert rank>=0
+ new.extend((0,role,before,f,rank,0));state[role]=f
+def emit(r):
+ op,a,b,c,f,z=r
+ if op==1:
+  move(a,f);move(b,f)
+  if c%2:cols[a]^=cols[b]
+ elif op==2:
+  move(a,c);assert b==n and cols[b]==0;cols[b]=cols[a];state[b]=f
+ elif op==3:
+  assert cols[a]==cols[b] and state[a]==c and state[b]==f;cols[b]=0;del state[b]
+ else:raise AssertionError(r)
+ new.extend(r)
+for i in range(len(old)//6):
+ if i==cut:
+  for e in edits:
+   emit((1,e['role'],e['donors'][0],old[6*e['incidences'][0][0]+3],e['frame'],32));assert cols[e['role']]==1<<e['role']
+ r=old[6*i:6*i+6]
+ if r[0]!=0 and i not in skip:emit(r)
+for role in range(n):move(role,final[role])
+expected=[(1<<i)^((1<<(i-v))if v<=i<2*v else 0)for i in range(n)]
+assert cols==expected+[0];assert state==final
+# Full reverse word with fresh COPY at each reverse ERASE and erase at each reverse COPY.
+def reverse(start):
+ cols=list(start)+[0];ss=dict(final)
+ for i in range(len(new)//6-1,-1,-1):
+  op,a,b,c,f,z=new[6*i:6*i+6]
+  if op==0:assert ss[a]==c;ss[a]=b
+  elif op==1:
+   assert ss[a]==ss[b]==f
+   if c%2:cols[a]^=cols[b]
+  elif op==3:assert cols[b]==0 and b not in ss and ss[a]==c;cols[b]=cols[a];ss[b]=f
+  elif op==2:assert cols[a]==cols[b] and ss[a]==c and ss[b]==f;cols[b]=0;del ss[b]
+ assert ss==initial
+ return cols
+assert reverse([1<<i for i in range(n)])==expected+[0]
+assert reverse(expected)==[1<<i for i in range(n)]+[0]
+# Omit one moved restoration: corruption must be detected on the full formal basis.
+bad=[1<<i for i in range(n)]+[0];omitted=False
+for i in range(0,len(new),6):
+ op,a,b,c,f,z=new[i:i+6]
+ if op==1:
+  if z==32 and not omitted:omitted=True
+  elif c%2:bad[a]^=bad[b]
+ elif op==2:bad[b]=bad[a]
+ elif op==3:assert bad[a]==bad[b];bad[b]=0
+wrong=sum(x!=y for x,y in zip(bad,expected+[0]));assert wrong
+
+def hist(r):
+ H=Counter()
+ for i in range(0,len(r),6):
+  op,a,b,c,f,z=r[i:i+6]
+  if op==0 and f:H[f]+=1
+  elif op==2:H[z]+=1
+ return H
+H0=hist(old);H=hist(new);delta=H.copy();delta.subtract(H0);delta={str(r):c for r,c in sorted(delta.items())if c};assert delta=={'1':3*len(edits),'2':-2*len(edits)};assert sum(int(r)*c for r,c in delta.items())==-len(edits)
+blob=new.tobytes();assert sha(blob)=='8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373';(out/'COHORT249-RECORDS.bin').write_bytes(blob);(out/'COHORT249-INITIAL.json').write_bytes((P/'COHORT249-INITIAL.json').read_bytes());(out/'COHORT249-FINAL.json').write_text(json.dumps(final,sort_keys=True)+'\n');extras.update({str(k):x for k,x in newfs.items()});(out/'COHORT249-FRAMES.json').write_text(json.dumps(extras,sort_keys=True)+'\n')
+newstates=dict(base);newstates['inherited_physical_provenance']=newstates.pop('physical');newstates.update(initial=initial,final=final,record_count=len(new)//6,record_sha256=sha(blob));(out/'249-states.json').write_text(json.dumps(newstates,sort_keys=True)+'\n')
+receipt=dict(status='PASS_EXACT_NEW_FRAMES_FORWARD_INVERSE_ROUNDTRIP',input_sha256=sha(raw),output_sha256=sha(blob),retired_helpers=len(edits),cut=cut,formal_columns=n,scalar_additions=len([i for i in range(0,len(new),6)if new[i]==1]),record_count=len(new)//6,histogram={str(r):c for r,c in sorted(H.items())},histogram_delta=delta,endpoint_rank_mass_drop=len(edits),exact_new_connector_pairs=len(checked),omission_wrong_rows=wrong,signed_scalar_operator_preserved_by_exact_commutation=True,maximum_formal_coefficient_bound_does_not_increase=True,frames_audit=aud,edits=edits,seconds=time.time()-t)
+(out/'CLEANUP-REPLAY.json').write_text(json.dumps(receipt,indent=2)+'\n');print({k:x for k,x in receipt.items()if k not in ('edits','frames_audit','histogram')},flush=True)
diff --git a/research/gen4-retiming-entrances/code/cleanup_reference.py b/research/gen4-retiming-entrances/code/cleanup_reference.py
new file mode 100644
index 0000000000..38eb6b6d09
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/cleanup_reference.py
@@ -0,0 +1,59 @@
+"""Exact basis helpers derived from PR271's sandwich263.py.
+
+Source: https://github.com/CrocSwap/integer-mult-bounds/pull/271
+Retained rational_basis, rank_mod_prime, and annihilator routines; no PR271
+cleanup selection or word rewrite is imported. The exact emitted-frame Gram
+and prime audits are independently performed in cleanup_emit.py.
+"""
+import sys
+if not __debug__: raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+from fractions import Fraction as Q
+from math import lcm
+H = 24
+PRIME = 1000003
+
+def rational_basis(rows):
+    """Reduced integer basis of the rational row space."""
+    basis = {}
+    for values in rows:
+        row = list(map(Q, values))
+        for p, b in sorted(basis.items()):
+            if row[p]:
+                row = [x - row[p] * y for x, y in zip(row, b)]
+        p = next((i for i, x in enumerate(row) if x), None)
+        if p is not None:
+            basis[p] = [x / row[p] for x in row]
+    out = []
+    for _, row in sorted(basis.items()):
+        d = lcm(*(x.denominator for x in row))
+        out.append([int(x * d) for x in row])
+    return out
+
+
+def rank_mod_prime(rows):
+    basis = {}
+    for row in rows:
+        row = [x % PRIME for x in row]
+        for p, b in sorted(basis.items()):
+            if row[p]:
+                c = row[p]
+                row = [(x - c * y) % PRIME for x, y in zip(row, b)]
+        p = next((i for i, x in enumerate(row) if x), None)
+        if p is not None:
+            inv = pow(row[p], -1, PRIME)
+            basis[p] = [x * inv % PRIME for x in row]
+    return len(basis)
+
+
+def annihilator(B):
+    """Rational basis of {x : B x = 0} for a reduced basis B."""
+    pivots = [next(i for i, x in enumerate(row) if x) for row in B]
+    out = []
+    for free in sorted(set(range(H)) - set(pivots)):
+        v = [Q(i == free) for i in range(H)]
+        for p, row in reversed(list(zip(pivots, B))):
+            v[p] = -sum(Q(row[j]) * v[j] for j in range(p + 1, H)) / row[p]
+        out.append([str(x) for x in v])
+    return out
+
diff --git a/research/gen4-retiming-entrances/code/cleanup_screen.py b/research/gen4-retiming-entrances/code/cleanup_screen.py
new file mode 100644
index 0000000000..705d1373f0
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/cleanup_screen.py
@@ -0,0 +1,54 @@
+#!/usr/bin/env python3
+"""Regenerate the fixed440 gen4 cleanup selection."""
+from pathlib import Path
+from array import array
+from collections import Counter,defaultdict
+import json,sys,argparse
+if not __debug__: raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+sys.path.insert(0,str(Path(__file__).parent))
+from cleanup_reference import rational_basis,rank_mod_prime,annihilator
+ap=argparse.ArgumentParser();ap.add_argument('--source-dir',type=Path,required=True);ap.add_argument('--export-dir',type=Path,required=True);ap.add_argument('--output-dir',type=Path,required=True);args=ap.parse_args();D=args.output_dir;D.mkdir(parents=True,exist_ok=True);P=args.source_dir;X=args.export_dir
+r=array('i');r.frombytes((P/'COHORT249-RECORDS.bin').read_bytes());st=json.loads((X/'gen4-states.json').read_text());n=st['n'];v=st['v'];rows=[1<<j for j in range(n)]+[0];fs=json.loads((X/'frames.json').read_text())['frames'];fs.update(json.loads((P/'COHORT249-FRAMES.json').read_text()));state={int(a):f for a,f in json.loads((P/'COHORT249-INITIAL.json').read_text()).items()}
+cut=next(i for i in range(len(r)//6) if r[6*i]==1 and r[6*i+5]==3)
+for i in range(cut):
+ op,a,b,c,f,z=r[6*i:6*i+6]
+ if op==0:state[a]=c
+ elif op==1:rows[a]^=rows[b]
+ elif op==2:rows[b]=rows[a];state[b]=f
+ elif op==3:rows[b]=0;state.pop(b,None)
+assert (n,v,cut)==(19930,1760,662145)
+assert all(rows[v+j]==(1<<(v+j))^(1<<j) for j in range(v))
+print('cut',cut,'target wrong',sum(rows[v+j]!=(1<<(v+j))^(1<<j) for j in range(v)),flush=True)
+affected=[0]*n
+for a,x in enumerate(rows[:n]):
+ x^=1<<a
+ if v<=a<2*v:x^=1<<(a-v)
+ while x:k=(x&-x).bit_length()-1;x&=x-1;affected[k]+=1
+cand=[a for a in range(2*v,n) if not affected[a] and fs[str(state[a])]['dim']<24]
+suffix=[1<<a for a in range(n)]+[0];inc=defaultdict(list)
+for i in range(cut,len(r)//6):
+ op,a,b,c,f,z=r[6*i:6*i+6]
+ if op==1:suffix[a]^=suffix[b];inc[a].append((i,a,b));inc[b].append((i,a,b))
+ elif op==2:suffix[b]=suffix[a]
+ elif op==3:suffix[b]=0
+census=Counter();cs=[];newframes={}
+for a in cand:
+ x=suffix[a]^(1<<a);don=[]
+ while x:k=(x&-x).bit_length()-1;x&=x-1;don.append(k)
+ census[len(don),max([fs[str(state[b])]['dim'] for b in don]+[0])]+=1
+ if len(don)!=1:continue
+ b=don[0]
+ B=rational_basis(fs[str(state[a])]['B']+fs[str(state[b])]['B']);d=len(B)
+ if d==24:continue
+ sums=[sum(u) for u in B];gram=[[9*sum(p*q for p,q in zip(u,w))-su*sw for w,sw in zip(B,sums)]for u,su in zip(B,sums)]
+ if rank_mod_prime(gram)!=d:continue
+ dim_a=fs[str(state[a])]['dim'];dim_b=fs[str(state[b])]['dim']
+ frame=900000+len(newframes);newframes[str(frame)]={'dim':d,'B':B,'A':annihilator(B)}
+ cs.append(dict(role=a,donors=[b],frame=frame,dim=d,dim_a=dim_a,dim_b=dim_b,incidences=inc[a]))
+print('isolated',len(cand),'donor census',census,flush=True)
+print('proper one donor',len(cs),'census',Counter((x['dim_a'],x['dim_b'],x['dim'],len(x['incidences']))for x in cs),flush=True)
+assert len(cs)==440 and all((e['dim_a'],e['dim_b'],e['dim'],len(e['incidences']))==(22,22,23,1) for e in cs)
+assert len({e['donors'][0] for e in cs})==440
+assert not {e['role'] for e in cs}.intersection(e['donors'][0] for e in cs)
+(D/'screen.json').write_text(json.dumps({'cut':cut,'n':n,'v':v,'candidates':cs,'newframes':newframes},indent=2))
diff --git a/research/gen4-retiming-entrances/code/entrances.py b/research/gen4-retiming-entrances/code/entrances.py
new file mode 100644
index 0000000000..7f4031a325
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/entrances.py
@@ -0,0 +1,121 @@
+"""Exact transport of 60 independent dirty entrances after center scatter.
+
+Frozen source words and selected stream/role identities are checked before replay.
+Each relocated elementary shear has a target destination and an unchanged helper
+source. Targets are never read by ADD or COPY; selected helpers are neither
+written nor copied before the transport cut. Consequently these240 shears commute
+with all intervening scalar/COPY instructions over every coefficient ring. Their
+original signed coefficients are retained. Literal projection and an independent
+integer replay of all60 selected dirty columns check the resulting equality.
+
+The physical frame change is checked separately: new entrance bases and their
+annihilators have full rank, zero pairing, and nonzero Gram determinant. Every
+changed movement is nested; each ADD has a common frame. The containment check
+also gives the reversed annihilator inclusion for the reflected ledger. Source
+and target endpoints are unchanged. The60 selected helper endpoints remainFULL24.
+
+The new residuals are12 of rank5 and48 of rank6, replacing60 of rank24. Sixty
+replicas tile120-coordinate banks exactly:30+144 banks per stage replace720.
+The full integrated finite invoice and chart audit are separate verifier steps.
+
+Substantial OpenAI Codex assistance. Apache-2.0; see repository notices.
+"""
+import argparse,json,hashlib,struct,functools,math
+from pathlib import Path
+from collections import Counter
+import sympy as sp
+if not __debug__:raise SystemExit('Assertions required')
+ap=argparse.ArgumentParser(description=__doc__)
+ap.add_argument('--source-dir',required=True,type=Path)
+ap.add_argument('--export-dir',required=True,type=Path)
+ap.add_argument('--output',required=True,type=Path)
+args=ap.parse_args();X=args.export_dir;D=args.output;D.mkdir(exist_ok=True,parents=True);base=args.source_dir
+st=json.loads((X/'gen4-states.json').read_text());n=st['n'];v=st['v'];zero=st['ZERO'];fs={int(k):x for k,x in json.loads((X/'frames.json').read_text())['frames'].items()};fs.update({int(k):x for k,x in json.loads((base/'COHORT249-FRAMES.json').read_text()).items()});extra={}
+selection_path=Path(__file__).resolve().parent.parent/'data'/'entrances60.json'
+selection=json.loads(selection_path.read_text());assert (n,v)==(19930,1760)
+assert hashlib.sha256((base/'COHORT249-RECORDS.bin').read_bytes()).hexdigest()==selection['source_word_sha256']
+assert st['record_sha256']==selection['export_word_sha256']
+selected={e['stream']:dict(e) for e in selection['entries']};assert len(selected)==len(selection['entries'])==60 and sum(e['rank']for e in selected.values())==1092
+raw=list(struct.iter_unpack('<6i',(base/'COHORT249-RECORDS.bin').read_bytes()));initial={int(k):x for k,x in json.loads((base/'COHORT249-INITIAL.json').read_text()).items()};final={int(k):x for k,x in json.loads((base/'COHORT249-FINAL.json').read_text()).items()};cut=max(j for j,e in enumerate(raw)if e[0]==3);read=st['physical']['category_names'].index('dirty_read');oldH=Counter();pairs=set();basepairs={(e[2],e[3])for e in raw if e[0]==0}
+def introw(row):
+ den=sp.ilcm(*[a.q for a in row]);z=[int(a*den)for a in row];g=math.gcd(*z);return [a//g for a in z]
+for h,e in selected.items():
+ assert 2*v<=h<n and st['regs'][h-2*v]==e['role'] and initial[h]==zero
+ B=sp.Matrix(e['basis']);rank=e['rank'];assert B.rank()==rank and (B*(9*sp.eye(24)-sp.ones(24))*B.T).det()!=0
+ A=[introw(row.T.tolist()[0])for row in B.nullspace()];assert len(A)+rank==24;assert sp.Matrix(A).rank()==24-rank and B*sp.Matrix(A).T==sp.zeros(rank,24-rank)
+ f=max(fs)+1;fs[f]=dict(B=e['basis'],A=A,dim=rank);extra[f]=fs[f];e['frame']=f;initial[h]=f
+@functools.lru_cache(None)
+def sub(a,b):return fs[a]['dim']<=fs[b]['dim'] and all(sum(x*y for x,y in zip(u,w))==0 for u in fs[a]['B']for w in fs[b]['A'])
+# Exact commutation contract: no target is ever read, each chosen helper is
+# untouched up to cut, and all its initial target reads are before that cut.
+reads=[];counter=Counter();helper_touches=Counter()
+for j,(op,a,b,c,f,z)in enumerate(raw):
+ if op==0:
+  if f:oldH[f]+=1
+ elif op==1:
+  assert not(v<=b<2*v),'Target read invalidates simple commutation proof'
+  if a in selected and j<=cut:raise AssertionError(('selected helper written before cut',a,j))
+  if b in selected and j<=cut:
+   assert v<=a<2*v and z==read and f==zero and abs(c)==1
+   reads.append((j,a,b,c,z));counter[b]+=1
+  if b in selected and f==zero:assert j<=cut
+ elif op==2:
+  assert not(v<=a<2*v),'Target COPY source invalidates simple commutation proof'
+  oldH[z]+=1
+  if j<=cut:assert a not in selected
+assert len(reads)==240 and set(counter)==set(selected) and set(counter.values())=={4}
+assert {a-v for _,a,b,c,z in reads}=={t for e in selected.values()for t in e['targets']}
+for h,e in selected.items():assert {a-v for _,a,b,c,z in reads if b==h}==set(e['targets'])
+state=dict(initial);out=[];temporary=None;H=Counter();changedpairs=set();skip={j for j,a,b,c,z in reads}
+def move(a,f):
+ old=state[a]
+ if old==f:return
+ if (old,f)not in basepairs:assert sub(old,f),('nonnested',a,old,f);changedpairs.add((old,f))
+ pairs.add((old,f));rank=fs[f]['dim']-fs[old]['dim'];assert rank>=0;out.append((0,a,old,f,rank,0));state[a]=f
+ if rank:H[rank]+=1
+for j,(op,a,b,c,f,z)in enumerate(raw):
+ if op==0:continue
+ if j in skip:continue
+ if op==1:move(a,f);move(b,f);out.append((op,a,b,c,f,z))
+ elif op==2:
+  assert temporary is None and b==n;move(a,c);state[b]=f;temporary=(a,b,c,f);H[z]+=1;out.append((op,a,b,c,f,z))
+ else:
+  assert op==3 and temporary==(a,b,c,f)and state[a]==c and state[b]==f;out.append((op,a,b,c,f,z));del state[b];temporary=None
+ if j==cut:
+  assert temporary is None
+  for oldj,a,b,c,z in reads:
+   f=selected[b]['frame'];assert state[b]==f;move(a,f);out.append((1,a,b,c,f,z))
+assert temporary is None
+for a in range(n):move(a,final[a])
+assert state==final
+# Full chronological projection with exactly the documented read relocation.
+expect=[]
+for j,(op,a,b,c,f,z) in enumerate(raw):
+ if op and j not in skip:expect.append((op,a,b,c,z))
+ if j==cut:expect.extend((1,a,b,c,z)for _,a,b,c,z in reads)
+assert [(op,a,b,c,z)for op,a,b,c,f,z in out if op]==expect
+# Selected 60 columns replay both source words over exact integers. This is
+# stronger than a parity test for the relocated arbitrary dirty payload.
+def columns(word):
+ cols=[{}for _ in range(n)];tmp=None
+ for h in selected:cols[h][h]=1
+ for op,a,b,c,f,z in word:
+  if op==1:
+   q=tmp if b==n else b
+   for h,x in list(cols[q].items()):
+    value=cols[a].get(h,0)+c*x
+    if value:cols[a][h]=value
+    elif h in cols[a]:del cols[a][h]
+  elif op==2:assert tmp is None;tmp=a
+  elif op==3:assert tmp==a;tmp=None
+ assert tmp is None
+ return cols
+assert columns(raw)==columns(out)
+delta=Counter(H);delta.subtract(oldH);delta={r:x for r,x in delta.items()if x};assert sum(r*x for r,x in delta.items())==-1092
+residual_before=Counter(fs[final[h]]['dim']-fs[zero]['dim']for h in selected);residual_after=Counter(fs[final[h]]['dim']-selected[h]['rank']for h in selected);assert residual_before=={24:60}and residual_after=={5:12,6:48}
+data=b''.join(struct.pack('<6i',*e)for e in out)
+assert hashlib.sha256(data).hexdigest()==selection['expected_output_sha256']
+(D/'COHORT249-RECORDS.bin').write_bytes(data)
+for name,value in [('INITIAL',initial),('FINAL',final),('FRAMES',{**json.loads((base/'COHORT249-FRAMES.json').read_text()),**extra})]:(D/f'COHORT249-{name}.json').write_text(json.dumps(value)+'\n')
+receipt=dict(selection_sha256=hashlib.sha256(selection_path.read_bytes()).hexdigest(),emitter_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),status='PASS_60_EXACT_INTEGER_DIRTY_COMPENSATION_TRANSPORT',source=str(base),source_sha256=hashlib.sha256((base/'COHORT249-RECORDS.bin').read_bytes()).hexdigest(),output_sha256=hashlib.sha256(data).hexdigest(),new_entrance_count=60,new_entrance_rank=1092,cut_record=cut,relocated_reads=reads,entries=list(selected.values()),all_selected_integer_columns_equal=True,only_documented_scalar_reordering=True,all_new_frames_exact_nondegenerate=True,changed_connector_pairs=sorted(changedpairs),paid_histogram=dict(H),histogram=dict(H),delta=delta,rank_mass=sum(r*x for r,x in H.items()),record_count=len(out),new_residual_histogram=dict(residual_after),local_entropy_delta=sum(x*r*math.log(120/r)for r,x in delta.items()))
+(D/'ENTRANCE-TRANSPORT.json').write_text(json.dumps(receipt,indent=2)+'\n');(D/'ENTRANCE-SELECTION.json').write_text(json.dumps(selection,indent=2)+'\n');print({k:v for k,v in receipt.items()if k not in ['entries','relocated_reads','changed_connector_pairs','paid_histogram','histogram']},flush=True)
diff --git a/research/gen4-retiming-entrances/code/export.py b/research/gen4-retiming-entrances/code/export.py
new file mode 100644
index 0000000000..e7b5c0ae30
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/export.py
@@ -0,0 +1,34 @@
+from pathlib import Path
+import json,sys,importlib.util,time,hashlib
+from collections import Counter
+import argparse, shutil
+if not __debug__: raise SystemExit('Assertions required; refusing -O')
+ap=argparse.ArgumentParser(); ap.add_argument('--base',type=Path,required=True); ap.add_argument('--output',type=Path,required=True); args=ap.parse_args()
+P=args.base.resolve(); D=args.output.resolve(); D.mkdir(parents=True,exist_ok=False)
+sys.dont_write_bytecode=True
+sys.path.insert(0,str(P));start=time.monotonic()
+def load(n):
+ s=importlib.util.spec_from_file_location('export_gen4_'+n.replace('/','_'),P/(n+'.py'));m=importlib.util.module_from_spec(s);sys.modules[s.name]=m;s.loader.exec_module(m);return m
+def save(n,j):(D/n).write_text(json.dumps(j,separators=(',',':'))+'\n')
+c=load('prepare').prepare();print('PREPARED',time.monotonic()-start,flush=True)
+p=load('code/physical527').run(c,c['SOURCE_TEXT'])
+p=load('parity_transform').run(p)
+records=p['records'];raw=records.tobytes();(D/'gen4-records.bin').write_bytes(raw)
+final=dict(p['initial_state']);used=set(final.values());hist=Counter();adds=Counter()
+for k in range(0,len(records),6):
+ op,a,b,cc,f,z=records[k:k+6]
+ if op==0:final[a]=cc;used.update((b,cc));hist[f]+=bool(f)
+ elif op==1:used.add(f);adds[cc]+=1
+ elif op in (2,3):used.update((cc,f));hist[z]+=op==2
+n=len(p['initial_state']);v=c['W'].v
+state=dict(initial=p['initial_state'],final=final,ZERO=p['ZERO'],FULL=p['FULL'],n=n,v=v,record_count=len(records)//6,record_sha256=hashlib.sha256(raw).hexdigest(),physical=p['physical'],regs=c['regs'],borrowed=list(c['borrow']),removed=list(c['removed']),source_owned_roles=sorted(c['borrow']),source_covectors=p['C'].cov)
+save('gen4-states.json',state)
+C=p['C'];save('frames.json',dict(h=24,frames={str(f):dict(B=C.B[f],A=C.A[f],dim=C.dimf[f])for f in sorted(used)}))
+save('gen4-ownership.json',dict(donor_keys=sorted(c['W'].donor),phys=c['W'].phys,idx=c['idx'],pairs=c['W'].pairs))
+save('EXPORT-RECEIPT.json',dict(status='FRESH_SOURCE_BOUND_EXPORT_NOT_FULL_VERIFICATION',head='d428ab0462b9dfd3131ab4e89999f0adcd6173dd',record_sha256=hashlib.sha256(raw).hexdigest(),n=n,v=v,frames=len(used),paid_histogram=dict(hist),adds=dict(adds),seconds=time.monotonic()-start))
+print('EXPORTED',n,len(records)//6,len(used),time.monotonic()-start,flush=True)
+
+assert state['record_sha256']=='60830cb24fbdd5a26942c4aa897d0ae30738ca5772ab83d6c57be666ddc95f7a'
+for name in ['249-records.bin','COHORT249-RECORDS.bin']: shutil.copyfile(D/'gen4-records.bin',D/name)
+shutil.copyfile(D/'gen4-states.json',D/'249-states.json')
+save('COHORT249-INITIAL.json',state['initial']);save('COHORT249-FINAL.json',state['final']);save('COHORT249-FRAMES.json',{})
diff --git a/research/gen4-retiming-entrances/code/five-stage-columns.cpp b/research/gen4-retiming-entrances/code/five-stage-columns.cpp
new file mode 100644
index 0000000000..187d969fc5
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/five-stage-columns.cpp
@@ -0,0 +1,42 @@
+#include "json.hpp"
+#include <map>
+#include <boost/multiprecision/cpp_int.hpp>
+using boost::multiprecision::cpp_int;
+#include <vector>
+#include <array>
+#include <fstream>
+#include <iostream>
+#include <chrono>
+#include <stdexcept>
+#include <cstring>
+using J=nlohmann::json;
+struct E{int kind,dst,src,c;};
+void need(bool x,const char*s){if(!x)throw std::runtime_error(s);}
+int main(int argc,char**argv){try{
+need(argc==5,"usage RAW6_RECORDS OUTPUT V HELPERS");std::string pre=argv[1];int v=std::stoi(argv[3]),r=std::stoi(argv[4]),loc=2*v+r,global=4*v+r,temp=global;need(v>0 && r>=0,"dimensions");
+struct Raw{int op,a,b,c,f,z;};std::ifstream f(pre,std::ios::binary|std::ios::ate);size_t sz=f.tellg();need(sz%sizeof(Raw)==0,"stream alignment");std::vector<Raw>p(sz/sizeof(Raw));f.seekg(0);f.read((char*)p.data(),sz);std::vector<E>e;std::map<int,long long>H;for(auto q:p){if(q.op==0){if(q.f)H[q.f]++;}else if(q.op==1)e.push_back({0,q.a,q.b,q.c});else if(q.op==2){H[q.z]++;e.push_back({1,loc,q.a,0});}else if(q.op==3)e.push_back({2,loc,q.a,0});else need(false,"opcode");}
+J prefix=J::array();cpp_int largestF=0,largestB=0;for(int rev=0;rev<2;rev++){std::vector<cpp_int>norms(loc+1,1);cpp_int maxrow=1;bool isopen=false;for(size_t z=0;z<e.size();z++){auto q=e[rev?e.size()-1-z:z];int k=q.kind;if(rev&&k)k=3-k;if(!k){norms[q.dst]+=std::abs(q.c)*norms[q.src];if(norms[q.dst]>maxrow)maxrow=norms[q.dst];}else if(k==1){need(!isopen,"boundcopy");norms[loc]=norms[q.src];isopen=true;}else {need(isopen,"bounderase");norms[loc]=0;isopen=false;}}need(!isopen,"prefix copy closure");if(rev)largestB=maxrow;else largestF=maxrow;prefix.push_back({{"reverse",bool(rev)},{"cancellation_free_signed_row_l1_upper",maxrow.convert_to<std::string>()},{"bits",boost::multiprecision::msb(maxrow)+1}});}
+cpp_int payload=64*largestF*largestF*largestF*largestB*largestB;need(payload>0,"positive finite prefix"); // Exact width is reported and must be included in the separate finite invoice.
+long long copies=0,adds=0,odd=0;bool open=false;int center=-1;long long reverseCopies=0;
+for(auto q:e){need(q.kind>=0&&q.kind<=2,"kind");need(q.dst>=0&&q.dst<=loc,"local dst");if(q.kind==0){need(q.src>=0&&q.src<=loc&&q.dst!=q.src,"source distinct");need(q.dst!=loc,"copy immutable");need(q.src!=loc||open,"temp not open");if(open)need(q.dst!=center,"source changes inside copied-center block");adds++;odd+=q.c&1;}
+else if(q.kind==1){need(!open&&q.dst==loc&&q.src>=0&&q.src<loc,"fresh copy shape");open=true;center=q.src;copies++;}
+else{need(open&&q.dst==loc&&q.src==center,"discard original-source binding");open=false;center=-1;}}
+need(!open&&copies==24,"center boundaries");
+int active[5][2]={{0,1},{1,0},{0,1},{3,2},{2,3}};
+int bridges[3][2][3]={{{0,2,1},{3,1,-1}},{{3,1,1},{0,2,-1}},{{1,3,-1},{2,0,1}}};
+size_t words=(global+63)/64;std::vector<unsigned long long>a((size_t)(global+1)*words);auto row=[&](int i){return a.data()+(size_t)i*words;};for(int i=0;i<global;i++)row(i)[i/64]|=1ull<<(i%64);
+auto xo=[&](int d,int s){auto*x=row(d);auto*y=row(s);for(size_t j=0;j<words;j++)x[j]^=y[j];};
+auto map=[&](int stage,int i){if(i<v)return active[stage][0]*v+i;if(i<2*v)return active[stage][1]*v+i-v;if(i<loc)return 4*v+i-2*v;return temp;};
+auto t0=std::chrono::steady_clock::now();J stages=J::array();
+for(int stage=0;stage<5;stage++){bool rev=stage==1||stage==3;bool opened=false;long long cp=0,ad=0;auto step=[&](E q){int k=q.kind;if(rev&&k)k=3-k;int d=map(stage,q.dst),s=map(stage,q.src);if(k==0){if(q.c&1)xo(d,s);ad++;}else if(k==1){need(!opened,"fresh physical work opening");std::memcpy(row(temp),row(s),words*8);opened=true;cp++;}else{need(opened,"physical work closing");std::memset(row(temp),0,words*8);opened=false;}};
+if(rev){for(auto it=e.rbegin();it!=e.rend();++it)step(*it);reverseCopies+=cp;}else for(auto q:e)step(q);need(!opened&&cp==24,"stage copied-center endpoint");
+if(stage==0){for(int i=0;i<global;i++){auto*x=row(i);for(size_t w=0;w<words;w++){unsigned long long want=(w==(size_t)i/64?1ull<<(i%64):0);if(i>=v&&i<2*v&&w==(size_t)(i-v)/64)want^=1ull<<((i-v)%64);need(x[w]==want,"local defining-decoder full formal column");}}}
+if(stage==1||stage==2||stage==4){int b=stage==1?0:stage==2?1:2;for(auto q:bridges[b])for(int i=0;i<v;i++)xo(q[0]*v+i,q[1]*v+i);}
+stages.push_back({{"stage",stage},{"signed_inverse",rev},{"fresh_copies",cp},{"scalar_additions",ad}});std::cerr<<"stage "<<stage<<" PASS elapsed "<<std::chrono::duration<double>(std::chrono::steady_clock::now()-t0).count()<<"s\n";}
+for(int bank=0;bank<4;bank+=2)for(int i=0;i<v;i++)for(size_t w=0;w<words;w++)std::swap(row(bank*v+i)[w],row((bank+1)*v+i)[w]);
+for(int i=0;i<=global;i++)for(size_t w=0;w<words;w++){unsigned long long want=(i<global&&w==(size_t)i/64?1ull<<(i%64):0);need(row(i)[w]==want,"five-stage all physical formal columns");}
+// Independent complete four-bank controls, each omitted bridge must change endpoint.
+J controls=J::array();for(int skip=0;skip<6;skip++){int b[4]={1,2,4,8},j=0;for(int s=0;s<5;s++){b[active[s][1]]^=b[active[s][0]];if(s==1||s==2||s==4){int k=s==1?0:s==2?1:2;for(auto q:bridges[k]){if(j++!=skip)b[q[0]]^=b[q[1]];}}}std::swap(b[0],b[1]);std::swap(b[2],b[3]);bool failed=false;for(int z=0;z<4;z++)failed|=b[z]!=(1<<z);need(failed,"vacuous omitted bridge control");controls.push_back({{"omit_bridge",skip},{"rejected",true}});}
+J out={{"status","PASS_GENERIC_FIVE_STAGE_FORMAL_COLUMNS_AND_COMPUTED_PREFIX"},{"local_scalar_stream",pre},{"local_registers",loc},{"global_live_registers",global},{"formal_columns_checked",global},{"independent_dirty_registers",r},{"local_scalar_additions",adds},{"local_odd_scalar_additions",odd},{"five_stage_additions",5*adds},{"bridge_additions",6*v},{"fresh_center_copies",120},{"reverse_fresh_center_copies",reverseCopies},{"copied_center_original_source_immutable",true},{"signed_reverse_semantics","Reverse ADD coefficient negated; reverse DISCARD is fresh COPY from recorded unchanged original center; reverse COPY is DISCARD. Each such block is inverse over every commutative coefficient ring, by elementary-shear induction."},{"scope","All computed global_live independent physical input columns over F2, including all arbitrary helper dirt, restored; external copied-center work closes to zero. New cohort scalar lift uses actual signed coefficients and computed cancellation-free bounds; unchanged source527 signed decoder remains separate defining evidence. Physical projector routing and paid rank/bank receipts are independently bound, not inferred from scalar check."},{"stages",stages},{"signed_lift_prefix",prefix},{"payload_prefix_upper",payload.convert_to<std::string>()},{"payload_prefix_bits",boost::multiprecision::msb(payload)+1},{"new_Q_categories",{28,29}},{"local_raw_H",H},{"negative_controls",controls},{"seconds",std::chrono::duration<double>(std::chrono::steady_clock::now()-t0).count()}};std::ofstream(argv[2])<<out.dump(2);std::cout<<out.dump(2)<<"\n";
+}catch(const std::exception&e){std::cerr<<e.what()<<"\n";return 2;}}
+
diff --git a/research/gen4-retiming-entrances/code/price.py b/research/gen4-retiming-entrances/code/price.py
new file mode 100644
index 0000000000..6c23fe7bad
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/price.py
@@ -0,0 +1,233 @@
+#!/usr/bin/env python3
+"""Recount and exactly price the literal gen4 candidate.
+
+The fixed-prime interval method follows the retained PR265 refinement; the
+moment and outer engines are dynamically loaded from the pinned PR276 package.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import sys
+if not __debug__:
+    raise SystemExit("Assertions required; refusing -O")
+sys.dont_write_bytecode = True
+sys.set_int_max_str_digits(0)
+
+from array import array
+from collections import Counter
+from decimal import Decimal, ROUND_FLOOR, localcontext
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import hashlib
+import importlib.util
+import json
+
+PRIME = (1 << 127) - 1
+M = 120
+RHO = Q(2 * M**3, PRIME)
+ETA = Q(1, 10**24)
+BETA = Q(1, 10**9)
+GRID = 10**27
+COMPLEX_SAVING = Q(747454944651775, 10**18)
+INITIAL_LEAF = Q(384599, 10**10)
+BASE_MANIFEST_SHA256 = "6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d"
+PUBLISHED_BASELINE = Q("0.000722869827347495")
+EXPECTED_KAPPA = Q(724189082265949363570532, GRID)
+
+
+def sha(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def load_engine(name, base):
+    path = base / (name + ".py")
+    manifest = json.loads((base / "MANIFEST.json").read_text())
+    assert sha(base / "MANIFEST.json") == BASE_MANIFEST_SHA256
+    assert sha(path) == manifest["files"][path.name]
+    spec = importlib.util.spec_from_file_location("gen4_pinned_" + name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def read_word(path):
+    blob = Path(path).read_bytes()
+    assert len(blob) % 24 == 0, "Bad six-int32 record alignment"
+    words = array("i")
+    assert words.itemsize == 4
+    words.frombytes(blob)
+    if sys.byteorder != "little":
+        words.byteswap()
+    records = list(zip(*[iter(words)] * 6))
+    assert all(record[0] in (0, 1, 2, 3) for record in records)
+    return records
+
+
+def word_inventory(candidate):
+    records = read_word(candidate / "COHORT249-RECORDS.bin")
+    histogram, opcounts, coefficients = Counter(), Counter(), Counter()
+    for op, a, b, c, frame, category in records:
+        opcounts[op] += 1
+        if op == 0 and frame:
+            histogram[frame] += 1
+        elif op == 2:
+            histogram[category] += 1
+        elif op == 1:
+            coefficients[abs(c)] += 1
+    assert histogram and min(histogram) > 0 and max(histogram) < 24
+    return records, histogram, opcounts, coefficients
+
+def serial(value):
+    if isinstance(value, Q):
+        return str(value)
+    if isinstance(value, dict):
+        return {str(k): serial(v) for k, v in value.items()}
+    if isinstance(value, (list, tuple)):
+        return [serial(v) for v in value]
+    return value
+
+def bridge_template():
+    # Literal retained bridge from source527 math_check.py, itself pinned in SOURCE.json.
+    return dict(
+        proof="PROOF.md",
+        representation="Exact powers with source-bound finite overcharges",
+        semantic=dict(G=dict(base=2, exponent=30000), E=dict(base=2, exponent=100000),
+                      B_upper=dict(base=2, exponent=100001), C0=dict(base=2, exponent=210000),
+                      C1=1, strict_literal_gap=1, induction_gap_lower=1),
+        rows=dict(coefficient=20161, degree=10**6, suffix_slope=4*10**6,
+                  degree_gap=Q(10**6) - Q(51*20161, 25)))
+
+def fixed_moment(histogram, m, stock, calls, saving, cost):
+    lo, hi = cost.moment(histogram, m, stock, saving, False)
+    log_lo, log_hi = cost.logarithm(Q(m))
+    exp_lo = cost.exponential(saving * log_lo, saving * log_lo)[0]
+    exp_hi = cost.exponential(saving * log_hi, saving * log_hi)[1]
+    fallback_weight = Q(32 * m * calls, stock) * RHO
+    return cost.floor(lo + fallback_weight * exp_lo), cost.ceil(hi + fallback_weight * exp_hi)
+
+def second_engine_with_fallback(histogram, m, stock, calls, saving, other):
+    lower, upper = other.moment(m, stock, list(histogram.items()), saving)
+    log_lo, log_hi = other.log_bounds(Q(m))
+    exp_lo = other.exp_bounds(saving * log_lo)[0]
+    exp_hi = other.exp_bounds(saving * log_hi)[1]
+    fallback_weight = Q(32 * m * calls, stock) * RHO
+    return lower + fallback_weight * exp_lo, upper + fallback_weight * exp_hi
+
+def certify_coarse(histogram, m, stock, calls, cost, other):
+    with localcontext() as ctx:
+        ctx.prec = 80
+        terms = [(Decimal(r*n) / Decimal(m*stock), (Decimal(m) / Decimal(r)).ln())
+                 for r, n in histogram.items()]
+        fallback = (Decimal(32*m*calls) / Decimal(stock)
+                    * Decimal(2*m**3) / Decimal(PRIME))
+        log_m = Decimal(m).ln()
+        lower, upper = Decimal(0), Decimal("0.003")
+        for _ in range(240):
+            candidate = (lower + upper) / 2
+            total = sum(p * (candidate * log_r).exp() for p, log_r in terms)
+            total += fallback * (candidate * log_m).exp()
+            if total < 1:
+                lower = candidate
+            else:
+                upper = candidate
+        endpoint = Q(int(((lower + upper) / 2 * GRID).to_integral_value(rounding=ROUND_FLOOR)), GRID)
+    next_endpoint = endpoint + Q(1, GRID)
+    first = fixed_moment(histogram, m, stock, calls, endpoint, cost)
+    first_next = fixed_moment(histogram, m, stock, calls, next_endpoint, cost)
+    second = second_engine_with_fallback(histogram, m, stock, calls, endpoint, other)
+    second_next = second_engine_with_fallback(histogram, m, stock, calls, next_endpoint, other)
+    assert first[1] < 1 < first_next[0]
+    assert second[1] < 1 < second_next[0]
+    return endpoint, next_endpoint, first, first_next, second, second_next
+
+def grid_kappa(bit_saving, eta=ETA):
+    q = bit_saving * (1 - 2*eta)
+    minimum = (1 - eta) * q / (1 + q)
+    ticks = minimum * GRID
+    return Q((ticks.numerator - 1) // ticks.denominator, GRID)
+
+def ceil_fraction(value):
+    assert value >= 0
+    return (value.numerator + value.denominator - 1) // value.denominator
+
+def compute(candidate, base):
+    candidate, base = Path(candidate).resolve(), Path(base).resolve()
+    cost = load_engine("moment", base)
+    other = load_engine("base_two_moment", base)
+    outer = load_engine("outer", base)
+    _, local, operations, coefficients = word_inventory(candidate)
+    histogram = Counter({rank: 60 * count for rank, count in local.items()})
+    histogram.update({rank: 24 * 1760 for rank in (4, 23, 46, 50)})
+    histogram = dict(sorted(histogram.items()))
+    stock = 255841  # Independently reconstructed from actual endpoints by admit.py.
+    calls = sum(histogram.values())
+    mass = sum(rank * count for rank, count in histogram.items())
+    assert (calls, mass, 120 * stock - mass) == (5808240, 30648120, 52800)
+    coarse, next_coarse, first, first_next, second, second_next = certify_coarse(
+        histogram, 120, stock, calls, cost, other
+    )
+    chain, gaps = [INITIAL_LEAF], []
+    for level in range(1, 9):
+        old = chain[-1]
+        new = (1 - coarse) * coarse + coarse * old
+        assert old < new < coarse < 1 - new
+        chain.append(new)
+        gap = dict(atom=coarse-new, borrowing=1-new-coarse,
+                   remainder=1-new-coarse*(1-old), stock=1-coarse)
+        assert min(gap.values()) > 0
+        gaps.append(dict(level=level, gaps=gap))
+    kappa = grid_kappa(chain[-1])
+    assembly = outer.assembly(chain[-1], COMPLEX_SAVING, bridge_template(),
+                              kappa, eta=ETA, beta=BETA)
+    assert len(assembly["strict_constraints"]) == 47
+    assert min(assembly["strict_constraints"].values()) > 0
+    try:
+        outer.assembly(chain[-1], COMPLEX_SAVING, bridge_template(),
+                       kappa + Q(1, GRID), eta=ETA, beta=BETA)
+    except AssertionError:
+        pass
+    else:
+        raise AssertionError("Adjacent finite-grid kappa admitted")
+    assert kappa == EXPECTED_KAPPA
+    target = PUBLISHED_BASELINE * Q(1001, 1000)
+    assert kappa > target
+    sources = [Path(__file__).resolve(), base / "MANIFEST.json"]
+    sources += [base / (name + ".py") for name in ("moment", "base_two_moment", "outer")]
+    sources += [candidate / name for name in ("COHORT249-RECORDS.bin", "COHORT249-INITIAL.json",
+                                            "COHORT249-FINAL.json", "COHORT249-FRAMES.json")]
+    return serial(dict(
+        status="PASS_EXACT_ACTUAL_WORD_PRICE_REQUIRES_SEPARATE_CONSTRUCTION_ADMISSION",
+        base_package=str(base), base_manifest_sha256=BASE_MANIFEST_SHA256,
+        source_word_sha256=sha(candidate / "COHORT249-RECORDS.bin"),
+        source_bindings={str(path): sha(path) for path in sources},
+        literal_replicas=60, normalization_factor=5, stock=stock, literal_stock=5*stock,
+        local_histogram=local, histogram=histogram, calls=calls, rank_mass=mass,
+        deficit=52800, operation_counts=operations, scalar_coefficient_counts=coefficients,
+        prime=PRIME, rare_density=RHO, full_fallback_kept=True,
+        coarse=coarse, coarse_bracket=[coarse, next_coarse],
+        first_engine_interval=first, first_engine_next_interval=first_next,
+        second_engine_interval=second, second_engine_next_interval=second_next,
+        ordinary_levels=8, ordinary_chain=chain, ordinary_gaps=gaps,
+        assembly=assembly, kappa=kappa, kappa_decimal=cost.decimal(kappa),
+        coarse_cap=grid_kappa(coarse), adjacent_grid_rejected_at_finite=True,
+        published_PR276_kappa=PUBLISHED_BASELINE, strict_PR276_0p1_percent_target=target,
+        gain_percent=100*(kappa-PUBLISHED_BASELINE)/PUBLISHED_BASELINE,
+        exceeds_PR276_0p1_percent=True,
+        scope="Exact pricing only. Source-bound scalar, geometry, chart, bank and finite "
+              "construction admission are separate mandatory checks."
+    ))
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("candidate", type=Path)
+    parser.add_argument("--base", type=Path, required=True)
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    result = compute(args.candidate, args.base)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(json.dumps(result, sort_keys=True, indent=2) + "\n")
+    print("PASS exact price", result["kappa_decimal"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/gen4-retiming-entrances/code/retime.py b/research/gen4-retiming-entrances/code/retime.py
new file mode 100644
index 0000000000..a0aed6a548
--- /dev/null
+++ b/research/gen4-retiming-entrances/code/retime.py
@@ -0,0 +1,86 @@
+from pathlib import Path
+import json,struct,hashlib,math,sys,argparse
+sys.dont_write_bytecode=True
+if not __debug__: raise SystemExit('Assertions required; refusing -O')
+from collections import Counter
+ap=argparse.ArgumentParser(); ap.add_argument('--export-dir',type=Path,required=True); ap.add_argument('--output',type=Path,required=True); args=ap.parse_args()
+X=args.export_dir.resolve(); D=args.output.resolve();D.mkdir(parents=True,exist_ok=False)
+st=json.loads((X/'gen4-states.json').read_text());n=st['n'];v=st['v'];fs={int(k):x for k,x in json.loads((X/'frames.json').read_text())['frames'].items()}
+rows=json.loads((Path(__file__).resolve().parents[1]/'data/retiming880.json').read_text());selected={}
+for r in rows:
+ if r['new_frame'] in fs and r['component'] not in selected:selected[r['component']]=r
+assert len(selected)==880
+roleuses=Counter(s for r in selected.values()for s in r['roles']);assert len(roleuses)==v and set(roleuses.values())=={1} and all(s<v for s in roleuses)
+replacements={g:r['new_frame']for r in selected.values()for g in r['gates']};assert len(replacements)==880
+raw=list(struct.iter_unpack('<6i',(X/'gen4-records.bin').read_bytes()));basepairs={(e[2],e[3])for e in raw if e[0]==0};initial={int(k):f for k,f in st['initial'].items()};final={int(k):f for k,f in st['final'].items()};state=dict(initial);out=[];pairs=set();changedpairs=set();core=0;copy=None;H=Counter();oldH=Counter()
+for op,a,b,c,f,z in raw:
+ if op==0 and f:oldH[f]+=1
+ elif op==2:oldH[z]+=1
+def sub(a,b):return fs[a]['dim']<=fs[b]['dim'] and all(sum(x*y for x,y in zip(u,w))==0 for u in fs[a]['B']for w in fs[b]['A'])
+# Data roles form a closed scalar subword. Track defining integer source
+# coefficients to audit both operands before and after each changed shear.
+source_columns=[{i:1} for i in range(v)]
+assert all(fs[initial[i]]['dim']==1 for i in range(v))
+source_vectors={i:fs[initial[i]]['B'][0] for i in range(v)}
+span_checks=0;span_sizes={}
+def span_in_frame(coefficients,f):
+ return all(all(sum(x*y for x,y in zip(source_vectors[i],w))==0 for w in fs[f]['A']) for i in coefficients)
+def move(a,f):
+ old=state[a]
+ if old==f:return
+ pair=(old,f)
+ if pair not in pairs:
+  if pair not in basepairs:assert sub(old,f);changedpairs.add(pair)
+  pairs.add(pair)
+ rank=fs[f]['dim']-fs[old]['dim'];assert rank>=0
+ out.append((0,a,old,f,rank,0));state[a]=f
+ if rank:H[rank]+=1
+for op,a,b,c,f,z in raw:
+ if op==0:continue
+ if op==1:
+
+  if core in replacements:
+   binding=selected[core];assert op==1 and f==binding['old_frame'] and sorted([a,b])==sorted(binding['roles'])
+   assert fs[f]['dim']==2 and fs[binding['new_frame']]['dim']==22
+   assert sub(f,binding['new_frame']), 'Retimed old frame must lie inside the new frame'
+   assert 0<=a<v and 0<=b<v
+   for operand in (a,b):
+    assert span_in_frame(source_columns[operand],f) and span_in_frame(source_columns[operand],binding['new_frame'])
+    span_checks+=len(source_columns[operand])
+  f=replacements.get(core,f);move(a,f);move(b,f);assert state[a]==state[b]==f
+  if a<v:
+   assert 0<=b<v, 'Data source roles must receive only data-source values'
+   for source,value in list(source_columns[b].items()):
+    value=source_columns[a].get(source,0)+c*value
+    if value:source_columns[a][source]=value
+    else:source_columns[a].pop(source,None)
+  if core in replacements:
+   assert span_in_frame(source_columns[a],f) and span_in_frame(source_columns[b],f)
+   span_checks+=len(source_columns[a])+len(source_columns[b]);span_sizes[core]=len(set(source_columns[a])|set(source_columns[b]))
+  out.append((op,a,b,c,f,z))
+ elif op==2:
+  assert copy is None and b==n;move(a,c);state[b]=f;copy=(a,b,c,f);H[z]+=1;out.append((op,a,b,c,f,z))
+ else:
+  assert op==3 and copy==(a,b,c,f) and state[a]==c and state[b]==f;out.append((op,a,b,c,f,z));del state[b];copy=None
+ core+=1
+assert copy is None and len(span_sizes)==880 and set(span_sizes.values())=={2}
+assert source_columns==[{i:1}for i in range(v)]
+for a in range(n):move(a,final[a])
+assert state==final
+def project(es):return [(op,a,b,c,z)for op,a,b,c,f,z in es if op]
+assert project(raw)==project(out)
+delta=Counter(H);delta.subtract(oldH);delta={r:x for r,x in delta.items()if x}
+assert delta=={21:1760,2:880,1:-1760,20:-880,22:-880}
+assert sum(r*x for r,x in delta.items())==0
+data=b''.join(struct.pack('<6i',*e)for e in out)
+(D/'COHORT249-RECORDS.bin').write_bytes(data)
+(D/'COHORT249-INITIAL.json').write_text(json.dumps(st['initial'])+'\n')
+(D/'COHORT249-FRAMES.json').write_text('{}\n')
+(D/'COHORT249-FINAL.json').write_text(json.dumps(st['final'])+'\n')
+(D/'RETIMING-SELECTION.json').write_text(json.dumps(list(selected.values()),indent=2)+'\n')
+receipt=dict(old_frame_containment_explicit=True,exact_integer_source_spans=True,checked_operand_source_inclusions=span_checks,max_changed_gate_source_support=max(span_sizes.values()),status='PASS_880_DISJOINT_RETIMINGS_LITERAL_SCALAR_EQUALITY_AND_NEW_CONNECTOR_GEOMETRY',base_sha256=hashlib.sha256((X/'gen4-records.bin').read_bytes()).hexdigest(),output_sha256=hashlib.sha256(data).hexdigest(),n=n,v=v,selected_gates=len(replacements),source_roles=len(roleuses),new_frame_ids=0,changed_connector_pairs=sorted(changedpairs),paid_histogram=dict(H),local_histogram_delta=delta,rank_mass=sum(r*x for r,x in H.items()),record_count=len(out),scope='Full baseline checks and fresh five-stage replay are separate; all changed connector inclusions checked by exact integer dot products. No exponent claimed by this emitter.')
+(D/'RETIMING-REPLAY.json').write_text(json.dumps(receipt,indent=2)+'\n')
+print({k:v for k,v in receipt.items()if k not in ['changed_connector_pairs','paid_histogram']},flush=True)
+
+assert receipt['output_sha256']=='2d22a9530f0b04a7a794d15077459234ef52183d6e7a70f813cfa849b79f2ebe'
+(D/'249-states.json').write_text(json.dumps(st)+'\n')
diff --git a/research/gen4-retiming-entrances/data/EXPECTED.json b/research/gen4-retiming-entrances/data/EXPECTED.json
new file mode 100644
index 0000000000..fb76988fc8
--- /dev/null
+++ b/research/gen4-retiming-entrances/data/EXPECTED.json
@@ -0,0 +1,14 @@
+{
+  "base_commit": "d428ab0462b9dfd3131ab4e89999f0adcd6173dd",
+  "base_manifest_sha256": "6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d",
+  "final_word_sha256": "71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48",
+  "kappa": "724189082265949363570532/1000000000000000000000000000",
+  "kappa_decimal": "0.000724189082265949363570532",
+  "comparator": {
+    "pull_request": 279,
+    "head": "2e2a38ba3f48edbda2152ed86691c75ff326b254",
+    "kappa_decimal": "0.000723571590007464",
+    "gain_percent_approx": 0.08533948361336213,
+    "observation": "Latest public bound at preparation; recheck separately at publication."
+  }
+}
diff --git a/research/gen4-retiming-entrances/data/entrances60.json b/research/gen4-retiming-entrances/data/entrances60.json
new file mode 100644
index 0000000000..db2d52ee8c
--- /dev/null
+++ b/research/gen4-retiming-entrances/data/entrances60.json
@@ -0,0 +1,29179 @@
+{
+  "source_word_sha256": "8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373",
+  "export_word_sha256": "60830cb24fbdd5a26942c4aa897d0ae30738ca5772ab83d6c57be666ddc95f7a",
+  "expected_output_sha256": "71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48",
+  "entries": [
+    {
+      "stream": 17213,
+      "role": 13693,
+      "rank": 19,
+      "basis": [
+        [
+          1,
+          2,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          1,
+          0,
+          2,
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+    "roles": [
+      1688,
+      1691
+    ]
+  },
+  {
+    "component": 583838,
+    "gates": [
+      583838
+    ],
+    "old_frame": 131053,
+    "new_frame": 28123,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1701,
+      1702
+    ]
+  },
+  {
+    "component": 583843,
+    "gates": [
+      583843
+    ],
+    "old_frame": 131057,
+    "new_frame": 28125,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1700,
+      1703
+    ]
+  },
+  {
+    "component": 583848,
+    "gates": [
+      583848
+    ],
+    "old_frame": 131055,
+    "new_frame": 28127,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1697,
+      1698
+    ]
+  },
+  {
+    "component": 583853,
+    "gates": [
+      583853
+    ],
+    "old_frame": 131051,
+    "new_frame": 28129,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1696,
+      1699
+    ]
+  },
+  {
+    "component": 583890,
+    "gates": [
+      583890
+    ],
+    "old_frame": 131061,
+    "new_frame": 28145,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1709,
+      1710
+    ]
+  },
+  {
+    "component": 583895,
+    "gates": [
+      583895
+    ],
+    "old_frame": 131065,
+    "new_frame": 28147,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1708,
+      1711
+    ]
+  },
+  {
+    "component": 583900,
+    "gates": [
+      583900
+    ],
+    "old_frame": 131063,
+    "new_frame": 28149,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1705,
+      1706
+    ]
+  },
+  {
+    "component": 583905,
+    "gates": [
+      583905
+    ],
+    "old_frame": 131059,
+    "new_frame": 28151,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1704,
+      1707
+    ]
+  },
+  {
+    "component": 583942,
+    "gates": [
+      583942
+    ],
+    "old_frame": 131069,
+    "new_frame": 28167,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1717,
+      1718
+    ]
+  },
+  {
+    "component": 583947,
+    "gates": [
+      583947
+    ],
+    "old_frame": 131073,
+    "new_frame": 28169,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1716,
+      1719
+    ]
+  },
+  {
+    "component": 583952,
+    "gates": [
+      583952
+    ],
+    "old_frame": 131071,
+    "new_frame": 28171,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1713,
+      1714
+    ]
+  },
+  {
+    "component": 583957,
+    "gates": [
+      583957
+    ],
+    "old_frame": 131067,
+    "new_frame": 28173,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1712,
+      1715
+    ]
+  },
+  {
+    "component": 583994,
+    "gates": [
+      583994
+    ],
+    "old_frame": 131077,
+    "new_frame": 28189,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1725,
+      1726
+    ]
+  },
+  {
+    "component": 583999,
+    "gates": [
+      583999
+    ],
+    "old_frame": 131081,
+    "new_frame": 28191,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1724,
+      1727
+    ]
+  },
+  {
+    "component": 584004,
+    "gates": [
+      584004
+    ],
+    "old_frame": 131079,
+    "new_frame": 28193,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1721,
+      1722
+    ]
+  },
+  {
+    "component": 584009,
+    "gates": [
+      584009
+    ],
+    "old_frame": 131075,
+    "new_frame": 28195,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1720,
+      1723
+    ]
+  },
+  {
+    "component": 584046,
+    "gates": [
+      584046
+    ],
+    "old_frame": 131085,
+    "new_frame": 28211,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1733,
+      1734
+    ]
+  },
+  {
+    "component": 584051,
+    "gates": [
+      584051
+    ],
+    "old_frame": 131089,
+    "new_frame": 28213,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1732,
+      1735
+    ]
+  },
+  {
+    "component": 584056,
+    "gates": [
+      584056
+    ],
+    "old_frame": 131087,
+    "new_frame": 28215,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1729,
+      1730
+    ]
+  },
+  {
+    "component": 584061,
+    "gates": [
+      584061
+    ],
+    "old_frame": 131083,
+    "new_frame": 28217,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1728,
+      1731
+    ]
+  },
+  {
+    "component": 584098,
+    "gates": [
+      584098
+    ],
+    "old_frame": 131093,
+    "new_frame": 28233,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1741,
+      1742
+    ]
+  },
+  {
+    "component": 584103,
+    "gates": [
+      584103
+    ],
+    "old_frame": 131097,
+    "new_frame": 28235,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1740,
+      1743
+    ]
+  },
+  {
+    "component": 584108,
+    "gates": [
+      584108
+    ],
+    "old_frame": 131095,
+    "new_frame": 28237,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1737,
+      1738
+    ]
+  },
+  {
+    "component": 584113,
+    "gates": [
+      584113
+    ],
+    "old_frame": 131091,
+    "new_frame": 28239,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1736,
+      1739
+    ]
+  },
+  {
+    "component": 584150,
+    "gates": [
+      584150
+    ],
+    "old_frame": 131101,
+    "new_frame": 28255,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1749,
+      1750
+    ]
+  },
+  {
+    "component": 584155,
+    "gates": [
+      584155
+    ],
+    "old_frame": 131105,
+    "new_frame": 28257,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1748,
+      1751
+    ]
+  },
+  {
+    "component": 584160,
+    "gates": [
+      584160
+    ],
+    "old_frame": 131103,
+    "new_frame": 28259,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1745,
+      1746
+    ]
+  },
+  {
+    "component": 584165,
+    "gates": [
+      584165
+    ],
+    "old_frame": 131099,
+    "new_frame": 28261,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1744,
+      1747
+    ]
+  },
+  {
+    "component": 584202,
+    "gates": [
+      584202
+    ],
+    "old_frame": 131109,
+    "new_frame": 28277,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1757,
+      1758
+    ]
+  },
+  {
+    "component": 584207,
+    "gates": [
+      584207
+    ],
+    "old_frame": 131113,
+    "new_frame": 28279,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1756,
+      1759
+    ]
+  },
+  {
+    "component": 584212,
+    "gates": [
+      584212
+    ],
+    "old_frame": 131111,
+    "new_frame": 28281,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1753,
+      1754
+    ]
+  },
+  {
+    "component": 584217,
+    "gates": [
+      584217
+    ],
+    "old_frame": 131107,
+    "new_frame": 28283,
+    "old_dim": 2,
+    "new_dim": 22,
+    "roles": [
+      1752,
+      1755
+    ]
+  }
+]
diff --git a/research/gen4-retiming-entrances/docs/cleanup-proof.md b/research/gen4-retiming-entrances/docs/cleanup-proof.md
new file mode 100644
index 0000000000..9561214162
--- /dev/null
+++ b/research/gen4-retiming-entrances/docs/cleanup-proof.md
@@ -0,0 +1,84 @@
+# Early restoration of 440 gen4 helpers
+
+The source word is the literal `retimed880/COHORT249-RECORDS.bin`, SHA256
+`2d22a9530f0b04a7a794d15077459234ef52183d6e7a70f813cfa849b79f2ebe`.
+This construction composes with its880 source-partner frame retimings.
+It changes no scalar coefficient and adds no scalar gate.
+
+At record662145, the first category3 cleanup ADD, all1,760 data targets
+already have their required scalar endpoints. There are440 helper roles a
+with the following properties, checked against the complete remaining word:
+
+* The only later scalar incidence of a is `a -= b`.
+* The donor b is never written between the cut and that incidence.
+* All440 destinations and440 donors are distinct, with the two sets disjoint.
+* Both roles have current frame dimension22. Their rational span is a
+  nondegenerate frame E of dimension23.
+* Helper a has entrance dimension20 and previously ended at FULL, dimension24.
+
+The ADD `a -= b` commutes over the integers with every intervening scalar
+gate. Moving it to the cut therefore preserves the exact signed scalar
+operator, including all dirty columns. There is no COPY/ERASE after this cut.
+These440 moves can be made simultaneously because their destinations and
+donors do not overlap. The original maximum formal coefficient bound does
+not increase: early-restored a has exactly its old value after the later
+restoration, while every other role has the same value at every unaffected
+event. No gate reads a on the crossed interval.
+
+For each pair, advance a and b from their rank22 frames to E, perform the
+unchanged `a -= b`, and retire a at E. Continue every remaining scalar gate
+in its original order and at its original frame. The donor later reaches
+FULL. Every new connector is checked by exact rational annihilator products;
+all other source, target, helper, and COPY endpoints remain unchanged.
+
+Per pair, two old rank2 climbs become three rank1 climbs: a→E, b→E, and
+b:E→FULL. Hence the local histogram change is exactly
+
+    ΔH[1] = +1320, ΔH[2] = -880.
+
+The local paid rank drops440. The helper endpoint changes from
+`D_(FULL-sigma)` of rank4 to `D_(E-sigma)` of rank3. Its reflected inverse
+goes from `I-E` to `I-sigma` and has the same residual rank3. The ordinary
+completed-bank construction must be repacked for these actual residuals;
+the old FULL-endpoint assumption may not be silently retained.
+
+With PR276's60 local replicas, each stage loses26,400 residual coordinates,
+or220 complete width120 banks. This is only the volume calculation: an exact
+block assignment and normalizer/selector invoice are separate required
+admission checks. The resulting five-stage literal stock drop is1,100 and
+the normalized stock drop220 if that tiling closes.
+
+`cleanup_emit.py` freshly checks every new frame's full annihilator, exact cleared
+Gram determinant and nonvanishing modulo the retained prime2^127−1. It
+replays all19,930 formal columns forward, backward with fresh copies in
+place of reversed erasures, and as a complete roundtrip. Omitting one moved
+restoration fails one formal row. It also independently checks the integer
+commutation conditions above. The complete global five-stage, bank, chart,
+and recurrence checks remain the caller's responsibility.
+
+The final all440 output word SHA256 is
+`8dfff69cc400256746443089817175a3345ac096c924957ef04b32c038964373`.
+The438-helper precursor is preserved separately; the all440 word is the
+intended final candidate under the60-replica normalization.
+
+
+## Portable reproduction
+
+Run from the package root with Python3 and SymPy (validated with SymPy1.14):
+
+```sh
+python code/cleanup.py --source-dir RETIMED --export-dir EXPORT --output CANDIDATE
+```
+
+`RETIMED` is the preceding880-retiming output. `EXPORT` contains the source
+`gen4-states.json` and `frames.json`. The fixed recipe freshly reconstructs
+all440 helper/donor pairs; it rejects a changed input word, changed candidate
+count/geometry, or changed emitted word hash. It preserves the source's COPY
+lifetimes and signed coefficients. No network access, NumPy, SciPy, or native
+compiler is needed for this cleanup step. Global verification remains in the
+package verifier.
+
+The rational basis utilities in `cleanup_reference.py` are derived from
+[PR271's sandwich263.py](https://github.com/CrocSwap/integer-mult-bounds/pull/271).
+This gen4 construction uses a single cleanup gate per retired helper rather
+than PR271's three-gate sandwich selection.
diff --git a/research/gen4-retiming-entrances/requirements.txt b/research/gen4-retiming-entrances/requirements.txt
new file mode 100644
index 0000000000..1ca5fd0616
--- /dev/null
+++ b/research/gen4-retiming-entrances/requirements.txt
@@ -0,0 +1 @@
+sympy==1.14.0
diff --git a/research/gen4-retiming-entrances/vendor/json.hpp b/research/gen4-retiming-entrances/vendor/json.hpp
new file mode 100644
index 0000000000..82d69f7c5d
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/json.hpp
@@ -0,0 +1,25526 @@
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+/****************************************************************************\
+ * Note on documentation: The source files contain links to the online      *
+ * documentation of the public API at https://json.nlohmann.me. This URL    *
+ * contains the most recent documentation and should also be applicable to  *
+ * previous versions; documentation for deprecated functions is not         *
+ * removed, but marked deprecated. See "Generate documentation" section in  *
+ * file docs/README.md.                                                     *
+\****************************************************************************/
+
+#ifndef INCLUDE_NLOHMANN_JSON_HPP_
+#define INCLUDE_NLOHMANN_JSON_HPP_
+
+#include <algorithm> // all_of, find, for_each
+#include <cstddef> // nullptr_t, ptrdiff_t, size_t
+#include <functional> // hash, less
+#include <initializer_list> // initializer_list
+#ifndef JSON_NO_IO
+    #include <iosfwd> // istream, ostream
+#endif  // JSON_NO_IO
+#include <iterator> // random_access_iterator_tag
+#include <memory> // unique_ptr
+#include <string> // string, stoi, to_string
+#include <utility> // declval, forward, move, pair, swap
+#include <vector> // vector
+
+// #include <nlohmann/adl_serializer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <utility>
+
+// #include <nlohmann/detail/abi_macros.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// This file contains all macro definitions affecting or depending on the ABI
+
+#ifndef JSON_SKIP_LIBRARY_VERSION_CHECK
+    #if defined(NLOHMANN_JSON_VERSION_MAJOR) && defined(NLOHMANN_JSON_VERSION_MINOR) && defined(NLOHMANN_JSON_VERSION_PATCH)
+        #if NLOHMANN_JSON_VERSION_MAJOR != 3 || NLOHMANN_JSON_VERSION_MINOR != 12 || NLOHMANN_JSON_VERSION_PATCH != 0
+            #warning "Already included a different version of the library!"
+        #endif
+    #endif
+#endif
+
+#define NLOHMANN_JSON_VERSION_MAJOR 3   // NOLINT(modernize-macro-to-enum)
+#define NLOHMANN_JSON_VERSION_MINOR 12  // NOLINT(modernize-macro-to-enum)
+#define NLOHMANN_JSON_VERSION_PATCH 0   // NOLINT(modernize-macro-to-enum)
+
+#ifndef JSON_DIAGNOSTICS
+    #define JSON_DIAGNOSTICS 0
+#endif
+
+#ifndef JSON_DIAGNOSTIC_POSITIONS
+    #define JSON_DIAGNOSTIC_POSITIONS 0
+#endif
+
+#ifndef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+    #define JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON 0
+#endif
+
+#if JSON_DIAGNOSTICS
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS _diag
+#else
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS
+#endif
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS _dp
+#else
+    #define NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS
+#endif
+
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+    #define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON _ldvcmp
+#else
+    #define NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_NO_VERSION
+    #define NLOHMANN_JSON_NAMESPACE_NO_VERSION 0
+#endif
+
+// Construct the namespace ABI tags component
+#define NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b, c) json_abi ## a ## b ## c
+#define NLOHMANN_JSON_ABI_TAGS_CONCAT(a, b, c) \
+    NLOHMANN_JSON_ABI_TAGS_CONCAT_EX(a, b, c)
+
+#define NLOHMANN_JSON_ABI_TAGS                                       \
+    NLOHMANN_JSON_ABI_TAGS_CONCAT(                                   \
+            NLOHMANN_JSON_ABI_TAG_DIAGNOSTICS,                       \
+            NLOHMANN_JSON_ABI_TAG_LEGACY_DISCARDED_VALUE_COMPARISON, \
+            NLOHMANN_JSON_ABI_TAG_DIAGNOSTIC_POSITIONS)
+
+// Construct the namespace version component
+#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch) \
+    _v ## major ## _ ## minor ## _ ## patch
+#define NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(major, minor, patch) \
+    NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT_EX(major, minor, patch)
+
+#if NLOHMANN_JSON_NAMESPACE_NO_VERSION
+#define NLOHMANN_JSON_NAMESPACE_VERSION
+#else
+#define NLOHMANN_JSON_NAMESPACE_VERSION                                 \
+    NLOHMANN_JSON_NAMESPACE_VERSION_CONCAT(NLOHMANN_JSON_VERSION_MAJOR, \
+                                           NLOHMANN_JSON_VERSION_MINOR, \
+                                           NLOHMANN_JSON_VERSION_PATCH)
+#endif
+
+// Combine namespace components
+#define NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b) a ## b
+#define NLOHMANN_JSON_NAMESPACE_CONCAT(a, b) \
+    NLOHMANN_JSON_NAMESPACE_CONCAT_EX(a, b)
+
+#ifndef NLOHMANN_JSON_NAMESPACE
+#define NLOHMANN_JSON_NAMESPACE               \
+    nlohmann::NLOHMANN_JSON_NAMESPACE_CONCAT( \
+            NLOHMANN_JSON_ABI_TAGS,           \
+            NLOHMANN_JSON_NAMESPACE_VERSION)
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_BEGIN
+#define NLOHMANN_JSON_NAMESPACE_BEGIN                \
+    namespace nlohmann                               \
+    {                                                \
+    inline namespace NLOHMANN_JSON_NAMESPACE_CONCAT( \
+                NLOHMANN_JSON_ABI_TAGS,              \
+                NLOHMANN_JSON_NAMESPACE_VERSION)     \
+    {
+#endif
+
+#ifndef NLOHMANN_JSON_NAMESPACE_END
+#define NLOHMANN_JSON_NAMESPACE_END                                     \
+    }  /* namespace (inline namespace) NOLINT(readability/namespace) */ \
+    }  // namespace nlohmann
+#endif
+
+// #include <nlohmann/detail/conversions/from_json.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // transform
+#include <array> // array
+#include <forward_list> // forward_list
+#include <iterator> // inserter, front_inserter, end
+#include <map> // map
+#ifdef JSON_HAS_CPP_17
+    #include <optional> // optional
+#endif
+#include <string> // string
+#include <tuple> // tuple, make_tuple
+#include <type_traits> // is_arithmetic, is_same, is_enum, underlying_type, is_convertible
+#include <unordered_map> // unordered_map
+#include <utility> // pair, declval
+#include <valarray> // valarray
+
+// #include <nlohmann/detail/exceptions.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // nullptr_t
+#include <exception> // exception
+#if JSON_DIAGNOSTICS
+    #include <numeric> // accumulate
+#endif
+#include <stdexcept> // runtime_error
+#include <string> // to_string
+#include <vector> // vector
+
+// #include <nlohmann/detail/value_t.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstddef> // size_t
+#include <cstdint> // uint8_t
+#include <string> // string
+
+// #include <nlohmann/detail/macro_scope.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <utility> // declval, pair
+// #include <nlohmann/detail/meta/detected.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <type_traits>
+
+// #include <nlohmann/detail/meta/void_t.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename ...Ts> struct make_void
+{
+    using type = void;
+};
+template<typename ...Ts> using void_t = typename make_void<Ts...>::type;
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// https://en.cppreference.com/w/cpp/experimental/is_detected
+struct nonesuch
+{
+    nonesuch() = delete;
+    ~nonesuch() = delete;
+    nonesuch(nonesuch const&) = delete;
+    nonesuch(nonesuch const&&) = delete;
+    void operator=(nonesuch const&) = delete;
+    void operator=(nonesuch&&) = delete;
+};
+
+template<class Default,
+         class AlwaysVoid,
+         template<class...> class Op,
+         class... Args>
+struct detector
+{
+    using value_t = std::false_type;
+    using type = Default;
+};
+
+template<class Default, template<class...> class Op, class... Args>
+struct detector<Default, void_t<Op<Args...>>, Op, Args...>
+{
+    using value_t = std::true_type;
+    using type = Op<Args...>;
+};
+
+template<template<class...> class Op, class... Args>
+using is_detected = typename detector<nonesuch, void, Op, Args...>::value_t;
+
+template<template<class...> class Op, class... Args>
+struct is_detected_lazy : is_detected<Op, Args...> { };
+
+template<template<class...> class Op, class... Args>
+using detected_t = typename detector<nonesuch, void, Op, Args...>::type;
+
+template<class Default, template<class...> class Op, class... Args>
+using detected_or = detector<Default, void, Op, Args...>;
+
+template<class Default, template<class...> class Op, class... Args>
+using detected_or_t = typename detected_or<Default, Op, Args...>::type;
+
+template<class Expected, template<class...> class Op, class... Args>
+using is_detected_exact = std::is_same<Expected, detected_t<Op, Args...>>;
+
+template<class To, template<class...> class Op, class... Args>
+using is_detected_convertible =
+    std::is_convertible<detected_t<Op, Args...>, To>;
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/thirdparty/hedley/hedley.hpp>
+
+
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-FileCopyrightText: 2016 - 2021 Evan Nemerson <evan@nemerson.com>
+// SPDX-License-Identifier: MIT
+
+/* Hedley - https://nemequ.github.io/hedley
+ * Created by Evan Nemerson <evan@nemerson.com>
+ */
+
+#if !defined(JSON_HEDLEY_VERSION) || (JSON_HEDLEY_VERSION < 15)
+#if defined(JSON_HEDLEY_VERSION)
+    #undef JSON_HEDLEY_VERSION
+#endif
+#define JSON_HEDLEY_VERSION 15
+
+#if defined(JSON_HEDLEY_STRINGIFY_EX)
+    #undef JSON_HEDLEY_STRINGIFY_EX
+#endif
+#define JSON_HEDLEY_STRINGIFY_EX(x) #x
+
+#if defined(JSON_HEDLEY_STRINGIFY)
+    #undef JSON_HEDLEY_STRINGIFY
+#endif
+#define JSON_HEDLEY_STRINGIFY(x) JSON_HEDLEY_STRINGIFY_EX(x)
+
+#if defined(JSON_HEDLEY_CONCAT_EX)
+    #undef JSON_HEDLEY_CONCAT_EX
+#endif
+#define JSON_HEDLEY_CONCAT_EX(a,b) a##b
+
+#if defined(JSON_HEDLEY_CONCAT)
+    #undef JSON_HEDLEY_CONCAT
+#endif
+#define JSON_HEDLEY_CONCAT(a,b) JSON_HEDLEY_CONCAT_EX(a,b)
+
+#if defined(JSON_HEDLEY_CONCAT3_EX)
+    #undef JSON_HEDLEY_CONCAT3_EX
+#endif
+#define JSON_HEDLEY_CONCAT3_EX(a,b,c) a##b##c
+
+#if defined(JSON_HEDLEY_CONCAT3)
+    #undef JSON_HEDLEY_CONCAT3
+#endif
+#define JSON_HEDLEY_CONCAT3(a,b,c) JSON_HEDLEY_CONCAT3_EX(a,b,c)
+
+#if defined(JSON_HEDLEY_VERSION_ENCODE)
+    #undef JSON_HEDLEY_VERSION_ENCODE
+#endif
+#define JSON_HEDLEY_VERSION_ENCODE(major,minor,revision) (((major) * 1000000) + ((minor) * 1000) + (revision))
+
+#if defined(JSON_HEDLEY_VERSION_DECODE_MAJOR)
+    #undef JSON_HEDLEY_VERSION_DECODE_MAJOR
+#endif
+#define JSON_HEDLEY_VERSION_DECODE_MAJOR(version) ((version) / 1000000)
+
+#if defined(JSON_HEDLEY_VERSION_DECODE_MINOR)
+    #undef JSON_HEDLEY_VERSION_DECODE_MINOR
+#endif
+#define JSON_HEDLEY_VERSION_DECODE_MINOR(version) (((version) % 1000000) / 1000)
+
+#if defined(JSON_HEDLEY_VERSION_DECODE_REVISION)
+    #undef JSON_HEDLEY_VERSION_DECODE_REVISION
+#endif
+#define JSON_HEDLEY_VERSION_DECODE_REVISION(version) ((version) % 1000)
+
+#if defined(JSON_HEDLEY_GNUC_VERSION)
+    #undef JSON_HEDLEY_GNUC_VERSION
+#endif
+#if defined(__GNUC__) && defined(__GNUC_PATCHLEVEL__)
+    #define JSON_HEDLEY_GNUC_VERSION JSON_HEDLEY_VERSION_ENCODE(__GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__)
+#elif defined(__GNUC__)
+    #define JSON_HEDLEY_GNUC_VERSION JSON_HEDLEY_VERSION_ENCODE(__GNUC__, __GNUC_MINOR__, 0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_VERSION_CHECK)
+    #undef JSON_HEDLEY_GNUC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_GNUC_VERSION)
+    #define JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_GNUC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_MSVC_VERSION)
+    #undef JSON_HEDLEY_MSVC_VERSION
+#endif
+#if defined(_MSC_FULL_VER) && (_MSC_FULL_VER >= 140000000) && !defined(__ICL)
+    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_FULL_VER / 10000000, (_MSC_FULL_VER % 10000000) / 100000, (_MSC_FULL_VER % 100000) / 100)
+#elif defined(_MSC_FULL_VER) && !defined(__ICL)
+    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_FULL_VER / 1000000, (_MSC_FULL_VER % 1000000) / 10000, (_MSC_FULL_VER % 10000) / 10)
+#elif defined(_MSC_VER) && !defined(__ICL)
+    #define JSON_HEDLEY_MSVC_VERSION JSON_HEDLEY_VERSION_ENCODE(_MSC_VER / 100, _MSC_VER % 100, 0)
+#endif
+
+#if defined(JSON_HEDLEY_MSVC_VERSION_CHECK)
+    #undef JSON_HEDLEY_MSVC_VERSION_CHECK
+#endif
+#if !defined(JSON_HEDLEY_MSVC_VERSION)
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (0)
+#elif defined(_MSC_VER) && (_MSC_VER >= 1400)
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_FULL_VER >= ((major * 10000000) + (minor * 100000) + (patch)))
+#elif defined(_MSC_VER) && (_MSC_VER >= 1200)
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_FULL_VER >= ((major * 1000000) + (minor * 10000) + (patch)))
+#else
+    #define JSON_HEDLEY_MSVC_VERSION_CHECK(major,minor,patch) (_MSC_VER >= ((major * 100) + (minor)))
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_VERSION)
+    #undef JSON_HEDLEY_INTEL_VERSION
+#endif
+#if defined(__INTEL_COMPILER) && defined(__INTEL_COMPILER_UPDATE) && !defined(__ICL)
+    #define JSON_HEDLEY_INTEL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER / 100, __INTEL_COMPILER % 100, __INTEL_COMPILER_UPDATE)
+#elif defined(__INTEL_COMPILER) && !defined(__ICL)
+    #define JSON_HEDLEY_INTEL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER / 100, __INTEL_COMPILER % 100, 0)
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_VERSION_CHECK)
+    #undef JSON_HEDLEY_INTEL_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_INTEL_VERSION)
+    #define JSON_HEDLEY_INTEL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_INTEL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_INTEL_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_CL_VERSION)
+    #undef JSON_HEDLEY_INTEL_CL_VERSION
+#endif
+#if defined(__INTEL_COMPILER) && defined(__INTEL_COMPILER_UPDATE) && defined(__ICL)
+    #define JSON_HEDLEY_INTEL_CL_VERSION JSON_HEDLEY_VERSION_ENCODE(__INTEL_COMPILER, __INTEL_COMPILER_UPDATE, 0)
+#endif
+
+#if defined(JSON_HEDLEY_INTEL_CL_VERSION_CHECK)
+    #undef JSON_HEDLEY_INTEL_CL_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_INTEL_CL_VERSION)
+    #define JSON_HEDLEY_INTEL_CL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_INTEL_CL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_INTEL_CL_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_PGI_VERSION)
+    #undef JSON_HEDLEY_PGI_VERSION
+#endif
+#if defined(__PGI) && defined(__PGIC__) && defined(__PGIC_MINOR__) && defined(__PGIC_PATCHLEVEL__)
+    #define JSON_HEDLEY_PGI_VERSION JSON_HEDLEY_VERSION_ENCODE(__PGIC__, __PGIC_MINOR__, __PGIC_PATCHLEVEL__)
+#endif
+
+#if defined(JSON_HEDLEY_PGI_VERSION_CHECK)
+    #undef JSON_HEDLEY_PGI_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_PGI_VERSION)
+    #define JSON_HEDLEY_PGI_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_PGI_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_PGI_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_SUNPRO_VERSION)
+    #undef JSON_HEDLEY_SUNPRO_VERSION
+#endif
+#if defined(__SUNPRO_C) && (__SUNPRO_C > 0x1000)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((((__SUNPRO_C >> 16) & 0xf) * 10) + ((__SUNPRO_C >> 12) & 0xf), (((__SUNPRO_C >> 8) & 0xf) * 10) + ((__SUNPRO_C >> 4) & 0xf), (__SUNPRO_C & 0xf) * 10)
+#elif defined(__SUNPRO_C)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((__SUNPRO_C >> 8) & 0xf, (__SUNPRO_C >> 4) & 0xf, (__SUNPRO_C) & 0xf)
+#elif defined(__SUNPRO_CC) && (__SUNPRO_CC > 0x1000)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((((__SUNPRO_CC >> 16) & 0xf) * 10) + ((__SUNPRO_CC >> 12) & 0xf), (((__SUNPRO_CC >> 8) & 0xf) * 10) + ((__SUNPRO_CC >> 4) & 0xf), (__SUNPRO_CC & 0xf) * 10)
+#elif defined(__SUNPRO_CC)
+    #define JSON_HEDLEY_SUNPRO_VERSION JSON_HEDLEY_VERSION_ENCODE((__SUNPRO_CC >> 8) & 0xf, (__SUNPRO_CC >> 4) & 0xf, (__SUNPRO_CC) & 0xf)
+#endif
+
+#if defined(JSON_HEDLEY_SUNPRO_VERSION_CHECK)
+    #undef JSON_HEDLEY_SUNPRO_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_SUNPRO_VERSION)
+    #define JSON_HEDLEY_SUNPRO_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_SUNPRO_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_SUNPRO_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION)
+    #undef JSON_HEDLEY_EMSCRIPTEN_VERSION
+#endif
+#if defined(__EMSCRIPTEN__)
+    #define JSON_HEDLEY_EMSCRIPTEN_VERSION JSON_HEDLEY_VERSION_ENCODE(__EMSCRIPTEN_major__, __EMSCRIPTEN_minor__, __EMSCRIPTEN_tiny__)
+#endif
+
+#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK)
+    #undef JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_EMSCRIPTEN_VERSION)
+    #define JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_EMSCRIPTEN_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_ARM_VERSION)
+    #undef JSON_HEDLEY_ARM_VERSION
+#endif
+#if defined(__CC_ARM) && defined(__ARMCOMPILER_VERSION)
+    #define JSON_HEDLEY_ARM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ARMCOMPILER_VERSION / 1000000, (__ARMCOMPILER_VERSION % 1000000) / 10000, (__ARMCOMPILER_VERSION % 10000) / 100)
+#elif defined(__CC_ARM) && defined(__ARMCC_VERSION)
+    #define JSON_HEDLEY_ARM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ARMCC_VERSION / 1000000, (__ARMCC_VERSION % 1000000) / 10000, (__ARMCC_VERSION % 10000) / 100)
+#endif
+
+#if defined(JSON_HEDLEY_ARM_VERSION_CHECK)
+    #undef JSON_HEDLEY_ARM_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_ARM_VERSION)
+    #define JSON_HEDLEY_ARM_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_ARM_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_ARM_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_IBM_VERSION)
+    #undef JSON_HEDLEY_IBM_VERSION
+#endif
+#if defined(__ibmxl__)
+    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__ibmxl_version__, __ibmxl_release__, __ibmxl_modification__)
+#elif defined(__xlC__) && defined(__xlC_ver__)
+    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__xlC__ >> 8, __xlC__ & 0xff, (__xlC_ver__ >> 8) & 0xff)
+#elif defined(__xlC__)
+    #define JSON_HEDLEY_IBM_VERSION JSON_HEDLEY_VERSION_ENCODE(__xlC__ >> 8, __xlC__ & 0xff, 0)
+#endif
+
+#if defined(JSON_HEDLEY_IBM_VERSION_CHECK)
+    #undef JSON_HEDLEY_IBM_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_IBM_VERSION)
+    #define JSON_HEDLEY_IBM_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_IBM_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_IBM_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_VERSION)
+    #undef JSON_HEDLEY_TI_VERSION
+#endif
+#if \
+    defined(__TI_COMPILER_VERSION__) && \
+    ( \
+      defined(__TMS470__) || defined(__TI_ARM__) || \
+      defined(__MSP430__) || \
+      defined(__TMS320C2000__) \
+    )
+#if (__TI_COMPILER_VERSION__ >= 16000000)
+    #define JSON_HEDLEY_TI_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+#endif
+
+#if defined(JSON_HEDLEY_TI_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_VERSION)
+    #define JSON_HEDLEY_TI_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL2000_VERSION)
+    #undef JSON_HEDLEY_TI_CL2000_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__TMS320C2000__)
+    #define JSON_HEDLEY_TI_CL2000_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL2000_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL2000_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL2000_VERSION)
+    #define JSON_HEDLEY_TI_CL2000_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL2000_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL2000_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL430_VERSION)
+    #undef JSON_HEDLEY_TI_CL430_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__MSP430__)
+    #define JSON_HEDLEY_TI_CL430_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL430_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL430_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL430_VERSION)
+    #define JSON_HEDLEY_TI_CL430_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL430_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL430_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_ARMCL_VERSION)
+    #undef JSON_HEDLEY_TI_ARMCL_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && (defined(__TMS470__) || defined(__TI_ARM__))
+    #define JSON_HEDLEY_TI_ARMCL_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_ARMCL_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_ARMCL_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_ARMCL_VERSION)
+    #define JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_ARMCL_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL6X_VERSION)
+    #undef JSON_HEDLEY_TI_CL6X_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__TMS320C6X__)
+    #define JSON_HEDLEY_TI_CL6X_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL6X_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL6X_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL6X_VERSION)
+    #define JSON_HEDLEY_TI_CL6X_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL6X_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL6X_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL7X_VERSION)
+    #undef JSON_HEDLEY_TI_CL7X_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__C7000__)
+    #define JSON_HEDLEY_TI_CL7X_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CL7X_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CL7X_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CL7X_VERSION)
+    #define JSON_HEDLEY_TI_CL7X_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CL7X_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CL7X_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TI_CLPRU_VERSION)
+    #undef JSON_HEDLEY_TI_CLPRU_VERSION
+#endif
+#if defined(__TI_COMPILER_VERSION__) && defined(__PRU__)
+    #define JSON_HEDLEY_TI_CLPRU_VERSION JSON_HEDLEY_VERSION_ENCODE(__TI_COMPILER_VERSION__ / 1000000, (__TI_COMPILER_VERSION__ % 1000000) / 1000, (__TI_COMPILER_VERSION__ % 1000))
+#endif
+
+#if defined(JSON_HEDLEY_TI_CLPRU_VERSION_CHECK)
+    #undef JSON_HEDLEY_TI_CLPRU_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TI_CLPRU_VERSION)
+    #define JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TI_CLPRU_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_CRAY_VERSION)
+    #undef JSON_HEDLEY_CRAY_VERSION
+#endif
+#if defined(_CRAYC)
+    #if defined(_RELEASE_PATCHLEVEL)
+        #define JSON_HEDLEY_CRAY_VERSION JSON_HEDLEY_VERSION_ENCODE(_RELEASE_MAJOR, _RELEASE_MINOR, _RELEASE_PATCHLEVEL)
+    #else
+        #define JSON_HEDLEY_CRAY_VERSION JSON_HEDLEY_VERSION_ENCODE(_RELEASE_MAJOR, _RELEASE_MINOR, 0)
+    #endif
+#endif
+
+#if defined(JSON_HEDLEY_CRAY_VERSION_CHECK)
+    #undef JSON_HEDLEY_CRAY_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_CRAY_VERSION)
+    #define JSON_HEDLEY_CRAY_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_CRAY_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_CRAY_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_IAR_VERSION)
+    #undef JSON_HEDLEY_IAR_VERSION
+#endif
+#if defined(__IAR_SYSTEMS_ICC__)
+    #if __VER__ > 1000
+        #define JSON_HEDLEY_IAR_VERSION JSON_HEDLEY_VERSION_ENCODE((__VER__ / 1000000), ((__VER__ / 1000) % 1000), (__VER__ % 1000))
+    #else
+        #define JSON_HEDLEY_IAR_VERSION JSON_HEDLEY_VERSION_ENCODE(__VER__ / 100, __VER__ % 100, 0)
+    #endif
+#endif
+
+#if defined(JSON_HEDLEY_IAR_VERSION_CHECK)
+    #undef JSON_HEDLEY_IAR_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_IAR_VERSION)
+    #define JSON_HEDLEY_IAR_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_IAR_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_IAR_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_TINYC_VERSION)
+    #undef JSON_HEDLEY_TINYC_VERSION
+#endif
+#if defined(__TINYC__)
+    #define JSON_HEDLEY_TINYC_VERSION JSON_HEDLEY_VERSION_ENCODE(__TINYC__ / 1000, (__TINYC__ / 100) % 10, __TINYC__ % 100)
+#endif
+
+#if defined(JSON_HEDLEY_TINYC_VERSION_CHECK)
+    #undef JSON_HEDLEY_TINYC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_TINYC_VERSION)
+    #define JSON_HEDLEY_TINYC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_TINYC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_TINYC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_DMC_VERSION)
+    #undef JSON_HEDLEY_DMC_VERSION
+#endif
+#if defined(__DMC__)
+    #define JSON_HEDLEY_DMC_VERSION JSON_HEDLEY_VERSION_ENCODE(__DMC__ >> 8, (__DMC__ >> 4) & 0xf, __DMC__ & 0xf)
+#endif
+
+#if defined(JSON_HEDLEY_DMC_VERSION_CHECK)
+    #undef JSON_HEDLEY_DMC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_DMC_VERSION)
+    #define JSON_HEDLEY_DMC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_DMC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_DMC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_COMPCERT_VERSION)
+    #undef JSON_HEDLEY_COMPCERT_VERSION
+#endif
+#if defined(__COMPCERT_VERSION__)
+    #define JSON_HEDLEY_COMPCERT_VERSION JSON_HEDLEY_VERSION_ENCODE(__COMPCERT_VERSION__ / 10000, (__COMPCERT_VERSION__ / 100) % 100, __COMPCERT_VERSION__ % 100)
+#endif
+
+#if defined(JSON_HEDLEY_COMPCERT_VERSION_CHECK)
+    #undef JSON_HEDLEY_COMPCERT_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_COMPCERT_VERSION)
+    #define JSON_HEDLEY_COMPCERT_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_COMPCERT_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_COMPCERT_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_PELLES_VERSION)
+    #undef JSON_HEDLEY_PELLES_VERSION
+#endif
+#if defined(__POCC__)
+    #define JSON_HEDLEY_PELLES_VERSION JSON_HEDLEY_VERSION_ENCODE(__POCC__ / 100, __POCC__ % 100, 0)
+#endif
+
+#if defined(JSON_HEDLEY_PELLES_VERSION_CHECK)
+    #undef JSON_HEDLEY_PELLES_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_PELLES_VERSION)
+    #define JSON_HEDLEY_PELLES_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_PELLES_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_PELLES_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_MCST_LCC_VERSION)
+    #undef JSON_HEDLEY_MCST_LCC_VERSION
+#endif
+#if defined(__LCC__) && defined(__LCC_MINOR__)
+    #define JSON_HEDLEY_MCST_LCC_VERSION JSON_HEDLEY_VERSION_ENCODE(__LCC__ / 100, __LCC__ % 100, __LCC_MINOR__)
+#endif
+
+#if defined(JSON_HEDLEY_MCST_LCC_VERSION_CHECK)
+    #undef JSON_HEDLEY_MCST_LCC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_MCST_LCC_VERSION)
+    #define JSON_HEDLEY_MCST_LCC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_MCST_LCC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_MCST_LCC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_VERSION)
+    #undef JSON_HEDLEY_GCC_VERSION
+#endif
+#if \
+    defined(JSON_HEDLEY_GNUC_VERSION) && \
+    !defined(__clang__) && \
+    !defined(JSON_HEDLEY_INTEL_VERSION) && \
+    !defined(JSON_HEDLEY_PGI_VERSION) && \
+    !defined(JSON_HEDLEY_ARM_VERSION) && \
+    !defined(JSON_HEDLEY_CRAY_VERSION) && \
+    !defined(JSON_HEDLEY_TI_VERSION) && \
+    !defined(JSON_HEDLEY_TI_ARMCL_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL430_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL2000_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL6X_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CL7X_VERSION) && \
+    !defined(JSON_HEDLEY_TI_CLPRU_VERSION) && \
+    !defined(__COMPCERT__) && \
+    !defined(JSON_HEDLEY_MCST_LCC_VERSION)
+    #define JSON_HEDLEY_GCC_VERSION JSON_HEDLEY_GNUC_VERSION
+#endif
+
+#if defined(JSON_HEDLEY_GCC_VERSION_CHECK)
+    #undef JSON_HEDLEY_GCC_VERSION_CHECK
+#endif
+#if defined(JSON_HEDLEY_GCC_VERSION)
+    #define JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch) (JSON_HEDLEY_GCC_VERSION >= JSON_HEDLEY_VERSION_ENCODE(major, minor, patch))
+#else
+    #define JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch) (0)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_HAS_ATTRIBUTE
+#endif
+#if \
+  defined(__has_attribute) && \
+  ( \
+    (!defined(JSON_HEDLEY_IAR_VERSION) || JSON_HEDLEY_IAR_VERSION_CHECK(8,5,9)) \
+  )
+#  define JSON_HEDLEY_HAS_ATTRIBUTE(attribute) __has_attribute(attribute)
+#else
+#  define JSON_HEDLEY_HAS_ATTRIBUTE(attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_GNUC_HAS_ATTRIBUTE
+#endif
+#if defined(__has_attribute)
+    #define JSON_HEDLEY_GNUC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_GCC_HAS_ATTRIBUTE
+#endif
+#if defined(__has_attribute)
+    #define JSON_HEDLEY_GCC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)
+#else
+    #define JSON_HEDLEY_GCC_HAS_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE
+#endif
+#if \
+    defined(__has_cpp_attribute) && \
+    defined(__cplusplus) && \
+    (!defined(JSON_HEDLEY_SUNPRO_VERSION) || JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0))
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute) __has_cpp_attribute(attribute)
+#else
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS)
+    #undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS
+#endif
+#if !defined(__cplusplus) || !defined(__has_cpp_attribute)
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) (0)
+#elif \
+    !defined(JSON_HEDLEY_PGI_VERSION) && \
+    !defined(JSON_HEDLEY_IAR_VERSION) && \
+    (!defined(JSON_HEDLEY_SUNPRO_VERSION) || JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0)) && \
+    (!defined(JSON_HEDLEY_MSVC_VERSION) || JSON_HEDLEY_MSVC_VERSION_CHECK(19,20,0))
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) JSON_HEDLEY_HAS_CPP_ATTRIBUTE(ns::attribute)
+#else
+    #define JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(ns,attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE
+#endif
+#if defined(__has_cpp_attribute) && defined(__cplusplus)
+    #define JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) __has_cpp_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE
+#endif
+#if defined(__has_cpp_attribute) && defined(__cplusplus)
+    #define JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) __has_cpp_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_BUILTIN)
+    #undef JSON_HEDLEY_HAS_BUILTIN
+#endif
+#if defined(__has_builtin)
+    #define JSON_HEDLEY_HAS_BUILTIN(builtin) __has_builtin(builtin)
+#else
+    #define JSON_HEDLEY_HAS_BUILTIN(builtin) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_BUILTIN)
+    #undef JSON_HEDLEY_GNUC_HAS_BUILTIN
+#endif
+#if defined(__has_builtin)
+    #define JSON_HEDLEY_GNUC_HAS_BUILTIN(builtin,major,minor,patch) __has_builtin(builtin)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_BUILTIN(builtin,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_BUILTIN)
+    #undef JSON_HEDLEY_GCC_HAS_BUILTIN
+#endif
+#if defined(__has_builtin)
+    #define JSON_HEDLEY_GCC_HAS_BUILTIN(builtin,major,minor,patch) __has_builtin(builtin)
+#else
+    #define JSON_HEDLEY_GCC_HAS_BUILTIN(builtin,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_FEATURE)
+    #undef JSON_HEDLEY_HAS_FEATURE
+#endif
+#if defined(__has_feature)
+    #define JSON_HEDLEY_HAS_FEATURE(feature) __has_feature(feature)
+#else
+    #define JSON_HEDLEY_HAS_FEATURE(feature) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_FEATURE)
+    #undef JSON_HEDLEY_GNUC_HAS_FEATURE
+#endif
+#if defined(__has_feature)
+    #define JSON_HEDLEY_GNUC_HAS_FEATURE(feature,major,minor,patch) __has_feature(feature)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_FEATURE(feature,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_FEATURE)
+    #undef JSON_HEDLEY_GCC_HAS_FEATURE
+#endif
+#if defined(__has_feature)
+    #define JSON_HEDLEY_GCC_HAS_FEATURE(feature,major,minor,patch) __has_feature(feature)
+#else
+    #define JSON_HEDLEY_GCC_HAS_FEATURE(feature,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_EXTENSION)
+    #undef JSON_HEDLEY_HAS_EXTENSION
+#endif
+#if defined(__has_extension)
+    #define JSON_HEDLEY_HAS_EXTENSION(extension) __has_extension(extension)
+#else
+    #define JSON_HEDLEY_HAS_EXTENSION(extension) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_EXTENSION)
+    #undef JSON_HEDLEY_GNUC_HAS_EXTENSION
+#endif
+#if defined(__has_extension)
+    #define JSON_HEDLEY_GNUC_HAS_EXTENSION(extension,major,minor,patch) __has_extension(extension)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_EXTENSION(extension,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_EXTENSION)
+    #undef JSON_HEDLEY_GCC_HAS_EXTENSION
+#endif
+#if defined(__has_extension)
+    #define JSON_HEDLEY_GCC_HAS_EXTENSION(extension,major,minor,patch) __has_extension(extension)
+#else
+    #define JSON_HEDLEY_GCC_HAS_EXTENSION(extension,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE
+#endif
+#if defined(__has_declspec_attribute)
+    #define JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute) __has_declspec_attribute(attribute)
+#else
+    #define JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE
+#endif
+#if defined(__has_declspec_attribute)
+    #define JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) __has_declspec_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE
+#endif
+#if defined(__has_declspec_attribute)
+    #define JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) __has_declspec_attribute(attribute)
+#else
+    #define JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE(attribute,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_HAS_WARNING)
+    #undef JSON_HEDLEY_HAS_WARNING
+#endif
+#if defined(__has_warning)
+    #define JSON_HEDLEY_HAS_WARNING(warning) __has_warning(warning)
+#else
+    #define JSON_HEDLEY_HAS_WARNING(warning) (0)
+#endif
+
+#if defined(JSON_HEDLEY_GNUC_HAS_WARNING)
+    #undef JSON_HEDLEY_GNUC_HAS_WARNING
+#endif
+#if defined(__has_warning)
+    #define JSON_HEDLEY_GNUC_HAS_WARNING(warning,major,minor,patch) __has_warning(warning)
+#else
+    #define JSON_HEDLEY_GNUC_HAS_WARNING(warning,major,minor,patch) JSON_HEDLEY_GNUC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_GCC_HAS_WARNING)
+    #undef JSON_HEDLEY_GCC_HAS_WARNING
+#endif
+#if defined(__has_warning)
+    #define JSON_HEDLEY_GCC_HAS_WARNING(warning,major,minor,patch) __has_warning(warning)
+#else
+    #define JSON_HEDLEY_GCC_HAS_WARNING(warning,major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if \
+    (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)) || \
+    defined(__clang__) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(18,4,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,7,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(2,0,1) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,0,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_CRAY_VERSION_CHECK(5,0,0) || \
+    JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,17) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(8,0,0) || \
+    (JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) && defined(__C99_PRAGMA_OPERATOR))
+    #define JSON_HEDLEY_PRAGMA(value) _Pragma(#value)
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)
+    #define JSON_HEDLEY_PRAGMA(value) __pragma(value)
+#else
+    #define JSON_HEDLEY_PRAGMA(value)
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_PUSH)
+    #undef JSON_HEDLEY_DIAGNOSTIC_PUSH
+#endif
+#if defined(JSON_HEDLEY_DIAGNOSTIC_POP)
+    #undef JSON_HEDLEY_DIAGNOSTIC_POP
+#endif
+#if defined(__clang__)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("clang diagnostic push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("clang diagnostic pop")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("warning(push)")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("warning(pop)")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("GCC diagnostic push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("GCC diagnostic pop")
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH __pragma(warning(push))
+    #define JSON_HEDLEY_DIAGNOSTIC_POP __pragma(warning(pop))
+#elif JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("pop")
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,4,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,1,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("diag_push")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("diag_pop")
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,90,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH _Pragma("warning(push)")
+    #define JSON_HEDLEY_DIAGNOSTIC_POP _Pragma("warning(pop)")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_PUSH
+    #define JSON_HEDLEY_DIAGNOSTIC_POP
+#endif
+
+/* JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_ is for
+   HEDLEY INTERNAL USE ONLY.  API subject to change without notice. */
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_
+#endif
+#if defined(__cplusplus)
+#  if JSON_HEDLEY_HAS_WARNING("-Wc++98-compat")
+#    if JSON_HEDLEY_HAS_WARNING("-Wc++17-extensions")
+#      if JSON_HEDLEY_HAS_WARNING("-Wc++1z-extensions")
+#        define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wc++98-compat\"") \
+    _Pragma("clang diagnostic ignored \"-Wc++17-extensions\"") \
+    _Pragma("clang diagnostic ignored \"-Wc++1z-extensions\"") \
+    xpr \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#      else
+#        define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wc++98-compat\"") \
+    _Pragma("clang diagnostic ignored \"-Wc++17-extensions\"") \
+    xpr \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#      endif
+#    else
+#      define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(xpr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wc++98-compat\"") \
+    xpr \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#    endif
+#  endif
+#endif
+#if !defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(x) x
+#endif
+
+#if defined(JSON_HEDLEY_CONST_CAST)
+    #undef JSON_HEDLEY_CONST_CAST
+#endif
+#if defined(__cplusplus)
+#  define JSON_HEDLEY_CONST_CAST(T, expr) (const_cast<T>(expr))
+#elif \
+  JSON_HEDLEY_HAS_WARNING("-Wcast-qual") || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+#  define JSON_HEDLEY_CONST_CAST(T, expr) (__extension__ ({ \
+        JSON_HEDLEY_DIAGNOSTIC_PUSH \
+        JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL \
+        ((T) (expr)); \
+        JSON_HEDLEY_DIAGNOSTIC_POP \
+    }))
+#else
+#  define JSON_HEDLEY_CONST_CAST(T, expr) ((T) (expr))
+#endif
+
+#if defined(JSON_HEDLEY_REINTERPRET_CAST)
+    #undef JSON_HEDLEY_REINTERPRET_CAST
+#endif
+#if defined(__cplusplus)
+    #define JSON_HEDLEY_REINTERPRET_CAST(T, expr) (reinterpret_cast<T>(expr))
+#else
+    #define JSON_HEDLEY_REINTERPRET_CAST(T, expr) ((T) (expr))
+#endif
+
+#if defined(JSON_HEDLEY_STATIC_CAST)
+    #undef JSON_HEDLEY_STATIC_CAST
+#endif
+#if defined(__cplusplus)
+    #define JSON_HEDLEY_STATIC_CAST(T, expr) (static_cast<T>(expr))
+#else
+    #define JSON_HEDLEY_STATIC_CAST(T, expr) ((T) (expr))
+#endif
+
+#if defined(JSON_HEDLEY_CPP_CAST)
+    #undef JSON_HEDLEY_CPP_CAST
+#endif
+#if defined(__cplusplus)
+#  if JSON_HEDLEY_HAS_WARNING("-Wold-style-cast")
+#    define JSON_HEDLEY_CPP_CAST(T, expr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wold-style-cast\"") \
+    ((T) (expr)) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#  elif JSON_HEDLEY_IAR_VERSION_CHECK(8,3,0)
+#    define JSON_HEDLEY_CPP_CAST(T, expr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("diag_suppress=Pe137") \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#  else
+#    define JSON_HEDLEY_CPP_CAST(T, expr) ((T) (expr))
+#  endif
+#else
+#  define JSON_HEDLEY_CPP_CAST(T, expr) (expr)
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wdeprecated-declarations")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("clang diagnostic ignored \"-Wdeprecated-declarations\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("warning(disable:1478 1786)")
+#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED __pragma(warning(disable:1478 1786))
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(20,7,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1215,1216,1444,1445")
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1215,1444")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("GCC diagnostic ignored \"-Wdeprecated-declarations\"")
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED __pragma(warning(disable:4996))
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1215,1444")
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress 1291,1718")
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) && !defined(__cplusplus)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("error_messages(off,E_DEPRECATED_ATT,E_DEPRECATED_ATT_MESS)")
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("error_messages(off,symdeprecated,symdeprecated2)")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("diag_suppress=Pe1444,Pe1215")
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,90,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED _Pragma("warn(disable:2241)")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-pragmas")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("clang diagnostic ignored \"-Wunknown-pragmas\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("warning(disable:161)")
+#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS __pragma(warning(disable:161))
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 1675")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("GCC diagnostic ignored \"-Wunknown-pragmas\"")
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS __pragma(warning(disable:4068))
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(16,9,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,3,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 163")
+#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 163")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress=Pe161")
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS _Pragma("diag_suppress 161")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-attributes")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("clang diagnostic ignored \"-Wunknown-attributes\"")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(4,6,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("GCC diagnostic ignored \"-Wdeprecated-declarations\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(17,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("warning(disable:1292)")
+#elif JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES __pragma(warning(disable:1292))
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(19,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES __pragma(warning(disable:5030))
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(20,7,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1097,1098")
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1097")
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,14,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("error_messages(off,attrskipunsup)")
+#elif \
+    JSON_HEDLEY_TI_VERSION_CHECK(18,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,3,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1173")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress=Pe1097")
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES _Pragma("diag_suppress 1097")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wcast-qual")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma("clang diagnostic ignored \"-Wcast-qual\"")
+#elif JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma("warning(disable:2203 2331)")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL _Pragma("GCC diagnostic ignored \"-Wcast-qual\"")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL
+#endif
+
+#if defined(JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION)
+    #undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunused-function")
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma("clang diagnostic ignored \"-Wunused-function\"")
+#elif JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma("GCC diagnostic ignored \"-Wunused-function\"")
+#elif JSON_HEDLEY_MSVC_VERSION_CHECK(1,0,0)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION __pragma(warning(disable:4505))
+#elif JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION _Pragma("diag_suppress 3142")
+#else
+    #define JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION
+#endif
+
+#if defined(JSON_HEDLEY_DEPRECATED)
+    #undef JSON_HEDLEY_DEPRECATED
+#endif
+#if defined(JSON_HEDLEY_DEPRECATED_FOR)
+    #undef JSON_HEDLEY_DEPRECATED_FOR
+#endif
+#if \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DEPRECATED(since) __declspec(deprecated("Since " # since))
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __declspec(deprecated("Since " #since "; use " #replacement))
+#elif \
+    (JSON_HEDLEY_HAS_EXTENSION(attribute_deprecated_with_message) && !defined(JSON_HEDLEY_IAR_VERSION)) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,5,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,13,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(18,1,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(18,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,3,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,3,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_DEPRECATED(since) __attribute__((__deprecated__("Since " #since)))
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __attribute__((__deprecated__("Since " #since "; use " #replacement)))
+#elif defined(__cplusplus) && (__cplusplus >= 201402L)
+    #define JSON_HEDLEY_DEPRECATED(since) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[deprecated("Since " #since)]])
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[deprecated("Since " #since "; use " #replacement)]])
+#elif \
+    JSON_HEDLEY_HAS_ATTRIBUTE(deprecated) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+    #define JSON_HEDLEY_DEPRECATED(since) __attribute__((__deprecated__))
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __attribute__((__deprecated__))
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_PELLES_VERSION_CHECK(6,50,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_DEPRECATED(since) __declspec(deprecated)
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) __declspec(deprecated)
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_DEPRECATED(since) _Pragma("deprecated")
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement) _Pragma("deprecated")
+#else
+    #define JSON_HEDLEY_DEPRECATED(since)
+    #define JSON_HEDLEY_DEPRECATED_FOR(since, replacement)
+#endif
+
+#if defined(JSON_HEDLEY_UNAVAILABLE)
+    #undef JSON_HEDLEY_UNAVAILABLE
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(warning) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,3,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_UNAVAILABLE(available_since) __attribute__((__warning__("Not available until " #available_since)))
+#else
+    #define JSON_HEDLEY_UNAVAILABLE(available_since)
+#endif
+
+#if defined(JSON_HEDLEY_WARN_UNUSED_RESULT)
+    #undef JSON_HEDLEY_WARN_UNUSED_RESULT
+#endif
+#if defined(JSON_HEDLEY_WARN_UNUSED_RESULT_MSG)
+    #undef JSON_HEDLEY_WARN_UNUSED_RESULT_MSG
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(warn_unused_result) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0) && defined(__cplusplus)) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT __attribute__((__warn_unused_result__))
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) __attribute__((__warn_unused_result__))
+#elif (JSON_HEDLEY_HAS_CPP_ATTRIBUTE(nodiscard) >= 201907L)
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard(msg)]])
+#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE(nodiscard)
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[nodiscard]])
+#elif defined(_Check_return_) /* SAL */
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT _Check_return_
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg) _Check_return_
+#else
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT
+    #define JSON_HEDLEY_WARN_UNUSED_RESULT_MSG(msg)
+#endif
+
+#if defined(JSON_HEDLEY_SENTINEL)
+    #undef JSON_HEDLEY_SENTINEL
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(sentinel) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(5,4,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_SENTINEL(position) __attribute__((__sentinel__(position)))
+#else
+    #define JSON_HEDLEY_SENTINEL(position)
+#endif
+
+#if defined(JSON_HEDLEY_NO_RETURN)
+    #undef JSON_HEDLEY_NO_RETURN
+#endif
+#if JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_NO_RETURN __noreturn
+#elif \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_NO_RETURN __attribute__((__noreturn__))
+#elif defined(__STDC_VERSION__) && __STDC_VERSION__ >= 201112L
+    #define JSON_HEDLEY_NO_RETURN _Noreturn
+#elif defined(__cplusplus) && (__cplusplus >= 201103L)
+    #define JSON_HEDLEY_NO_RETURN JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[noreturn]])
+#elif \
+    JSON_HEDLEY_HAS_ATTRIBUTE(noreturn) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,2,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+    #define JSON_HEDLEY_NO_RETURN __attribute__((__noreturn__))
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+    #define JSON_HEDLEY_NO_RETURN _Pragma("does_not_return")
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_NO_RETURN __declspec(noreturn)
+#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,0,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_NO_RETURN _Pragma("FUNC_NEVER_RETURNS;")
+#elif JSON_HEDLEY_COMPCERT_VERSION_CHECK(3,2,0)
+    #define JSON_HEDLEY_NO_RETURN __attribute((noreturn))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(9,0,0)
+    #define JSON_HEDLEY_NO_RETURN __declspec(noreturn)
+#else
+    #define JSON_HEDLEY_NO_RETURN
+#endif
+
+#if defined(JSON_HEDLEY_NO_ESCAPE)
+    #undef JSON_HEDLEY_NO_ESCAPE
+#endif
+#if JSON_HEDLEY_HAS_ATTRIBUTE(noescape)
+    #define JSON_HEDLEY_NO_ESCAPE __attribute__((__noescape__))
+#else
+    #define JSON_HEDLEY_NO_ESCAPE
+#endif
+
+#if defined(JSON_HEDLEY_UNREACHABLE)
+    #undef JSON_HEDLEY_UNREACHABLE
+#endif
+#if defined(JSON_HEDLEY_UNREACHABLE_RETURN)
+    #undef JSON_HEDLEY_UNREACHABLE_RETURN
+#endif
+#if defined(JSON_HEDLEY_ASSUME)
+    #undef JSON_HEDLEY_ASSUME
+#endif
+#if \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_ASSUME(expr) __assume(expr)
+#elif JSON_HEDLEY_HAS_BUILTIN(__builtin_assume)
+    #define JSON_HEDLEY_ASSUME(expr) __builtin_assume(expr)
+#elif \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0)
+    #if defined(__cplusplus)
+        #define JSON_HEDLEY_ASSUME(expr) std::_nassert(expr)
+    #else
+        #define JSON_HEDLEY_ASSUME(expr) _nassert(expr)
+    #endif
+#endif
+#if \
+    (JSON_HEDLEY_HAS_BUILTIN(__builtin_unreachable) && (!defined(JSON_HEDLEY_ARM_VERSION))) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,5,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(18,10,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,5) || \
+    JSON_HEDLEY_CRAY_VERSION_CHECK(10,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_UNREACHABLE() __builtin_unreachable()
+#elif defined(JSON_HEDLEY_ASSUME)
+    #define JSON_HEDLEY_UNREACHABLE() JSON_HEDLEY_ASSUME(0)
+#endif
+#if !defined(JSON_HEDLEY_ASSUME)
+    #if defined(JSON_HEDLEY_UNREACHABLE)
+        #define JSON_HEDLEY_ASSUME(expr) JSON_HEDLEY_STATIC_CAST(void, ((expr) ? 1 : (JSON_HEDLEY_UNREACHABLE(), 1)))
+    #else
+        #define JSON_HEDLEY_ASSUME(expr) JSON_HEDLEY_STATIC_CAST(void, expr)
+    #endif
+#endif
+#if defined(JSON_HEDLEY_UNREACHABLE)
+    #if  \
+        JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \
+        JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0)
+        #define JSON_HEDLEY_UNREACHABLE_RETURN(value) return (JSON_HEDLEY_STATIC_CAST(void, JSON_HEDLEY_ASSUME(0)), (value))
+    #else
+        #define JSON_HEDLEY_UNREACHABLE_RETURN(value) JSON_HEDLEY_UNREACHABLE()
+    #endif
+#else
+    #define JSON_HEDLEY_UNREACHABLE_RETURN(value) return (value)
+#endif
+#if !defined(JSON_HEDLEY_UNREACHABLE)
+    #define JSON_HEDLEY_UNREACHABLE() JSON_HEDLEY_ASSUME(0)
+#endif
+
+JSON_HEDLEY_DIAGNOSTIC_PUSH
+#if JSON_HEDLEY_HAS_WARNING("-Wpedantic")
+    #pragma clang diagnostic ignored "-Wpedantic"
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wc++98-compat-pedantic") && defined(__cplusplus)
+    #pragma clang diagnostic ignored "-Wc++98-compat-pedantic"
+#endif
+#if JSON_HEDLEY_GCC_HAS_WARNING("-Wvariadic-macros",4,0,0)
+    #if defined(__clang__)
+        #pragma clang diagnostic ignored "-Wvariadic-macros"
+    #elif defined(JSON_HEDLEY_GCC_VERSION)
+        #pragma GCC diagnostic ignored "-Wvariadic-macros"
+    #endif
+#endif
+#if defined(JSON_HEDLEY_NON_NULL)
+    #undef JSON_HEDLEY_NON_NULL
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(nonnull) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0)
+    #define JSON_HEDLEY_NON_NULL(...) __attribute__((__nonnull__(__VA_ARGS__)))
+#else
+    #define JSON_HEDLEY_NON_NULL(...)
+#endif
+JSON_HEDLEY_DIAGNOSTIC_POP
+
+#if defined(JSON_HEDLEY_PRINTF_FORMAT)
+    #undef JSON_HEDLEY_PRINTF_FORMAT
+#endif
+#if defined(__MINGW32__) && JSON_HEDLEY_GCC_HAS_ATTRIBUTE(format,4,4,0) && !defined(__USE_MINGW_ANSI_STDIO)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(ms_printf, string_idx, first_to_check)))
+#elif defined(__MINGW32__) && JSON_HEDLEY_GCC_HAS_ATTRIBUTE(format,4,4,0) && defined(__USE_MINGW_ANSI_STDIO)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(gnu_printf, string_idx, first_to_check)))
+#elif \
+    JSON_HEDLEY_HAS_ATTRIBUTE(format) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(5,6,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __attribute__((__format__(__printf__, string_idx, first_to_check)))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(6,0,0)
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check) __declspec(vaformat(printf,string_idx,first_to_check))
+#else
+    #define JSON_HEDLEY_PRINTF_FORMAT(string_idx,first_to_check)
+#endif
+
+#if defined(JSON_HEDLEY_CONSTEXPR)
+    #undef JSON_HEDLEY_CONSTEXPR
+#endif
+#if defined(__cplusplus)
+    #if __cplusplus >= 201103L
+        #define JSON_HEDLEY_CONSTEXPR JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(constexpr)
+    #endif
+#endif
+#if !defined(JSON_HEDLEY_CONSTEXPR)
+    #define JSON_HEDLEY_CONSTEXPR
+#endif
+
+#if defined(JSON_HEDLEY_PREDICT)
+    #undef JSON_HEDLEY_PREDICT
+#endif
+#if defined(JSON_HEDLEY_LIKELY)
+    #undef JSON_HEDLEY_LIKELY
+#endif
+#if defined(JSON_HEDLEY_UNLIKELY)
+    #undef JSON_HEDLEY_UNLIKELY
+#endif
+#if defined(JSON_HEDLEY_UNPREDICTABLE)
+    #undef JSON_HEDLEY_UNPREDICTABLE
+#endif
+#if JSON_HEDLEY_HAS_BUILTIN(__builtin_unpredictable)
+    #define JSON_HEDLEY_UNPREDICTABLE(expr) __builtin_unpredictable((expr))
+#endif
+#if \
+  (JSON_HEDLEY_HAS_BUILTIN(__builtin_expect_with_probability) && !defined(JSON_HEDLEY_PGI_VERSION)) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(9,0,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#  define JSON_HEDLEY_PREDICT(expr, value, probability) __builtin_expect_with_probability(  (expr), (value), (probability))
+#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability)   __builtin_expect_with_probability(!!(expr),    1   , (probability))
+#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability)  __builtin_expect_with_probability(!!(expr),    0   , (probability))
+#  define JSON_HEDLEY_LIKELY(expr)                      __builtin_expect                 (!!(expr),    1                  )
+#  define JSON_HEDLEY_UNLIKELY(expr)                    __builtin_expect                 (!!(expr),    0                  )
+#elif \
+  (JSON_HEDLEY_HAS_BUILTIN(__builtin_expect) && !defined(JSON_HEDLEY_INTEL_CL_VERSION)) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(3,0,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+  (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,15,0) && defined(__cplusplus)) || \
+  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,7,0) || \
+  JSON_HEDLEY_TI_CL430_VERSION_CHECK(3,1,0) || \
+  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,1,0) || \
+  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \
+  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+  JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,27) || \
+  JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#  define JSON_HEDLEY_PREDICT(expr, expected, probability) \
+    (((probability) >= 0.9) ? __builtin_expect((expr), (expected)) : (JSON_HEDLEY_STATIC_CAST(void, expected), (expr)))
+#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability) \
+    (__extension__ ({ \
+        double hedley_probability_ = (probability); \
+        ((hedley_probability_ >= 0.9) ? __builtin_expect(!!(expr), 1) : ((hedley_probability_ <= 0.1) ? __builtin_expect(!!(expr), 0) : !!(expr))); \
+    }))
+#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability) \
+    (__extension__ ({ \
+        double hedley_probability_ = (probability); \
+        ((hedley_probability_ >= 0.9) ? __builtin_expect(!!(expr), 0) : ((hedley_probability_ <= 0.1) ? __builtin_expect(!!(expr), 1) : !!(expr))); \
+    }))
+#  define JSON_HEDLEY_LIKELY(expr)   __builtin_expect(!!(expr), 1)
+#  define JSON_HEDLEY_UNLIKELY(expr) __builtin_expect(!!(expr), 0)
+#else
+#  define JSON_HEDLEY_PREDICT(expr, expected, probability) (JSON_HEDLEY_STATIC_CAST(void, expected), (expr))
+#  define JSON_HEDLEY_PREDICT_TRUE(expr, probability) (!!(expr))
+#  define JSON_HEDLEY_PREDICT_FALSE(expr, probability) (!!(expr))
+#  define JSON_HEDLEY_LIKELY(expr) (!!(expr))
+#  define JSON_HEDLEY_UNLIKELY(expr) (!!(expr))
+#endif
+#if !defined(JSON_HEDLEY_UNPREDICTABLE)
+    #define JSON_HEDLEY_UNPREDICTABLE(expr) JSON_HEDLEY_PREDICT(expr, 1, 0.5)
+#endif
+
+#if defined(JSON_HEDLEY_MALLOC)
+    #undef JSON_HEDLEY_MALLOC
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(malloc) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(12,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_MALLOC __attribute__((__malloc__))
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+    #define JSON_HEDLEY_MALLOC _Pragma("returns_new_memory")
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_MALLOC __declspec(restrict)
+#else
+    #define JSON_HEDLEY_MALLOC
+#endif
+
+#if defined(JSON_HEDLEY_PURE)
+    #undef JSON_HEDLEY_PURE
+#endif
+#if \
+  JSON_HEDLEY_HAS_ATTRIBUTE(pure) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(2,96,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+  JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+  (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+  (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+  (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+  (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+  JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#  define JSON_HEDLEY_PURE __attribute__((__pure__))
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+#  define JSON_HEDLEY_PURE _Pragma("does_not_write_global_data")
+#elif defined(__cplusplus) && \
+    ( \
+      JSON_HEDLEY_TI_CL430_VERSION_CHECK(2,0,1) || \
+      JSON_HEDLEY_TI_CL6X_VERSION_CHECK(4,0,0) || \
+      JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) \
+    )
+#  define JSON_HEDLEY_PURE _Pragma("FUNC_IS_PURE;")
+#else
+#  define JSON_HEDLEY_PURE
+#endif
+
+#if defined(JSON_HEDLEY_CONST)
+    #undef JSON_HEDLEY_CONST
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(const) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(2,5,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_CONST __attribute__((__const__))
+#elif \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0)
+    #define JSON_HEDLEY_CONST _Pragma("no_side_effect")
+#else
+    #define JSON_HEDLEY_CONST JSON_HEDLEY_PURE
+#endif
+
+#if defined(JSON_HEDLEY_RESTRICT)
+    #undef JSON_HEDLEY_RESTRICT
+#endif
+#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) && !defined(__cplusplus)
+    #define JSON_HEDLEY_RESTRICT restrict
+#elif \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(14,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_PGI_VERSION_CHECK(17,10,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,4) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,1,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,14,0) && defined(__cplusplus)) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0) || \
+    defined(__clang__) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_RESTRICT __restrict
+#elif JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,3,0) && !defined(__cplusplus)
+    #define JSON_HEDLEY_RESTRICT _Restrict
+#else
+    #define JSON_HEDLEY_RESTRICT
+#endif
+
+#if defined(JSON_HEDLEY_INLINE)
+    #undef JSON_HEDLEY_INLINE
+#endif
+#if \
+    (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)) || \
+    (defined(__cplusplus) && (__cplusplus >= 199711L))
+    #define JSON_HEDLEY_INLINE inline
+#elif \
+    defined(JSON_HEDLEY_GCC_VERSION) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(6,2,0)
+    #define JSON_HEDLEY_INLINE __inline__
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(12,0,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,1,0) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(3,1,0) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,2,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(8,0,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_INLINE __inline
+#else
+    #define JSON_HEDLEY_INLINE
+#endif
+
+#if defined(JSON_HEDLEY_ALWAYS_INLINE)
+    #undef JSON_HEDLEY_ALWAYS_INLINE
+#endif
+#if \
+  JSON_HEDLEY_HAS_ATTRIBUTE(always_inline) || \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+  JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+  JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+  JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+  JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+  (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+  (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+  (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+  (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+  JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+  JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+  JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+  JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \
+  JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+#  define JSON_HEDLEY_ALWAYS_INLINE __attribute__((__always_inline__)) JSON_HEDLEY_INLINE
+#elif \
+  JSON_HEDLEY_MSVC_VERSION_CHECK(12,0,0) || \
+  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+#  define JSON_HEDLEY_ALWAYS_INLINE __forceinline
+#elif defined(__cplusplus) && \
+    ( \
+      JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+      JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+      JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+      JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \
+      JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+      JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) \
+    )
+#  define JSON_HEDLEY_ALWAYS_INLINE _Pragma("FUNC_ALWAYS_INLINE;")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+#  define JSON_HEDLEY_ALWAYS_INLINE _Pragma("inline=forced")
+#else
+#  define JSON_HEDLEY_ALWAYS_INLINE JSON_HEDLEY_INLINE
+#endif
+
+#if defined(JSON_HEDLEY_NEVER_INLINE)
+    #undef JSON_HEDLEY_NEVER_INLINE
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(noinline) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,0,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(10,1,0) || \
+    JSON_HEDLEY_TI_VERSION_CHECK(15,12,0) || \
+    (JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(4,8,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_ARMCL_VERSION_CHECK(5,2,0) || \
+    (JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL2000_VERSION_CHECK(6,4,0) || \
+    (JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,0,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL430_VERSION_CHECK(4,3,0) || \
+    (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) || \
+    JSON_HEDLEY_TI_CL7X_VERSION_CHECK(1,2,0) || \
+    JSON_HEDLEY_TI_CLPRU_VERSION_CHECK(2,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10) || \
+    JSON_HEDLEY_IAR_VERSION_CHECK(8,10,0)
+    #define JSON_HEDLEY_NEVER_INLINE __attribute__((__noinline__))
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,10,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_NEVER_INLINE __declspec(noinline)
+#elif JSON_HEDLEY_PGI_VERSION_CHECK(10,2,0)
+    #define JSON_HEDLEY_NEVER_INLINE _Pragma("noinline")
+#elif JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,0,0) && defined(__cplusplus)
+    #define JSON_HEDLEY_NEVER_INLINE _Pragma("FUNC_CANNOT_INLINE;")
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+    #define JSON_HEDLEY_NEVER_INLINE _Pragma("inline=never")
+#elif JSON_HEDLEY_COMPCERT_VERSION_CHECK(3,2,0)
+    #define JSON_HEDLEY_NEVER_INLINE __attribute((noinline))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(9,0,0)
+    #define JSON_HEDLEY_NEVER_INLINE __declspec(noinline)
+#else
+    #define JSON_HEDLEY_NEVER_INLINE
+#endif
+
+#if defined(JSON_HEDLEY_PRIVATE)
+    #undef JSON_HEDLEY_PRIVATE
+#endif
+#if defined(JSON_HEDLEY_PUBLIC)
+    #undef JSON_HEDLEY_PUBLIC
+#endif
+#if defined(JSON_HEDLEY_IMPORT)
+    #undef JSON_HEDLEY_IMPORT
+#endif
+#if defined(_WIN32) || defined(__CYGWIN__)
+#  define JSON_HEDLEY_PRIVATE
+#  define JSON_HEDLEY_PUBLIC   __declspec(dllexport)
+#  define JSON_HEDLEY_IMPORT   __declspec(dllimport)
+#else
+#  if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(visibility) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \
+    JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,11,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \
+    ( \
+      defined(__TI_EABI__) && \
+      ( \
+        (JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,2,0) && defined(__TI_GNU_ATTRIBUTE_SUPPORT__)) || \
+        JSON_HEDLEY_TI_CL6X_VERSION_CHECK(7,5,0) \
+      ) \
+    ) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+#    define JSON_HEDLEY_PRIVATE __attribute__((__visibility__("hidden")))
+#    define JSON_HEDLEY_PUBLIC  __attribute__((__visibility__("default")))
+#  else
+#    define JSON_HEDLEY_PRIVATE
+#    define JSON_HEDLEY_PUBLIC
+#  endif
+#  define JSON_HEDLEY_IMPORT    extern
+#endif
+
+#if defined(JSON_HEDLEY_NO_THROW)
+    #undef JSON_HEDLEY_NO_THROW
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(nothrow) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,3,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_NO_THROW __attribute__((__nothrow__))
+#elif \
+    JSON_HEDLEY_MSVC_VERSION_CHECK(13,1,0) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0)
+    #define JSON_HEDLEY_NO_THROW __declspec(nothrow)
+#else
+    #define JSON_HEDLEY_NO_THROW
+#endif
+
+#if defined(JSON_HEDLEY_FALL_THROUGH)
+    #undef JSON_HEDLEY_FALL_THROUGH
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(fallthrough) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(7,0,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_FALL_THROUGH __attribute__((__fallthrough__))
+#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS(clang,fallthrough)
+    #define JSON_HEDLEY_FALL_THROUGH JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[clang::fallthrough]])
+#elif JSON_HEDLEY_HAS_CPP_ATTRIBUTE(fallthrough)
+    #define JSON_HEDLEY_FALL_THROUGH JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_([[fallthrough]])
+#elif defined(__fallthrough) /* SAL */
+    #define JSON_HEDLEY_FALL_THROUGH __fallthrough
+#else
+    #define JSON_HEDLEY_FALL_THROUGH
+#endif
+
+#if defined(JSON_HEDLEY_RETURNS_NON_NULL)
+    #undef JSON_HEDLEY_RETURNS_NON_NULL
+#endif
+#if \
+    JSON_HEDLEY_HAS_ATTRIBUTE(returns_nonnull) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_RETURNS_NON_NULL __attribute__((__returns_nonnull__))
+#elif defined(_Ret_notnull_) /* SAL */
+    #define JSON_HEDLEY_RETURNS_NON_NULL _Ret_notnull_
+#else
+    #define JSON_HEDLEY_RETURNS_NON_NULL
+#endif
+
+#if defined(JSON_HEDLEY_ARRAY_PARAM)
+    #undef JSON_HEDLEY_ARRAY_PARAM
+#endif
+#if \
+    defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L) && \
+    !defined(__STDC_NO_VLA__) && \
+    !defined(__cplusplus) && \
+    !defined(JSON_HEDLEY_PGI_VERSION) && \
+    !defined(JSON_HEDLEY_TINYC_VERSION)
+    #define JSON_HEDLEY_ARRAY_PARAM(name) (name)
+#else
+    #define JSON_HEDLEY_ARRAY_PARAM(name)
+#endif
+
+#if defined(JSON_HEDLEY_IS_CONSTANT)
+    #undef JSON_HEDLEY_IS_CONSTANT
+#endif
+#if defined(JSON_HEDLEY_REQUIRE_CONSTEXPR)
+    #undef JSON_HEDLEY_REQUIRE_CONSTEXPR
+#endif
+/* JSON_HEDLEY_IS_CONSTEXPR_ is for
+   HEDLEY INTERNAL USE ONLY.  API subject to change without notice. */
+#if defined(JSON_HEDLEY_IS_CONSTEXPR_)
+    #undef JSON_HEDLEY_IS_CONSTEXPR_
+#endif
+#if \
+    JSON_HEDLEY_HAS_BUILTIN(__builtin_constant_p) || \
+    JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \
+    JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+    JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,19) || \
+    JSON_HEDLEY_ARM_VERSION_CHECK(4,1,0) || \
+    JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \
+    JSON_HEDLEY_TI_CL6X_VERSION_CHECK(6,1,0) || \
+    (JSON_HEDLEY_SUNPRO_VERSION_CHECK(5,10,0) && !defined(__cplusplus)) || \
+    JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \
+    JSON_HEDLEY_MCST_LCC_VERSION_CHECK(1,25,10)
+    #define JSON_HEDLEY_IS_CONSTANT(expr) __builtin_constant_p(expr)
+#endif
+#if !defined(__cplusplus)
+#  if \
+       JSON_HEDLEY_HAS_BUILTIN(__builtin_types_compatible_p) || \
+       JSON_HEDLEY_GCC_VERSION_CHECK(3,4,0) || \
+       JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+       JSON_HEDLEY_IBM_VERSION_CHECK(13,1,0) || \
+       JSON_HEDLEY_CRAY_VERSION_CHECK(8,1,0) || \
+       JSON_HEDLEY_ARM_VERSION_CHECK(5,4,0) || \
+       JSON_HEDLEY_TINYC_VERSION_CHECK(0,9,24)
+#if defined(__INTPTR_TYPE__)
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) __builtin_types_compatible_p(__typeof__((1 ? (void*) ((__INTPTR_TYPE__) ((expr) * 0)) : (int*) 0)), int*)
+#else
+    #include <stdint.h>
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) __builtin_types_compatible_p(__typeof__((1 ? (void*) ((intptr_t) ((expr) * 0)) : (int*) 0)), int*)
+#endif
+#  elif \
+       ( \
+          defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L) && \
+          !defined(JSON_HEDLEY_SUNPRO_VERSION) && \
+          !defined(JSON_HEDLEY_PGI_VERSION) && \
+          !defined(JSON_HEDLEY_IAR_VERSION)) || \
+       (JSON_HEDLEY_HAS_EXTENSION(c_generic_selections) && !defined(JSON_HEDLEY_IAR_VERSION)) || \
+       JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0) || \
+       JSON_HEDLEY_INTEL_VERSION_CHECK(17,0,0) || \
+       JSON_HEDLEY_IBM_VERSION_CHECK(12,1,0) || \
+       JSON_HEDLEY_ARM_VERSION_CHECK(5,3,0)
+#if defined(__INTPTR_TYPE__)
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) _Generic((1 ? (void*) ((__INTPTR_TYPE__) ((expr) * 0)) : (int*) 0), int*: 1, void*: 0)
+#else
+    #include <stdint.h>
+    #define JSON_HEDLEY_IS_CONSTEXPR_(expr) _Generic((1 ? (void*) ((intptr_t) * 0) : (int*) 0), int*: 1, void*: 0)
+#endif
+#  elif \
+       defined(JSON_HEDLEY_GCC_VERSION) || \
+       defined(JSON_HEDLEY_INTEL_VERSION) || \
+       defined(JSON_HEDLEY_TINYC_VERSION) || \
+       defined(JSON_HEDLEY_TI_ARMCL_VERSION) || \
+       JSON_HEDLEY_TI_CL430_VERSION_CHECK(18,12,0) || \
+       defined(JSON_HEDLEY_TI_CL2000_VERSION) || \
+       defined(JSON_HEDLEY_TI_CL6X_VERSION) || \
+       defined(JSON_HEDLEY_TI_CL7X_VERSION) || \
+       defined(JSON_HEDLEY_TI_CLPRU_VERSION) || \
+       defined(__clang__)
+#    define JSON_HEDLEY_IS_CONSTEXPR_(expr) ( \
+        sizeof(void) != \
+        sizeof(*( \
+                  1 ? \
+                  ((void*) ((expr) * 0L) ) : \
+((struct { char v[sizeof(void) * 2]; } *) 1) \
+                ) \
+              ) \
+                                            )
+#  endif
+#endif
+#if defined(JSON_HEDLEY_IS_CONSTEXPR_)
+    #if !defined(JSON_HEDLEY_IS_CONSTANT)
+        #define JSON_HEDLEY_IS_CONSTANT(expr) JSON_HEDLEY_IS_CONSTEXPR_(expr)
+    #endif
+    #define JSON_HEDLEY_REQUIRE_CONSTEXPR(expr) (JSON_HEDLEY_IS_CONSTEXPR_(expr) ? (expr) : (-1))
+#else
+    #if !defined(JSON_HEDLEY_IS_CONSTANT)
+        #define JSON_HEDLEY_IS_CONSTANT(expr) (0)
+    #endif
+    #define JSON_HEDLEY_REQUIRE_CONSTEXPR(expr) (expr)
+#endif
+
+#if defined(JSON_HEDLEY_BEGIN_C_DECLS)
+    #undef JSON_HEDLEY_BEGIN_C_DECLS
+#endif
+#if defined(JSON_HEDLEY_END_C_DECLS)
+    #undef JSON_HEDLEY_END_C_DECLS
+#endif
+#if defined(JSON_HEDLEY_C_DECL)
+    #undef JSON_HEDLEY_C_DECL
+#endif
+#if defined(__cplusplus)
+    #define JSON_HEDLEY_BEGIN_C_DECLS extern "C" {
+    #define JSON_HEDLEY_END_C_DECLS }
+    #define JSON_HEDLEY_C_DECL extern "C"
+#else
+    #define JSON_HEDLEY_BEGIN_C_DECLS
+    #define JSON_HEDLEY_END_C_DECLS
+    #define JSON_HEDLEY_C_DECL
+#endif
+
+#if defined(JSON_HEDLEY_STATIC_ASSERT)
+    #undef JSON_HEDLEY_STATIC_ASSERT
+#endif
+#if \
+  !defined(__cplusplus) && ( \
+      (defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 201112L)) || \
+      (JSON_HEDLEY_HAS_FEATURE(c_static_assert) && !defined(JSON_HEDLEY_INTEL_CL_VERSION)) || \
+      JSON_HEDLEY_GCC_VERSION_CHECK(6,0,0) || \
+      JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0) || \
+      defined(_Static_assert) \
+    )
+#  define JSON_HEDLEY_STATIC_ASSERT(expr, message) _Static_assert(expr, message)
+#elif \
+  (defined(__cplusplus) && (__cplusplus >= 201103L)) || \
+  JSON_HEDLEY_MSVC_VERSION_CHECK(16,0,0) || \
+  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+#  define JSON_HEDLEY_STATIC_ASSERT(expr, message) JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(static_assert(expr, message))
+#else
+#  define JSON_HEDLEY_STATIC_ASSERT(expr, message)
+#endif
+
+#if defined(JSON_HEDLEY_NULL)
+    #undef JSON_HEDLEY_NULL
+#endif
+#if defined(__cplusplus)
+    #if __cplusplus >= 201103L
+        #define JSON_HEDLEY_NULL JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_(nullptr)
+    #elif defined(NULL)
+        #define JSON_HEDLEY_NULL NULL
+    #else
+        #define JSON_HEDLEY_NULL JSON_HEDLEY_STATIC_CAST(void*, 0)
+    #endif
+#elif defined(NULL)
+    #define JSON_HEDLEY_NULL NULL
+#else
+    #define JSON_HEDLEY_NULL ((void*) 0)
+#endif
+
+#if defined(JSON_HEDLEY_MESSAGE)
+    #undef JSON_HEDLEY_MESSAGE
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-pragmas")
+#  define JSON_HEDLEY_MESSAGE(msg) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS \
+    JSON_HEDLEY_PRAGMA(message msg) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#elif \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,4,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message msg)
+#elif JSON_HEDLEY_CRAY_VERSION_CHECK(5,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(_CRI message msg)
+#elif JSON_HEDLEY_IAR_VERSION_CHECK(8,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message(msg))
+#elif JSON_HEDLEY_PELLES_VERSION_CHECK(2,0,0)
+#  define JSON_HEDLEY_MESSAGE(msg) JSON_HEDLEY_PRAGMA(message(msg))
+#else
+#  define JSON_HEDLEY_MESSAGE(msg)
+#endif
+
+#if defined(JSON_HEDLEY_WARNING)
+    #undef JSON_HEDLEY_WARNING
+#endif
+#if JSON_HEDLEY_HAS_WARNING("-Wunknown-pragmas")
+#  define JSON_HEDLEY_WARNING(msg) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS \
+    JSON_HEDLEY_PRAGMA(clang warning msg) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#elif \
+  JSON_HEDLEY_GCC_VERSION_CHECK(4,8,0) || \
+  JSON_HEDLEY_PGI_VERSION_CHECK(18,4,0) || \
+  JSON_HEDLEY_INTEL_VERSION_CHECK(13,0,0)
+#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_PRAGMA(GCC warning msg)
+#elif \
+  JSON_HEDLEY_MSVC_VERSION_CHECK(15,0,0) || \
+  JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_PRAGMA(message(msg))
+#else
+#  define JSON_HEDLEY_WARNING(msg) JSON_HEDLEY_MESSAGE(msg)
+#endif
+
+#if defined(JSON_HEDLEY_REQUIRE)
+    #undef JSON_HEDLEY_REQUIRE
+#endif
+#if defined(JSON_HEDLEY_REQUIRE_MSG)
+    #undef JSON_HEDLEY_REQUIRE_MSG
+#endif
+#if JSON_HEDLEY_HAS_ATTRIBUTE(diagnose_if)
+#  if JSON_HEDLEY_HAS_WARNING("-Wgcc-compat")
+#    define JSON_HEDLEY_REQUIRE(expr) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wgcc-compat\"") \
+    __attribute__((diagnose_if(!(expr), #expr, "error"))) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#    define JSON_HEDLEY_REQUIRE_MSG(expr,msg) \
+    JSON_HEDLEY_DIAGNOSTIC_PUSH \
+    _Pragma("clang diagnostic ignored \"-Wgcc-compat\"") \
+    __attribute__((diagnose_if(!(expr), msg, "error"))) \
+    JSON_HEDLEY_DIAGNOSTIC_POP
+#  else
+#    define JSON_HEDLEY_REQUIRE(expr) __attribute__((diagnose_if(!(expr), #expr, "error")))
+#    define JSON_HEDLEY_REQUIRE_MSG(expr,msg) __attribute__((diagnose_if(!(expr), msg, "error")))
+#  endif
+#else
+#  define JSON_HEDLEY_REQUIRE(expr)
+#  define JSON_HEDLEY_REQUIRE_MSG(expr,msg)
+#endif
+
+#if defined(JSON_HEDLEY_FLAGS)
+    #undef JSON_HEDLEY_FLAGS
+#endif
+#if JSON_HEDLEY_HAS_ATTRIBUTE(flag_enum) && (!defined(__cplusplus) || JSON_HEDLEY_HAS_WARNING("-Wbitfield-enum-conversion"))
+    #define JSON_HEDLEY_FLAGS __attribute__((__flag_enum__))
+#else
+    #define JSON_HEDLEY_FLAGS
+#endif
+
+#if defined(JSON_HEDLEY_FLAGS_CAST)
+    #undef JSON_HEDLEY_FLAGS_CAST
+#endif
+#if JSON_HEDLEY_INTEL_VERSION_CHECK(19,0,0)
+#  define JSON_HEDLEY_FLAGS_CAST(T, expr) (__extension__ ({ \
+        JSON_HEDLEY_DIAGNOSTIC_PUSH \
+        _Pragma("warning(disable:188)") \
+        ((T) (expr)); \
+        JSON_HEDLEY_DIAGNOSTIC_POP \
+    }))
+#else
+#  define JSON_HEDLEY_FLAGS_CAST(T, expr) JSON_HEDLEY_STATIC_CAST(T, expr)
+#endif
+
+#if defined(JSON_HEDLEY_EMPTY_BASES)
+    #undef JSON_HEDLEY_EMPTY_BASES
+#endif
+#if \
+    (JSON_HEDLEY_MSVC_VERSION_CHECK(19,0,23918) && !JSON_HEDLEY_MSVC_VERSION_CHECK(20,0,0)) || \
+    JSON_HEDLEY_INTEL_CL_VERSION_CHECK(2021,1,0)
+    #define JSON_HEDLEY_EMPTY_BASES __declspec(empty_bases)
+#else
+    #define JSON_HEDLEY_EMPTY_BASES
+#endif
+
+/* Remaining macros are deprecated. */
+
+#if defined(JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK)
+    #undef JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK
+#endif
+#if defined(__clang__)
+    #define JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK(major,minor,patch) (0)
+#else
+    #define JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK(major,minor,patch) JSON_HEDLEY_GCC_VERSION_CHECK(major,minor,patch)
+#endif
+
+#if defined(JSON_HEDLEY_CLANG_HAS_ATTRIBUTE)
+    #undef JSON_HEDLEY_CLANG_HAS_ATTRIBUTE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_ATTRIBUTE(attribute)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE)
+    #undef JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_CPP_ATTRIBUTE(attribute)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_BUILTIN)
+    #undef JSON_HEDLEY_CLANG_HAS_BUILTIN
+#endif
+#define JSON_HEDLEY_CLANG_HAS_BUILTIN(builtin) JSON_HEDLEY_HAS_BUILTIN(builtin)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_FEATURE)
+    #undef JSON_HEDLEY_CLANG_HAS_FEATURE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_FEATURE(feature) JSON_HEDLEY_HAS_FEATURE(feature)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_EXTENSION)
+    #undef JSON_HEDLEY_CLANG_HAS_EXTENSION
+#endif
+#define JSON_HEDLEY_CLANG_HAS_EXTENSION(extension) JSON_HEDLEY_HAS_EXTENSION(extension)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE)
+    #undef JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE
+#endif
+#define JSON_HEDLEY_CLANG_HAS_DECLSPEC_ATTRIBUTE(attribute) JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE(attribute)
+
+#if defined(JSON_HEDLEY_CLANG_HAS_WARNING)
+    #undef JSON_HEDLEY_CLANG_HAS_WARNING
+#endif
+#define JSON_HEDLEY_CLANG_HAS_WARNING(warning) JSON_HEDLEY_HAS_WARNING(warning)
+
+#endif /* !defined(JSON_HEDLEY_VERSION) || (JSON_HEDLEY_VERSION < X) */
+
+
+// This file contains all internal macro definitions (except those affecting ABI)
+// You MUST include macro_unscope.hpp at the end of json.hpp to undef all of them
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+// exclude unsupported compilers
+#if !defined(JSON_SKIP_UNSUPPORTED_COMPILER_CHECK)
+    #if defined(__clang__)
+        #if (__clang_major__ * 10000 + __clang_minor__ * 100 + __clang_patchlevel__) < 30400
+            #error "unsupported Clang version - see https://github.com/nlohmann/json#supported-compilers"
+        #endif
+    #elif defined(__GNUC__) && !(defined(__ICC) || defined(__INTEL_COMPILER))
+        #if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) < 40800
+            #error "unsupported GCC version - see https://github.com/nlohmann/json#supported-compilers"
+        #endif
+    #endif
+#endif
+
+// C++ language standard detection
+// if the user manually specified the used c++ version this is skipped
+#if !defined(JSON_HAS_CPP_23) && !defined(JSON_HAS_CPP_20) && !defined(JSON_HAS_CPP_17) && !defined(JSON_HAS_CPP_14) && !defined(JSON_HAS_CPP_11)
+    #if (defined(__cplusplus) && __cplusplus > 202002L) || (defined(_MSVC_LANG) && _MSVC_LANG > 202002L)
+        #define JSON_HAS_CPP_23
+        #define JSON_HAS_CPP_20
+        #define JSON_HAS_CPP_17
+        #define JSON_HAS_CPP_14
+    #elif (defined(__cplusplus) && __cplusplus > 201703L) || (defined(_MSVC_LANG) && _MSVC_LANG > 201703L)
+        #define JSON_HAS_CPP_20
+        #define JSON_HAS_CPP_17
+        #define JSON_HAS_CPP_14
+    #elif (defined(__cplusplus) && __cplusplus > 201402L) || (defined(_HAS_CXX17) && _HAS_CXX17 == 1) // fix for issue #464
+        #define JSON_HAS_CPP_17
+        #define JSON_HAS_CPP_14
+    #elif (defined(__cplusplus) && __cplusplus > 201103L) || (defined(_HAS_CXX14) && _HAS_CXX14 == 1)
+        #define JSON_HAS_CPP_14
+    #endif
+    // the cpp 11 flag is always specified because it is the minimal required version
+    #define JSON_HAS_CPP_11
+#endif
+
+#ifdef __has_include
+    #if __has_include(<version>)
+        #include <version>
+    #endif
+#endif
+
+#if !defined(JSON_HAS_FILESYSTEM) && !defined(JSON_HAS_EXPERIMENTAL_FILESYSTEM)
+    #ifdef JSON_HAS_CPP_17
+        #if defined(__cpp_lib_filesystem)
+            #define JSON_HAS_FILESYSTEM 1
+        #elif defined(__cpp_lib_experimental_filesystem)
+            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1
+        #elif !defined(__has_include)
+            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1
+        #elif __has_include(<filesystem>)
+            #define JSON_HAS_FILESYSTEM 1
+        #elif __has_include(<experimental/filesystem>)
+            #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 1
+        #endif
+
+        // std::filesystem does not work on MinGW GCC 8: https://sourceforge.net/p/mingw-w64/bugs/737/
+        #if defined(__MINGW32__) && defined(__GNUC__) && __GNUC__ == 8
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before GCC 8: https://en.cppreference.com/w/cpp/compiler_support
+        #if defined(__GNUC__) && !defined(__clang__) && __GNUC__ < 8
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before Clang 7: https://en.cppreference.com/w/cpp/compiler_support
+        #if defined(__clang_major__) && __clang_major__ < 7
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before MSVC 19.14: https://en.cppreference.com/w/cpp/compiler_support
+        #if defined(_MSC_VER) && _MSC_VER < 1914
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before iOS 13
+        #if defined(__IPHONE_OS_VERSION_MIN_REQUIRED) && __IPHONE_OS_VERSION_MIN_REQUIRED < 130000
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+
+        // no filesystem support before macOS Catalina
+        #if defined(__MAC_OS_X_VERSION_MIN_REQUIRED) && __MAC_OS_X_VERSION_MIN_REQUIRED < 101500
+            #undef JSON_HAS_FILESYSTEM
+            #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+        #endif
+    #endif
+#endif
+
+#ifndef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+    #define JSON_HAS_EXPERIMENTAL_FILESYSTEM 0
+#endif
+
+#ifndef JSON_HAS_FILESYSTEM
+    #define JSON_HAS_FILESYSTEM 0
+#endif
+
+#ifndef JSON_HAS_THREE_WAY_COMPARISON
+    #if defined(__cpp_impl_three_way_comparison) && __cpp_impl_three_way_comparison >= 201907L \
+        && defined(__cpp_lib_three_way_comparison) && __cpp_lib_three_way_comparison >= 201907L
+        #define JSON_HAS_THREE_WAY_COMPARISON 1
+    #else
+        #define JSON_HAS_THREE_WAY_COMPARISON 0
+    #endif
+#endif
+
+#ifndef JSON_HAS_RANGES
+    // ranges header shipping in GCC 11.1.0 (released 2021-04-27) has syntax error
+    #if defined(__GLIBCXX__) && __GLIBCXX__ == 20210427
+        #define JSON_HAS_RANGES 0
+    #elif defined(__cpp_lib_ranges)
+        #define JSON_HAS_RANGES 1
+    #else
+        #define JSON_HAS_RANGES 0
+    #endif
+#endif
+
+#ifndef JSON_HAS_STATIC_RTTI
+    #if !defined(_HAS_STATIC_RTTI) || _HAS_STATIC_RTTI != 0
+        #define JSON_HAS_STATIC_RTTI 1
+    #else
+        #define JSON_HAS_STATIC_RTTI 0
+    #endif
+#endif
+
+#ifdef JSON_HAS_CPP_17
+    #define JSON_INLINE_VARIABLE inline
+#else
+    #define JSON_INLINE_VARIABLE
+#endif
+
+#if JSON_HEDLEY_HAS_ATTRIBUTE(no_unique_address)
+    #define JSON_NO_UNIQUE_ADDRESS [[no_unique_address]]
+#else
+    #define JSON_NO_UNIQUE_ADDRESS
+#endif
+
+// disable documentation warnings on clang
+#if defined(__clang__)
+    #pragma clang diagnostic push
+    #pragma clang diagnostic ignored "-Wdocumentation"
+    #pragma clang diagnostic ignored "-Wdocumentation-unknown-command"
+#endif
+
+// allow disabling exceptions
+#if (defined(__cpp_exceptions) || defined(__EXCEPTIONS) || defined(_CPPUNWIND)) && !defined(JSON_NOEXCEPTION)
+    #define JSON_THROW(exception) throw exception
+    #define JSON_TRY try
+    #define JSON_CATCH(exception) catch(exception)
+    #define JSON_INTERNAL_CATCH(exception) catch(exception)
+#else
+    #include <cstdlib>
+    #define JSON_THROW(exception) std::abort()
+    #define JSON_TRY if(true)
+    #define JSON_CATCH(exception) if(false)
+    #define JSON_INTERNAL_CATCH(exception) if(false)
+#endif
+
+// override exception macros
+#if defined(JSON_THROW_USER)
+    #undef JSON_THROW
+    #define JSON_THROW JSON_THROW_USER
+#endif
+#if defined(JSON_TRY_USER)
+    #undef JSON_TRY
+    #define JSON_TRY JSON_TRY_USER
+#endif
+#if defined(JSON_CATCH_USER)
+    #undef JSON_CATCH
+    #define JSON_CATCH JSON_CATCH_USER
+    #undef JSON_INTERNAL_CATCH
+    #define JSON_INTERNAL_CATCH JSON_CATCH_USER
+#endif
+#if defined(JSON_INTERNAL_CATCH_USER)
+    #undef JSON_INTERNAL_CATCH
+    #define JSON_INTERNAL_CATCH JSON_INTERNAL_CATCH_USER
+#endif
+
+// allow overriding assert
+#if !defined(JSON_ASSERT)
+    #include <cassert> // assert
+    #define JSON_ASSERT(x) assert(x)
+#endif
+
+// allow to access some private functions (needed by the test suite)
+#if defined(JSON_TESTS_PRIVATE)
+    #define JSON_PRIVATE_UNLESS_TESTED public
+#else
+    #define JSON_PRIVATE_UNLESS_TESTED private
+#endif
+
+/*!
+@brief macro to briefly define a mapping between an enum and JSON
+@def NLOHMANN_JSON_SERIALIZE_ENUM
+@since version 3.4.0
+*/
+#define NLOHMANN_JSON_SERIALIZE_ENUM(ENUM_TYPE, ...)                                            \
+    template<typename BasicJsonType>                                                            \
+    inline void to_json(BasicJsonType& j, const ENUM_TYPE& e)                                   \
+    {                                                                                           \
+        /* NOLINTNEXTLINE(modernize-type-traits) we use C++11 */                                \
+        static_assert(std::is_enum<ENUM_TYPE>::value, #ENUM_TYPE " must be an enum!");          \
+        /* NOLINTNEXTLINE(modernize-avoid-c-arrays) we don't want to depend on <array> */       \
+        static const std::pair<ENUM_TYPE, BasicJsonType> m[] = __VA_ARGS__;                     \
+        auto it = std::find_if(std::begin(m), std::end(m),                                      \
+                               [e](const std::pair<ENUM_TYPE, BasicJsonType>& ej_pair) -> bool  \
+        {                                                                                       \
+            return ej_pair.first == e;                                                          \
+        });                                                                                     \
+        j = ((it != std::end(m)) ? it : std::begin(m))->second;                                 \
+    }                                                                                           \
+    template<typename BasicJsonType>                                                            \
+    inline void from_json(const BasicJsonType& j, ENUM_TYPE& e)                                 \
+    {                                                                                           \
+        /* NOLINTNEXTLINE(modernize-type-traits) we use C++11 */                                \
+        static_assert(std::is_enum<ENUM_TYPE>::value, #ENUM_TYPE " must be an enum!");          \
+        /* NOLINTNEXTLINE(modernize-avoid-c-arrays) we don't want to depend on <array> */       \
+        static const std::pair<ENUM_TYPE, BasicJsonType> m[] = __VA_ARGS__;                     \
+        auto it = std::find_if(std::begin(m), std::end(m),                                      \
+                               [&j](const std::pair<ENUM_TYPE, BasicJsonType>& ej_pair) -> bool \
+        {                                                                                       \
+            return ej_pair.second == j;                                                         \
+        });                                                                                     \
+        e = ((it != std::end(m)) ? it : std::begin(m))->first;                                  \
+    }
+
+// Ugly macros to avoid uglier copy-paste when specializing basic_json. They
+// may be removed in the future once the class is split.
+
+#define NLOHMANN_BASIC_JSON_TPL_DECLARATION                                \
+    template<template<typename, typename, typename...> class ObjectType,   \
+             template<typename, typename...> class ArrayType,              \
+             class StringType, class BooleanType, class NumberIntegerType, \
+             class NumberUnsignedType, class NumberFloatType,              \
+             template<typename> class AllocatorType,                       \
+             template<typename, typename = void> class JSONSerializer,     \
+             class BinaryType,                                             \
+             class CustomBaseClass>
+
+#define NLOHMANN_BASIC_JSON_TPL                                            \
+    basic_json<ObjectType, ArrayType, StringType, BooleanType,             \
+    NumberIntegerType, NumberUnsignedType, NumberFloatType,                \
+    AllocatorType, JSONSerializer, BinaryType, CustomBaseClass>
+
+// Macros to simplify conversion from/to types
+
+#define NLOHMANN_JSON_EXPAND( x ) x
+#define NLOHMANN_JSON_GET_MACRO(_1, _2, _3, _4, _5, _6, _7, _8, _9, _10, _11, _12, _13, _14, _15, _16, _17, _18, _19, _20, _21, _22, _23, _24, _25, _26, _27, _28, _29, _30, _31, _32, _33, _34, _35, _36, _37, _38, _39, _40, _41, _42, _43, _44, _45, _46, _47, _48, _49, _50, _51, _52, _53, _54, _55, _56, _57, _58, _59, _60, _61, _62, _63, _64, NAME,...) NAME
+#define NLOHMANN_JSON_PASTE(...) NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_GET_MACRO(__VA_ARGS__, \
+        NLOHMANN_JSON_PASTE64, \
+        NLOHMANN_JSON_PASTE63, \
+        NLOHMANN_JSON_PASTE62, \
+        NLOHMANN_JSON_PASTE61, \
+        NLOHMANN_JSON_PASTE60, \
+        NLOHMANN_JSON_PASTE59, \
+        NLOHMANN_JSON_PASTE58, \
+        NLOHMANN_JSON_PASTE57, \
+        NLOHMANN_JSON_PASTE56, \
+        NLOHMANN_JSON_PASTE55, \
+        NLOHMANN_JSON_PASTE54, \
+        NLOHMANN_JSON_PASTE53, \
+        NLOHMANN_JSON_PASTE52, \
+        NLOHMANN_JSON_PASTE51, \
+        NLOHMANN_JSON_PASTE50, \
+        NLOHMANN_JSON_PASTE49, \
+        NLOHMANN_JSON_PASTE48, \
+        NLOHMANN_JSON_PASTE47, \
+        NLOHMANN_JSON_PASTE46, \
+        NLOHMANN_JSON_PASTE45, \
+        NLOHMANN_JSON_PASTE44, \
+        NLOHMANN_JSON_PASTE43, \
+        NLOHMANN_JSON_PASTE42, \
+        NLOHMANN_JSON_PASTE41, \
+        NLOHMANN_JSON_PASTE40, \
+        NLOHMANN_JSON_PASTE39, \
+        NLOHMANN_JSON_PASTE38, \
+        NLOHMANN_JSON_PASTE37, \
+        NLOHMANN_JSON_PASTE36, \
+        NLOHMANN_JSON_PASTE35, \
+        NLOHMANN_JSON_PASTE34, \
+        NLOHMANN_JSON_PASTE33, \
+        NLOHMANN_JSON_PASTE32, \
+        NLOHMANN_JSON_PASTE31, \
+        NLOHMANN_JSON_PASTE30, \
+        NLOHMANN_JSON_PASTE29, \
+        NLOHMANN_JSON_PASTE28, \
+        NLOHMANN_JSON_PASTE27, \
+        NLOHMANN_JSON_PASTE26, \
+        NLOHMANN_JSON_PASTE25, \
+        NLOHMANN_JSON_PASTE24, \
+        NLOHMANN_JSON_PASTE23, \
+        NLOHMANN_JSON_PASTE22, \
+        NLOHMANN_JSON_PASTE21, \
+        NLOHMANN_JSON_PASTE20, \
+        NLOHMANN_JSON_PASTE19, \
+        NLOHMANN_JSON_PASTE18, \
+        NLOHMANN_JSON_PASTE17, \
+        NLOHMANN_JSON_PASTE16, \
+        NLOHMANN_JSON_PASTE15, \
+        NLOHMANN_JSON_PASTE14, \
+        NLOHMANN_JSON_PASTE13, \
+        NLOHMANN_JSON_PASTE12, \
+        NLOHMANN_JSON_PASTE11, \
+        NLOHMANN_JSON_PASTE10, \
+        NLOHMANN_JSON_PASTE9, \
+        NLOHMANN_JSON_PASTE8, \
+        NLOHMANN_JSON_PASTE7, \
+        NLOHMANN_JSON_PASTE6, \
+        NLOHMANN_JSON_PASTE5, \
+        NLOHMANN_JSON_PASTE4, \
+        NLOHMANN_JSON_PASTE3, \
+        NLOHMANN_JSON_PASTE2, \
+        NLOHMANN_JSON_PASTE1)(__VA_ARGS__))
+#define NLOHMANN_JSON_PASTE2(func, v1) func(v1)
+#define NLOHMANN_JSON_PASTE3(func, v1, v2) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE2(func, v2)
+#define NLOHMANN_JSON_PASTE4(func, v1, v2, v3) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE3(func, v2, v3)
+#define NLOHMANN_JSON_PASTE5(func, v1, v2, v3, v4) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE4(func, v2, v3, v4)
+#define NLOHMANN_JSON_PASTE6(func, v1, v2, v3, v4, v5) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE5(func, v2, v3, v4, v5)
+#define NLOHMANN_JSON_PASTE7(func, v1, v2, v3, v4, v5, v6) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE6(func, v2, v3, v4, v5, v6)
+#define NLOHMANN_JSON_PASTE8(func, v1, v2, v3, v4, v5, v6, v7) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE7(func, v2, v3, v4, v5, v6, v7)
+#define NLOHMANN_JSON_PASTE9(func, v1, v2, v3, v4, v5, v6, v7, v8) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE8(func, v2, v3, v4, v5, v6, v7, v8)
+#define NLOHMANN_JSON_PASTE10(func, v1, v2, v3, v4, v5, v6, v7, v8, v9) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE9(func, v2, v3, v4, v5, v6, v7, v8, v9)
+#define NLOHMANN_JSON_PASTE11(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE10(func, v2, v3, v4, v5, v6, v7, v8, v9, v10)
+#define NLOHMANN_JSON_PASTE12(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE11(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11)
+#define NLOHMANN_JSON_PASTE13(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE12(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12)
+#define NLOHMANN_JSON_PASTE14(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE13(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13)
+#define NLOHMANN_JSON_PASTE15(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE14(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14)
+#define NLOHMANN_JSON_PASTE16(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE15(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15)
+#define NLOHMANN_JSON_PASTE17(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE16(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16)
+#define NLOHMANN_JSON_PASTE18(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE17(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17)
+#define NLOHMANN_JSON_PASTE19(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE18(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18)
+#define NLOHMANN_JSON_PASTE20(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE19(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19)
+#define NLOHMANN_JSON_PASTE21(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE20(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20)
+#define NLOHMANN_JSON_PASTE22(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE21(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21)
+#define NLOHMANN_JSON_PASTE23(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE22(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22)
+#define NLOHMANN_JSON_PASTE24(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE23(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23)
+#define NLOHMANN_JSON_PASTE25(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE24(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24)
+#define NLOHMANN_JSON_PASTE26(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE25(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25)
+#define NLOHMANN_JSON_PASTE27(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE26(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26)
+#define NLOHMANN_JSON_PASTE28(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE27(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27)
+#define NLOHMANN_JSON_PASTE29(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE28(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28)
+#define NLOHMANN_JSON_PASTE30(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE29(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29)
+#define NLOHMANN_JSON_PASTE31(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE30(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30)
+#define NLOHMANN_JSON_PASTE32(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE31(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31)
+#define NLOHMANN_JSON_PASTE33(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE32(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32)
+#define NLOHMANN_JSON_PASTE34(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE33(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33)
+#define NLOHMANN_JSON_PASTE35(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE34(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34)
+#define NLOHMANN_JSON_PASTE36(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE35(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35)
+#define NLOHMANN_JSON_PASTE37(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE36(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36)
+#define NLOHMANN_JSON_PASTE38(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE37(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37)
+#define NLOHMANN_JSON_PASTE39(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE38(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38)
+#define NLOHMANN_JSON_PASTE40(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE39(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39)
+#define NLOHMANN_JSON_PASTE41(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE40(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40)
+#define NLOHMANN_JSON_PASTE42(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE41(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41)
+#define NLOHMANN_JSON_PASTE43(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE42(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42)
+#define NLOHMANN_JSON_PASTE44(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE43(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43)
+#define NLOHMANN_JSON_PASTE45(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE44(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44)
+#define NLOHMANN_JSON_PASTE46(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE45(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45)
+#define NLOHMANN_JSON_PASTE47(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE46(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46)
+#define NLOHMANN_JSON_PASTE48(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE47(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47)
+#define NLOHMANN_JSON_PASTE49(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE48(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48)
+#define NLOHMANN_JSON_PASTE50(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE49(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49)
+#define NLOHMANN_JSON_PASTE51(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE50(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50)
+#define NLOHMANN_JSON_PASTE52(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE51(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51)
+#define NLOHMANN_JSON_PASTE53(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE52(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52)
+#define NLOHMANN_JSON_PASTE54(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE53(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53)
+#define NLOHMANN_JSON_PASTE55(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE54(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54)
+#define NLOHMANN_JSON_PASTE56(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE55(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55)
+#define NLOHMANN_JSON_PASTE57(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE56(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56)
+#define NLOHMANN_JSON_PASTE58(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE57(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57)
+#define NLOHMANN_JSON_PASTE59(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE58(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58)
+#define NLOHMANN_JSON_PASTE60(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE59(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59)
+#define NLOHMANN_JSON_PASTE61(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE60(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60)
+#define NLOHMANN_JSON_PASTE62(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE61(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61)
+#define NLOHMANN_JSON_PASTE63(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE62(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62)
+#define NLOHMANN_JSON_PASTE64(func, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63) NLOHMANN_JSON_PASTE2(func, v1) NLOHMANN_JSON_PASTE63(func, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27, v28, v29, v30, v31, v32, v33, v34, v35, v36, v37, v38, v39, v40, v41, v42, v43, v44, v45, v46, v47, v48, v49, v50, v51, v52, v53, v54, v55, v56, v57, v58, v59, v60, v61, v62, v63)
+
+#define NLOHMANN_JSON_TO(v1) nlohmann_json_j[#v1] = nlohmann_json_t.v1;
+#define NLOHMANN_JSON_FROM(v1) nlohmann_json_j.at(#v1).get_to(nlohmann_json_t.v1);
+#define NLOHMANN_JSON_FROM_WITH_DEFAULT(v1) nlohmann_json_t.v1 = !nlohmann_json_j.is_null() ? nlohmann_json_j.value(#v1, nlohmann_json_default_obj.v1) : nlohmann_json_default_obj.v1;
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_INTRUSIVE
+@since version 3.9.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_INTRUSIVE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_INTRUSIVE_WITH_DEFAULT
+@since version 3.11.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_INTRUSIVE_WITH_DEFAULT(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.11.3
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_INTRUSIVE_ONLY_SERIALIZE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE
+@since version 3.9.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_non_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_WITH_DEFAULT
+@since version 3.11.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_non_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_WITH_DEFAULT(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.11.3
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_type_non_intrusive/
+*/
+#define NLOHMANN_DEFINE_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE(Type, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_WITH_DEFAULT
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_WITH_DEFAULT(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType&>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_INTRUSIVE_ONLY_SERIALIZE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    friend void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_WITH_DEFAULT
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_WITH_DEFAULT(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) } \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void from_json(const BasicJsonType& nlohmann_json_j, Type& nlohmann_json_t) { nlohmann::from_json(nlohmann_json_j, static_cast<BaseType&>(nlohmann_json_t)); const Type nlohmann_json_default_obj{}; NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_FROM_WITH_DEFAULT, __VA_ARGS__)) }
+
+/*!
+@brief macro
+@def NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE
+@since version 3.12.0
+@sa https://json.nlohmann.me/api/macros/nlohmann_define_derived_type/
+*/
+#define NLOHMANN_DEFINE_DERIVED_TYPE_NON_INTRUSIVE_ONLY_SERIALIZE(Type, BaseType, ...)  \
+    template<typename BasicJsonType, nlohmann::detail::enable_if_t<nlohmann::detail::is_basic_json<BasicJsonType>::value, int> = 0> \
+    void to_json(BasicJsonType& nlohmann_json_j, const Type& nlohmann_json_t) { nlohmann::to_json(nlohmann_json_j, static_cast<const BaseType &>(nlohmann_json_t)); NLOHMANN_JSON_EXPAND(NLOHMANN_JSON_PASTE(NLOHMANN_JSON_TO, __VA_ARGS__)) }
+
+// inspired from https://stackoverflow.com/a/26745591
+// allows calling any std function as if (e.g., with begin):
+// using std::begin; begin(x);
+//
+// it allows using the detected idiom to retrieve the return type
+// of such an expression
+#define NLOHMANN_CAN_CALL_STD_FUNC_IMPL(std_name)                                 \
+    namespace detail {                                                            \
+    using std::std_name;                                                          \
+    \
+    template<typename... T>                                                       \
+    using result_of_##std_name = decltype(std_name(std::declval<T>()...));        \
+    }                                                                             \
+    \
+    namespace detail2 {                                                           \
+    struct std_name##_tag                                                         \
+    {                                                                             \
+    };                                                                            \
+    \
+    template<typename... T>                                                       \
+    std_name##_tag std_name(T&&...);                                              \
+    \
+    template<typename... T>                                                       \
+    using result_of_##std_name = decltype(std_name(std::declval<T>()...));        \
+    \
+    template<typename... T>                                                       \
+    struct would_call_std_##std_name                                              \
+    {                                                                             \
+        static constexpr auto const value = ::nlohmann::detail::                  \
+                                            is_detected_exact<std_name##_tag, result_of_##std_name, T...>::value; \
+    };                                                                            \
+    } /* namespace detail2 */ \
+    \
+    template<typename... T>                                                       \
+    struct would_call_std_##std_name : detail2::would_call_std_##std_name<T...>   \
+    {                                                                             \
+    }
+
+#ifndef JSON_USE_IMPLICIT_CONVERSIONS
+    #define JSON_USE_IMPLICIT_CONVERSIONS 1
+#endif
+
+#if JSON_USE_IMPLICIT_CONVERSIONS
+    #define JSON_EXPLICIT
+#else
+    #define JSON_EXPLICIT explicit
+#endif
+
+#ifndef JSON_DISABLE_ENUM_SERIALIZATION
+    #define JSON_DISABLE_ENUM_SERIALIZATION 0
+#endif
+
+#ifndef JSON_USE_GLOBAL_UDLS
+    #define JSON_USE_GLOBAL_UDLS 1
+#endif
+
+#if JSON_HAS_THREE_WAY_COMPARISON
+    #include <compare> // partial_ordering
+#endif
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+///////////////////////////
+// JSON type enumeration //
+///////////////////////////
+
+/*!
+@brief the JSON type enumeration
+
+This enumeration collects the different JSON types. It is internally used to
+distinguish the stored values, and the functions @ref basic_json::is_null(),
+@ref basic_json::is_object(), @ref basic_json::is_array(),
+@ref basic_json::is_string(), @ref basic_json::is_boolean(),
+@ref basic_json::is_number() (with @ref basic_json::is_number_integer(),
+@ref basic_json::is_number_unsigned(), and @ref basic_json::is_number_float()),
+@ref basic_json::is_discarded(), @ref basic_json::is_primitive(), and
+@ref basic_json::is_structured() rely on it.
+
+@note There are three enumeration entries (number_integer, number_unsigned, and
+number_float), because the library distinguishes these three types for numbers:
+@ref basic_json::number_unsigned_t is used for unsigned integers,
+@ref basic_json::number_integer_t is used for signed integers, and
+@ref basic_json::number_float_t is used for floating-point numbers or to
+approximate integers which do not fit in the limits of their respective type.
+
+@sa see @ref basic_json::basic_json(const value_t value_type) -- create a JSON
+value with the default value for a given type
+
+@since version 1.0.0
+*/
+enum class value_t : std::uint8_t
+{
+    null,             ///< null value
+    object,           ///< object (unordered set of name/value pairs)
+    array,            ///< array (ordered collection of values)
+    string,           ///< string value
+    boolean,          ///< boolean value
+    number_integer,   ///< number value (signed integer)
+    number_unsigned,  ///< number value (unsigned integer)
+    number_float,     ///< number value (floating-point)
+    binary,           ///< binary array (ordered collection of bytes)
+    discarded         ///< discarded by the parser callback function
+};
+
+/*!
+@brief comparison operator for JSON types
+
+Returns an ordering that is similar to Python:
+- order: null < boolean < number < object < array < string < binary
+- furthermore, each type is not smaller than itself
+- discarded values are not comparable
+- binary is represented as a b"" string in python and directly comparable to a
+  string; however, making a binary array directly comparable with a string would
+  be surprising behavior in a JSON file.
+
+@since version 1.0.0
+*/
+#if JSON_HAS_THREE_WAY_COMPARISON
+    inline std::partial_ordering operator<=>(const value_t lhs, const value_t rhs) noexcept // *NOPAD*
+#else
+    inline bool operator<(const value_t lhs, const value_t rhs) noexcept
+#endif
+{
+    static constexpr std::array<std::uint8_t, 9> order = {{
+            0 /* null */, 3 /* object */, 4 /* array */, 5 /* string */,
+            1 /* boolean */, 2 /* integer */, 2 /* unsigned */, 2 /* float */,
+            6 /* binary */
+        }
+    };
+
+    const auto l_index = static_cast<std::size_t>(lhs);
+    const auto r_index = static_cast<std::size_t>(rhs);
+#if JSON_HAS_THREE_WAY_COMPARISON
+    if (l_index < order.size() && r_index < order.size())
+    {
+        return order[l_index] <=> order[r_index]; // *NOPAD*
+    }
+    return std::partial_ordering::unordered;
+#else
+    return l_index < order.size() && r_index < order.size() && order[l_index] < order[r_index];
+#endif
+}
+
+// GCC selects the built-in operator< over an operator rewritten from
+// a user-defined spaceship operator
+// Clang, MSVC, and ICC select the rewritten candidate
+// (see GCC bug https://gcc.gnu.org/bugzilla/show_bug.cgi?id=105200)
+#if JSON_HAS_THREE_WAY_COMPARISON && defined(__GNUC__)
+inline bool operator<(const value_t lhs, const value_t rhs) noexcept
+{
+    return std::is_lt(lhs <=> rhs); // *NOPAD*
+}
+#endif
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/string_escape.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief replace all occurrences of a substring by another string
+
+@param[in,out] s  the string to manipulate; changed so that all
+               occurrences of @a f are replaced with @a t
+@param[in]     f  the substring to replace with @a t
+@param[in]     t  the string to replace @a f
+
+@pre The search string @a f must not be empty. **This precondition is
+enforced with an assertion.**
+
+@since version 2.0.0
+*/
+template<typename StringType>
+inline void replace_substring(StringType& s, const StringType& f,
+                              const StringType& t)
+{
+    JSON_ASSERT(!f.empty());
+    for (auto pos = s.find(f);                // find first occurrence of f
+            pos != StringType::npos;          // make sure f was found
+            s.replace(pos, f.size(), t),      // replace with t, and
+            pos = s.find(f, pos + t.size()))  // find next occurrence of f
+    {}
+}
+
+/*!
+ * @brief string escaping as described in RFC 6901 (Sect. 4)
+ * @param[in] s string to escape
+ * @return    escaped string
+ *
+ * Note the order of escaping "~" to "~0" and "/" to "~1" is important.
+ */
+template<typename StringType>
+inline StringType escape(StringType s)
+{
+    replace_substring(s, StringType{"~"}, StringType{"~0"});
+    replace_substring(s, StringType{"/"}, StringType{"~1"});
+    return s;
+}
+
+/*!
+ * @brief string unescaping as described in RFC 6901 (Sect. 4)
+ * @param[in] s string to unescape
+ * @return    unescaped string
+ *
+ * Note the order of escaping "~1" to "/" and "~0" to "~" is important.
+ */
+template<typename StringType>
+static void unescape(StringType& s)
+{
+    replace_substring(s, StringType{"~1"}, StringType{"/"});
+    replace_substring(s, StringType{"~0"}, StringType{"~"});
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/position_t.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // size_t
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// struct to capture the start position of the current token
+struct position_t
+{
+    /// the total number of characters read
+    std::size_t chars_read_total = 0;
+    /// the number of characters read in the current line
+    std::size_t chars_read_current_line = 0;
+    /// the number of lines read
+    std::size_t lines_read = 0;
+
+    /// conversion to size_t to preserve SAX interface
+    constexpr operator size_t() const
+    {
+        return chars_read_total;
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-FileCopyrightText: 2018 The Abseil Authors
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstddef> // size_t
+#include <type_traits> // conditional, enable_if, false_type, integral_constant, is_constructible, is_integral, is_same, remove_cv, remove_reference, true_type
+#include <utility> // index_sequence, make_index_sequence, index_sequence_for
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename T>
+using uncvref_t = typename std::remove_cv<typename std::remove_reference<T>::type>::type;
+
+#ifdef JSON_HAS_CPP_14
+
+// the following utilities are natively available in C++14
+using std::enable_if_t;
+using std::index_sequence;
+using std::make_index_sequence;
+using std::index_sequence_for;
+
+#else
+
+// alias templates to reduce boilerplate
+template<bool B, typename T = void>
+using enable_if_t = typename std::enable_if<B, T>::type;
+
+// The following code is taken from https://github.com/abseil/abseil-cpp/blob/10cb35e459f5ecca5b2ff107635da0bfa41011b4/absl/utility/utility.h
+// which is part of Google Abseil (https://github.com/abseil/abseil-cpp), licensed under the Apache License 2.0.
+
+//// START OF CODE FROM GOOGLE ABSEIL
+
+// integer_sequence
+//
+// Class template representing a compile-time integer sequence. An instantiation
+// of `integer_sequence<T, Ints...>` has a sequence of integers encoded in its
+// type through its template arguments (which is a common need when
+// working with C++11 variadic templates). `absl::integer_sequence` is designed
+// to be a drop-in replacement for C++14's `std::integer_sequence`.
+//
+// Example:
+//
+//   template< class T, T... Ints >
+//   void user_function(integer_sequence<T, Ints...>);
+//
+//   int main()
+//   {
+//     // user_function's `T` will be deduced to `int` and `Ints...`
+//     // will be deduced to `0, 1, 2, 3, 4`.
+//     user_function(make_integer_sequence<int, 5>());
+//   }
+template <typename T, T... Ints>
+struct integer_sequence
+{
+    using value_type = T;
+    static constexpr std::size_t size() noexcept
+    {
+        return sizeof...(Ints);
+    }
+};
+
+// index_sequence
+//
+// A helper template for an `integer_sequence` of `size_t`,
+// `absl::index_sequence` is designed to be a drop-in replacement for C++14's
+// `std::index_sequence`.
+template <size_t... Ints>
+using index_sequence = integer_sequence<size_t, Ints...>;
+
+namespace utility_internal
+{
+
+template <typename Seq, size_t SeqSize, size_t Rem>
+struct Extend;
+
+// Note that SeqSize == sizeof...(Ints). It's passed explicitly for efficiency.
+template <typename T, T... Ints, size_t SeqSize>
+struct Extend<integer_sequence<T, Ints...>, SeqSize, 0>
+{
+    using type = integer_sequence < T, Ints..., (Ints + SeqSize)... >;
+};
+
+template <typename T, T... Ints, size_t SeqSize>
+struct Extend<integer_sequence<T, Ints...>, SeqSize, 1>
+{
+    using type = integer_sequence < T, Ints..., (Ints + SeqSize)..., 2 * SeqSize >;
+};
+
+// Recursion helper for 'make_integer_sequence<T, N>'.
+// 'Gen<T, N>::type' is an alias for 'integer_sequence<T, 0, 1, ... N-1>'.
+template <typename T, size_t N>
+struct Gen
+{
+    using type =
+        typename Extend < typename Gen < T, N / 2 >::type, N / 2, N % 2 >::type;
+};
+
+template <typename T>
+struct Gen<T, 0>
+{
+    using type = integer_sequence<T>;
+};
+
+}  // namespace utility_internal
+
+// Compile-time sequences of integers
+
+// make_integer_sequence
+//
+// This template alias is equivalent to
+// `integer_sequence<int, 0, 1, ..., N-1>`, and is designed to be a drop-in
+// replacement for C++14's `std::make_integer_sequence`.
+template <typename T, T N>
+using make_integer_sequence = typename utility_internal::Gen<T, N>::type;
+
+// make_index_sequence
+//
+// This template alias is equivalent to `index_sequence<0, 1, ..., N-1>`,
+// and is designed to be a drop-in replacement for C++14's
+// `std::make_index_sequence`.
+template <size_t N>
+using make_index_sequence = make_integer_sequence<size_t, N>;
+
+// index_sequence_for
+//
+// Converts a typename pack into an index sequence of the same length, and
+// is designed to be a drop-in replacement for C++14's
+// `std::index_sequence_for()`
+template <typename... Ts>
+using index_sequence_for = make_index_sequence<sizeof...(Ts)>;
+
+//// END OF CODE FROM GOOGLE ABSEIL
+
+#endif
+
+// dispatch utility (taken from ranges-v3)
+template<unsigned N> struct priority_tag : priority_tag < N - 1 > {};
+template<> struct priority_tag<0> {};
+
+// taken from ranges-v3
+template<typename T>
+struct static_const
+{
+    static JSON_INLINE_VARIABLE constexpr T value{};
+};
+
+#ifndef JSON_HAS_CPP_17
+    template<typename T>
+    constexpr T static_const<T>::value;
+#endif
+
+template<typename T, typename... Args>
+constexpr std::array<T, sizeof...(Args)> make_array(Args&& ... args)
+{
+    return std::array<T, sizeof...(Args)> {{static_cast<T>(std::forward<Args>(args))...}};
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <limits> // numeric_limits
+#include <string> // char_traits
+#include <tuple> // tuple
+#include <type_traits> // false_type, is_constructible, is_integral, is_same, true_type
+#include <utility> // declval
+
+// #include <nlohmann/detail/iterators/iterator_traits.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <iterator> // random_access_iterator_tag
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/void_t.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename It, typename = void>
+struct iterator_types {};
+
+template<typename It>
+struct iterator_types <
+    It,
+    void_t<typename It::difference_type, typename It::value_type, typename It::pointer,
+    typename It::reference, typename It::iterator_category >>
+{
+    using difference_type = typename It::difference_type;
+    using value_type = typename It::value_type;
+    using pointer = typename It::pointer;
+    using reference = typename It::reference;
+    using iterator_category = typename It::iterator_category;
+};
+
+// This is required as some compilers implement std::iterator_traits in a way that
+// doesn't work with SFINAE. See https://github.com/nlohmann/json/issues/1341.
+template<typename T, typename = void>
+struct iterator_traits
+{
+};
+
+template<typename T>
+struct iterator_traits < T, enable_if_t < !std::is_pointer<T>::value >>
+    : iterator_types<T>
+{
+};
+
+template<typename T>
+struct iterator_traits<T*, enable_if_t<std::is_object<T>::value>>
+{
+    using iterator_category = std::random_access_iterator_tag;
+    using value_type = T;
+    using difference_type = ptrdiff_t;
+    using pointer = T*;
+    using reference = T&;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/call_std/begin.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+NLOHMANN_CAN_CALL_STD_FUNC_IMPL(begin);
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/call_std/end.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+NLOHMANN_CAN_CALL_STD_FUNC_IMPL(end);
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/detected.hpp>
+
+// #include <nlohmann/json_fwd.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+#ifndef INCLUDE_NLOHMANN_JSON_FWD_HPP_
+    #define INCLUDE_NLOHMANN_JSON_FWD_HPP_
+
+    #include <cstdint> // int64_t, uint64_t
+    #include <map> // map
+    #include <memory> // allocator
+    #include <string> // string
+    #include <vector> // vector
+
+    // #include <nlohmann/detail/abi_macros.hpp>
+
+
+    /*!
+    @brief namespace for Niels Lohmann
+    @see https://github.com/nlohmann
+    @since version 1.0.0
+    */
+    NLOHMANN_JSON_NAMESPACE_BEGIN
+
+    /*!
+    @brief default JSONSerializer template argument
+
+    This serializer ignores the template arguments and uses ADL
+    ([argument-dependent lookup](https://en.cppreference.com/w/cpp/language/adl))
+    for serialization.
+    */
+    template<typename T = void, typename SFINAE = void>
+    struct adl_serializer;
+
+    /// a class to store JSON values
+    /// @sa https://json.nlohmann.me/api/basic_json/
+    template<template<typename U, typename V, typename... Args> class ObjectType =
+    std::map,
+    template<typename U, typename... Args> class ArrayType = std::vector,
+    class StringType = std::string, class BooleanType = bool,
+    class NumberIntegerType = std::int64_t,
+    class NumberUnsignedType = std::uint64_t,
+    class NumberFloatType = double,
+    template<typename U> class AllocatorType = std::allocator,
+    template<typename T, typename SFINAE = void> class JSONSerializer =
+    adl_serializer,
+    class BinaryType = std::vector<std::uint8_t>, // cppcheck-suppress syntaxError
+    class CustomBaseClass = void>
+    class basic_json;
+
+    /// @brief JSON Pointer defines a string syntax for identifying a specific value within a JSON document
+    /// @sa https://json.nlohmann.me/api/json_pointer/
+    template<typename RefStringType>
+    class json_pointer;
+
+    /*!
+    @brief default specialization
+    @sa https://json.nlohmann.me/api/json/
+    */
+    using json = basic_json<>;
+
+    /// @brief a minimal map-like container that preserves insertion order
+    /// @sa https://json.nlohmann.me/api/ordered_map/
+    template<class Key, class T, class IgnoredLess, class Allocator>
+    struct ordered_map;
+
+    /// @brief specialization that maintains the insertion order of object keys
+    /// @sa https://json.nlohmann.me/api/ordered_json/
+    using ordered_json = basic_json<nlohmann::ordered_map>;
+
+    NLOHMANN_JSON_NAMESPACE_END
+
+#endif  // INCLUDE_NLOHMANN_JSON_FWD_HPP_
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+/*!
+@brief detail namespace with internal helper functions
+
+This namespace collects functions that should not be exposed,
+implementations of some @ref basic_json methods, and meta-programming helpers.
+
+@since version 2.1.0
+*/
+namespace detail
+{
+
+/////////////
+// helpers //
+/////////////
+
+// Note to maintainers:
+//
+// Every trait in this file expects a non CV-qualified type.
+// The only exceptions are in the 'aliases for detected' section
+// (i.e. those of the form: decltype(T::member_function(std::declval<T>())))
+//
+// In this case, T has to be properly CV-qualified to constraint the function arguments
+// (e.g. to_json(BasicJsonType&, const T&))
+
+template<typename> struct is_basic_json : std::false_type {};
+
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+struct is_basic_json<NLOHMANN_BASIC_JSON_TPL> : std::true_type {};
+
+// used by exceptions create() member functions
+// true_type for pointer to possibly cv-qualified basic_json or std::nullptr_t
+// false_type otherwise
+template<typename BasicJsonContext>
+struct is_basic_json_context :
+    std::integral_constant < bool,
+    is_basic_json<typename std::remove_cv<typename std::remove_pointer<BasicJsonContext>::type>::type>::value
+    || std::is_same<BasicJsonContext, std::nullptr_t>::value >
+{};
+
+//////////////////////
+// json_ref helpers //
+//////////////////////
+
+template<typename>
+class json_ref;
+
+template<typename>
+struct is_json_ref : std::false_type {};
+
+template<typename T>
+struct is_json_ref<json_ref<T>> : std::true_type {};
+
+//////////////////////////
+// aliases for detected //
+//////////////////////////
+
+template<typename T>
+using mapped_type_t = typename T::mapped_type;
+
+template<typename T>
+using key_type_t = typename T::key_type;
+
+template<typename T>
+using value_type_t = typename T::value_type;
+
+template<typename T>
+using difference_type_t = typename T::difference_type;
+
+template<typename T>
+using pointer_t = typename T::pointer;
+
+template<typename T>
+using reference_t = typename T::reference;
+
+template<typename T>
+using iterator_category_t = typename T::iterator_category;
+
+template<typename T, typename... Args>
+using to_json_function = decltype(T::to_json(std::declval<Args>()...));
+
+template<typename T, typename... Args>
+using from_json_function = decltype(T::from_json(std::declval<Args>()...));
+
+template<typename T, typename U>
+using get_template_function = decltype(std::declval<T>().template get<U>());
+
+// trait checking if JSONSerializer<T>::from_json(json const&, udt&) exists
+template<typename BasicJsonType, typename T, typename = void>
+struct has_from_json : std::false_type {};
+
+// trait checking if j.get<T> is valid
+// use this trait instead of std::is_constructible or std::is_convertible,
+// both rely on, or make use of implicit conversions, and thus fail when T
+// has several constructors/operator= (see https://github.com/nlohmann/json/issues/958)
+template <typename BasicJsonType, typename T>
+struct is_getable
+{
+    static constexpr bool value = is_detected<get_template_function, const BasicJsonType&, T>::value;
+};
+
+template<typename BasicJsonType, typename T>
+struct has_from_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>
+{
+    using serializer = typename BasicJsonType::template json_serializer<T, void>;
+
+    static constexpr bool value =
+        is_detected_exact<void, from_json_function, serializer,
+        const BasicJsonType&, T&>::value;
+};
+
+// This trait checks if JSONSerializer<T>::from_json(json const&) exists
+// this overload is used for non-default-constructible user-defined-types
+template<typename BasicJsonType, typename T, typename = void>
+struct has_non_default_from_json : std::false_type {};
+
+template<typename BasicJsonType, typename T>
+struct has_non_default_from_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>
+{
+    using serializer = typename BasicJsonType::template json_serializer<T, void>;
+
+    static constexpr bool value =
+        is_detected_exact<T, from_json_function, serializer,
+        const BasicJsonType&>::value;
+};
+
+// This trait checks if BasicJsonType::json_serializer<T>::to_json exists
+// Do not evaluate the trait when T is a basic_json type, to avoid template instantiation infinite recursion.
+template<typename BasicJsonType, typename T, typename = void>
+struct has_to_json : std::false_type {};
+
+template<typename BasicJsonType, typename T>
+struct has_to_json < BasicJsonType, T, enable_if_t < !is_basic_json<T>::value >>
+{
+    using serializer = typename BasicJsonType::template json_serializer<T, void>;
+
+    static constexpr bool value =
+        is_detected_exact<void, to_json_function, serializer, BasicJsonType&,
+        T>::value;
+};
+
+template<typename T>
+using detect_key_compare = typename T::key_compare;
+
+template<typename T>
+struct has_key_compare : std::integral_constant<bool, is_detected<detect_key_compare, T>::value> {};
+
+// obtains the actual object key comparator
+template<typename BasicJsonType>
+struct actual_object_comparator
+{
+    using object_t = typename BasicJsonType::object_t;
+    using object_comparator_t = typename BasicJsonType::default_object_comparator_t;
+    using type = typename std::conditional < has_key_compare<object_t>::value,
+          typename object_t::key_compare, object_comparator_t>::type;
+};
+
+template<typename BasicJsonType>
+using actual_object_comparator_t = typename actual_object_comparator<BasicJsonType>::type;
+
+/////////////////
+// char_traits //
+/////////////////
+
+// Primary template of char_traits calls std char_traits
+template<typename T>
+struct char_traits : std::char_traits<T>
+{};
+
+// Explicitly define char traits for unsigned char since it is not standard
+template<>
+struct char_traits<unsigned char> : std::char_traits<char>
+{
+    using char_type = unsigned char;
+    using int_type = uint64_t;
+
+    // Redefine to_int_type function
+    static int_type to_int_type(char_type c) noexcept
+    {
+        return static_cast<int_type>(c);
+    }
+
+    static char_type to_char_type(int_type i) noexcept
+    {
+        return static_cast<char_type>(i);
+    }
+
+    static constexpr int_type eof() noexcept
+    {
+        return static_cast<int_type>(std::char_traits<char>::eof());
+    }
+};
+
+// Explicitly define char traits for signed char since it is not standard
+template<>
+struct char_traits<signed char> : std::char_traits<char>
+{
+    using char_type = signed char;
+    using int_type = uint64_t;
+
+    // Redefine to_int_type function
+    static int_type to_int_type(char_type c) noexcept
+    {
+        return static_cast<int_type>(c);
+    }
+
+    static char_type to_char_type(int_type i) noexcept
+    {
+        return static_cast<char_type>(i);
+    }
+
+    static constexpr int_type eof() noexcept
+    {
+        return static_cast<int_type>(std::char_traits<char>::eof());
+    }
+};
+
+///////////////////
+// is_ functions //
+///////////////////
+
+// https://en.cppreference.com/w/cpp/types/conjunction
+template<class...> struct conjunction : std::true_type { };
+template<class B> struct conjunction<B> : B { };
+template<class B, class... Bn>
+struct conjunction<B, Bn...>
+: std::conditional<static_cast<bool>(B::value), conjunction<Bn...>, B>::type {};
+
+// https://en.cppreference.com/w/cpp/types/negation
+template<class B> struct negation : std::integral_constant < bool, !B::value > { };
+
+// Reimplementation of is_constructible and is_default_constructible, due to them being broken for
+// std::pair and std::tuple until LWG 2367 fix (see https://cplusplus.github.io/LWG/lwg-defects.html#2367).
+// This causes compile errors in e.g. clang 3.5 or gcc 4.9.
+template <typename T>
+struct is_default_constructible : std::is_default_constructible<T> {};
+
+template <typename T1, typename T2>
+struct is_default_constructible<std::pair<T1, T2>>
+    : conjunction<is_default_constructible<T1>, is_default_constructible<T2>> {};
+
+template <typename T1, typename T2>
+struct is_default_constructible<const std::pair<T1, T2>>
+    : conjunction<is_default_constructible<T1>, is_default_constructible<T2>> {};
+
+template <typename... Ts>
+struct is_default_constructible<std::tuple<Ts...>>
+    : conjunction<is_default_constructible<Ts>...> {};
+
+template <typename... Ts>
+struct is_default_constructible<const std::tuple<Ts...>>
+    : conjunction<is_default_constructible<Ts>...> {};
+
+template <typename T, typename... Args>
+struct is_constructible : std::is_constructible<T, Args...> {};
+
+template <typename T1, typename T2>
+struct is_constructible<std::pair<T1, T2>> : is_default_constructible<std::pair<T1, T2>> {};
+
+template <typename T1, typename T2>
+struct is_constructible<const std::pair<T1, T2>> : is_default_constructible<const std::pair<T1, T2>> {};
+
+template <typename... Ts>
+struct is_constructible<std::tuple<Ts...>> : is_default_constructible<std::tuple<Ts...>> {};
+
+template <typename... Ts>
+struct is_constructible<const std::tuple<Ts...>> : is_default_constructible<const std::tuple<Ts...>> {};
+
+template<typename T, typename = void>
+struct is_iterator_traits : std::false_type {};
+
+template<typename T>
+struct is_iterator_traits<iterator_traits<T>>
+{
+  private:
+    using traits = iterator_traits<T>;
+
+  public:
+    static constexpr auto value =
+        is_detected<value_type_t, traits>::value &&
+        is_detected<difference_type_t, traits>::value &&
+        is_detected<pointer_t, traits>::value &&
+        is_detected<iterator_category_t, traits>::value &&
+        is_detected<reference_t, traits>::value;
+};
+
+template<typename T>
+struct is_range
+{
+  private:
+    using t_ref = typename std::add_lvalue_reference<T>::type;
+
+    using iterator = detected_t<result_of_begin, t_ref>;
+    using sentinel = detected_t<result_of_end, t_ref>;
+
+    // to be 100% correct, it should use https://en.cppreference.com/w/cpp/iterator/input_or_output_iterator
+    // and https://en.cppreference.com/w/cpp/iterator/sentinel_for
+    // but reimplementing these would be too much work, as a lot of other concepts are used underneath
+    static constexpr auto is_iterator_begin =
+        is_iterator_traits<iterator_traits<iterator>>::value;
+
+  public:
+    static constexpr bool value = !std::is_same<iterator, nonesuch>::value && !std::is_same<sentinel, nonesuch>::value && is_iterator_begin;
+};
+
+template<typename R>
+using iterator_t = enable_if_t<is_range<R>::value, result_of_begin<decltype(std::declval<R&>())>>;
+
+template<typename T>
+using range_value_t = value_type_t<iterator_traits<iterator_t<T>>>;
+
+// The following implementation of is_complete_type is taken from
+// https://blogs.msdn.microsoft.com/vcblog/2015/12/02/partial-support-for-expression-sfinae-in-vs-2015-update-1/
+// and is written by Xiang Fan who agreed to using it in this library.
+
+template<typename T, typename = void>
+struct is_complete_type : std::false_type {};
+
+template<typename T>
+struct is_complete_type<T, decltype(void(sizeof(T)))> : std::true_type {};
+
+template<typename BasicJsonType, typename CompatibleObjectType,
+         typename = void>
+struct is_compatible_object_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename CompatibleObjectType>
+struct is_compatible_object_type_impl <
+    BasicJsonType, CompatibleObjectType,
+    enable_if_t < is_detected<mapped_type_t, CompatibleObjectType>::value&&
+    is_detected<key_type_t, CompatibleObjectType>::value >>
+{
+    using object_t = typename BasicJsonType::object_t;
+
+    // macOS's is_constructible does not play well with nonesuch...
+    static constexpr bool value =
+        is_constructible<typename object_t::key_type,
+        typename CompatibleObjectType::key_type>::value &&
+        is_constructible<typename object_t::mapped_type,
+        typename CompatibleObjectType::mapped_type>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleObjectType>
+struct is_compatible_object_type
+    : is_compatible_object_type_impl<BasicJsonType, CompatibleObjectType> {};
+
+template<typename BasicJsonType, typename ConstructibleObjectType,
+         typename = void>
+struct is_constructible_object_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename ConstructibleObjectType>
+struct is_constructible_object_type_impl <
+    BasicJsonType, ConstructibleObjectType,
+    enable_if_t < is_detected<mapped_type_t, ConstructibleObjectType>::value&&
+    is_detected<key_type_t, ConstructibleObjectType>::value >>
+{
+    using object_t = typename BasicJsonType::object_t;
+
+    static constexpr bool value =
+        (is_default_constructible<ConstructibleObjectType>::value &&
+         (std::is_move_assignable<ConstructibleObjectType>::value ||
+          std::is_copy_assignable<ConstructibleObjectType>::value) &&
+         (is_constructible<typename ConstructibleObjectType::key_type,
+          typename object_t::key_type>::value &&
+          std::is_same <
+          typename object_t::mapped_type,
+          typename ConstructibleObjectType::mapped_type >::value)) ||
+        (has_from_json<BasicJsonType,
+         typename ConstructibleObjectType::mapped_type>::value ||
+         has_non_default_from_json <
+         BasicJsonType,
+         typename ConstructibleObjectType::mapped_type >::value);
+};
+
+template<typename BasicJsonType, typename ConstructibleObjectType>
+struct is_constructible_object_type
+    : is_constructible_object_type_impl<BasicJsonType,
+      ConstructibleObjectType> {};
+
+template<typename BasicJsonType, typename CompatibleStringType>
+struct is_compatible_string_type
+{
+    static constexpr auto value =
+        is_constructible<typename BasicJsonType::string_t, CompatibleStringType>::value;
+};
+
+template<typename BasicJsonType, typename ConstructibleStringType>
+struct is_constructible_string_type
+{
+    // launder type through decltype() to fix compilation failure on ICPC
+#ifdef __INTEL_COMPILER
+    using laundered_type = decltype(std::declval<ConstructibleStringType>());
+#else
+    using laundered_type = ConstructibleStringType;
+#endif
+
+    static constexpr auto value =
+        conjunction <
+        is_constructible<laundered_type, typename BasicJsonType::string_t>,
+        is_detected_exact<typename BasicJsonType::string_t::value_type,
+        value_type_t, laundered_type >>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleArrayType, typename = void>
+struct is_compatible_array_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename CompatibleArrayType>
+struct is_compatible_array_type_impl <
+    BasicJsonType, CompatibleArrayType,
+    enable_if_t <
+    is_detected<iterator_t, CompatibleArrayType>::value&&
+    is_iterator_traits<iterator_traits<detected_t<iterator_t, CompatibleArrayType>>>::value&&
+// special case for types like std::filesystem::path whose iterator's value_type are themselves
+// c.f. https://github.com/nlohmann/json/pull/3073
+    !std::is_same<CompatibleArrayType, detected_t<range_value_t, CompatibleArrayType>>::value >>
+{
+    static constexpr bool value =
+        is_constructible<BasicJsonType,
+        range_value_t<CompatibleArrayType>>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleArrayType>
+struct is_compatible_array_type
+    : is_compatible_array_type_impl<BasicJsonType, CompatibleArrayType> {};
+
+template<typename BasicJsonType, typename ConstructibleArrayType, typename = void>
+struct is_constructible_array_type_impl : std::false_type {};
+
+template<typename BasicJsonType, typename ConstructibleArrayType>
+struct is_constructible_array_type_impl <
+    BasicJsonType, ConstructibleArrayType,
+    enable_if_t<std::is_same<ConstructibleArrayType,
+    typename BasicJsonType::value_type>::value >>
+            : std::true_type {};
+
+template<typename BasicJsonType, typename ConstructibleArrayType>
+struct is_constructible_array_type_impl <
+    BasicJsonType, ConstructibleArrayType,
+    enable_if_t < !std::is_same<ConstructibleArrayType,
+    typename BasicJsonType::value_type>::value&&
+    !is_compatible_string_type<BasicJsonType, ConstructibleArrayType>::value&&
+    is_default_constructible<ConstructibleArrayType>::value&&
+(std::is_move_assignable<ConstructibleArrayType>::value ||
+ std::is_copy_assignable<ConstructibleArrayType>::value)&&
+is_detected<iterator_t, ConstructibleArrayType>::value&&
+is_iterator_traits<iterator_traits<detected_t<iterator_t, ConstructibleArrayType>>>::value&&
+is_detected<range_value_t, ConstructibleArrayType>::value&&
+// special case for types like std::filesystem::path whose iterator's value_type are themselves
+// c.f. https://github.com/nlohmann/json/pull/3073
+!std::is_same<ConstructibleArrayType, detected_t<range_value_t, ConstructibleArrayType>>::value&&
+is_complete_type <
+detected_t<range_value_t, ConstructibleArrayType >>::value >>
+{
+    using value_type = range_value_t<ConstructibleArrayType>;
+
+    static constexpr bool value =
+        std::is_same<value_type,
+        typename BasicJsonType::array_t::value_type>::value ||
+        has_from_json<BasicJsonType,
+        value_type>::value ||
+        has_non_default_from_json <
+        BasicJsonType,
+        value_type >::value;
+};
+
+template<typename BasicJsonType, typename ConstructibleArrayType>
+struct is_constructible_array_type
+    : is_constructible_array_type_impl<BasicJsonType, ConstructibleArrayType> {};
+
+template<typename RealIntegerType, typename CompatibleNumberIntegerType,
+         typename = void>
+struct is_compatible_integer_type_impl : std::false_type {};
+
+template<typename RealIntegerType, typename CompatibleNumberIntegerType>
+struct is_compatible_integer_type_impl <
+    RealIntegerType, CompatibleNumberIntegerType,
+    enable_if_t < std::is_integral<RealIntegerType>::value&&
+    std::is_integral<CompatibleNumberIntegerType>::value&&
+    !std::is_same<bool, CompatibleNumberIntegerType>::value >>
+{
+    // is there an assert somewhere on overflows?
+    using RealLimits = std::numeric_limits<RealIntegerType>;
+    using CompatibleLimits = std::numeric_limits<CompatibleNumberIntegerType>;
+
+    static constexpr auto value =
+        is_constructible<RealIntegerType,
+        CompatibleNumberIntegerType>::value &&
+        CompatibleLimits::is_integer &&
+        RealLimits::is_signed == CompatibleLimits::is_signed;
+};
+
+template<typename RealIntegerType, typename CompatibleNumberIntegerType>
+struct is_compatible_integer_type
+    : is_compatible_integer_type_impl<RealIntegerType,
+      CompatibleNumberIntegerType> {};
+
+template<typename BasicJsonType, typename CompatibleType, typename = void>
+struct is_compatible_type_impl: std::false_type {};
+
+template<typename BasicJsonType, typename CompatibleType>
+struct is_compatible_type_impl <
+    BasicJsonType, CompatibleType,
+    enable_if_t<is_complete_type<CompatibleType>::value >>
+{
+    static constexpr bool value =
+        has_to_json<BasicJsonType, CompatibleType>::value;
+};
+
+template<typename BasicJsonType, typename CompatibleType>
+struct is_compatible_type
+    : is_compatible_type_impl<BasicJsonType, CompatibleType> {};
+
+template<typename T1, typename T2>
+struct is_constructible_tuple : std::false_type {};
+
+template<typename T1, typename... Args>
+struct is_constructible_tuple<T1, std::tuple<Args...>> : conjunction<is_constructible<T1, Args>...> {};
+
+template<typename BasicJsonType, typename T>
+struct is_json_iterator_of : std::false_type {};
+
+template<typename BasicJsonType>
+struct is_json_iterator_of<BasicJsonType, typename BasicJsonType::iterator> : std::true_type {};
+
+template<typename BasicJsonType>
+struct is_json_iterator_of<BasicJsonType, typename BasicJsonType::const_iterator> : std::true_type
+{};
+
+// checks if a given type T is a template specialization of Primary
+template<template <typename...> class Primary, typename T>
+struct is_specialization_of : std::false_type {};
+
+template<template <typename...> class Primary, typename... Args>
+struct is_specialization_of<Primary, Primary<Args...>> : std::true_type {};
+
+template<typename T>
+using is_json_pointer = is_specialization_of<::nlohmann::json_pointer, uncvref_t<T>>;
+
+// checks if A and B are comparable using Compare functor
+template<typename Compare, typename A, typename B, typename = void>
+struct is_comparable : std::false_type {};
+
+template<typename Compare, typename A, typename B>
+struct is_comparable<Compare, A, B, void_t<
+decltype(std::declval<Compare>()(std::declval<A>(), std::declval<B>())),
+decltype(std::declval<Compare>()(std::declval<B>(), std::declval<A>()))
+>> : std::true_type {};
+
+template<typename T>
+using detect_is_transparent = typename T::is_transparent;
+
+// type trait to check if KeyType can be used as object key (without a BasicJsonType)
+// see is_usable_as_basic_json_key_type below
+template<typename Comparator, typename ObjectKeyType, typename KeyTypeCVRef, bool RequireTransparentComparator = true,
+         bool ExcludeObjectKeyType = RequireTransparentComparator, typename KeyType = uncvref_t<KeyTypeCVRef>>
+using is_usable_as_key_type = typename std::conditional <
+                              is_comparable<Comparator, ObjectKeyType, KeyTypeCVRef>::value
+                              && !(ExcludeObjectKeyType && std::is_same<KeyType,
+                                   ObjectKeyType>::value)
+                              && (!RequireTransparentComparator
+                                  || is_detected <detect_is_transparent, Comparator>::value)
+                              && !is_json_pointer<KeyType>::value,
+                              std::true_type,
+                              std::false_type >::type;
+
+// type trait to check if KeyType can be used as object key
+// true if:
+//   - KeyType is comparable with BasicJsonType::object_t::key_type
+//   - if ExcludeObjectKeyType is true, KeyType is not BasicJsonType::object_t::key_type
+//   - the comparator is transparent or RequireTransparentComparator is false
+//   - KeyType is not a JSON iterator or json_pointer
+template<typename BasicJsonType, typename KeyTypeCVRef, bool RequireTransparentComparator = true,
+         bool ExcludeObjectKeyType = RequireTransparentComparator, typename KeyType = uncvref_t<KeyTypeCVRef>>
+using is_usable_as_basic_json_key_type = typename std::conditional <
+    is_usable_as_key_type<typename BasicJsonType::object_comparator_t,
+    typename BasicJsonType::object_t::key_type, KeyTypeCVRef,
+    RequireTransparentComparator, ExcludeObjectKeyType>::value
+    && !is_json_iterator_of<BasicJsonType, KeyType>::value,
+    std::true_type,
+    std::false_type >::type;
+
+template<typename ObjectType, typename KeyType>
+using detect_erase_with_key_type = decltype(std::declval<ObjectType&>().erase(std::declval<KeyType>()));
+
+// type trait to check if object_t has an erase() member functions accepting KeyType
+template<typename BasicJsonType, typename KeyType>
+using has_erase_with_key_type = typename std::conditional <
+                                is_detected <
+                                detect_erase_with_key_type,
+                                typename BasicJsonType::object_t, KeyType >::value,
+                                std::true_type,
+                                std::false_type >::type;
+
+// a naive helper to check if a type is an ordered_map (exploits the fact that
+// ordered_map inherits capacity() from std::vector)
+template <typename T>
+struct is_ordered_map
+{
+    using one = char;
+
+    struct two
+    {
+        char x[2]; // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+    };
+
+    template <typename C> static one test( decltype(&C::capacity) ) ;
+    template <typename C> static two test(...);
+
+    enum { value = sizeof(test<T>(nullptr)) == sizeof(char) }; // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+};
+
+// to avoid useless casts (see https://github.com/nlohmann/json/issues/2893#issuecomment-889152324)
+template < typename T, typename U, enable_if_t < !std::is_same<T, U>::value, int > = 0 >
+T conditional_static_cast(U value)
+{
+    return static_cast<T>(value);
+}
+
+template<typename T, typename U, enable_if_t<std::is_same<T, U>::value, int> = 0>
+T conditional_static_cast(U value)
+{
+    return value;
+}
+
+template<typename... Types>
+using all_integral = conjunction<std::is_integral<Types>...>;
+
+template<typename... Types>
+using all_signed = conjunction<std::is_signed<Types>...>;
+
+template<typename... Types>
+using all_unsigned = conjunction<std::is_unsigned<Types>...>;
+
+// there's a disjunction trait in another PR; replace when merged
+template<typename... Types>
+using same_sign = std::integral_constant < bool,
+      all_signed<Types...>::value || all_unsigned<Types...>::value >;
+
+template<typename OfType, typename T>
+using never_out_of_range = std::integral_constant < bool,
+      (std::is_signed<OfType>::value && (sizeof(T) < sizeof(OfType)))
+      || (same_sign<OfType, T>::value && sizeof(OfType) == sizeof(T)) >;
+
+template<typename OfType, typename T,
+         bool OfTypeSigned = std::is_signed<OfType>::value,
+         bool TSigned = std::is_signed<T>::value>
+struct value_in_range_of_impl2;
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, false, false>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, true, false>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, false, true>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return val >= 0 && static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl2<OfType, T, true, true>
+{
+    static constexpr bool test(T val)
+    {
+        using CommonType = typename std::common_type<OfType, T>::type;
+        return static_cast<CommonType>(val) >= static_cast<CommonType>((std::numeric_limits<OfType>::min)())
+               && static_cast<CommonType>(val) <= static_cast<CommonType>((std::numeric_limits<OfType>::max)());
+    }
+};
+
+template<typename OfType, typename T,
+         bool NeverOutOfRange = never_out_of_range<OfType, T>::value,
+         typename = detail::enable_if_t<all_integral<OfType, T>::value>>
+struct value_in_range_of_impl1;
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl1<OfType, T, false>
+{
+    static constexpr bool test(T val)
+    {
+        return value_in_range_of_impl2<OfType, T>::test(val);
+    }
+};
+
+template<typename OfType, typename T>
+struct value_in_range_of_impl1<OfType, T, true>
+{
+    static constexpr bool test(T /*val*/)
+    {
+        return true;
+    }
+};
+
+template<typename OfType, typename T>
+constexpr bool value_in_range_of(T val)
+{
+    return value_in_range_of_impl1<OfType, T>::test(val);
+}
+
+template<bool Value>
+using bool_constant = std::integral_constant<bool, Value>;
+
+///////////////////////////////////////////////////////////////////////////////
+// is_c_string
+///////////////////////////////////////////////////////////////////////////////
+
+namespace impl
+{
+
+template<typename T>
+constexpr bool is_c_string()
+{
+    using TUnExt = typename std::remove_extent<T>::type;
+    using TUnCVExt = typename std::remove_cv<TUnExt>::type;
+    using TUnPtr = typename std::remove_pointer<T>::type;
+    using TUnCVPtr = typename std::remove_cv<TUnPtr>::type;
+    return
+        (std::is_array<T>::value && std::is_same<TUnCVExt, char>::value)
+        || (std::is_pointer<T>::value && std::is_same<TUnCVPtr, char>::value);
+}
+
+}  // namespace impl
+
+// checks whether T is a [cv] char */[cv] char[] C string
+template<typename T>
+struct is_c_string : bool_constant<impl::is_c_string<T>()> {};
+
+template<typename T>
+using is_c_string_uncvref = is_c_string<uncvref_t<T>>;
+
+///////////////////////////////////////////////////////////////////////////////
+// is_transparent
+///////////////////////////////////////////////////////////////////////////////
+
+namespace impl
+{
+
+template<typename T>
+constexpr bool is_transparent()
+{
+    return is_detected<detect_is_transparent, T>::value;
+}
+
+}  // namespace impl
+
+// checks whether T has a member named is_transparent
+template<typename T>
+struct is_transparent : bool_constant<impl::is_transparent<T>()> {};
+
+///////////////////////////////////////////////////////////////////////////////
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/string_concat.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstring> // strlen
+#include <string> // string
+#include <utility> // forward
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/detected.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+inline std::size_t concat_length()
+{
+    return 0;
+}
+
+template<typename... Args>
+inline std::size_t concat_length(const char* cstr, const Args& ... rest);
+
+template<typename StringType, typename... Args>
+inline std::size_t concat_length(const StringType& str, const Args& ... rest);
+
+template<typename... Args>
+inline std::size_t concat_length(const char /*c*/, const Args& ... rest)
+{
+    return 1 + concat_length(rest...);
+}
+
+template<typename... Args>
+inline std::size_t concat_length(const char* cstr, const Args& ... rest)
+{
+    // cppcheck-suppress ignoredReturnValue
+    return ::strlen(cstr) + concat_length(rest...);
+}
+
+template<typename StringType, typename... Args>
+inline std::size_t concat_length(const StringType& str, const Args& ... rest)
+{
+    return str.size() + concat_length(rest...);
+}
+
+template<typename OutStringType>
+inline void concat_into(OutStringType& /*out*/)
+{}
+
+template<typename StringType, typename Arg>
+using string_can_append = decltype(std::declval<StringType&>().append(std::declval < Arg && > ()));
+
+template<typename StringType, typename Arg>
+using detect_string_can_append = is_detected<string_can_append, StringType, Arg>;
+
+template<typename StringType, typename Arg>
+using string_can_append_op = decltype(std::declval<StringType&>() += std::declval < Arg && > ());
+
+template<typename StringType, typename Arg>
+using detect_string_can_append_op = is_detected<string_can_append_op, StringType, Arg>;
+
+template<typename StringType, typename Arg>
+using string_can_append_iter = decltype(std::declval<StringType&>().append(std::declval<const Arg&>().begin(), std::declval<const Arg&>().end()));
+
+template<typename StringType, typename Arg>
+using detect_string_can_append_iter = is_detected<string_can_append_iter, StringType, Arg>;
+
+template<typename StringType, typename Arg>
+using string_can_append_data = decltype(std::declval<StringType&>().append(std::declval<const Arg&>().data(), std::declval<const Arg&>().size()));
+
+template<typename StringType, typename Arg>
+using detect_string_can_append_data = is_detected<string_can_append_data, StringType, Arg>;
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && detect_string_can_append_op<OutStringType, Arg>::value, int > = 0 >
+inline void concat_into(OutStringType& out, Arg && arg, Args && ... rest);
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && detect_string_can_append_iter<OutStringType, Arg>::value, int > = 0 >
+inline void concat_into(OutStringType& out, const Arg& arg, Args && ... rest);
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && !detect_string_can_append_iter<OutStringType, Arg>::value
+                         && detect_string_can_append_data<OutStringType, Arg>::value, int > = 0 >
+inline void concat_into(OutStringType& out, const Arg& arg, Args && ... rest);
+
+template<typename OutStringType, typename Arg, typename... Args,
+         enable_if_t<detect_string_can_append<OutStringType, Arg>::value, int> = 0>
+inline void concat_into(OutStringType& out, Arg && arg, Args && ... rest)
+{
+    out.append(std::forward<Arg>(arg));
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && detect_string_can_append_op<OutStringType, Arg>::value, int > >
+inline void concat_into(OutStringType& out, Arg&& arg, Args&& ... rest)
+{
+    out += std::forward<Arg>(arg);
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && detect_string_can_append_iter<OutStringType, Arg>::value, int > >
+inline void concat_into(OutStringType& out, const Arg& arg, Args&& ... rest)
+{
+    out.append(arg.begin(), arg.end());
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template < typename OutStringType, typename Arg, typename... Args,
+           enable_if_t < !detect_string_can_append<OutStringType, Arg>::value
+                         && !detect_string_can_append_op<OutStringType, Arg>::value
+                         && !detect_string_can_append_iter<OutStringType, Arg>::value
+                         && detect_string_can_append_data<OutStringType, Arg>::value, int > >
+inline void concat_into(OutStringType& out, const Arg& arg, Args&& ... rest)
+{
+    out.append(arg.data(), arg.size());
+    concat_into(out, std::forward<Args>(rest)...);
+}
+
+template<typename OutStringType = std::string, typename... Args>
+inline OutStringType concat(Args && ... args)
+{
+    OutStringType str;
+    str.reserve(concat_length(args...));
+    concat_into(str, std::forward<Args>(args)...);
+    return str;
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+
+// With -Wweak-vtables, Clang will complain about the exception classes as they
+// have no out-of-line virtual method definitions and their vtable will be
+// emitted in every translation unit. This issue cannot be fixed with a
+// header-only library as there is no implementation file to move these
+// functions to. As a result, we suppress this warning here to avoid client
+// code to stumble over this. See https://github.com/nlohmann/json/issues/4087
+// for a discussion.
+#if defined(__clang__)
+    #pragma clang diagnostic push
+    #pragma clang diagnostic ignored "-Wweak-vtables"
+#endif
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+////////////////
+// exceptions //
+////////////////
+
+/// @brief general exception of the @ref basic_json class
+/// @sa https://json.nlohmann.me/api/basic_json/exception/
+class exception : public std::exception
+{
+  public:
+    /// returns the explanatory string
+    const char* what() const noexcept override
+    {
+        return m.what();
+    }
+
+    /// the id of the exception
+    const int id; // NOLINT(cppcoreguidelines-non-private-member-variables-in-classes)
+
+  protected:
+    JSON_HEDLEY_NON_NULL(3)
+    exception(int id_, const char* what_arg) : id(id_), m(what_arg) {} // NOLINT(bugprone-throw-keyword-missing)
+
+    static std::string name(const std::string& ename, int id_)
+    {
+        return concat("[json.exception.", ename, '.', std::to_string(id_), "] ");
+    }
+
+    static std::string diagnostics(std::nullptr_t /*leaf_element*/)
+    {
+        return "";
+    }
+
+    template<typename BasicJsonType>
+    static std::string diagnostics(const BasicJsonType* leaf_element)
+    {
+#if JSON_DIAGNOSTICS
+        std::vector<std::string> tokens;
+        for (const auto* current = leaf_element; current != nullptr && current->m_parent != nullptr; current = current->m_parent)
+        {
+            switch (current->m_parent->type())
+            {
+                case value_t::array:
+                {
+                    for (std::size_t i = 0; i < current->m_parent->m_data.m_value.array->size(); ++i)
+                    {
+                        if (&current->m_parent->m_data.m_value.array->operator[](i) == current)
+                        {
+                            tokens.emplace_back(std::to_string(i));
+                            break;
+                        }
+                    }
+                    break;
+                }
+
+                case value_t::object:
+                {
+                    for (const auto& element : *current->m_parent->m_data.m_value.object)
+                    {
+                        if (&element.second == current)
+                        {
+                            tokens.emplace_back(element.first.c_str());
+                            break;
+                        }
+                    }
+                    break;
+                }
+
+                case value_t::null: // LCOV_EXCL_LINE
+                case value_t::string: // LCOV_EXCL_LINE
+                case value_t::boolean: // LCOV_EXCL_LINE
+                case value_t::number_integer: // LCOV_EXCL_LINE
+                case value_t::number_unsigned: // LCOV_EXCL_LINE
+                case value_t::number_float: // LCOV_EXCL_LINE
+                case value_t::binary: // LCOV_EXCL_LINE
+                case value_t::discarded: // LCOV_EXCL_LINE
+                default:   // LCOV_EXCL_LINE
+                    break; // LCOV_EXCL_LINE
+            }
+        }
+
+        if (tokens.empty())
+        {
+            return "";
+        }
+
+        auto str = std::accumulate(tokens.rbegin(), tokens.rend(), std::string{},
+                                   [](const std::string & a, const std::string & b)
+        {
+            return concat(a, '/', detail::escape(b));
+        });
+
+        return concat('(', str, ") ", get_byte_positions(leaf_element));
+#else
+        return get_byte_positions(leaf_element);
+#endif
+    }
+
+  private:
+    /// an exception object as storage for error messages
+    std::runtime_error m;
+#if JSON_DIAGNOSTIC_POSITIONS
+    template<typename BasicJsonType>
+    static std::string get_byte_positions(const BasicJsonType* leaf_element)
+    {
+        if ((leaf_element->start_pos() != std::string::npos) && (leaf_element->end_pos() != std::string::npos))
+        {
+            return concat("(bytes ", std::to_string(leaf_element->start_pos()), "-", std::to_string(leaf_element->end_pos()), ") ");
+        }
+        return "";
+    }
+#else
+    template<typename BasicJsonType>
+    static std::string get_byte_positions(const BasicJsonType* leaf_element)
+    {
+        static_cast<void>(leaf_element);
+        return "";
+    }
+#endif
+};
+
+/// @brief exception indicating a parse error
+/// @sa https://json.nlohmann.me/api/basic_json/parse_error/
+class parse_error : public exception
+{
+  public:
+    /*!
+    @brief create a parse error exception
+    @param[in] id_       the id of the exception
+    @param[in] pos       the position where the error occurred (or with
+                         chars_read_total=0 if the position cannot be
+                         determined)
+    @param[in] what_arg  the explanatory string
+    @return parse_error object
+    */
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static parse_error create(int id_, const position_t& pos, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("parse_error", id_), "parse error",
+                                     position_string(pos), ": ", exception::diagnostics(context), what_arg);
+        return {id_, pos.chars_read_total, w.c_str()};
+    }
+
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static parse_error create(int id_, std::size_t byte_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("parse_error", id_), "parse error",
+                                     (byte_ != 0 ? (concat(" at byte ", std::to_string(byte_))) : ""),
+                                     ": ", exception::diagnostics(context), what_arg);
+        return {id_, byte_, w.c_str()};
+    }
+
+    /*!
+    @brief byte index of the parse error
+
+    The byte index of the last read character in the input file.
+
+    @note For an input with n bytes, 1 is the index of the first character and
+          n+1 is the index of the terminating null byte or the end of file.
+          This also holds true when reading a byte vector (CBOR or MessagePack).
+    */
+    const std::size_t byte;
+
+  private:
+    parse_error(int id_, std::size_t byte_, const char* what_arg)
+        : exception(id_, what_arg), byte(byte_) {}
+
+    static std::string position_string(const position_t& pos)
+    {
+        return concat(" at line ", std::to_string(pos.lines_read + 1),
+                      ", column ", std::to_string(pos.chars_read_current_line));
+    }
+};
+
+/// @brief exception indicating errors with iterators
+/// @sa https://json.nlohmann.me/api/basic_json/invalid_iterator/
+class invalid_iterator : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static invalid_iterator create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("invalid_iterator", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    invalid_iterator(int id_, const char* what_arg)
+        : exception(id_, what_arg) {}
+};
+
+/// @brief exception indicating executing a member function with a wrong type
+/// @sa https://json.nlohmann.me/api/basic_json/type_error/
+class type_error : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static type_error create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("type_error", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    type_error(int id_, const char* what_arg) : exception(id_, what_arg) {}
+};
+
+/// @brief exception indicating access out of the defined range
+/// @sa https://json.nlohmann.me/api/basic_json/out_of_range/
+class out_of_range : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static out_of_range create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("out_of_range", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    out_of_range(int id_, const char* what_arg) : exception(id_, what_arg) {}
+};
+
+/// @brief exception indicating other library errors
+/// @sa https://json.nlohmann.me/api/basic_json/other_error/
+class other_error : public exception
+{
+  public:
+    template<typename BasicJsonContext, enable_if_t<is_basic_json_context<BasicJsonContext>::value, int> = 0>
+    static other_error create(int id_, const std::string& what_arg, BasicJsonContext context)
+    {
+        const std::string w = concat(exception::name("other_error", id_), exception::diagnostics(context), what_arg);
+        return {id_, w.c_str()};
+    }
+
+  private:
+    JSON_HEDLEY_NON_NULL(3)
+    other_error(int id_, const char* what_arg) : exception(id_, what_arg) {}
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+#if defined(__clang__)
+    #pragma clang diagnostic pop
+#endif
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/identity_tag.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// dispatching helper struct
+template <class T> struct identity_tag {};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/std_fs.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+#if JSON_HAS_EXPERIMENTAL_FILESYSTEM
+#include <experimental/filesystem>
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+namespace std_fs = std::experimental::filesystem;
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+#elif JSON_HAS_FILESYSTEM
+#include <filesystem> // NOLINT(build/c++17)
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+namespace std_fs = std::filesystem;
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+#endif
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename std::nullptr_t& n)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_null()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be null, but is ", j.type_name()), &j));
+    }
+    n = nullptr;
+}
+
+#ifdef JSON_HAS_CPP_17
+#ifndef JSON_USE_IMPLICIT_CONVERSIONS
+template<typename BasicJsonType, typename T>
+void from_json(const BasicJsonType& j, std::optional<T>& opt)
+{
+    if (j.is_null())
+    {
+        opt = std::nullopt;
+    }
+    else
+    {
+        opt.emplace(j.template get<T>());
+    }
+}
+
+#endif // JSON_USE_IMPLICIT_CONVERSIONS
+#endif // JSON_HAS_CPP_17
+
+// overloads for basic_json template parameters
+template < typename BasicJsonType, typename ArithmeticType,
+           enable_if_t < std::is_arithmetic<ArithmeticType>::value&&
+                         !std::is_same<ArithmeticType, typename BasicJsonType::boolean_t>::value,
+                         int > = 0 >
+void get_arithmetic_value(const BasicJsonType& j, ArithmeticType& val)
+{
+    switch (static_cast<value_t>(j))
+    {
+        case value_t::number_unsigned:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_unsigned_t*>());
+            break;
+        }
+        case value_t::number_integer:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_integer_t*>());
+            break;
+        }
+        case value_t::number_float:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_float_t*>());
+            break;
+        }
+
+        case value_t::null:
+        case value_t::object:
+        case value_t::array:
+        case value_t::string:
+        case value_t::boolean:
+        case value_t::binary:
+        case value_t::discarded:
+        default:
+            JSON_THROW(type_error::create(302, concat("type must be number, but is ", j.type_name()), &j));
+    }
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::boolean_t& b)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_boolean()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be boolean, but is ", j.type_name()), &j));
+    }
+    b = *j.template get_ptr<const typename BasicJsonType::boolean_t*>();
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::string_t& s)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be string, but is ", j.type_name()), &j));
+    }
+    s = *j.template get_ptr<const typename BasicJsonType::string_t*>();
+}
+
+template <
+    typename BasicJsonType, typename StringType,
+    enable_if_t <
+        std::is_assignable<StringType&, const typename BasicJsonType::string_t>::value
+        && is_detected_exact<typename BasicJsonType::string_t::value_type, value_type_t, StringType>::value
+        && !std::is_same<typename BasicJsonType::string_t, StringType>::value
+        && !is_json_ref<StringType>::value, int > = 0 >
+inline void from_json(const BasicJsonType& j, StringType& s)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be string, but is ", j.type_name()), &j));
+    }
+
+    s = *j.template get_ptr<const typename BasicJsonType::string_t*>();
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::number_float_t& val)
+{
+    get_arithmetic_value(j, val);
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::number_unsigned_t& val)
+{
+    get_arithmetic_value(j, val);
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::number_integer_t& val)
+{
+    get_arithmetic_value(j, val);
+}
+
+#if !JSON_DISABLE_ENUM_SERIALIZATION
+template<typename BasicJsonType, typename EnumType,
+         enable_if_t<std::is_enum<EnumType>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, EnumType& e)
+{
+    typename std::underlying_type<EnumType>::type val;
+    get_arithmetic_value(j, val);
+    e = static_cast<EnumType>(val);
+}
+#endif  // JSON_DISABLE_ENUM_SERIALIZATION
+
+// forward_list doesn't have an insert method
+template<typename BasicJsonType, typename T, typename Allocator,
+         enable_if_t<is_getable<BasicJsonType, T>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, std::forward_list<T, Allocator>& l)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    l.clear();
+    std::transform(j.rbegin(), j.rend(),
+                   std::front_inserter(l), [](const BasicJsonType & i)
+    {
+        return i.template get<T>();
+    });
+}
+
+// valarray doesn't have an insert method
+template<typename BasicJsonType, typename T,
+         enable_if_t<is_getable<BasicJsonType, T>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, std::valarray<T>& l)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    l.resize(j.size());
+    std::transform(j.begin(), j.end(), std::begin(l),
+                   [](const BasicJsonType & elem)
+    {
+        return elem.template get<T>();
+    });
+}
+
+template<typename BasicJsonType, typename T, std::size_t N>
+auto from_json(const BasicJsonType& j, T (&arr)[N])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i = 0; i < N; ++i)
+    {
+        arr[i] = j.at(i).template get<T>();
+    }
+}
+
+template<typename BasicJsonType, typename T, std::size_t N1, std::size_t N2>
+auto from_json(const BasicJsonType& j, T (&arr)[N1][N2])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i1 = 0; i1 < N1; ++i1)
+    {
+        for (std::size_t i2 = 0; i2 < N2; ++i2)
+        {
+            arr[i1][i2] = j.at(i1).at(i2).template get<T>();
+        }
+    }
+}
+
+template<typename BasicJsonType, typename T, std::size_t N1, std::size_t N2, std::size_t N3>
+auto from_json(const BasicJsonType& j, T (&arr)[N1][N2][N3])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i1 = 0; i1 < N1; ++i1)
+    {
+        for (std::size_t i2 = 0; i2 < N2; ++i2)
+        {
+            for (std::size_t i3 = 0; i3 < N3; ++i3)
+            {
+                arr[i1][i2][i3] = j.at(i1).at(i2).at(i3).template get<T>();
+            }
+        }
+    }
+}
+
+template<typename BasicJsonType, typename T, std::size_t N1, std::size_t N2, std::size_t N3, std::size_t N4>
+auto from_json(const BasicJsonType& j, T (&arr)[N1][N2][N3][N4])  // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i1 = 0; i1 < N1; ++i1)
+    {
+        for (std::size_t i2 = 0; i2 < N2; ++i2)
+        {
+            for (std::size_t i3 = 0; i3 < N3; ++i3)
+            {
+                for (std::size_t i4 = 0; i4 < N4; ++i4)
+                {
+                    arr[i1][i2][i3][i4] = j.at(i1).at(i2).at(i3).at(i4).template get<T>();
+                }
+            }
+        }
+    }
+}
+
+template<typename BasicJsonType>
+inline void from_json_array_impl(const BasicJsonType& j, typename BasicJsonType::array_t& arr, priority_tag<3> /*unused*/)
+{
+    arr = *j.template get_ptr<const typename BasicJsonType::array_t*>();
+}
+
+template<typename BasicJsonType, typename T, std::size_t N>
+auto from_json_array_impl(const BasicJsonType& j, std::array<T, N>& arr,
+                          priority_tag<2> /*unused*/)
+-> decltype(j.template get<T>(), void())
+{
+    for (std::size_t i = 0; i < N; ++i)
+    {
+        arr[i] = j.at(i).template get<T>();
+    }
+}
+
+template<typename BasicJsonType, typename ConstructibleArrayType,
+         enable_if_t<
+             std::is_assignable<ConstructibleArrayType&, ConstructibleArrayType>::value,
+             int> = 0>
+auto from_json_array_impl(const BasicJsonType& j, ConstructibleArrayType& arr, priority_tag<1> /*unused*/)
+-> decltype(
+    arr.reserve(std::declval<typename ConstructibleArrayType::size_type>()),
+    j.template get<typename ConstructibleArrayType::value_type>(),
+    void())
+{
+    using std::end;
+
+    ConstructibleArrayType ret;
+    ret.reserve(j.size());
+    std::transform(j.begin(), j.end(),
+                   std::inserter(ret, end(ret)), [](const BasicJsonType & i)
+    {
+        // get<BasicJsonType>() returns *this, this won't call a from_json
+        // method when value_type is BasicJsonType
+        return i.template get<typename ConstructibleArrayType::value_type>();
+    });
+    arr = std::move(ret);
+}
+
+template<typename BasicJsonType, typename ConstructibleArrayType,
+         enable_if_t<
+             std::is_assignable<ConstructibleArrayType&, ConstructibleArrayType>::value,
+             int> = 0>
+inline void from_json_array_impl(const BasicJsonType& j, ConstructibleArrayType& arr,
+                                 priority_tag<0> /*unused*/)
+{
+    using std::end;
+
+    ConstructibleArrayType ret;
+    std::transform(
+        j.begin(), j.end(), std::inserter(ret, end(ret)),
+        [](const BasicJsonType & i)
+    {
+        // get<BasicJsonType>() returns *this, this won't call a from_json
+        // method when value_type is BasicJsonType
+        return i.template get<typename ConstructibleArrayType::value_type>();
+    });
+    arr = std::move(ret);
+}
+
+template < typename BasicJsonType, typename ConstructibleArrayType,
+           enable_if_t <
+               is_constructible_array_type<BasicJsonType, ConstructibleArrayType>::value&&
+               !is_constructible_object_type<BasicJsonType, ConstructibleArrayType>::value&&
+               !is_constructible_string_type<BasicJsonType, ConstructibleArrayType>::value&&
+               !std::is_same<ConstructibleArrayType, typename BasicJsonType::binary_t>::value&&
+               !is_basic_json<ConstructibleArrayType>::value,
+               int > = 0 >
+auto from_json(const BasicJsonType& j, ConstructibleArrayType& arr)
+-> decltype(from_json_array_impl(j, arr, priority_tag<3> {}),
+j.template get<typename ConstructibleArrayType::value_type>(),
+void())
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+
+    from_json_array_impl(j, arr, priority_tag<3> {});
+}
+
+template < typename BasicJsonType, typename T, std::size_t... Idx >
+std::array<T, sizeof...(Idx)> from_json_inplace_array_impl(BasicJsonType&& j,
+                     identity_tag<std::array<T, sizeof...(Idx)>> /*unused*/, index_sequence<Idx...> /*unused*/)
+{
+    return { { std::forward<BasicJsonType>(j).at(Idx).template get<T>()... } };
+}
+
+template < typename BasicJsonType, typename T, std::size_t N >
+auto from_json(BasicJsonType&& j, identity_tag<std::array<T, N>> tag)
+-> decltype(from_json_inplace_array_impl(std::forward<BasicJsonType>(j), tag, make_index_sequence<N> {}))
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+
+    return from_json_inplace_array_impl(std::forward<BasicJsonType>(j), tag, make_index_sequence<N> {});
+}
+
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, typename BasicJsonType::binary_t& bin)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_binary()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be binary, but is ", j.type_name()), &j));
+    }
+
+    bin = *j.template get_ptr<const typename BasicJsonType::binary_t*>();
+}
+
+template<typename BasicJsonType, typename ConstructibleObjectType,
+         enable_if_t<is_constructible_object_type<BasicJsonType, ConstructibleObjectType>::value, int> = 0>
+inline void from_json(const BasicJsonType& j, ConstructibleObjectType& obj)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_object()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be object, but is ", j.type_name()), &j));
+    }
+
+    ConstructibleObjectType ret;
+    const auto* inner_object = j.template get_ptr<const typename BasicJsonType::object_t*>();
+    using value_type = typename ConstructibleObjectType::value_type;
+    std::transform(
+        inner_object->begin(), inner_object->end(),
+        std::inserter(ret, ret.begin()),
+        [](typename BasicJsonType::object_t::value_type const & p)
+    {
+        return value_type(p.first, p.second.template get<typename ConstructibleObjectType::mapped_type>());
+    });
+    obj = std::move(ret);
+}
+
+// overload for arithmetic types, not chosen for basic_json template arguments
+// (BooleanType, etc..); note: Is it really necessary to provide explicit
+// overloads for boolean_t etc. in case of a custom BooleanType which is not
+// an arithmetic type?
+template < typename BasicJsonType, typename ArithmeticType,
+           enable_if_t <
+               std::is_arithmetic<ArithmeticType>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::number_unsigned_t>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::number_integer_t>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::number_float_t>::value&&
+               !std::is_same<ArithmeticType, typename BasicJsonType::boolean_t>::value,
+               int > = 0 >
+inline void from_json(const BasicJsonType& j, ArithmeticType& val)
+{
+    switch (static_cast<value_t>(j))
+    {
+        case value_t::number_unsigned:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_unsigned_t*>());
+            break;
+        }
+        case value_t::number_integer:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_integer_t*>());
+            break;
+        }
+        case value_t::number_float:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::number_float_t*>());
+            break;
+        }
+        case value_t::boolean:
+        {
+            val = static_cast<ArithmeticType>(*j.template get_ptr<const typename BasicJsonType::boolean_t*>());
+            break;
+        }
+
+        case value_t::null:
+        case value_t::object:
+        case value_t::array:
+        case value_t::string:
+        case value_t::binary:
+        case value_t::discarded:
+        default:
+            JSON_THROW(type_error::create(302, concat("type must be number, but is ", j.type_name()), &j));
+    }
+}
+
+template<typename BasicJsonType, typename... Args, std::size_t... Idx>
+std::tuple<Args...> from_json_tuple_impl_base(BasicJsonType&& j, index_sequence<Idx...> /*unused*/)
+{
+    return std::make_tuple(std::forward<BasicJsonType>(j).at(Idx).template get<Args>()...);
+}
+
+template<typename BasicJsonType>
+std::tuple<> from_json_tuple_impl_base(BasicJsonType& /*unused*/, index_sequence<> /*unused*/)
+{
+    return {};
+}
+
+template < typename BasicJsonType, class A1, class A2 >
+std::pair<A1, A2> from_json_tuple_impl(BasicJsonType&& j, identity_tag<std::pair<A1, A2>> /*unused*/, priority_tag<0> /*unused*/)
+{
+    return {std::forward<BasicJsonType>(j).at(0).template get<A1>(),
+            std::forward<BasicJsonType>(j).at(1).template get<A2>()};
+}
+
+template<typename BasicJsonType, typename A1, typename A2>
+inline void from_json_tuple_impl(BasicJsonType&& j, std::pair<A1, A2>& p, priority_tag<1> /*unused*/)
+{
+    p = from_json_tuple_impl(std::forward<BasicJsonType>(j), identity_tag<std::pair<A1, A2>> {}, priority_tag<0> {});
+}
+
+template<typename BasicJsonType, typename... Args>
+std::tuple<Args...> from_json_tuple_impl(BasicJsonType&& j, identity_tag<std::tuple<Args...>> /*unused*/, priority_tag<2> /*unused*/)
+{
+    return from_json_tuple_impl_base<BasicJsonType, Args...>(std::forward<BasicJsonType>(j), index_sequence_for<Args...> {});
+}
+
+template<typename BasicJsonType, typename... Args>
+inline void from_json_tuple_impl(BasicJsonType&& j, std::tuple<Args...>& t, priority_tag<3> /*unused*/)
+{
+    t = from_json_tuple_impl_base<BasicJsonType, Args...>(std::forward<BasicJsonType>(j), index_sequence_for<Args...> {});
+}
+
+template<typename BasicJsonType, typename TupleRelated>
+auto from_json(BasicJsonType&& j, TupleRelated&& t)
+-> decltype(from_json_tuple_impl(std::forward<BasicJsonType>(j), std::forward<TupleRelated>(t), priority_tag<3> {}))
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+
+    return from_json_tuple_impl(std::forward<BasicJsonType>(j), std::forward<TupleRelated>(t), priority_tag<3> {});
+}
+
+template < typename BasicJsonType, typename Key, typename Value, typename Compare, typename Allocator,
+           typename = enable_if_t < !std::is_constructible <
+                                        typename BasicJsonType::string_t, Key >::value >>
+inline void from_json(const BasicJsonType& j, std::map<Key, Value, Compare, Allocator>& m)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    m.clear();
+    for (const auto& p : j)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!p.is_array()))
+        {
+            JSON_THROW(type_error::create(302, concat("type must be array, but is ", p.type_name()), &j));
+        }
+        m.emplace(p.at(0).template get<Key>(), p.at(1).template get<Value>());
+    }
+}
+
+template < typename BasicJsonType, typename Key, typename Value, typename Hash, typename KeyEqual, typename Allocator,
+           typename = enable_if_t < !std::is_constructible <
+                                        typename BasicJsonType::string_t, Key >::value >>
+inline void from_json(const BasicJsonType& j, std::unordered_map<Key, Value, Hash, KeyEqual, Allocator>& m)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_array()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be array, but is ", j.type_name()), &j));
+    }
+    m.clear();
+    for (const auto& p : j)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!p.is_array()))
+        {
+            JSON_THROW(type_error::create(302, concat("type must be array, but is ", p.type_name()), &j));
+        }
+        m.emplace(p.at(0).template get<Key>(), p.at(1).template get<Value>());
+    }
+}
+
+#if JSON_HAS_FILESYSTEM || JSON_HAS_EXPERIMENTAL_FILESYSTEM
+template<typename BasicJsonType>
+inline void from_json(const BasicJsonType& j, std_fs::path& p)
+{
+    if (JSON_HEDLEY_UNLIKELY(!j.is_string()))
+    {
+        JSON_THROW(type_error::create(302, concat("type must be string, but is ", j.type_name()), &j));
+    }
+    const auto& s = *j.template get_ptr<const typename BasicJsonType::string_t*>();
+#ifdef JSON_HAS_CPP_20
+    p = std_fs::path(std::u8string_view(reinterpret_cast<const char8_t*>(s.data()), s.size()));
+#else
+    p = std_fs::u8path(s); // accepts UTF-8 encoded std::string in C++17, deprecated in C++20
+#endif
+}
+#endif
+
+struct from_json_fn
+{
+    template<typename BasicJsonType, typename T>
+    auto operator()(const BasicJsonType& j, T&& val) const
+    noexcept(noexcept(from_json(j, std::forward<T>(val))))
+    -> decltype(from_json(j, std::forward<T>(val)))
+    {
+        return from_json(j, std::forward<T>(val));
+    }
+};
+
+}  // namespace detail
+
+#ifndef JSON_HAS_CPP_17
+/// namespace to hold default `from_json` function
+/// to see why this is required:
+/// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/n4381.html
+namespace // NOLINT(cert-dcl59-cpp,fuchsia-header-anon-namespaces,google-build-namespaces)
+{
+#endif
+JSON_INLINE_VARIABLE constexpr const auto& from_json = // NOLINT(misc-definitions-in-headers)
+    detail::static_const<detail::from_json_fn>::value;
+#ifndef JSON_HAS_CPP_17
+}  // namespace
+#endif
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/conversions/to_json.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/macro_scope.hpp>
+// JSON_HAS_CPP_17
+#ifdef JSON_HAS_CPP_17
+    #include <optional> // optional
+#endif
+
+#include <algorithm> // copy
+#include <iterator> // begin, end
+#include <string> // string
+#include <tuple> // tuple, get
+#include <type_traits> // is_same, is_constructible, is_floating_point, is_enum, underlying_type
+#include <utility> // move, forward, declval, pair
+#include <valarray> // valarray
+#include <vector> // vector
+
+// #include <nlohmann/detail/iterators/iteration_proxy.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // size_t
+#include <iterator> // forward_iterator_tag
+#include <tuple> // tuple_size, get, tuple_element
+#include <utility> // move
+
+#if JSON_HAS_RANGES
+    #include <ranges> // enable_borrowed_range
+#endif
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/string_utils.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // size_t
+#include <string> // string, to_string
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename StringType>
+void int_to_string(StringType& target, std::size_t value)
+{
+    // For ADL
+    using std::to_string;
+    target = to_string(value);
+}
+
+template<typename StringType>
+StringType to_string(std::size_t value)
+{
+    StringType result;
+    int_to_string(result, value);
+    return result;
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename IteratorType> class iteration_proxy_value
+{
+  public:
+    using difference_type = std::ptrdiff_t;
+    using value_type = iteration_proxy_value;
+    using pointer = value_type *;
+    using reference = value_type &;
+    using iterator_category = std::forward_iterator_tag;
+    using string_type = typename std::remove_cv< typename std::remove_reference<decltype( std::declval<IteratorType>().key() ) >::type >::type;
+
+  private:
+    /// the iterator
+    IteratorType anchor{};
+    /// an index for arrays (used to create key names)
+    std::size_t array_index = 0;
+    /// last stringified array index
+    mutable std::size_t array_index_last = 0;
+    /// a string representation of the array index
+    mutable string_type array_index_str = "0";
+    /// an empty string (to return a reference for primitive values)
+    string_type empty_str{};
+
+  public:
+    explicit iteration_proxy_value() = default;
+    explicit iteration_proxy_value(IteratorType it, std::size_t array_index_ = 0)
+    noexcept(std::is_nothrow_move_constructible<IteratorType>::value
+             && std::is_nothrow_default_constructible<string_type>::value)
+        : anchor(std::move(it))
+        , array_index(array_index_)
+    {}
+
+    iteration_proxy_value(iteration_proxy_value const&) = default;
+    iteration_proxy_value& operator=(iteration_proxy_value const&) = default;
+    // older GCCs are a bit fussy and require explicit noexcept specifiers on defaulted functions
+    iteration_proxy_value(iteration_proxy_value&&)
+    noexcept(std::is_nothrow_move_constructible<IteratorType>::value
+             && std::is_nothrow_move_constructible<string_type>::value) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor,cppcoreguidelines-noexcept-move-operations)
+    iteration_proxy_value& operator=(iteration_proxy_value&&)
+    noexcept(std::is_nothrow_move_assignable<IteratorType>::value
+             && std::is_nothrow_move_assignable<string_type>::value) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor,cppcoreguidelines-noexcept-move-operations)
+    ~iteration_proxy_value() = default;
+
+    /// dereference operator (needed for range-based for)
+    const iteration_proxy_value& operator*() const
+    {
+        return *this;
+    }
+
+    /// increment operator (needed for range-based for)
+    iteration_proxy_value& operator++()
+    {
+        ++anchor;
+        ++array_index;
+
+        return *this;
+    }
+
+    iteration_proxy_value operator++(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        auto tmp = iteration_proxy_value(anchor, array_index);
+        ++anchor;
+        ++array_index;
+        return tmp;
+    }
+
+    /// equality operator (needed for InputIterator)
+    bool operator==(const iteration_proxy_value& o) const
+    {
+        return anchor == o.anchor;
+    }
+
+    /// inequality operator (needed for range-based for)
+    bool operator!=(const iteration_proxy_value& o) const
+    {
+        return anchor != o.anchor;
+    }
+
+    /// return key of the iterator
+    const string_type& key() const
+    {
+        JSON_ASSERT(anchor.m_object != nullptr);
+
+        switch (anchor.m_object->type())
+        {
+            // use integer array index as key
+            case value_t::array:
+            {
+                if (array_index != array_index_last)
+                {
+                    int_to_string( array_index_str, array_index );
+                    array_index_last = array_index;
+                }
+                return array_index_str;
+            }
+
+            // use key from the object
+            case value_t::object:
+                return anchor.key();
+
+            // use an empty key for all primitive types
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return empty_str;
+        }
+    }
+
+    /// return value of the iterator
+    typename IteratorType::reference value() const
+    {
+        return anchor.value();
+    }
+};
+
+/// proxy class for the items() function
+template<typename IteratorType> class iteration_proxy
+{
+  private:
+    /// the container to iterate
+    typename IteratorType::pointer container = nullptr;
+
+  public:
+    explicit iteration_proxy() = default;
+
+    /// construct iteration proxy from a container
+    explicit iteration_proxy(typename IteratorType::reference cont) noexcept
+        : container(&cont) {}
+
+    iteration_proxy(iteration_proxy const&) = default;
+    iteration_proxy& operator=(iteration_proxy const&) = default;
+    iteration_proxy(iteration_proxy&&) noexcept = default;
+    iteration_proxy& operator=(iteration_proxy&&) noexcept = default;
+    ~iteration_proxy() = default;
+
+    /// return iterator begin (needed for range-based for)
+    iteration_proxy_value<IteratorType> begin() const noexcept
+    {
+        return iteration_proxy_value<IteratorType>(container->begin());
+    }
+
+    /// return iterator end (needed for range-based for)
+    iteration_proxy_value<IteratorType> end() const noexcept
+    {
+        return iteration_proxy_value<IteratorType>(container->end());
+    }
+};
+
+// Structured Bindings Support
+// For further reference see https://blog.tartanllama.xyz/structured-bindings/
+// And see https://github.com/nlohmann/json/pull/1391
+template<std::size_t N, typename IteratorType, enable_if_t<N == 0, int> = 0>
+auto get(const nlohmann::detail::iteration_proxy_value<IteratorType>& i) -> decltype(i.key())
+{
+    return i.key();
+}
+// Structured Bindings Support
+// For further reference see https://blog.tartanllama.xyz/structured-bindings/
+// And see https://github.com/nlohmann/json/pull/1391
+template<std::size_t N, typename IteratorType, enable_if_t<N == 1, int> = 0>
+auto get(const nlohmann::detail::iteration_proxy_value<IteratorType>& i) -> decltype(i.value())
+{
+    return i.value();
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// The Addition to the STD Namespace is required to add
+// Structured Bindings Support to the iteration_proxy_value class
+// For further reference see https://blog.tartanllama.xyz/structured-bindings/
+// And see https://github.com/nlohmann/json/pull/1391
+namespace std
+{
+
+#if defined(__clang__)
+    // Fix: https://github.com/nlohmann/json/issues/1401
+    #pragma clang diagnostic push
+    #pragma clang diagnostic ignored "-Wmismatched-tags"
+#endif
+template<typename IteratorType>
+class tuple_size<::nlohmann::detail::iteration_proxy_value<IteratorType>> // NOLINT(cert-dcl58-cpp)
+    : public std::integral_constant<std::size_t, 2> {};
+
+template<std::size_t N, typename IteratorType>
+class tuple_element<N, ::nlohmann::detail::iteration_proxy_value<IteratorType >> // NOLINT(cert-dcl58-cpp)
+{
+  public:
+    using type = decltype(
+                     get<N>(std::declval <
+                            ::nlohmann::detail::iteration_proxy_value<IteratorType >> ()));
+};
+#if defined(__clang__)
+    #pragma clang diagnostic pop
+#endif
+
+}  // namespace std
+
+#if JSON_HAS_RANGES
+    template <typename IteratorType>
+    inline constexpr bool ::std::ranges::enable_borrowed_range<::nlohmann::detail::iteration_proxy<IteratorType>> = true;
+#endif
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/std_fs.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+//////////////////
+// constructors //
+//////////////////
+
+/*
+ * Note all external_constructor<>::construct functions need to call
+ * j.m_data.m_value.destroy(j.m_data.m_type) to avoid a memory leak in case j contains an
+ * allocated value (e.g., a string). See bug issue
+ * https://github.com/nlohmann/json/issues/2865 for more information.
+ */
+
+template<value_t> struct external_constructor;
+
+template<>
+struct external_constructor<value_t::boolean>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::boolean_t b) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::boolean;
+        j.m_data.m_value = b;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::string>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::string_t& s)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::string;
+        j.m_data.m_value = s;
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::string_t&& s)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::string;
+        j.m_data.m_value = std::move(s);
+        j.assert_invariant();
+    }
+
+    template < typename BasicJsonType, typename CompatibleStringType,
+               enable_if_t < !std::is_same<CompatibleStringType, typename BasicJsonType::string_t>::value,
+                             int > = 0 >
+    static void construct(BasicJsonType& j, const CompatibleStringType& str)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::string;
+        j.m_data.m_value.string = j.template create<typename BasicJsonType::string_t>(str);
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::binary>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::binary_t& b)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::binary;
+        j.m_data.m_value = typename BasicJsonType::binary_t(b);
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::binary_t&& b)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::binary;
+        j.m_data.m_value = typename BasicJsonType::binary_t(std::move(b));
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::number_float>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::number_float_t val) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::number_float;
+        j.m_data.m_value = val;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::number_unsigned>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::number_unsigned_t val) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::number_unsigned;
+        j.m_data.m_value = val;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::number_integer>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::number_integer_t val) noexcept
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::number_integer;
+        j.m_data.m_value = val;
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::array>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::array_t& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = arr;
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::array_t&& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = std::move(arr);
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template < typename BasicJsonType, typename CompatibleArrayType,
+               enable_if_t < !std::is_same<CompatibleArrayType, typename BasicJsonType::array_t>::value,
+                             int > = 0 >
+    static void construct(BasicJsonType& j, const CompatibleArrayType& arr)
+    {
+        using std::begin;
+        using std::end;
+
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value.array = j.template create<typename BasicJsonType::array_t>(begin(arr), end(arr));
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const std::vector<bool>& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = value_t::array;
+        j.m_data.m_value.array->reserve(arr.size());
+        for (const bool x : arr)
+        {
+            j.m_data.m_value.array->push_back(x);
+            j.set_parent(j.m_data.m_value.array->back());
+        }
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType, typename T,
+             enable_if_t<std::is_convertible<T, BasicJsonType>::value, int> = 0>
+    static void construct(BasicJsonType& j, const std::valarray<T>& arr)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::array;
+        j.m_data.m_value = value_t::array;
+        j.m_data.m_value.array->resize(arr.size());
+        if (arr.size() > 0)
+        {
+            std::copy(std::begin(arr), std::end(arr), j.m_data.m_value.array->begin());
+        }
+        j.set_parents();
+        j.assert_invariant();
+    }
+};
+
+template<>
+struct external_constructor<value_t::object>
+{
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, const typename BasicJsonType::object_t& obj)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::object;
+        j.m_data.m_value = obj;
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template<typename BasicJsonType>
+    static void construct(BasicJsonType& j, typename BasicJsonType::object_t&& obj)
+    {
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::object;
+        j.m_data.m_value = std::move(obj);
+        j.set_parents();
+        j.assert_invariant();
+    }
+
+    template < typename BasicJsonType, typename CompatibleObjectType,
+               enable_if_t < !std::is_same<CompatibleObjectType, typename BasicJsonType::object_t>::value, int > = 0 >
+    static void construct(BasicJsonType& j, const CompatibleObjectType& obj)
+    {
+        using std::begin;
+        using std::end;
+
+        j.m_data.m_value.destroy(j.m_data.m_type);
+        j.m_data.m_type = value_t::object;
+        j.m_data.m_value.object = j.template create<typename BasicJsonType::object_t>(begin(obj), end(obj));
+        j.set_parents();
+        j.assert_invariant();
+    }
+};
+
+/////////////
+// to_json //
+/////////////
+
+#ifdef JSON_HAS_CPP_17
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_constructible<BasicJsonType, T>::value, int> = 0>
+void to_json(BasicJsonType& j, const std::optional<T>& opt)
+{
+    if (opt.has_value())
+    {
+        j = *opt;
+    }
+    else
+    {
+        j = nullptr;
+    }
+}
+#endif
+
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_same<T, typename BasicJsonType::boolean_t>::value, int> = 0>
+inline void to_json(BasicJsonType& j, T b) noexcept
+{
+    external_constructor<value_t::boolean>::construct(j, b);
+}
+
+template < typename BasicJsonType, typename BoolRef,
+           enable_if_t <
+               ((std::is_same<std::vector<bool>::reference, BoolRef>::value
+                 && !std::is_same <std::vector<bool>::reference, typename BasicJsonType::boolean_t&>::value)
+                || (std::is_same<std::vector<bool>::const_reference, BoolRef>::value
+                    && !std::is_same <detail::uncvref_t<std::vector<bool>::const_reference>,
+                                      typename BasicJsonType::boolean_t >::value))
+               && std::is_convertible<const BoolRef&, typename BasicJsonType::boolean_t>::value, int > = 0 >
+inline void to_json(BasicJsonType& j, const BoolRef& b) noexcept
+{
+    external_constructor<value_t::boolean>::construct(j, static_cast<typename BasicJsonType::boolean_t>(b));
+}
+
+template<typename BasicJsonType, typename CompatibleString,
+         enable_if_t<std::is_constructible<typename BasicJsonType::string_t, CompatibleString>::value, int> = 0>
+inline void to_json(BasicJsonType& j, const CompatibleString& s)
+{
+    external_constructor<value_t::string>::construct(j, s);
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, typename BasicJsonType::string_t&& s)
+{
+    external_constructor<value_t::string>::construct(j, std::move(s));
+}
+
+template<typename BasicJsonType, typename FloatType,
+         enable_if_t<std::is_floating_point<FloatType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, FloatType val) noexcept
+{
+    external_constructor<value_t::number_float>::construct(j, static_cast<typename BasicJsonType::number_float_t>(val));
+}
+
+template<typename BasicJsonType, typename CompatibleNumberUnsignedType,
+         enable_if_t<is_compatible_integer_type<typename BasicJsonType::number_unsigned_t, CompatibleNumberUnsignedType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, CompatibleNumberUnsignedType val) noexcept
+{
+    external_constructor<value_t::number_unsigned>::construct(j, static_cast<typename BasicJsonType::number_unsigned_t>(val));
+}
+
+template<typename BasicJsonType, typename CompatibleNumberIntegerType,
+         enable_if_t<is_compatible_integer_type<typename BasicJsonType::number_integer_t, CompatibleNumberIntegerType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, CompatibleNumberIntegerType val) noexcept
+{
+    external_constructor<value_t::number_integer>::construct(j, static_cast<typename BasicJsonType::number_integer_t>(val));
+}
+
+#if !JSON_DISABLE_ENUM_SERIALIZATION
+template<typename BasicJsonType, typename EnumType,
+         enable_if_t<std::is_enum<EnumType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, EnumType e) noexcept
+{
+    using underlying_type = typename std::underlying_type<EnumType>::type;
+    static constexpr value_t integral_value_t = std::is_unsigned<underlying_type>::value ? value_t::number_unsigned : value_t::number_integer;
+    external_constructor<integral_value_t>::construct(j, static_cast<underlying_type>(e));
+}
+#endif  // JSON_DISABLE_ENUM_SERIALIZATION
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, const std::vector<bool>& e)
+{
+    external_constructor<value_t::array>::construct(j, e);
+}
+
+template < typename BasicJsonType, typename CompatibleArrayType,
+           enable_if_t < is_compatible_array_type<BasicJsonType,
+                         CompatibleArrayType>::value&&
+                         !is_compatible_object_type<BasicJsonType, CompatibleArrayType>::value&&
+                         !is_compatible_string_type<BasicJsonType, CompatibleArrayType>::value&&
+                         !std::is_same<typename BasicJsonType::binary_t, CompatibleArrayType>::value&&
+                         !is_basic_json<CompatibleArrayType>::value,
+                         int > = 0 >
+inline void to_json(BasicJsonType& j, const CompatibleArrayType& arr)
+{
+    external_constructor<value_t::array>::construct(j, arr);
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, const typename BasicJsonType::binary_t& bin)
+{
+    external_constructor<value_t::binary>::construct(j, bin);
+}
+
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_convertible<T, BasicJsonType>::value, int> = 0>
+inline void to_json(BasicJsonType& j, const std::valarray<T>& arr)
+{
+    external_constructor<value_t::array>::construct(j, std::move(arr));
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, typename BasicJsonType::array_t&& arr)
+{
+    external_constructor<value_t::array>::construct(j, std::move(arr));
+}
+
+template < typename BasicJsonType, typename CompatibleObjectType,
+           enable_if_t < is_compatible_object_type<BasicJsonType, CompatibleObjectType>::value&& !is_basic_json<CompatibleObjectType>::value, int > = 0 >
+inline void to_json(BasicJsonType& j, const CompatibleObjectType& obj)
+{
+    external_constructor<value_t::object>::construct(j, obj);
+}
+
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, typename BasicJsonType::object_t&& obj)
+{
+    external_constructor<value_t::object>::construct(j, std::move(obj));
+}
+
+template <
+    typename BasicJsonType, typename T, std::size_t N,
+    enable_if_t < !std::is_constructible<typename BasicJsonType::string_t,
+                  const T(&)[N]>::value, // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+                  int > = 0 >
+inline void to_json(BasicJsonType& j, const T(&arr)[N]) // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+{
+    external_constructor<value_t::array>::construct(j, arr);
+}
+
+template < typename BasicJsonType, typename T1, typename T2, enable_if_t < std::is_constructible<BasicJsonType, T1>::value&& std::is_constructible<BasicJsonType, T2>::value, int > = 0 >
+inline void to_json(BasicJsonType& j, const std::pair<T1, T2>& p)
+{
+    j = { p.first, p.second };
+}
+
+// for https://github.com/nlohmann/json/pull/1134
+template<typename BasicJsonType, typename T,
+         enable_if_t<std::is_same<T, iteration_proxy_value<typename BasicJsonType::iterator>>::value, int> = 0>
+inline void to_json(BasicJsonType& j, const T& b)
+{
+    j = { {b.key(), b.value()} };
+}
+
+template<typename BasicJsonType, typename Tuple, std::size_t... Idx>
+inline void to_json_tuple_impl(BasicJsonType& j, const Tuple& t, index_sequence<Idx...> /*unused*/)
+{
+    j = { std::get<Idx>(t)... };
+}
+
+template<typename BasicJsonType, typename Tuple>
+inline void to_json_tuple_impl(BasicJsonType& j, const Tuple& /*unused*/, index_sequence<> /*unused*/)
+{
+    using array_t = typename BasicJsonType::array_t;
+    j = array_t();
+}
+
+template<typename BasicJsonType, typename T, enable_if_t<is_constructible_tuple<BasicJsonType, T>::value, int > = 0>
+inline void to_json(BasicJsonType& j, const T& t)
+{
+    to_json_tuple_impl(j, t, make_index_sequence<std::tuple_size<T>::value> {});
+}
+
+#if JSON_HAS_FILESYSTEM || JSON_HAS_EXPERIMENTAL_FILESYSTEM
+template<typename BasicJsonType>
+inline void to_json(BasicJsonType& j, const std_fs::path& p)
+{
+#ifdef JSON_HAS_CPP_20
+    const std::u8string s = p.u8string();
+    j = std::string(s.begin(), s.end());
+#else
+    j = p.u8string(); // returns std::string in C++17
+#endif
+}
+#endif
+
+struct to_json_fn
+{
+    template<typename BasicJsonType, typename T>
+    auto operator()(BasicJsonType& j, T&& val) const noexcept(noexcept(to_json(j, std::forward<T>(val))))
+    -> decltype(to_json(j, std::forward<T>(val)), void())
+    {
+        return to_json(j, std::forward<T>(val));
+    }
+};
+}  // namespace detail
+
+#ifndef JSON_HAS_CPP_17
+/// namespace to hold default `to_json` function
+/// to see why this is required:
+/// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/n4381.html
+namespace // NOLINT(cert-dcl59-cpp,fuchsia-header-anon-namespaces,google-build-namespaces)
+{
+#endif
+JSON_INLINE_VARIABLE constexpr const auto& to_json = // NOLINT(misc-definitions-in-headers)
+    detail::static_const<detail::to_json_fn>::value;
+#ifndef JSON_HAS_CPP_17
+}  // namespace
+#endif
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/identity_tag.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// @sa https://json.nlohmann.me/api/adl_serializer/
+template<typename ValueType, typename>
+struct adl_serializer
+{
+    /// @brief convert a JSON value to any value type
+    /// @sa https://json.nlohmann.me/api/adl_serializer/from_json/
+    template<typename BasicJsonType, typename TargetType = ValueType>
+    static auto from_json(BasicJsonType && j, TargetType& val) noexcept(
+        noexcept(::nlohmann::from_json(std::forward<BasicJsonType>(j), val)))
+    -> decltype(::nlohmann::from_json(std::forward<BasicJsonType>(j), val), void())
+    {
+        ::nlohmann::from_json(std::forward<BasicJsonType>(j), val);
+    }
+
+    /// @brief convert a JSON value to any value type
+    /// @sa https://json.nlohmann.me/api/adl_serializer/from_json/
+    template<typename BasicJsonType, typename TargetType = ValueType>
+    static auto from_json(BasicJsonType && j) noexcept(
+    noexcept(::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {})))
+    -> decltype(::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {}))
+    {
+        return ::nlohmann::from_json(std::forward<BasicJsonType>(j), detail::identity_tag<TargetType> {});
+    }
+
+    /// @brief convert any value type to a JSON value
+    /// @sa https://json.nlohmann.me/api/adl_serializer/to_json/
+    template<typename BasicJsonType, typename TargetType = ValueType>
+    static auto to_json(BasicJsonType& j, TargetType && val) noexcept(
+        noexcept(::nlohmann::to_json(j, std::forward<TargetType>(val))))
+    -> decltype(::nlohmann::to_json(j, std::forward<TargetType>(val)), void())
+    {
+        ::nlohmann::to_json(j, std::forward<TargetType>(val));
+    }
+};
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/byte_container_with_subtype.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // uint8_t, uint64_t
+#include <tuple> // tie
+#include <utility> // move
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// @brief an internal type for a backed binary type
+/// @sa https://json.nlohmann.me/api/byte_container_with_subtype/
+template<typename BinaryType>
+class byte_container_with_subtype : public BinaryType
+{
+  public:
+    using container_type = BinaryType;
+    using subtype_type = std::uint64_t;
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype() noexcept(noexcept(container_type()))
+        : container_type()
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(const container_type& b) noexcept(noexcept(container_type(b)))
+        : container_type(b)
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(container_type&& b) noexcept(noexcept(container_type(std::move(b))))
+        : container_type(std::move(b))
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(const container_type& b, subtype_type subtype_) noexcept(noexcept(container_type(b)))
+        : container_type(b)
+        , m_subtype(subtype_)
+        , m_has_subtype(true)
+    {}
+
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/byte_container_with_subtype/
+    byte_container_with_subtype(container_type&& b, subtype_type subtype_) noexcept(noexcept(container_type(std::move(b))))
+        : container_type(std::move(b))
+        , m_subtype(subtype_)
+        , m_has_subtype(true)
+    {}
+
+    bool operator==(const byte_container_with_subtype& rhs) const
+    {
+        return std::tie(static_cast<const BinaryType&>(*this), m_subtype, m_has_subtype) ==
+               std::tie(static_cast<const BinaryType&>(rhs), rhs.m_subtype, rhs.m_has_subtype);
+    }
+
+    bool operator!=(const byte_container_with_subtype& rhs) const
+    {
+        return !(rhs == *this);
+    }
+
+    /// @brief sets the binary subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/set_subtype/
+    void set_subtype(subtype_type subtype_) noexcept
+    {
+        m_subtype = subtype_;
+        m_has_subtype = true;
+    }
+
+    /// @brief return the binary subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/subtype/
+    constexpr subtype_type subtype() const noexcept
+    {
+        return m_has_subtype ? m_subtype : static_cast<subtype_type>(-1);
+    }
+
+    /// @brief return whether the value has a subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/has_subtype/
+    constexpr bool has_subtype() const noexcept
+    {
+        return m_has_subtype;
+    }
+
+    /// @brief clears the binary subtype
+    /// @sa https://json.nlohmann.me/api/byte_container_with_subtype/clear_subtype/
+    void clear_subtype() noexcept
+    {
+        m_subtype = 0;
+        m_has_subtype = false;
+    }
+
+  private:
+    subtype_type m_subtype = 0;
+    bool m_has_subtype = false;
+};
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/conversions/from_json.hpp>
+
+// #include <nlohmann/detail/conversions/to_json.hpp>
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/hash.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // uint8_t
+#include <cstddef> // size_t
+#include <functional> // hash
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// boost::hash_combine
+inline std::size_t combine(std::size_t seed, std::size_t h) noexcept
+{
+    seed ^= h + 0x9e3779b9 + (seed << 6U) + (seed >> 2U);
+    return seed;
+}
+
+/*!
+@brief hash a JSON value
+
+The hash function tries to rely on std::hash where possible. Furthermore, the
+type of the JSON value is taken into account to have different hash values for
+null, 0, 0U, and false, etc.
+
+@tparam BasicJsonType basic_json specialization
+@param j JSON value to hash
+@return hash value of j
+*/
+template<typename BasicJsonType>
+std::size_t hash(const BasicJsonType& j)
+{
+    using string_t = typename BasicJsonType::string_t;
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+
+    const auto type = static_cast<std::size_t>(j.type());
+    switch (j.type())
+    {
+        case BasicJsonType::value_t::null:
+        case BasicJsonType::value_t::discarded:
+        {
+            return combine(type, 0);
+        }
+
+        case BasicJsonType::value_t::object:
+        {
+            auto seed = combine(type, j.size());
+            for (const auto& element : j.items())
+            {
+                const auto h = std::hash<string_t> {}(element.key());
+                seed = combine(seed, h);
+                seed = combine(seed, hash(element.value()));
+            }
+            return seed;
+        }
+
+        case BasicJsonType::value_t::array:
+        {
+            auto seed = combine(type, j.size());
+            for (const auto& element : j)
+            {
+                seed = combine(seed, hash(element));
+            }
+            return seed;
+        }
+
+        case BasicJsonType::value_t::string:
+        {
+            const auto h = std::hash<string_t> {}(j.template get_ref<const string_t&>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::boolean:
+        {
+            const auto h = std::hash<bool> {}(j.template get<bool>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::number_integer:
+        {
+            const auto h = std::hash<number_integer_t> {}(j.template get<number_integer_t>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::number_unsigned:
+        {
+            const auto h = std::hash<number_unsigned_t> {}(j.template get<number_unsigned_t>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::number_float:
+        {
+            const auto h = std::hash<number_float_t> {}(j.template get<number_float_t>());
+            return combine(type, h);
+        }
+
+        case BasicJsonType::value_t::binary:
+        {
+            auto seed = combine(type, j.get_binary().size());
+            const auto h = std::hash<bool> {}(j.get_binary().has_subtype());
+            seed = combine(seed, h);
+            seed = combine(seed, static_cast<std::size_t>(j.get_binary().subtype()));
+            for (const auto byte : j.get_binary())
+            {
+                seed = combine(seed, std::hash<std::uint8_t> {}(byte));
+            }
+            return seed;
+        }
+
+        default:                   // LCOV_EXCL_LINE
+            JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+            return 0;              // LCOV_EXCL_LINE
+    }
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/binary_reader.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // generate_n
+#include <array> // array
+#include <cmath> // ldexp
+#include <cstddef> // size_t
+#include <cstdint> // uint8_t, uint16_t, uint32_t, uint64_t
+#include <cstdio> // snprintf
+#include <cstring> // memcpy
+#include <iterator> // back_inserter
+#include <limits> // numeric_limits
+#include <string> // char_traits, string
+#include <utility> // make_pair, move
+#include <vector> // vector
+#ifdef __cpp_lib_byteswap
+    #include <bit>  //byteswap
+#endif
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cstddef> // size_t
+#include <cstring> // strlen
+#include <iterator> // begin, end, iterator_traits, random_access_iterator_tag, distance, next
+#include <memory> // shared_ptr, make_shared, addressof
+#include <numeric> // accumulate
+#include <string> // string, char_traits
+#include <type_traits> // enable_if, is_base_of, is_pointer, is_integral, remove_pointer
+#include <utility> // pair, declval
+
+#ifndef JSON_NO_IO
+    #include <cstdio>   // FILE *
+    #include <istream>  // istream
+#endif                  // JSON_NO_IO
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/iterators/iterator_traits.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// the supported input formats
+enum class input_format_t { json, cbor, msgpack, ubjson, bson, bjdata };
+
+////////////////////
+// input adapters //
+////////////////////
+
+#ifndef JSON_NO_IO
+/*!
+Input adapter for stdio file access. This adapter read only 1 byte and do not use any
+ buffer. This adapter is a very low level adapter.
+*/
+class file_input_adapter
+{
+  public:
+    using char_type = char;
+
+    JSON_HEDLEY_NON_NULL(2)
+    explicit file_input_adapter(std::FILE* f) noexcept
+        : m_file(f)
+    {
+        JSON_ASSERT(m_file != nullptr);
+    }
+
+    // make class move-only
+    file_input_adapter(const file_input_adapter&) = delete;
+    file_input_adapter(file_input_adapter&&) noexcept = default;
+    file_input_adapter& operator=(const file_input_adapter&) = delete;
+    file_input_adapter& operator=(file_input_adapter&&) = delete;
+    ~file_input_adapter() = default;
+
+    std::char_traits<char>::int_type get_character() noexcept
+    {
+        return std::fgetc(m_file);
+    }
+
+    // returns the number of characters successfully read
+    template<class T>
+    std::size_t get_elements(T* dest, std::size_t count = 1)
+    {
+        return fread(dest, 1, sizeof(T) * count, m_file);
+    }
+
+  private:
+    /// the file pointer to read from
+    std::FILE* m_file;
+};
+
+/*!
+Input adapter for a (caching) istream. Ignores a UFT Byte Order Mark at
+beginning of input. Does not support changing the underlying std::streambuf
+in mid-input. Maintains underlying std::istream and std::streambuf to support
+subsequent use of standard std::istream operations to process any input
+characters following those used in parsing the JSON input.  Clears the
+std::istream flags; any input errors (e.g., EOF) will be detected by the first
+subsequent call for input from the std::istream.
+*/
+class input_stream_adapter
+{
+  public:
+    using char_type = char;
+
+    ~input_stream_adapter()
+    {
+        // clear stream flags; we use underlying streambuf I/O, do not
+        // maintain ifstream flags, except eof
+        if (is != nullptr)
+        {
+            is->clear(is->rdstate() & std::ios::eofbit);
+        }
+    }
+
+    explicit input_stream_adapter(std::istream& i)
+        : is(&i), sb(i.rdbuf())
+    {}
+
+    // delete because of pointer members
+    input_stream_adapter(const input_stream_adapter&) = delete;
+    input_stream_adapter& operator=(input_stream_adapter&) = delete;
+    input_stream_adapter& operator=(input_stream_adapter&&) = delete;
+
+    input_stream_adapter(input_stream_adapter&& rhs) noexcept
+        : is(rhs.is), sb(rhs.sb)
+    {
+        rhs.is = nullptr;
+        rhs.sb = nullptr;
+    }
+
+    // std::istream/std::streambuf use std::char_traits<char>::to_int_type, to
+    // ensure that std::char_traits<char>::eof() and the character 0xFF do not
+    // end up as the same value, e.g. 0xFFFFFFFF.
+    std::char_traits<char>::int_type get_character()
+    {
+        auto res = sb->sbumpc();
+        // set eof manually, as we don't use the istream interface.
+        if (JSON_HEDLEY_UNLIKELY(res == std::char_traits<char>::eof()))
+        {
+            is->clear(is->rdstate() | std::ios::eofbit);
+        }
+        return res;
+    }
+
+    template<class T>
+    std::size_t get_elements(T* dest, std::size_t count = 1)
+    {
+        auto res = static_cast<std::size_t>(sb->sgetn(reinterpret_cast<char*>(dest), static_cast<std::streamsize>(count * sizeof(T))));
+        if (JSON_HEDLEY_UNLIKELY(res < count * sizeof(T)))
+        {
+            is->clear(is->rdstate() | std::ios::eofbit);
+        }
+        return res;
+    }
+
+  private:
+    /// the associated input stream
+    std::istream* is = nullptr;
+    std::streambuf* sb = nullptr;
+};
+#endif  // JSON_NO_IO
+
+// General-purpose iterator-based adapter. It might not be as fast as
+// theoretically possible for some containers, but it is extremely versatile.
+template<typename IteratorType>
+class iterator_input_adapter
+{
+  public:
+    using char_type = typename std::iterator_traits<IteratorType>::value_type;
+
+    iterator_input_adapter(IteratorType first, IteratorType last)
+        : current(std::move(first)), end(std::move(last))
+    {}
+
+    typename char_traits<char_type>::int_type get_character()
+    {
+        if (JSON_HEDLEY_LIKELY(current != end))
+        {
+            auto result = char_traits<char_type>::to_int_type(*current);
+            std::advance(current, 1);
+            return result;
+        }
+
+        return char_traits<char_type>::eof();
+    }
+
+    // for general iterators, we cannot really do something better than falling back to processing the range one-by-one
+    template<class T>
+    std::size_t get_elements(T* dest, std::size_t count = 1)
+    {
+        auto* ptr = reinterpret_cast<char*>(dest);
+        for (std::size_t read_index = 0; read_index < count * sizeof(T); ++read_index)
+        {
+            if (JSON_HEDLEY_LIKELY(current != end))
+            {
+                ptr[read_index] = static_cast<char>(*current);
+                std::advance(current, 1);
+            }
+            else
+            {
+                return read_index;
+            }
+        }
+        return count * sizeof(T);
+    }
+
+  private:
+    IteratorType current;
+    IteratorType end;
+
+    template<typename BaseInputAdapter, size_t T>
+    friend struct wide_string_input_helper;
+
+    bool empty() const
+    {
+        return current == end;
+    }
+};
+
+template<typename BaseInputAdapter, size_t T>
+struct wide_string_input_helper;
+
+template<typename BaseInputAdapter>
+struct wide_string_input_helper<BaseInputAdapter, 4>
+{
+    // UTF-32
+    static void fill_buffer(BaseInputAdapter& input,
+                            std::array<std::char_traits<char>::int_type, 4>& utf8_bytes,
+                            size_t& utf8_bytes_index,
+                            size_t& utf8_bytes_filled)
+    {
+        utf8_bytes_index = 0;
+
+        if (JSON_HEDLEY_UNLIKELY(input.empty()))
+        {
+            utf8_bytes[0] = std::char_traits<char>::eof();
+            utf8_bytes_filled = 1;
+        }
+        else
+        {
+            // get the current character
+            const auto wc = input.get_character();
+
+            // UTF-32 to UTF-8 encoding
+            if (wc < 0x80)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                utf8_bytes_filled = 1;
+            }
+            else if (wc <= 0x7FF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xC0u | ((static_cast<unsigned int>(wc) >> 6u) & 0x1Fu));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 2;
+            }
+            else if (wc <= 0xFFFF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xE0u | ((static_cast<unsigned int>(wc) >> 12u) & 0x0Fu));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));
+                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 3;
+            }
+            else if (wc <= 0x10FFFF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xF0u | ((static_cast<unsigned int>(wc) >> 18u) & 0x07u));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 12u) & 0x3Fu));
+                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));
+                utf8_bytes[3] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 4;
+            }
+            else
+            {
+                // unknown character
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                utf8_bytes_filled = 1;
+            }
+        }
+    }
+};
+
+template<typename BaseInputAdapter>
+struct wide_string_input_helper<BaseInputAdapter, 2>
+{
+    // UTF-16
+    static void fill_buffer(BaseInputAdapter& input,
+                            std::array<std::char_traits<char>::int_type, 4>& utf8_bytes,
+                            size_t& utf8_bytes_index,
+                            size_t& utf8_bytes_filled)
+    {
+        utf8_bytes_index = 0;
+
+        if (JSON_HEDLEY_UNLIKELY(input.empty()))
+        {
+            utf8_bytes[0] = std::char_traits<char>::eof();
+            utf8_bytes_filled = 1;
+        }
+        else
+        {
+            // get the current character
+            const auto wc = input.get_character();
+
+            // UTF-16 to UTF-8 encoding
+            if (wc < 0x80)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                utf8_bytes_filled = 1;
+            }
+            else if (wc <= 0x7FF)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xC0u | ((static_cast<unsigned int>(wc) >> 6u)));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 2;
+            }
+            else if (0xD800 > wc || wc >= 0xE000)
+            {
+                utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xE0u | ((static_cast<unsigned int>(wc) >> 12u)));
+                utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((static_cast<unsigned int>(wc) >> 6u) & 0x3Fu));
+                utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | (static_cast<unsigned int>(wc) & 0x3Fu));
+                utf8_bytes_filled = 3;
+            }
+            else
+            {
+                if (JSON_HEDLEY_UNLIKELY(!input.empty()))
+                {
+                    const auto wc2 = static_cast<unsigned int>(input.get_character());
+                    const auto charcode = 0x10000u + (((static_cast<unsigned int>(wc) & 0x3FFu) << 10u) | (wc2 & 0x3FFu));
+                    utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(0xF0u | (charcode >> 18u));
+                    utf8_bytes[1] = static_cast<std::char_traits<char>::int_type>(0x80u | ((charcode >> 12u) & 0x3Fu));
+                    utf8_bytes[2] = static_cast<std::char_traits<char>::int_type>(0x80u | ((charcode >> 6u) & 0x3Fu));
+                    utf8_bytes[3] = static_cast<std::char_traits<char>::int_type>(0x80u | (charcode & 0x3Fu));
+                    utf8_bytes_filled = 4;
+                }
+                else
+                {
+                    utf8_bytes[0] = static_cast<std::char_traits<char>::int_type>(wc);
+                    utf8_bytes_filled = 1;
+                }
+            }
+        }
+    }
+};
+
+// Wraps another input adapter to convert wide character types into individual bytes.
+template<typename BaseInputAdapter, typename WideCharType>
+class wide_string_input_adapter
+{
+  public:
+    using char_type = char;
+
+    wide_string_input_adapter(BaseInputAdapter base)
+        : base_adapter(base) {}
+
+    typename std::char_traits<char>::int_type get_character() noexcept
+    {
+        // check if buffer needs to be filled
+        if (utf8_bytes_index == utf8_bytes_filled)
+        {
+            fill_buffer<sizeof(WideCharType)>();
+
+            JSON_ASSERT(utf8_bytes_filled > 0);
+            JSON_ASSERT(utf8_bytes_index == 0);
+        }
+
+        // use buffer
+        JSON_ASSERT(utf8_bytes_filled > 0);
+        JSON_ASSERT(utf8_bytes_index < utf8_bytes_filled);
+        return utf8_bytes[utf8_bytes_index++];
+    }
+
+    // parsing binary with wchar doesn't make sense, but since the parsing mode can be runtime, we need something here
+    template<class T>
+    std::size_t get_elements(T* /*dest*/, std::size_t /*count*/ = 1)
+    {
+        JSON_THROW(parse_error::create(112, 1, "wide string type cannot be interpreted as binary data", nullptr));
+    }
+
+  private:
+    BaseInputAdapter base_adapter;
+
+    template<size_t T>
+    void fill_buffer()
+    {
+        wide_string_input_helper<BaseInputAdapter, T>::fill_buffer(base_adapter, utf8_bytes, utf8_bytes_index, utf8_bytes_filled);
+    }
+
+    /// a buffer for UTF-8 bytes
+    std::array<std::char_traits<char>::int_type, 4> utf8_bytes = {{0, 0, 0, 0}};
+
+    /// index to the utf8_codes array for the next valid byte
+    std::size_t utf8_bytes_index = 0;
+    /// number of valid bytes in the utf8_codes array
+    std::size_t utf8_bytes_filled = 0;
+};
+
+template<typename IteratorType, typename Enable = void>
+struct iterator_input_adapter_factory
+{
+    using iterator_type = IteratorType;
+    using char_type = typename std::iterator_traits<iterator_type>::value_type;
+    using adapter_type = iterator_input_adapter<iterator_type>;
+
+    static adapter_type create(IteratorType first, IteratorType last)
+    {
+        return adapter_type(std::move(first), std::move(last));
+    }
+};
+
+template<typename T>
+struct is_iterator_of_multibyte
+{
+    using value_type = typename std::iterator_traits<T>::value_type;
+    enum
+    {
+        value = sizeof(value_type) > 1
+    };
+};
+
+template<typename IteratorType>
+struct iterator_input_adapter_factory<IteratorType, enable_if_t<is_iterator_of_multibyte<IteratorType>::value>>
+{
+    using iterator_type = IteratorType;
+    using char_type = typename std::iterator_traits<iterator_type>::value_type;
+    using base_adapter_type = iterator_input_adapter<iterator_type>;
+    using adapter_type = wide_string_input_adapter<base_adapter_type, char_type>;
+
+    static adapter_type create(IteratorType first, IteratorType last)
+    {
+        return adapter_type(base_adapter_type(std::move(first), std::move(last)));
+    }
+};
+
+// General purpose iterator-based input
+template<typename IteratorType>
+typename iterator_input_adapter_factory<IteratorType>::adapter_type input_adapter(IteratorType first, IteratorType last)
+{
+    using factory_type = iterator_input_adapter_factory<IteratorType>;
+    return factory_type::create(first, last);
+}
+
+// Convenience shorthand from container to iterator
+// Enables ADL on begin(container) and end(container)
+// Encloses the using declarations in namespace for not to leak them to outside scope
+
+namespace container_input_adapter_factory_impl
+{
+
+using std::begin;
+using std::end;
+
+template<typename ContainerType, typename Enable = void>
+struct container_input_adapter_factory {};
+
+template<typename ContainerType>
+struct container_input_adapter_factory< ContainerType,
+       void_t<decltype(begin(std::declval<ContainerType>()), end(std::declval<ContainerType>()))>>
+       {
+           using adapter_type = decltype(input_adapter(begin(std::declval<ContainerType>()), end(std::declval<ContainerType>())));
+
+           static adapter_type create(const ContainerType& container)
+{
+    return input_adapter(begin(container), end(container));
+}
+       };
+
+}  // namespace container_input_adapter_factory_impl
+
+template<typename ContainerType>
+typename container_input_adapter_factory_impl::container_input_adapter_factory<ContainerType>::adapter_type input_adapter(const ContainerType& container)
+{
+    return container_input_adapter_factory_impl::container_input_adapter_factory<ContainerType>::create(container);
+}
+
+// specialization for std::string
+using string_input_adapter_type = decltype(input_adapter(std::declval<std::string>()));
+
+#ifndef JSON_NO_IO
+// Special cases with fast paths
+inline file_input_adapter input_adapter(std::FILE* file)
+{
+    if (file == nullptr)
+    {
+        JSON_THROW(parse_error::create(101, 0, "attempting to parse an empty input; check that your input string or stream contains the expected JSON", nullptr));
+    }
+    return file_input_adapter(file);
+}
+
+inline input_stream_adapter input_adapter(std::istream& stream)
+{
+    return input_stream_adapter(stream);
+}
+
+inline input_stream_adapter input_adapter(std::istream&& stream)
+{
+    return input_stream_adapter(stream);
+}
+#endif  // JSON_NO_IO
+
+using contiguous_bytes_input_adapter = decltype(input_adapter(std::declval<const char*>(), std::declval<const char*>()));
+
+// Null-delimited strings, and the like.
+template < typename CharT,
+           typename std::enable_if <
+               std::is_pointer<CharT>::value&&
+               !std::is_array<CharT>::value&&
+               std::is_integral<typename std::remove_pointer<CharT>::type>::value&&
+               sizeof(typename std::remove_pointer<CharT>::type) == 1,
+               int >::type = 0 >
+contiguous_bytes_input_adapter input_adapter(CharT b)
+{
+    if (b == nullptr)
+    {
+        JSON_THROW(parse_error::create(101, 0, "attempting to parse an empty input; check that your input string or stream contains the expected JSON", nullptr));
+    }
+    auto length = std::strlen(reinterpret_cast<const char*>(b));
+    const auto* ptr = reinterpret_cast<const char*>(b);
+    return input_adapter(ptr, ptr + length); // cppcheck-suppress[nullPointerArithmeticRedundantCheck]
+}
+
+template<typename T, std::size_t N>
+auto input_adapter(T (&array)[N]) -> decltype(input_adapter(array, array + N)) // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+{
+    return input_adapter(array, array + N);
+}
+
+// This class only handles inputs of input_buffer_adapter type.
+// It's required so that expressions like {ptr, len} can be implicitly cast
+// to the correct adapter.
+class span_input_adapter
+{
+  public:
+    template < typename CharT,
+               typename std::enable_if <
+                   std::is_pointer<CharT>::value&&
+                   std::is_integral<typename std::remove_pointer<CharT>::type>::value&&
+                   sizeof(typename std::remove_pointer<CharT>::type) == 1,
+                   int >::type = 0 >
+    span_input_adapter(CharT b, std::size_t l)
+        : ia(reinterpret_cast<const char*>(b), reinterpret_cast<const char*>(b) + l) {}
+
+    template<class IteratorType,
+             typename std::enable_if<
+                 std::is_same<typename iterator_traits<IteratorType>::iterator_category, std::random_access_iterator_tag>::value,
+                 int>::type = 0>
+    span_input_adapter(IteratorType first, IteratorType last)
+        : ia(input_adapter(first, last)) {}
+
+    contiguous_bytes_input_adapter&& get()
+    {
+        return std::move(ia); // NOLINT(hicpp-move-const-arg,performance-move-const-arg)
+    }
+
+  private:
+    contiguous_bytes_input_adapter ia;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/json_sax.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef>
+#include <string> // string
+#include <type_traits> // enable_if_t
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/input/lexer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <clocale> // localeconv
+#include <cstddef> // size_t
+#include <cstdio> // snprintf
+#include <cstdlib> // strtof, strtod, strtold, strtoll, strtoull
+#include <initializer_list> // initializer_list
+#include <string> // char_traits, string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+
+// #include <nlohmann/detail/input/position_t.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+///////////
+// lexer //
+///////////
+
+template<typename BasicJsonType>
+class lexer_base
+{
+  public:
+    /// token types for the parser
+    enum class token_type
+    {
+        uninitialized,    ///< indicating the scanner is uninitialized
+        literal_true,     ///< the `true` literal
+        literal_false,    ///< the `false` literal
+        literal_null,     ///< the `null` literal
+        value_string,     ///< a string -- use get_string() for actual value
+        value_unsigned,   ///< an unsigned integer -- use get_number_unsigned() for actual value
+        value_integer,    ///< a signed integer -- use get_number_integer() for actual value
+        value_float,      ///< an floating point number -- use get_number_float() for actual value
+        begin_array,      ///< the character for array begin `[`
+        begin_object,     ///< the character for object begin `{`
+        end_array,        ///< the character for array end `]`
+        end_object,       ///< the character for object end `}`
+        name_separator,   ///< the name separator `:`
+        value_separator,  ///< the value separator `,`
+        parse_error,      ///< indicating a parse error
+        end_of_input,     ///< indicating the end of the input buffer
+        literal_or_value  ///< a literal or the begin of a value (only for diagnostics)
+    };
+
+    /// return name of values of type token_type (only used for errors)
+    JSON_HEDLEY_RETURNS_NON_NULL
+    JSON_HEDLEY_CONST
+    static const char* token_type_name(const token_type t) noexcept
+    {
+        switch (t)
+        {
+            case token_type::uninitialized:
+                return "<uninitialized>";
+            case token_type::literal_true:
+                return "true literal";
+            case token_type::literal_false:
+                return "false literal";
+            case token_type::literal_null:
+                return "null literal";
+            case token_type::value_string:
+                return "string literal";
+            case token_type::value_unsigned:
+            case token_type::value_integer:
+            case token_type::value_float:
+                return "number literal";
+            case token_type::begin_array:
+                return "'['";
+            case token_type::begin_object:
+                return "'{'";
+            case token_type::end_array:
+                return "']'";
+            case token_type::end_object:
+                return "'}'";
+            case token_type::name_separator:
+                return "':'";
+            case token_type::value_separator:
+                return "','";
+            case token_type::parse_error:
+                return "<parse error>";
+            case token_type::end_of_input:
+                return "end of input";
+            case token_type::literal_or_value:
+                return "'[', '{', or a literal";
+            // LCOV_EXCL_START
+            default: // catch non-enum values
+                return "unknown token";
+                // LCOV_EXCL_STOP
+        }
+    }
+};
+/*!
+@brief lexical analysis
+
+This class organizes the lexical analysis during JSON deserialization.
+*/
+template<typename BasicJsonType, typename InputAdapterType>
+class lexer : public lexer_base<BasicJsonType>
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using char_type = typename InputAdapterType::char_type;
+    using char_int_type = typename char_traits<char_type>::int_type;
+
+  public:
+    using token_type = typename lexer_base<BasicJsonType>::token_type;
+
+    explicit lexer(InputAdapterType&& adapter, bool ignore_comments_ = false) noexcept
+        : ia(std::move(adapter))
+        , ignore_comments(ignore_comments_)
+        , decimal_point_char(static_cast<char_int_type>(get_decimal_point()))
+    {}
+
+    // delete because of pointer members
+    lexer(const lexer&) = delete;
+    lexer(lexer&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    lexer& operator=(lexer&) = delete;
+    lexer& operator=(lexer&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~lexer() = default;
+
+  private:
+    /////////////////////
+    // locales
+    /////////////////////
+
+    /// return the locale-dependent decimal point
+    JSON_HEDLEY_PURE
+    static char get_decimal_point() noexcept
+    {
+        const auto* loc = localeconv();
+        JSON_ASSERT(loc != nullptr);
+        return (loc->decimal_point == nullptr) ? '.' : *(loc->decimal_point);
+    }
+
+    /////////////////////
+    // scan functions
+    /////////////////////
+
+    /*!
+    @brief get codepoint from 4 hex characters following `\u`
+
+    For input "\u c1 c2 c3 c4" the codepoint is:
+      (c1 * 0x1000) + (c2 * 0x0100) + (c3 * 0x0010) + c4
+    = (c1 << 12) + (c2 << 8) + (c3 << 4) + (c4 << 0)
+
+    Furthermore, the possible characters '0'..'9', 'A'..'F', and 'a'..'f'
+    must be converted to the integers 0x0..0x9, 0xA..0xF, 0xA..0xF, resp. The
+    conversion is done by subtracting the offset (0x30, 0x37, and 0x57)
+    between the ASCII value of the character and the desired integer value.
+
+    @return codepoint (0x0000..0xFFFF) or -1 in case of an error (e.g. EOF or
+            non-hex character)
+    */
+    int get_codepoint()
+    {
+        // this function only makes sense after reading `\u`
+        JSON_ASSERT(current == 'u');
+        int codepoint = 0;
+
+        const auto factors = { 12u, 8u, 4u, 0u };
+        for (const auto factor : factors)
+        {
+            get();
+
+            if (current >= '0' && current <= '9')
+            {
+                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x30u) << factor);
+            }
+            else if (current >= 'A' && current <= 'F')
+            {
+                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x37u) << factor);
+            }
+            else if (current >= 'a' && current <= 'f')
+            {
+                codepoint += static_cast<int>((static_cast<unsigned int>(current) - 0x57u) << factor);
+            }
+            else
+            {
+                return -1;
+            }
+        }
+
+        JSON_ASSERT(0x0000 <= codepoint && codepoint <= 0xFFFF);
+        return codepoint;
+    }
+
+    /*!
+    @brief check if the next byte(s) are inside a given range
+
+    Adds the current byte and, for each passed range, reads a new byte and
+    checks if it is inside the range. If a violation was detected, set up an
+    error message and return false. Otherwise, return true.
+
+    @param[in] ranges  list of integers; interpreted as list of pairs of
+                       inclusive lower and upper bound, respectively
+
+    @pre The passed list @a ranges must have 2, 4, or 6 elements; that is,
+         1, 2, or 3 pairs. This precondition is enforced by an assertion.
+
+    @return true if and only if no range violation was detected
+    */
+    bool next_byte_in_range(std::initializer_list<char_int_type> ranges)
+    {
+        JSON_ASSERT(ranges.size() == 2 || ranges.size() == 4 || ranges.size() == 6);
+        add(current);
+
+        for (auto range = ranges.begin(); range != ranges.end(); ++range)
+        {
+            get();
+            if (JSON_HEDLEY_LIKELY(*range <= current && current <= *(++range))) // NOLINT(bugprone-inc-dec-in-conditions)
+            {
+                add(current);
+            }
+            else
+            {
+                error_message = "invalid string: ill-formed UTF-8 byte";
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    /*!
+    @brief scan a string literal
+
+    This function scans a string according to Sect. 7 of RFC 8259. While
+    scanning, bytes are escaped and copied into buffer token_buffer. Then the
+    function returns successfully, token_buffer is *not* null-terminated (as it
+    may contain \0 bytes), and token_buffer.size() is the number of bytes in the
+    string.
+
+    @return token_type::value_string if string could be successfully scanned,
+            token_type::parse_error otherwise
+
+    @note In case of errors, variable error_message contains a textual
+          description.
+    */
+    token_type scan_string()
+    {
+        // reset token_buffer (ignore opening quote)
+        reset();
+
+        // we entered the function by reading an open quote
+        JSON_ASSERT(current == '\"');
+
+        while (true)
+        {
+            // get next character
+            switch (get())
+            {
+                // end of file while parsing string
+                case char_traits<char_type>::eof():
+                {
+                    error_message = "invalid string: missing closing quote";
+                    return token_type::parse_error;
+                }
+
+                // closing quote
+                case '\"':
+                {
+                    return token_type::value_string;
+                }
+
+                // escapes
+                case '\\':
+                {
+                    switch (get())
+                    {
+                        // quotation mark
+                        case '\"':
+                            add('\"');
+                            break;
+                        // reverse solidus
+                        case '\\':
+                            add('\\');
+                            break;
+                        // solidus
+                        case '/':
+                            add('/');
+                            break;
+                        // backspace
+                        case 'b':
+                            add('\b');
+                            break;
+                        // form feed
+                        case 'f':
+                            add('\f');
+                            break;
+                        // line feed
+                        case 'n':
+                            add('\n');
+                            break;
+                        // carriage return
+                        case 'r':
+                            add('\r');
+                            break;
+                        // tab
+                        case 't':
+                            add('\t');
+                            break;
+
+                        // unicode escapes
+                        case 'u':
+                        {
+                            const int codepoint1 = get_codepoint();
+                            int codepoint = codepoint1; // start with codepoint1
+
+                            if (JSON_HEDLEY_UNLIKELY(codepoint1 == -1))
+                            {
+                                error_message = "invalid string: '\\u' must be followed by 4 hex digits";
+                                return token_type::parse_error;
+                            }
+
+                            // check if code point is a high surrogate
+                            if (0xD800 <= codepoint1 && codepoint1 <= 0xDBFF)
+                            {
+                                // expect next \uxxxx entry
+                                if (JSON_HEDLEY_LIKELY(get() == '\\' && get() == 'u'))
+                                {
+                                    const int codepoint2 = get_codepoint();
+
+                                    if (JSON_HEDLEY_UNLIKELY(codepoint2 == -1))
+                                    {
+                                        error_message = "invalid string: '\\u' must be followed by 4 hex digits";
+                                        return token_type::parse_error;
+                                    }
+
+                                    // check if codepoint2 is a low surrogate
+                                    if (JSON_HEDLEY_LIKELY(0xDC00 <= codepoint2 && codepoint2 <= 0xDFFF))
+                                    {
+                                        // overwrite codepoint
+                                        codepoint = static_cast<int>(
+                                                        // high surrogate occupies the most significant 22 bits
+                                                        (static_cast<unsigned int>(codepoint1) << 10u)
+                                                        // low surrogate occupies the least significant 15 bits
+                                                        + static_cast<unsigned int>(codepoint2)
+                                                        // there is still the 0xD800, 0xDC00 and 0x10000 noise
+                                                        // in the result, so we have to subtract with:
+                                                        // (0xD800 << 10) + DC00 - 0x10000 = 0x35FDC00
+                                                        - 0x35FDC00u);
+                                    }
+                                    else
+                                    {
+                                        error_message = "invalid string: surrogate U+D800..U+DBFF must be followed by U+DC00..U+DFFF";
+                                        return token_type::parse_error;
+                                    }
+                                }
+                                else
+                                {
+                                    error_message = "invalid string: surrogate U+D800..U+DBFF must be followed by U+DC00..U+DFFF";
+                                    return token_type::parse_error;
+                                }
+                            }
+                            else
+                            {
+                                if (JSON_HEDLEY_UNLIKELY(0xDC00 <= codepoint1 && codepoint1 <= 0xDFFF))
+                                {
+                                    error_message = "invalid string: surrogate U+DC00..U+DFFF must follow U+D800..U+DBFF";
+                                    return token_type::parse_error;
+                                }
+                            }
+
+                            // result of the above calculation yields a proper codepoint
+                            JSON_ASSERT(0x00 <= codepoint && codepoint <= 0x10FFFF);
+
+                            // translate codepoint into bytes
+                            if (codepoint < 0x80)
+                            {
+                                // 1-byte characters: 0xxxxxxx (ASCII)
+                                add(static_cast<char_int_type>(codepoint));
+                            }
+                            else if (codepoint <= 0x7FF)
+                            {
+                                // 2-byte characters: 110xxxxx 10xxxxxx
+                                add(static_cast<char_int_type>(0xC0u | (static_cast<unsigned int>(codepoint) >> 6u)));
+                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));
+                            }
+                            else if (codepoint <= 0xFFFF)
+                            {
+                                // 3-byte characters: 1110xxxx 10xxxxxx 10xxxxxx
+                                add(static_cast<char_int_type>(0xE0u | (static_cast<unsigned int>(codepoint) >> 12u)));
+                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 6u) & 0x3Fu)));
+                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));
+                            }
+                            else
+                            {
+                                // 4-byte characters: 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx
+                                add(static_cast<char_int_type>(0xF0u | (static_cast<unsigned int>(codepoint) >> 18u)));
+                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 12u) & 0x3Fu)));
+                                add(static_cast<char_int_type>(0x80u | ((static_cast<unsigned int>(codepoint) >> 6u) & 0x3Fu)));
+                                add(static_cast<char_int_type>(0x80u | (static_cast<unsigned int>(codepoint) & 0x3Fu)));
+                            }
+
+                            break;
+                        }
+
+                        // other characters after escape
+                        default:
+                            error_message = "invalid string: forbidden character after backslash";
+                            return token_type::parse_error;
+                    }
+
+                    break;
+                }
+
+                // invalid control characters
+                case 0x00:
+                {
+                    error_message = "invalid string: control character U+0000 (NUL) must be escaped to \\u0000";
+                    return token_type::parse_error;
+                }
+
+                case 0x01:
+                {
+                    error_message = "invalid string: control character U+0001 (SOH) must be escaped to \\u0001";
+                    return token_type::parse_error;
+                }
+
+                case 0x02:
+                {
+                    error_message = "invalid string: control character U+0002 (STX) must be escaped to \\u0002";
+                    return token_type::parse_error;
+                }
+
+                case 0x03:
+                {
+                    error_message = "invalid string: control character U+0003 (ETX) must be escaped to \\u0003";
+                    return token_type::parse_error;
+                }
+
+                case 0x04:
+                {
+                    error_message = "invalid string: control character U+0004 (EOT) must be escaped to \\u0004";
+                    return token_type::parse_error;
+                }
+
+                case 0x05:
+                {
+                    error_message = "invalid string: control character U+0005 (ENQ) must be escaped to \\u0005";
+                    return token_type::parse_error;
+                }
+
+                case 0x06:
+                {
+                    error_message = "invalid string: control character U+0006 (ACK) must be escaped to \\u0006";
+                    return token_type::parse_error;
+                }
+
+                case 0x07:
+                {
+                    error_message = "invalid string: control character U+0007 (BEL) must be escaped to \\u0007";
+                    return token_type::parse_error;
+                }
+
+                case 0x08:
+                {
+                    error_message = "invalid string: control character U+0008 (BS) must be escaped to \\u0008 or \\b";
+                    return token_type::parse_error;
+                }
+
+                case 0x09:
+                {
+                    error_message = "invalid string: control character U+0009 (HT) must be escaped to \\u0009 or \\t";
+                    return token_type::parse_error;
+                }
+
+                case 0x0A:
+                {
+                    error_message = "invalid string: control character U+000A (LF) must be escaped to \\u000A or \\n";
+                    return token_type::parse_error;
+                }
+
+                case 0x0B:
+                {
+                    error_message = "invalid string: control character U+000B (VT) must be escaped to \\u000B";
+                    return token_type::parse_error;
+                }
+
+                case 0x0C:
+                {
+                    error_message = "invalid string: control character U+000C (FF) must be escaped to \\u000C or \\f";
+                    return token_type::parse_error;
+                }
+
+                case 0x0D:
+                {
+                    error_message = "invalid string: control character U+000D (CR) must be escaped to \\u000D or \\r";
+                    return token_type::parse_error;
+                }
+
+                case 0x0E:
+                {
+                    error_message = "invalid string: control character U+000E (SO) must be escaped to \\u000E";
+                    return token_type::parse_error;
+                }
+
+                case 0x0F:
+                {
+                    error_message = "invalid string: control character U+000F (SI) must be escaped to \\u000F";
+                    return token_type::parse_error;
+                }
+
+                case 0x10:
+                {
+                    error_message = "invalid string: control character U+0010 (DLE) must be escaped to \\u0010";
+                    return token_type::parse_error;
+                }
+
+                case 0x11:
+                {
+                    error_message = "invalid string: control character U+0011 (DC1) must be escaped to \\u0011";
+                    return token_type::parse_error;
+                }
+
+                case 0x12:
+                {
+                    error_message = "invalid string: control character U+0012 (DC2) must be escaped to \\u0012";
+                    return token_type::parse_error;
+                }
+
+                case 0x13:
+                {
+                    error_message = "invalid string: control character U+0013 (DC3) must be escaped to \\u0013";
+                    return token_type::parse_error;
+                }
+
+                case 0x14:
+                {
+                    error_message = "invalid string: control character U+0014 (DC4) must be escaped to \\u0014";
+                    return token_type::parse_error;
+                }
+
+                case 0x15:
+                {
+                    error_message = "invalid string: control character U+0015 (NAK) must be escaped to \\u0015";
+                    return token_type::parse_error;
+                }
+
+                case 0x16:
+                {
+                    error_message = "invalid string: control character U+0016 (SYN) must be escaped to \\u0016";
+                    return token_type::parse_error;
+                }
+
+                case 0x17:
+                {
+                    error_message = "invalid string: control character U+0017 (ETB) must be escaped to \\u0017";
+                    return token_type::parse_error;
+                }
+
+                case 0x18:
+                {
+                    error_message = "invalid string: control character U+0018 (CAN) must be escaped to \\u0018";
+                    return token_type::parse_error;
+                }
+
+                case 0x19:
+                {
+                    error_message = "invalid string: control character U+0019 (EM) must be escaped to \\u0019";
+                    return token_type::parse_error;
+                }
+
+                case 0x1A:
+                {
+                    error_message = "invalid string: control character U+001A (SUB) must be escaped to \\u001A";
+                    return token_type::parse_error;
+                }
+
+                case 0x1B:
+                {
+                    error_message = "invalid string: control character U+001B (ESC) must be escaped to \\u001B";
+                    return token_type::parse_error;
+                }
+
+                case 0x1C:
+                {
+                    error_message = "invalid string: control character U+001C (FS) must be escaped to \\u001C";
+                    return token_type::parse_error;
+                }
+
+                case 0x1D:
+                {
+                    error_message = "invalid string: control character U+001D (GS) must be escaped to \\u001D";
+                    return token_type::parse_error;
+                }
+
+                case 0x1E:
+                {
+                    error_message = "invalid string: control character U+001E (RS) must be escaped to \\u001E";
+                    return token_type::parse_error;
+                }
+
+                case 0x1F:
+                {
+                    error_message = "invalid string: control character U+001F (US) must be escaped to \\u001F";
+                    return token_type::parse_error;
+                }
+
+                // U+0020..U+007F (except U+0022 (quote) and U+005C (backspace))
+                case 0x20:
+                case 0x21:
+                case 0x23:
+                case 0x24:
+                case 0x25:
+                case 0x26:
+                case 0x27:
+                case 0x28:
+                case 0x29:
+                case 0x2A:
+                case 0x2B:
+                case 0x2C:
+                case 0x2D:
+                case 0x2E:
+                case 0x2F:
+                case 0x30:
+                case 0x31:
+                case 0x32:
+                case 0x33:
+                case 0x34:
+                case 0x35:
+                case 0x36:
+                case 0x37:
+                case 0x38:
+                case 0x39:
+                case 0x3A:
+                case 0x3B:
+                case 0x3C:
+                case 0x3D:
+                case 0x3E:
+                case 0x3F:
+                case 0x40:
+                case 0x41:
+                case 0x42:
+                case 0x43:
+                case 0x44:
+                case 0x45:
+                case 0x46:
+                case 0x47:
+                case 0x48:
+                case 0x49:
+                case 0x4A:
+                case 0x4B:
+                case 0x4C:
+                case 0x4D:
+                case 0x4E:
+                case 0x4F:
+                case 0x50:
+                case 0x51:
+                case 0x52:
+                case 0x53:
+                case 0x54:
+                case 0x55:
+                case 0x56:
+                case 0x57:
+                case 0x58:
+                case 0x59:
+                case 0x5A:
+                case 0x5B:
+                case 0x5D:
+                case 0x5E:
+                case 0x5F:
+                case 0x60:
+                case 0x61:
+                case 0x62:
+                case 0x63:
+                case 0x64:
+                case 0x65:
+                case 0x66:
+                case 0x67:
+                case 0x68:
+                case 0x69:
+                case 0x6A:
+                case 0x6B:
+                case 0x6C:
+                case 0x6D:
+                case 0x6E:
+                case 0x6F:
+                case 0x70:
+                case 0x71:
+                case 0x72:
+                case 0x73:
+                case 0x74:
+                case 0x75:
+                case 0x76:
+                case 0x77:
+                case 0x78:
+                case 0x79:
+                case 0x7A:
+                case 0x7B:
+                case 0x7C:
+                case 0x7D:
+                case 0x7E:
+                case 0x7F:
+                {
+                    add(current);
+                    break;
+                }
+
+                // U+0080..U+07FF: bytes C2..DF 80..BF
+                case 0xC2:
+                case 0xC3:
+                case 0xC4:
+                case 0xC5:
+                case 0xC6:
+                case 0xC7:
+                case 0xC8:
+                case 0xC9:
+                case 0xCA:
+                case 0xCB:
+                case 0xCC:
+                case 0xCD:
+                case 0xCE:
+                case 0xCF:
+                case 0xD0:
+                case 0xD1:
+                case 0xD2:
+                case 0xD3:
+                case 0xD4:
+                case 0xD5:
+                case 0xD6:
+                case 0xD7:
+                case 0xD8:
+                case 0xD9:
+                case 0xDA:
+                case 0xDB:
+                case 0xDC:
+                case 0xDD:
+                case 0xDE:
+                case 0xDF:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!next_byte_in_range({0x80, 0xBF})))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+0800..U+0FFF: bytes E0 A0..BF 80..BF
+                case 0xE0:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0xA0, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+1000..U+CFFF: bytes E1..EC 80..BF 80..BF
+                // U+E000..U+FFFF: bytes EE..EF 80..BF 80..BF
+                case 0xE1:
+                case 0xE2:
+                case 0xE3:
+                case 0xE4:
+                case 0xE5:
+                case 0xE6:
+                case 0xE7:
+                case 0xE8:
+                case 0xE9:
+                case 0xEA:
+                case 0xEB:
+                case 0xEC:
+                case 0xEE:
+                case 0xEF:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+D000..U+D7FF: bytes ED 80..9F 80..BF
+                case 0xED:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0x9F, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+10000..U+3FFFF F0 90..BF 80..BF 80..BF
+                case 0xF0:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x90, 0xBF, 0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+40000..U+FFFFF F1..F3 80..BF 80..BF 80..BF
+                case 0xF1:
+                case 0xF2:
+                case 0xF3:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0xBF, 0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // U+100000..U+10FFFF F4 80..8F 80..BF 80..BF
+                case 0xF4:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!(next_byte_in_range({0x80, 0x8F, 0x80, 0xBF, 0x80, 0xBF}))))
+                    {
+                        return token_type::parse_error;
+                    }
+                    break;
+                }
+
+                // remaining bytes (80..C1 and F5..FF) are ill-formed
+                default:
+                {
+                    error_message = "invalid string: ill-formed UTF-8 byte";
+                    return token_type::parse_error;
+                }
+            }
+        }
+    }
+
+    /*!
+     * @brief scan a comment
+     * @return whether comment could be scanned successfully
+     */
+    bool scan_comment()
+    {
+        switch (get())
+        {
+            // single-line comments skip input until a newline or EOF is read
+            case '/':
+            {
+                while (true)
+                {
+                    switch (get())
+                    {
+                        case '\n':
+                        case '\r':
+                        case char_traits<char_type>::eof():
+                        case '\0':
+                            return true;
+
+                        default:
+                            break;
+                    }
+                }
+            }
+
+            // multi-line comments skip input until */ is read
+            case '*':
+            {
+                while (true)
+                {
+                    switch (get())
+                    {
+                        case char_traits<char_type>::eof():
+                        case '\0':
+                        {
+                            error_message = "invalid comment; missing closing '*/'";
+                            return false;
+                        }
+
+                        case '*':
+                        {
+                            switch (get())
+                            {
+                                case '/':
+                                    return true;
+
+                                default:
+                                {
+                                    unget();
+                                    continue;
+                                }
+                            }
+                        }
+
+                        default:
+                            continue;
+                    }
+                }
+            }
+
+            // unexpected character after reading '/'
+            default:
+            {
+                error_message = "invalid comment; expecting '/' or '*' after '/'";
+                return false;
+            }
+        }
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    static void strtof(float& f, const char* str, char** endptr) noexcept
+    {
+        f = std::strtof(str, endptr);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    static void strtof(double& f, const char* str, char** endptr) noexcept
+    {
+        f = std::strtod(str, endptr);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    static void strtof(long double& f, const char* str, char** endptr) noexcept
+    {
+        f = std::strtold(str, endptr);
+    }
+
+    /*!
+    @brief scan a number literal
+
+    This function scans a string according to Sect. 6 of RFC 8259.
+
+    The function is realized with a deterministic finite state machine derived
+    from the grammar described in RFC 8259. Starting in state "init", the
+    input is read and used to determined the next state. Only state "done"
+    accepts the number. State "error" is a trap state to model errors. In the
+    table below, "anything" means any character but the ones listed before.
+
+    state    | 0        | 1-9      | e E      | +       | -       | .        | anything
+    ---------|----------|----------|----------|---------|---------|----------|-----------
+    init     | zero     | any1     | [error]  | [error] | minus   | [error]  | [error]
+    minus    | zero     | any1     | [error]  | [error] | [error] | [error]  | [error]
+    zero     | done     | done     | exponent | done    | done    | decimal1 | done
+    any1     | any1     | any1     | exponent | done    | done    | decimal1 | done
+    decimal1 | decimal2 | decimal2 | [error]  | [error] | [error] | [error]  | [error]
+    decimal2 | decimal2 | decimal2 | exponent | done    | done    | done     | done
+    exponent | any2     | any2     | [error]  | sign    | sign    | [error]  | [error]
+    sign     | any2     | any2     | [error]  | [error] | [error] | [error]  | [error]
+    any2     | any2     | any2     | done     | done    | done    | done     | done
+
+    The state machine is realized with one label per state (prefixed with
+    "scan_number_") and `goto` statements between them. The state machine
+    contains cycles, but any cycle can be left when EOF is read. Therefore,
+    the function is guaranteed to terminate.
+
+    During scanning, the read bytes are stored in token_buffer. This string is
+    then converted to a signed integer, an unsigned integer, or a
+    floating-point number.
+
+    @return token_type::value_unsigned, token_type::value_integer, or
+            token_type::value_float if number could be successfully scanned,
+            token_type::parse_error otherwise
+
+    @note The scanner is independent of the current locale. Internally, the
+          locale's decimal point is used instead of `.` to work with the
+          locale-dependent converters.
+    */
+    token_type scan_number()  // lgtm [cpp/use-of-goto] `goto` is used in this function to implement the number-parsing state machine described above. By design, any finite input will eventually reach the "done" state or return token_type::parse_error. In each intermediate state, 1 byte of the input is appended to the token_buffer vector, and only the already initialized variables token_buffer, number_type, and error_message are manipulated.
+    {
+        // reset token_buffer to store the number's bytes
+        reset();
+
+        // the type of the parsed number; initially set to unsigned; will be
+        // changed if minus sign, decimal point or exponent is read
+        token_type number_type = token_type::value_unsigned;
+
+        // state (init): we just found out we need to scan a number
+        switch (current)
+        {
+            case '-':
+            {
+                add(current);
+                goto scan_number_minus;
+            }
+
+            case '0':
+            {
+                add(current);
+                goto scan_number_zero;
+            }
+
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any1;
+            }
+
+            // all other characters are rejected outside scan_number()
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+
+scan_number_minus:
+        // state: we just parsed a leading minus sign
+        number_type = token_type::value_integer;
+        switch (get())
+        {
+            case '0':
+            {
+                add(current);
+                goto scan_number_zero;
+            }
+
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any1;
+            }
+
+            default:
+            {
+                error_message = "invalid number; expected digit after '-'";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_zero:
+        // state: we just parse a zero (maybe with a leading minus sign)
+        switch (get())
+        {
+            case '.':
+            {
+                add(decimal_point_char);
+                decimal_point_position = token_buffer.size() - 1;
+                goto scan_number_decimal1;
+            }
+
+            case 'e':
+            case 'E':
+            {
+                add(current);
+                goto scan_number_exponent;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_any1:
+        // state: we just parsed a number 0-9 (maybe with a leading minus sign)
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any1;
+            }
+
+            case '.':
+            {
+                add(decimal_point_char);
+                decimal_point_position = token_buffer.size() - 1;
+                goto scan_number_decimal1;
+            }
+
+            case 'e':
+            case 'E':
+            {
+                add(current);
+                goto scan_number_exponent;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_decimal1:
+        // state: we just parsed a decimal point
+        number_type = token_type::value_float;
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_decimal2;
+            }
+
+            default:
+            {
+                error_message = "invalid number; expected digit after '.'";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_decimal2:
+        // we just parsed at least one number after a decimal point
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_decimal2;
+            }
+
+            case 'e':
+            case 'E':
+            {
+                add(current);
+                goto scan_number_exponent;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_exponent:
+        // we just parsed an exponent
+        number_type = token_type::value_float;
+        switch (get())
+        {
+            case '+':
+            case '-':
+            {
+                add(current);
+                goto scan_number_sign;
+            }
+
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any2;
+            }
+
+            default:
+            {
+                error_message =
+                    "invalid number; expected '+', '-', or digit after exponent";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_sign:
+        // we just parsed an exponent sign
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any2;
+            }
+
+            default:
+            {
+                error_message = "invalid number; expected digit after exponent sign";
+                return token_type::parse_error;
+            }
+        }
+
+scan_number_any2:
+        // we just parsed a number after the exponent or exponent sign
+        switch (get())
+        {
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+            {
+                add(current);
+                goto scan_number_any2;
+            }
+
+            default:
+                goto scan_number_done;
+        }
+
+scan_number_done:
+        // unget the character after the number (we only read it to know that
+        // we are done scanning a number)
+        unget();
+
+        char* endptr = nullptr; // NOLINT(misc-const-correctness,cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+        errno = 0;
+
+        // try to parse integers first and fall back to floats
+        if (number_type == token_type::value_unsigned)
+        {
+            const auto x = std::strtoull(token_buffer.data(), &endptr, 10);
+
+            // we checked the number format before
+            JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());
+
+            if (errno != ERANGE)
+            {
+                value_unsigned = static_cast<number_unsigned_t>(x);
+                if (value_unsigned == x)
+                {
+                    return token_type::value_unsigned;
+                }
+            }
+        }
+        else if (number_type == token_type::value_integer)
+        {
+            const auto x = std::strtoll(token_buffer.data(), &endptr, 10);
+
+            // we checked the number format before
+            JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());
+
+            if (errno != ERANGE)
+            {
+                value_integer = static_cast<number_integer_t>(x);
+                if (value_integer == x)
+                {
+                    return token_type::value_integer;
+                }
+            }
+        }
+
+        // this code is reached if we parse a floating-point number or if an
+        // integer conversion above failed
+        strtof(value_float, token_buffer.data(), &endptr);
+
+        // we checked the number format before
+        JSON_ASSERT(endptr == token_buffer.data() + token_buffer.size());
+
+        return token_type::value_float;
+    }
+
+    /*!
+    @param[in] literal_text  the literal text to expect
+    @param[in] length        the length of the passed literal text
+    @param[in] return_type   the token type to return on success
+    */
+    JSON_HEDLEY_NON_NULL(2)
+    token_type scan_literal(const char_type* literal_text, const std::size_t length,
+                            token_type return_type)
+    {
+        JSON_ASSERT(char_traits<char_type>::to_char_type(current) == literal_text[0]);
+        for (std::size_t i = 1; i < length; ++i)
+        {
+            if (JSON_HEDLEY_UNLIKELY(char_traits<char_type>::to_char_type(get()) != literal_text[i]))
+            {
+                error_message = "invalid literal";
+                return token_type::parse_error;
+            }
+        }
+        return return_type;
+    }
+
+    /////////////////////
+    // input management
+    /////////////////////
+
+    /// reset token_buffer; current character is beginning of token
+    void reset() noexcept
+    {
+        token_buffer.clear();
+        token_string.clear();
+        decimal_point_position = std::string::npos;
+        token_string.push_back(char_traits<char_type>::to_char_type(current));
+    }
+
+    /*
+    @brief get next character from the input
+
+    This function provides the interface to the used input adapter. It does
+    not throw in case the input reached EOF, but returns a
+    `char_traits<char>::eof()` in that case.  Stores the scanned characters
+    for use in error messages.
+
+    @return character read from the input
+    */
+    char_int_type get()
+    {
+        ++position.chars_read_total;
+        ++position.chars_read_current_line;
+
+        if (next_unget)
+        {
+            // just reset the next_unget variable and work with current
+            next_unget = false;
+        }
+        else
+        {
+            current = ia.get_character();
+        }
+
+        if (JSON_HEDLEY_LIKELY(current != char_traits<char_type>::eof()))
+        {
+            token_string.push_back(char_traits<char_type>::to_char_type(current));
+        }
+
+        if (current == '\n')
+        {
+            ++position.lines_read;
+            position.chars_read_current_line = 0;
+        }
+
+        return current;
+    }
+
+    /*!
+    @brief unget current character (read it again on next get)
+
+    We implement unget by setting variable next_unget to true. The input is not
+    changed - we just simulate ungetting by modifying chars_read_total,
+    chars_read_current_line, and token_string. The next call to get() will
+    behave as if the unget character is read again.
+    */
+    void unget()
+    {
+        next_unget = true;
+
+        --position.chars_read_total;
+
+        // in case we "unget" a newline, we have to also decrement the lines_read
+        if (position.chars_read_current_line == 0)
+        {
+            if (position.lines_read > 0)
+            {
+                --position.lines_read;
+            }
+        }
+        else
+        {
+            --position.chars_read_current_line;
+        }
+
+        if (JSON_HEDLEY_LIKELY(current != char_traits<char_type>::eof()))
+        {
+            JSON_ASSERT(!token_string.empty());
+            token_string.pop_back();
+        }
+    }
+
+    /// add a character to token_buffer
+    void add(char_int_type c)
+    {
+        token_buffer.push_back(static_cast<typename string_t::value_type>(c));
+    }
+
+  public:
+    /////////////////////
+    // value getters
+    /////////////////////
+
+    /// return integer value
+    constexpr number_integer_t get_number_integer() const noexcept
+    {
+        return value_integer;
+    }
+
+    /// return unsigned integer value
+    constexpr number_unsigned_t get_number_unsigned() const noexcept
+    {
+        return value_unsigned;
+    }
+
+    /// return floating-point value
+    constexpr number_float_t get_number_float() const noexcept
+    {
+        return value_float;
+    }
+
+    /// return current string value (implicitly resets the token; useful only once)
+    string_t& get_string()
+    {
+        // translate decimal points from locale back to '.' (#4084)
+        if (decimal_point_char != '.' && decimal_point_position != std::string::npos)
+        {
+            token_buffer[decimal_point_position] = '.';
+        }
+        return token_buffer;
+    }
+
+    /////////////////////
+    // diagnostics
+    /////////////////////
+
+    /// return position of last read token
+    constexpr position_t get_position() const noexcept
+    {
+        return position;
+    }
+
+    /// return the last read token (for errors only).  Will never contain EOF
+    /// (an arbitrary value that is not a valid char value, often -1), because
+    /// 255 may legitimately occur.  May contain NUL, which should be escaped.
+    std::string get_token_string() const
+    {
+        // escape control characters
+        std::string result;
+        for (const auto c : token_string)
+        {
+            if (static_cast<unsigned char>(c) <= '\x1F')
+            {
+                // escape control characters
+                std::array<char, 9> cs{{}};
+                static_cast<void>((std::snprintf)(cs.data(), cs.size(), "<U+%.4X>", static_cast<unsigned char>(c))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                result += cs.data();
+            }
+            else
+            {
+                // add character as is
+                result.push_back(static_cast<std::string::value_type>(c));
+            }
+        }
+
+        return result;
+    }
+
+    /// return syntax error message
+    JSON_HEDLEY_RETURNS_NON_NULL
+    constexpr const char* get_error_message() const noexcept
+    {
+        return error_message;
+    }
+
+    /////////////////////
+    // actual scanner
+    /////////////////////
+
+    /*!
+    @brief skip the UTF-8 byte order mark
+    @return true iff there is no BOM or the correct BOM has been skipped
+    */
+    bool skip_bom()
+    {
+        if (get() == 0xEF)
+        {
+            // check if we completely parse the BOM
+            return get() == 0xBB && get() == 0xBF;
+        }
+
+        // the first character is not the beginning of the BOM; unget it to
+        // process is later
+        unget();
+        return true;
+    }
+
+    void skip_whitespace()
+    {
+        do
+        {
+            get();
+        }
+        while (current == ' ' || current == '\t' || current == '\n' || current == '\r');
+    }
+
+    token_type scan()
+    {
+        // initially, skip the BOM
+        if (position.chars_read_total == 0 && !skip_bom())
+        {
+            error_message = "invalid BOM; must be 0xEF 0xBB 0xBF if given";
+            return token_type::parse_error;
+        }
+
+        // read next character and ignore whitespace
+        skip_whitespace();
+
+        // ignore comments
+        while (ignore_comments && current == '/')
+        {
+            if (!scan_comment())
+            {
+                return token_type::parse_error;
+            }
+
+            // skip following whitespace
+            skip_whitespace();
+        }
+
+        switch (current)
+        {
+            // structural characters
+            case '[':
+                return token_type::begin_array;
+            case ']':
+                return token_type::end_array;
+            case '{':
+                return token_type::begin_object;
+            case '}':
+                return token_type::end_object;
+            case ':':
+                return token_type::name_separator;
+            case ',':
+                return token_type::value_separator;
+
+            // literals
+            case 't':
+            {
+                std::array<char_type, 4> true_literal = {{static_cast<char_type>('t'), static_cast<char_type>('r'), static_cast<char_type>('u'), static_cast<char_type>('e')}};
+                return scan_literal(true_literal.data(), true_literal.size(), token_type::literal_true);
+            }
+            case 'f':
+            {
+                std::array<char_type, 5> false_literal = {{static_cast<char_type>('f'), static_cast<char_type>('a'), static_cast<char_type>('l'), static_cast<char_type>('s'), static_cast<char_type>('e')}};
+                return scan_literal(false_literal.data(), false_literal.size(), token_type::literal_false);
+            }
+            case 'n':
+            {
+                std::array<char_type, 4> null_literal = {{static_cast<char_type>('n'), static_cast<char_type>('u'), static_cast<char_type>('l'), static_cast<char_type>('l')}};
+                return scan_literal(null_literal.data(), null_literal.size(), token_type::literal_null);
+            }
+
+            // string
+            case '\"':
+                return scan_string();
+
+            // number
+            case '-':
+            case '0':
+            case '1':
+            case '2':
+            case '3':
+            case '4':
+            case '5':
+            case '6':
+            case '7':
+            case '8':
+            case '9':
+                return scan_number();
+
+            // end of input (the null byte is needed when parsing from
+            // string literals)
+            case '\0':
+            case char_traits<char_type>::eof():
+                return token_type::end_of_input;
+
+            // error
+            default:
+                error_message = "invalid literal";
+                return token_type::parse_error;
+        }
+    }
+
+  private:
+    /// input adapter
+    InputAdapterType ia;
+
+    /// whether comments should be ignored (true) or signaled as errors (false)
+    const bool ignore_comments = false;
+
+    /// the current character
+    char_int_type current = char_traits<char_type>::eof();
+
+    /// whether the next get() call should just return current
+    bool next_unget = false;
+
+    /// the start position of the current token
+    position_t position {};
+
+    /// raw input token string (for error messages)
+    std::vector<char_type> token_string {};
+
+    /// buffer for variable-length tokens (numbers, strings)
+    string_t token_buffer {};
+
+    /// a description of occurred lexer errors
+    const char* error_message = "";
+
+    // number values
+    number_integer_t value_integer = 0;
+    number_unsigned_t value_unsigned = 0;
+    number_float_t value_float = 0;
+
+    /// the decimal point
+    const char_int_type decimal_point_char = '.';
+    /// the position of the decimal point in the input
+    std::size_t decimal_point_position = std::string::npos;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/*!
+@brief SAX interface
+
+This class describes the SAX interface used by @ref nlohmann::json::sax_parse.
+Each function is called in different situations while the input is parsed. The
+boolean return value informs the parser whether to continue processing the
+input.
+*/
+template<typename BasicJsonType>
+struct json_sax
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+
+    /*!
+    @brief a null value was read
+    @return whether parsing should proceed
+    */
+    virtual bool null() = 0;
+
+    /*!
+    @brief a boolean value was read
+    @param[in] val  boolean value
+    @return whether parsing should proceed
+    */
+    virtual bool boolean(bool val) = 0;
+
+    /*!
+    @brief an integer number was read
+    @param[in] val  integer value
+    @return whether parsing should proceed
+    */
+    virtual bool number_integer(number_integer_t val) = 0;
+
+    /*!
+    @brief an unsigned integer number was read
+    @param[in] val  unsigned integer value
+    @return whether parsing should proceed
+    */
+    virtual bool number_unsigned(number_unsigned_t val) = 0;
+
+    /*!
+    @brief a floating-point number was read
+    @param[in] val  floating-point value
+    @param[in] s    raw token value
+    @return whether parsing should proceed
+    */
+    virtual bool number_float(number_float_t val, const string_t& s) = 0;
+
+    /*!
+    @brief a string value was read
+    @param[in] val  string value
+    @return whether parsing should proceed
+    @note It is safe to move the passed string value.
+    */
+    virtual bool string(string_t& val) = 0;
+
+    /*!
+    @brief a binary value was read
+    @param[in] val  binary value
+    @return whether parsing should proceed
+    @note It is safe to move the passed binary value.
+    */
+    virtual bool binary(binary_t& val) = 0;
+
+    /*!
+    @brief the beginning of an object was read
+    @param[in] elements  number of object elements or -1 if unknown
+    @return whether parsing should proceed
+    @note binary formats may report the number of elements
+    */
+    virtual bool start_object(std::size_t elements) = 0;
+
+    /*!
+    @brief an object key was read
+    @param[in] val  object key
+    @return whether parsing should proceed
+    @note It is safe to move the passed string.
+    */
+    virtual bool key(string_t& val) = 0;
+
+    /*!
+    @brief the end of an object was read
+    @return whether parsing should proceed
+    */
+    virtual bool end_object() = 0;
+
+    /*!
+    @brief the beginning of an array was read
+    @param[in] elements  number of array elements or -1 if unknown
+    @return whether parsing should proceed
+    @note binary formats may report the number of elements
+    */
+    virtual bool start_array(std::size_t elements) = 0;
+
+    /*!
+    @brief the end of an array was read
+    @return whether parsing should proceed
+    */
+    virtual bool end_array() = 0;
+
+    /*!
+    @brief a parse error occurred
+    @param[in] position    the position in the input where the error occurs
+    @param[in] last_token  the last read token
+    @param[in] ex          an exception object describing the error
+    @return whether parsing should proceed (must return false)
+    */
+    virtual bool parse_error(std::size_t position,
+                             const std::string& last_token,
+                             const detail::exception& ex) = 0;
+
+    json_sax() = default;
+    json_sax(const json_sax&) = default;
+    json_sax(json_sax&&) noexcept = default;
+    json_sax& operator=(const json_sax&) = default;
+    json_sax& operator=(json_sax&&) noexcept = default;
+    virtual ~json_sax() = default;
+};
+
+namespace detail
+{
+constexpr std::size_t unknown_size()
+{
+    return (std::numeric_limits<std::size_t>::max)();
+}
+
+/*!
+@brief SAX implementation to create a JSON value from SAX events
+
+This class implements the @ref json_sax interface and processes the SAX events
+to create a JSON value which makes it basically a DOM parser. The structure or
+hierarchy of the JSON value is managed by the stack `ref_stack` which contains
+a pointer to the respective array or object for each recursion depth.
+
+After successful parsing, the value that is passed by reference to the
+constructor contains the parsed value.
+
+@tparam BasicJsonType  the JSON type
+*/
+template<typename BasicJsonType, typename InputAdapterType>
+class json_sax_dom_parser
+{
+  public:
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using lexer_t = lexer<BasicJsonType, InputAdapterType>;
+
+    /*!
+    @param[in,out] r  reference to a JSON value that is manipulated while
+                       parsing
+    @param[in] allow_exceptions_  whether parse errors yield exceptions
+    */
+    explicit json_sax_dom_parser(BasicJsonType& r, const bool allow_exceptions_ = true, lexer_t* lexer_ = nullptr)
+        : root(r), allow_exceptions(allow_exceptions_), m_lexer_ref(lexer_)
+    {}
+
+    // make class move-only
+    json_sax_dom_parser(const json_sax_dom_parser&) = delete;
+    json_sax_dom_parser(json_sax_dom_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    json_sax_dom_parser& operator=(const json_sax_dom_parser&) = delete;
+    json_sax_dom_parser& operator=(json_sax_dom_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~json_sax_dom_parser() = default;
+
+    bool null()
+    {
+        handle_value(nullptr);
+        return true;
+    }
+
+    bool boolean(bool val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_integer(number_integer_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_unsigned(number_unsigned_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_float(number_float_t val, const string_t& /*unused*/)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool string(string_t& val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool binary(binary_t& val)
+    {
+        handle_value(std::move(val));
+        return true;
+    }
+
+    bool start_object(std::size_t len)
+    {
+        ref_stack.push_back(handle_value(BasicJsonType::value_t::object));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        // Manually set the start position of the object here.
+        // Ensure this is after the call to handle_value to ensure correct start position.
+        if (m_lexer_ref)
+        {
+            // Lexer has read the first character of the object, so
+            // subtract 1 from the position to get the correct start position.
+            ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+        }
+#endif
+
+        if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+        {
+            JSON_THROW(out_of_range::create(408, concat("excessive object size: ", std::to_string(len)), ref_stack.back()));
+        }
+
+        return true;
+    }
+
+    bool key(string_t& val)
+    {
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(ref_stack.back()->is_object());
+
+        // add null at given key and store the reference for later
+        object_element = &(ref_stack.back()->m_data.m_value.object->operator[](val));
+        return true;
+    }
+
+    bool end_object()
+    {
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(ref_stack.back()->is_object());
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        if (m_lexer_ref)
+        {
+            // Lexer's position is past the closing brace, so set that as the end position.
+            ref_stack.back()->end_position = m_lexer_ref->get_position();
+        }
+#endif
+
+        ref_stack.back()->set_parents();
+        ref_stack.pop_back();
+        return true;
+    }
+
+    bool start_array(std::size_t len)
+    {
+        ref_stack.push_back(handle_value(BasicJsonType::value_t::array));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        // Manually set the start position of the array here.
+        // Ensure this is after the call to handle_value to ensure correct start position.
+        if (m_lexer_ref)
+        {
+            ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+        }
+#endif
+
+        if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+        {
+            JSON_THROW(out_of_range::create(408, concat("excessive array size: ", std::to_string(len)), ref_stack.back()));
+        }
+
+        return true;
+    }
+
+    bool end_array()
+    {
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(ref_stack.back()->is_array());
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        if (m_lexer_ref)
+        {
+            // Lexer's position is past the closing bracket, so set that as the end position.
+            ref_stack.back()->end_position = m_lexer_ref->get_position();
+        }
+#endif
+
+        ref_stack.back()->set_parents();
+        ref_stack.pop_back();
+        return true;
+    }
+
+    template<class Exception>
+    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/,
+                     const Exception& ex)
+    {
+        errored = true;
+        static_cast<void>(ex);
+        if (allow_exceptions)
+        {
+            JSON_THROW(ex);
+        }
+        return false;
+    }
+
+    constexpr bool is_errored() const
+    {
+        return errored;
+    }
+
+  private:
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    void handle_diagnostic_positions_for_json_value(BasicJsonType& v)
+    {
+        if (m_lexer_ref)
+        {
+            // Lexer has read past the current field value, so set the end position to the current position.
+            // The start position will be set below based on the length of the string representation
+            // of the value.
+            v.end_position = m_lexer_ref->get_position();
+
+            switch (v.type())
+            {
+                case value_t::boolean:
+                {
+                    // 4 and 5 are the string length of "true" and "false"
+                    v.start_position = v.end_position - (v.m_data.m_value.boolean ? 4 : 5);
+                    break;
+                }
+
+                case value_t::null:
+                {
+                    // 4 is the string length of "null"
+                    v.start_position = v.end_position - 4;
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    // include the length of the quotes, which is 2
+                    v.start_position = v.end_position - v.m_data.m_value.string->size() - 2;
+                    break;
+                }
+
+                // As we handle the start and end positions for values created during parsing,
+                // we do not expect the following value type to be called. Regardless, set the positions
+                // in case this is created manually or through a different constructor. Exclude from lcov
+                // since the exact condition of this switch is esoteric.
+                // LCOV_EXCL_START
+                case value_t::discarded:
+                {
+                    v.end_position = std::string::npos;
+                    v.start_position = v.end_position;
+                    break;
+                }
+                // LCOV_EXCL_STOP
+                case value_t::binary:
+                case value_t::number_integer:
+                case value_t::number_unsigned:
+                case value_t::number_float:
+                {
+                    v.start_position = v.end_position - m_lexer_ref->get_string().size();
+                    break;
+                }
+                case value_t::object:
+                case value_t::array:
+                {
+                    // object and array are handled in start_object() and start_array() handlers
+                    // skip setting the values here.
+                    break;
+                }
+                default: // LCOV_EXCL_LINE
+                    // Handle all possible types discretely, default handler should never be reached.
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert,-warnings-as-errors) LCOV_EXCL_LINE
+            }
+        }
+    }
+#endif
+
+    /*!
+    @invariant If the ref stack is empty, then the passed value will be the new
+               root.
+    @invariant If the ref stack contains a value, then it is an array or an
+               object to which we can add elements
+    */
+    template<typename Value>
+    JSON_HEDLEY_RETURNS_NON_NULL
+    BasicJsonType* handle_value(Value&& v)
+    {
+        if (ref_stack.empty())
+        {
+            root = BasicJsonType(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            handle_diagnostic_positions_for_json_value(root);
+#endif
+
+            return &root;
+        }
+
+        JSON_ASSERT(ref_stack.back()->is_array() || ref_stack.back()->is_object());
+
+        if (ref_stack.back()->is_array())
+        {
+            ref_stack.back()->m_data.m_value.array->emplace_back(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            handle_diagnostic_positions_for_json_value(ref_stack.back()->m_data.m_value.array->back());
+#endif
+
+            return &(ref_stack.back()->m_data.m_value.array->back());
+        }
+
+        JSON_ASSERT(ref_stack.back()->is_object());
+        JSON_ASSERT(object_element);
+        *object_element = BasicJsonType(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        handle_diagnostic_positions_for_json_value(*object_element);
+#endif
+
+        return object_element;
+    }
+
+    /// the parsed JSON value
+    BasicJsonType& root;
+    /// stack to model hierarchy of values
+    std::vector<BasicJsonType*> ref_stack {};
+    /// helper to hold the reference for the next object element
+    BasicJsonType* object_element = nullptr;
+    /// whether a syntax error occurred
+    bool errored = false;
+    /// whether to throw exceptions in case of errors
+    const bool allow_exceptions = true;
+    /// the lexer reference to obtain the current position
+    lexer_t* m_lexer_ref = nullptr;
+};
+
+template<typename BasicJsonType, typename InputAdapterType>
+class json_sax_dom_callback_parser
+{
+  public:
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using parser_callback_t = typename BasicJsonType::parser_callback_t;
+    using parse_event_t = typename BasicJsonType::parse_event_t;
+    using lexer_t = lexer<BasicJsonType, InputAdapterType>;
+
+    json_sax_dom_callback_parser(BasicJsonType& r,
+                                 parser_callback_t cb,
+                                 const bool allow_exceptions_ = true,
+                                 lexer_t* lexer_ = nullptr)
+        : root(r), callback(std::move(cb)), allow_exceptions(allow_exceptions_), m_lexer_ref(lexer_)
+    {
+        keep_stack.push_back(true);
+    }
+
+    // make class move-only
+    json_sax_dom_callback_parser(const json_sax_dom_callback_parser&) = delete;
+    json_sax_dom_callback_parser(json_sax_dom_callback_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    json_sax_dom_callback_parser& operator=(const json_sax_dom_callback_parser&) = delete;
+    json_sax_dom_callback_parser& operator=(json_sax_dom_callback_parser&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~json_sax_dom_callback_parser() = default;
+
+    bool null()
+    {
+        handle_value(nullptr);
+        return true;
+    }
+
+    bool boolean(bool val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_integer(number_integer_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_unsigned(number_unsigned_t val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool number_float(number_float_t val, const string_t& /*unused*/)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool string(string_t& val)
+    {
+        handle_value(val);
+        return true;
+    }
+
+    bool binary(binary_t& val)
+    {
+        handle_value(std::move(val));
+        return true;
+    }
+
+    bool start_object(std::size_t len)
+    {
+        // check callback for object start
+        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::object_start, discarded);
+        keep_stack.push_back(keep);
+
+        auto val = handle_value(BasicJsonType::value_t::object, true);
+        ref_stack.push_back(val.second);
+
+        if (ref_stack.back())
+        {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            // Manually set the start position of the object here.
+            // Ensure this is after the call to handle_value to ensure correct start position.
+            if (m_lexer_ref)
+            {
+                // Lexer has read the first character of the object, so
+                // subtract 1 from the position to get the correct start position.
+                ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+            }
+#endif
+
+            // check object limit
+            if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+            {
+                JSON_THROW(out_of_range::create(408, concat("excessive object size: ", std::to_string(len)), ref_stack.back()));
+            }
+        }
+        return true;
+    }
+
+    bool key(string_t& val)
+    {
+        BasicJsonType k = BasicJsonType(val);
+
+        // check callback for key
+        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::key, k);
+        key_keep_stack.push_back(keep);
+
+        // add discarded value at given key and store the reference for later
+        if (keep && ref_stack.back())
+        {
+            object_element = &(ref_stack.back()->m_data.m_value.object->operator[](val) = discarded);
+        }
+
+        return true;
+    }
+
+    bool end_object()
+    {
+        if (ref_stack.back())
+        {
+            if (!callback(static_cast<int>(ref_stack.size()) - 1, parse_event_t::object_end, *ref_stack.back()))
+            {
+                // discard object
+                *ref_stack.back() = discarded;
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                // Set start/end positions for discarded object.
+                handle_diagnostic_positions_for_json_value(*ref_stack.back());
+#endif
+            }
+            else
+            {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                if (m_lexer_ref)
+                {
+                    // Lexer's position is past the closing brace, so set that as the end position.
+                    ref_stack.back()->end_position = m_lexer_ref->get_position();
+                }
+#endif
+
+                ref_stack.back()->set_parents();
+            }
+        }
+
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(!keep_stack.empty());
+        ref_stack.pop_back();
+        keep_stack.pop_back();
+
+        if (!ref_stack.empty() && ref_stack.back() && ref_stack.back()->is_structured())
+        {
+            // remove discarded value
+            for (auto it = ref_stack.back()->begin(); it != ref_stack.back()->end(); ++it)
+            {
+                if (it->is_discarded())
+                {
+                    ref_stack.back()->erase(it);
+                    break;
+                }
+            }
+        }
+
+        return true;
+    }
+
+    bool start_array(std::size_t len)
+    {
+        const bool keep = callback(static_cast<int>(ref_stack.size()), parse_event_t::array_start, discarded);
+        keep_stack.push_back(keep);
+
+        auto val = handle_value(BasicJsonType::value_t::array, true);
+        ref_stack.push_back(val.second);
+
+        if (ref_stack.back())
+        {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+            // Manually set the start position of the array here.
+            // Ensure this is after the call to handle_value to ensure correct start position.
+            if (m_lexer_ref)
+            {
+                // Lexer has read the first character of the array, so
+                // subtract 1 from the position to get the correct start position.
+                ref_stack.back()->start_position = m_lexer_ref->get_position() - 1;
+            }
+#endif
+
+            // check array limit
+            if (JSON_HEDLEY_UNLIKELY(len != detail::unknown_size() && len > ref_stack.back()->max_size()))
+            {
+                JSON_THROW(out_of_range::create(408, concat("excessive array size: ", std::to_string(len)), ref_stack.back()));
+            }
+        }
+
+        return true;
+    }
+
+    bool end_array()
+    {
+        bool keep = true;
+
+        if (ref_stack.back())
+        {
+            keep = callback(static_cast<int>(ref_stack.size()) - 1, parse_event_t::array_end, *ref_stack.back());
+            if (keep)
+            {
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                if (m_lexer_ref)
+                {
+                    // Lexer's position is past the closing bracket, so set that as the end position.
+                    ref_stack.back()->end_position = m_lexer_ref->get_position();
+                }
+#endif
+
+                ref_stack.back()->set_parents();
+            }
+            else
+            {
+                // discard array
+                *ref_stack.back() = discarded;
+
+#if JSON_DIAGNOSTIC_POSITIONS
+                // Set start/end positions for discarded array.
+                handle_diagnostic_positions_for_json_value(*ref_stack.back());
+#endif
+            }
+        }
+
+        JSON_ASSERT(!ref_stack.empty());
+        JSON_ASSERT(!keep_stack.empty());
+        ref_stack.pop_back();
+        keep_stack.pop_back();
+
+        // remove discarded value
+        if (!keep && !ref_stack.empty() && ref_stack.back()->is_array())
+        {
+            ref_stack.back()->m_data.m_value.array->pop_back();
+        }
+
+        return true;
+    }
+
+    template<class Exception>
+    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/,
+                     const Exception& ex)
+    {
+        errored = true;
+        static_cast<void>(ex);
+        if (allow_exceptions)
+        {
+            JSON_THROW(ex);
+        }
+        return false;
+    }
+
+    constexpr bool is_errored() const
+    {
+        return errored;
+    }
+
+  private:
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    void handle_diagnostic_positions_for_json_value(BasicJsonType& v)
+    {
+        if (m_lexer_ref)
+        {
+            // Lexer has read past the current field value, so set the end position to the current position.
+            // The start position will be set below based on the length of the string representation
+            // of the value.
+            v.end_position = m_lexer_ref->get_position();
+
+            switch (v.type())
+            {
+                case value_t::boolean:
+                {
+                    // 4 and 5 are the string length of "true" and "false"
+                    v.start_position = v.end_position - (v.m_data.m_value.boolean ? 4 : 5);
+                    break;
+                }
+
+                case value_t::null:
+                {
+                    // 4 is the string length of "null"
+                    v.start_position = v.end_position - 4;
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    // include the length of the quotes, which is 2
+                    v.start_position = v.end_position - v.m_data.m_value.string->size() - 2;
+                    break;
+                }
+
+                case value_t::discarded:
+                {
+                    v.end_position = std::string::npos;
+                    v.start_position = v.end_position;
+                    break;
+                }
+
+                case value_t::binary:
+                case value_t::number_integer:
+                case value_t::number_unsigned:
+                case value_t::number_float:
+                {
+                    v.start_position = v.end_position - m_lexer_ref->get_string().size();
+                    break;
+                }
+
+                case value_t::object:
+                case value_t::array:
+                {
+                    // object and array are handled in start_object() and start_array() handlers
+                    // skip setting the values here.
+                    break;
+                }
+                default: // LCOV_EXCL_LINE
+                    // Handle all possible types discretely, default handler should never be reached.
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert,-warnings-as-errors) LCOV_EXCL_LINE
+            }
+        }
+    }
+#endif
+
+    /*!
+    @param[in] v  value to add to the JSON value we build during parsing
+    @param[in] skip_callback  whether we should skip calling the callback
+               function; this is required after start_array() and
+               start_object() SAX events, because otherwise we would call the
+               callback function with an empty array or object, respectively.
+
+    @invariant If the ref stack is empty, then the passed value will be the new
+               root.
+    @invariant If the ref stack contains a value, then it is an array or an
+               object to which we can add elements
+
+    @return pair of boolean (whether value should be kept) and pointer (to the
+            passed value in the ref_stack hierarchy; nullptr if not kept)
+    */
+    template<typename Value>
+    std::pair<bool, BasicJsonType*> handle_value(Value&& v, const bool skip_callback = false)
+    {
+        JSON_ASSERT(!keep_stack.empty());
+
+        // do not handle this value if we know it would be added to a discarded
+        // container
+        if (!keep_stack.back())
+        {
+            return {false, nullptr};
+        }
+
+        // create value
+        auto value = BasicJsonType(std::forward<Value>(v));
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        handle_diagnostic_positions_for_json_value(value);
+#endif
+
+        // check callback
+        const bool keep = skip_callback || callback(static_cast<int>(ref_stack.size()), parse_event_t::value, value);
+
+        // do not handle this value if we just learnt it shall be discarded
+        if (!keep)
+        {
+            return {false, nullptr};
+        }
+
+        if (ref_stack.empty())
+        {
+            root = std::move(value);
+            return {true, & root};
+        }
+
+        // skip this value if we already decided to skip the parent
+        // (https://github.com/nlohmann/json/issues/971#issuecomment-413678360)
+        if (!ref_stack.back())
+        {
+            return {false, nullptr};
+        }
+
+        // we now only expect arrays and objects
+        JSON_ASSERT(ref_stack.back()->is_array() || ref_stack.back()->is_object());
+
+        // array
+        if (ref_stack.back()->is_array())
+        {
+            ref_stack.back()->m_data.m_value.array->emplace_back(std::move(value));
+            return {true, & (ref_stack.back()->m_data.m_value.array->back())};
+        }
+
+        // object
+        JSON_ASSERT(ref_stack.back()->is_object());
+        // check if we should store an element for the current key
+        JSON_ASSERT(!key_keep_stack.empty());
+        const bool store_element = key_keep_stack.back();
+        key_keep_stack.pop_back();
+
+        if (!store_element)
+        {
+            return {false, nullptr};
+        }
+
+        JSON_ASSERT(object_element);
+        *object_element = std::move(value);
+        return {true, object_element};
+    }
+
+    /// the parsed JSON value
+    BasicJsonType& root;
+    /// stack to model hierarchy of values
+    std::vector<BasicJsonType*> ref_stack {};
+    /// stack to manage which values to keep
+    std::vector<bool> keep_stack {}; // NOLINT(readability-redundant-member-init)
+    /// stack to manage which object keys to keep
+    std::vector<bool> key_keep_stack {}; // NOLINT(readability-redundant-member-init)
+    /// helper to hold the reference for the next object element
+    BasicJsonType* object_element = nullptr;
+    /// whether a syntax error occurred
+    bool errored = false;
+    /// callback function
+    const parser_callback_t callback = nullptr;
+    /// whether to throw exceptions in case of errors
+    const bool allow_exceptions = true;
+    /// a discarded value for the callback
+    BasicJsonType discarded = BasicJsonType::value_t::discarded;
+    /// the lexer reference to obtain the current position
+    lexer_t* m_lexer_ref = nullptr;
+};
+
+template<typename BasicJsonType>
+class json_sax_acceptor
+{
+  public:
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+
+    bool null()
+    {
+        return true;
+    }
+
+    bool boolean(bool /*unused*/)
+    {
+        return true;
+    }
+
+    bool number_integer(number_integer_t /*unused*/)
+    {
+        return true;
+    }
+
+    bool number_unsigned(number_unsigned_t /*unused*/)
+    {
+        return true;
+    }
+
+    bool number_float(number_float_t /*unused*/, const string_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool string(string_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool binary(binary_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool start_object(std::size_t /*unused*/ = detail::unknown_size())
+    {
+        return true;
+    }
+
+    bool key(string_t& /*unused*/)
+    {
+        return true;
+    }
+
+    bool end_object()
+    {
+        return true;
+    }
+
+    bool start_array(std::size_t /*unused*/ = detail::unknown_size())
+    {
+        return true;
+    }
+
+    bool end_array()
+    {
+        return true;
+    }
+
+    bool parse_error(std::size_t /*unused*/, const std::string& /*unused*/, const detail::exception& /*unused*/)
+    {
+        return false;
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/lexer.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/is_sax.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstdint> // size_t
+#include <utility> // declval
+#include <string> // string
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/detected.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename T>
+using null_function_t = decltype(std::declval<T&>().null());
+
+template<typename T>
+using boolean_function_t =
+    decltype(std::declval<T&>().boolean(std::declval<bool>()));
+
+template<typename T, typename Integer>
+using number_integer_function_t =
+    decltype(std::declval<T&>().number_integer(std::declval<Integer>()));
+
+template<typename T, typename Unsigned>
+using number_unsigned_function_t =
+    decltype(std::declval<T&>().number_unsigned(std::declval<Unsigned>()));
+
+template<typename T, typename Float, typename String>
+using number_float_function_t = decltype(std::declval<T&>().number_float(
+                                    std::declval<Float>(), std::declval<const String&>()));
+
+template<typename T, typename String>
+using string_function_t =
+    decltype(std::declval<T&>().string(std::declval<String&>()));
+
+template<typename T, typename Binary>
+using binary_function_t =
+    decltype(std::declval<T&>().binary(std::declval<Binary&>()));
+
+template<typename T>
+using start_object_function_t =
+    decltype(std::declval<T&>().start_object(std::declval<std::size_t>()));
+
+template<typename T, typename String>
+using key_function_t =
+    decltype(std::declval<T&>().key(std::declval<String&>()));
+
+template<typename T>
+using end_object_function_t = decltype(std::declval<T&>().end_object());
+
+template<typename T>
+using start_array_function_t =
+    decltype(std::declval<T&>().start_array(std::declval<std::size_t>()));
+
+template<typename T>
+using end_array_function_t = decltype(std::declval<T&>().end_array());
+
+template<typename T, typename Exception>
+using parse_error_function_t = decltype(std::declval<T&>().parse_error(
+        std::declval<std::size_t>(), std::declval<const std::string&>(),
+        std::declval<const Exception&>()));
+
+template<typename SAX, typename BasicJsonType>
+struct is_sax
+{
+  private:
+    static_assert(is_basic_json<BasicJsonType>::value,
+                  "BasicJsonType must be of type basic_json<...>");
+
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using exception_t = typename BasicJsonType::exception;
+
+  public:
+    static constexpr bool value =
+        is_detected_exact<bool, null_function_t, SAX>::value &&
+        is_detected_exact<bool, boolean_function_t, SAX>::value &&
+        is_detected_exact<bool, number_integer_function_t, SAX, number_integer_t>::value &&
+        is_detected_exact<bool, number_unsigned_function_t, SAX, number_unsigned_t>::value &&
+        is_detected_exact<bool, number_float_function_t, SAX, number_float_t, string_t>::value &&
+        is_detected_exact<bool, string_function_t, SAX, string_t>::value &&
+        is_detected_exact<bool, binary_function_t, SAX, binary_t>::value &&
+        is_detected_exact<bool, start_object_function_t, SAX>::value &&
+        is_detected_exact<bool, key_function_t, SAX, string_t>::value &&
+        is_detected_exact<bool, end_object_function_t, SAX>::value &&
+        is_detected_exact<bool, start_array_function_t, SAX>::value &&
+        is_detected_exact<bool, end_array_function_t, SAX>::value &&
+        is_detected_exact<bool, parse_error_function_t, SAX, exception_t>::value;
+};
+
+template<typename SAX, typename BasicJsonType>
+struct is_sax_static_asserts
+{
+  private:
+    static_assert(is_basic_json<BasicJsonType>::value,
+                  "BasicJsonType must be of type basic_json<...>");
+
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using exception_t = typename BasicJsonType::exception;
+
+  public:
+    static_assert(is_detected_exact<bool, null_function_t, SAX>::value,
+                  "Missing/invalid function: bool null()");
+    static_assert(is_detected_exact<bool, boolean_function_t, SAX>::value,
+                  "Missing/invalid function: bool boolean(bool)");
+    static_assert(is_detected_exact<bool, boolean_function_t, SAX>::value,
+                  "Missing/invalid function: bool boolean(bool)");
+    static_assert(
+        is_detected_exact<bool, number_integer_function_t, SAX,
+        number_integer_t>::value,
+        "Missing/invalid function: bool number_integer(number_integer_t)");
+    static_assert(
+        is_detected_exact<bool, number_unsigned_function_t, SAX,
+        number_unsigned_t>::value,
+        "Missing/invalid function: bool number_unsigned(number_unsigned_t)");
+    static_assert(is_detected_exact<bool, number_float_function_t, SAX,
+                  number_float_t, string_t>::value,
+                  "Missing/invalid function: bool number_float(number_float_t, const string_t&)");
+    static_assert(
+        is_detected_exact<bool, string_function_t, SAX, string_t>::value,
+        "Missing/invalid function: bool string(string_t&)");
+    static_assert(
+        is_detected_exact<bool, binary_function_t, SAX, binary_t>::value,
+        "Missing/invalid function: bool binary(binary_t&)");
+    static_assert(is_detected_exact<bool, start_object_function_t, SAX>::value,
+                  "Missing/invalid function: bool start_object(std::size_t)");
+    static_assert(is_detected_exact<bool, key_function_t, SAX, string_t>::value,
+                  "Missing/invalid function: bool key(string_t&)");
+    static_assert(is_detected_exact<bool, end_object_function_t, SAX>::value,
+                  "Missing/invalid function: bool end_object()");
+    static_assert(is_detected_exact<bool, start_array_function_t, SAX>::value,
+                  "Missing/invalid function: bool start_array(std::size_t)");
+    static_assert(is_detected_exact<bool, end_array_function_t, SAX>::value,
+                  "Missing/invalid function: bool end_array()");
+    static_assert(
+        is_detected_exact<bool, parse_error_function_t, SAX, exception_t>::value,
+        "Missing/invalid function: bool parse_error(std::size_t, const "
+        "std::string&, const exception&)");
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// how to treat CBOR tags
+enum class cbor_tag_handler_t
+{
+    error,   ///< throw a parse_error exception in case of a tag
+    ignore,  ///< ignore tags
+    store    ///< store tags as binary type
+};
+
+/*!
+@brief determine system byte order
+
+@return true if and only if system's byte order is little endian
+
+@note from https://stackoverflow.com/a/1001328/266378
+*/
+static inline bool little_endianness(int num = 1) noexcept
+{
+    return *reinterpret_cast<char*>(&num) == 1;
+}
+
+///////////////////
+// binary reader //
+///////////////////
+
+/*!
+@brief deserialization of CBOR, MessagePack, and UBJSON values
+*/
+template<typename BasicJsonType, typename InputAdapterType, typename SAX = json_sax_dom_parser<BasicJsonType, InputAdapterType>>
+class binary_reader
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using json_sax_t = SAX;
+    using char_type = typename InputAdapterType::char_type;
+    using char_int_type = typename char_traits<char_type>::int_type;
+
+  public:
+    /*!
+    @brief create a binary reader
+
+    @param[in] adapter  input adapter to read from
+    */
+    explicit binary_reader(InputAdapterType&& adapter, const input_format_t format = input_format_t::json) noexcept : ia(std::move(adapter)), input_format(format)
+    {
+        (void)detail::is_sax_static_asserts<SAX, BasicJsonType> {};
+    }
+
+    // make class move-only
+    binary_reader(const binary_reader&) = delete;
+    binary_reader(binary_reader&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    binary_reader& operator=(const binary_reader&) = delete;
+    binary_reader& operator=(binary_reader&&) = default; // NOLINT(hicpp-noexcept-move,performance-noexcept-move-constructor)
+    ~binary_reader() = default;
+
+    /*!
+    @param[in] format  the binary format to parse
+    @param[in] sax_    a SAX event processor
+    @param[in] strict  whether to expect the input to be consumed completed
+    @param[in] tag_handler  how to treat CBOR tags
+
+    @return whether parsing was successful
+    */
+    JSON_HEDLEY_NON_NULL(3)
+    bool sax_parse(const input_format_t format,
+                   json_sax_t* sax_,
+                   const bool strict = true,
+                   const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        sax = sax_;
+        bool result = false;
+
+        switch (format)
+        {
+            case input_format_t::bson:
+                result = parse_bson_internal();
+                break;
+
+            case input_format_t::cbor:
+                result = parse_cbor_internal(true, tag_handler);
+                break;
+
+            case input_format_t::msgpack:
+                result = parse_msgpack_internal();
+                break;
+
+            case input_format_t::ubjson:
+            case input_format_t::bjdata:
+                result = parse_ubjson_internal();
+                break;
+
+            case input_format_t::json: // LCOV_EXCL_LINE
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+
+        // strict mode: next byte must be EOF
+        if (result && strict)
+        {
+            if (input_format == input_format_t::ubjson || input_format == input_format_t::bjdata)
+            {
+                get_ignore_noop();
+            }
+            else
+            {
+                get();
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(current != char_traits<char_type>::eof()))
+            {
+                return sax->parse_error(chars_read, get_token_string(), parse_error::create(110, chars_read,
+                                        exception_message(input_format, concat("expected end of input; last byte: 0x", get_token_string()), "value"), nullptr));
+            }
+        }
+
+        return result;
+    }
+
+  private:
+    //////////
+    // BSON //
+    //////////
+
+    /*!
+    @brief Reads in a BSON-object and passes it to the SAX-parser.
+    @return whether a valid BSON-value was passed to the SAX parser
+    */
+    bool parse_bson_internal()
+    {
+        std::int32_t document_size{};
+        get_number<std::int32_t, true>(input_format_t::bson, document_size);
+
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(detail::unknown_size())))
+        {
+            return false;
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_list(/*is_array*/false)))
+        {
+            return false;
+        }
+
+        return sax->end_object();
+    }
+
+    /*!
+    @brief Parses a C-style string from the BSON input.
+    @param[in,out] result  A reference to the string variable where the read
+                            string is to be stored.
+    @return `true` if the \x00-byte indicating the end of the string was
+             encountered before the EOF; false` indicates an unexpected EOF.
+    */
+    bool get_bson_cstr(string_t& result)
+    {
+        auto out = std::back_inserter(result);
+        while (true)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::bson, "cstring")))
+            {
+                return false;
+            }
+            if (current == 0x00)
+            {
+                return true;
+            }
+            *out++ = static_cast<typename string_t::value_type>(current);
+        }
+    }
+
+    /*!
+    @brief Parses a zero-terminated string of length @a len from the BSON
+           input.
+    @param[in] len  The length (including the zero-byte at the end) of the
+                    string to be read.
+    @param[in,out] result  A reference to the string variable where the read
+                            string is to be stored.
+    @tparam NumberType The type of the length @a len
+    @pre len >= 1
+    @return `true` if the string was successfully parsed
+    */
+    template<typename NumberType>
+    bool get_bson_string(const NumberType len, string_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(len < 1))
+        {
+            auto last_token = get_token_string();
+            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                    exception_message(input_format_t::bson, concat("string length must be at least 1, is ", std::to_string(len)), "string"), nullptr));
+        }
+
+        return get_string(input_format_t::bson, len - static_cast<NumberType>(1), result) && get() != char_traits<char_type>::eof();
+    }
+
+    /*!
+    @brief Parses a byte array input of length @a len from the BSON input.
+    @param[in] len  The length of the byte array to be read.
+    @param[in,out] result  A reference to the binary variable where the read
+                            array is to be stored.
+    @tparam NumberType The type of the length @a len
+    @pre len >= 0
+    @return `true` if the byte array was successfully parsed
+    */
+    template<typename NumberType>
+    bool get_bson_binary(const NumberType len, binary_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(len < 0))
+        {
+            auto last_token = get_token_string();
+            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                    exception_message(input_format_t::bson, concat("byte array length cannot be negative, is ", std::to_string(len)), "binary"), nullptr));
+        }
+
+        // All BSON binary values have a subtype
+        std::uint8_t subtype{};
+        get_number<std::uint8_t>(input_format_t::bson, subtype);
+        result.set_subtype(subtype);
+
+        return get_binary(input_format_t::bson, len, result);
+    }
+
+    /*!
+    @brief Read a BSON document element of the given @a element_type.
+    @param[in] element_type The BSON element type, c.f. http://bsonspec.org/spec.html
+    @param[in] element_type_parse_position The position in the input stream,
+               where the `element_type` was read.
+    @warning Not all BSON element types are supported yet. An unsupported
+             @a element_type will give rise to a parse_error.114:
+             Unsupported BSON record type 0x...
+    @return whether a valid BSON-object/array was passed to the SAX parser
+    */
+    bool parse_bson_element_internal(const char_int_type element_type,
+                                     const std::size_t element_type_parse_position)
+    {
+        switch (element_type)
+        {
+            case 0x01: // double
+            {
+                double number{};
+                return get_number<double, true>(input_format_t::bson, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0x02: // string
+            {
+                std::int32_t len{};
+                string_t value;
+                return get_number<std::int32_t, true>(input_format_t::bson, len) && get_bson_string(len, value) && sax->string(value);
+            }
+
+            case 0x03: // object
+            {
+                return parse_bson_internal();
+            }
+
+            case 0x04: // array
+            {
+                return parse_bson_array();
+            }
+
+            case 0x05: // binary
+            {
+                std::int32_t len{};
+                binary_t value;
+                return get_number<std::int32_t, true>(input_format_t::bson, len) && get_bson_binary(len, value) && sax->binary(value);
+            }
+
+            case 0x08: // boolean
+            {
+                return sax->boolean(get() != 0);
+            }
+
+            case 0x0A: // null
+            {
+                return sax->null();
+            }
+
+            case 0x10: // int32
+            {
+                std::int32_t value{};
+                return get_number<std::int32_t, true>(input_format_t::bson, value) && sax->number_integer(value);
+            }
+
+            case 0x12: // int64
+            {
+                std::int64_t value{};
+                return get_number<std::int64_t, true>(input_format_t::bson, value) && sax->number_integer(value);
+            }
+
+            case 0x11: // uint64
+            {
+                std::uint64_t value{};
+                return get_number<std::uint64_t, true>(input_format_t::bson, value) && sax->number_unsigned(value);
+            }
+
+            default: // anything else not supported (yet)
+            {
+                std::array<char, 3> cr{{}};
+                static_cast<void>((std::snprintf)(cr.data(), cr.size(), "%.2hhX", static_cast<unsigned char>(element_type))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                const std::string cr_str{cr.data()};
+                return sax->parse_error(element_type_parse_position, cr_str,
+                                        parse_error::create(114, element_type_parse_position, concat("Unsupported BSON record type 0x", cr_str), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief Read a BSON element list (as specified in the BSON-spec)
+
+    The same binary layout is used for objects and arrays, hence it must be
+    indicated with the argument @a is_array which one is expected
+    (true --> array, false --> object).
+
+    @param[in] is_array Determines if the element list being read is to be
+                        treated as an object (@a is_array == false), or as an
+                        array (@a is_array == true).
+    @return whether a valid BSON-object/array was passed to the SAX parser
+    */
+    bool parse_bson_element_list(const bool is_array)
+    {
+        string_t key;
+
+        while (auto element_type = get())
+        {
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::bson, "element list")))
+            {
+                return false;
+            }
+
+            const std::size_t element_type_parse_position = chars_read;
+            if (JSON_HEDLEY_UNLIKELY(!get_bson_cstr(key)))
+            {
+                return false;
+            }
+
+            if (!is_array && !sax->key(key))
+            {
+                return false;
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_internal(element_type, element_type_parse_position)))
+            {
+                return false;
+            }
+
+            // get_bson_cstr only appends
+            key.clear();
+        }
+
+        return true;
+    }
+
+    /*!
+    @brief Reads an array from the BSON input and passes it to the SAX-parser.
+    @return whether a valid BSON-array was passed to the SAX parser
+    */
+    bool parse_bson_array()
+    {
+        std::int32_t document_size{};
+        get_number<std::int32_t, true>(input_format_t::bson, document_size);
+
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(detail::unknown_size())))
+        {
+            return false;
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!parse_bson_element_list(/*is_array*/true)))
+        {
+            return false;
+        }
+
+        return sax->end_array();
+    }
+
+    //////////
+    // CBOR //
+    //////////
+
+    /*!
+    @param[in] get_char  whether a new character should be retrieved from the
+                         input (true) or whether the last read character should
+                         be considered instead (false)
+    @param[in] tag_handler how CBOR tags should be treated
+
+    @return whether a valid CBOR value was passed to the SAX parser
+    */
+    bool parse_cbor_internal(const bool get_char,
+                             const cbor_tag_handler_t tag_handler)
+    {
+        switch (get_char ? get() : current)
+        {
+            // EOF
+            case char_traits<char_type>::eof():
+                return unexpect_eof(input_format_t::cbor, "value");
+
+            // Integer 0x00..0x17 (0..23)
+            case 0x00:
+            case 0x01:
+            case 0x02:
+            case 0x03:
+            case 0x04:
+            case 0x05:
+            case 0x06:
+            case 0x07:
+            case 0x08:
+            case 0x09:
+            case 0x0A:
+            case 0x0B:
+            case 0x0C:
+            case 0x0D:
+            case 0x0E:
+            case 0x0F:
+            case 0x10:
+            case 0x11:
+            case 0x12:
+            case 0x13:
+            case 0x14:
+            case 0x15:
+            case 0x16:
+            case 0x17:
+                return sax->number_unsigned(static_cast<number_unsigned_t>(current));
+
+            case 0x18: // Unsigned integer (one-byte uint8_t follows)
+            {
+                std::uint8_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            case 0x19: // Unsigned integer (two-byte uint16_t follows)
+            {
+                std::uint16_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            case 0x1A: // Unsigned integer (four-byte uint32_t follows)
+            {
+                std::uint32_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            case 0x1B: // Unsigned integer (eight-byte uint64_t follows)
+            {
+                std::uint64_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_unsigned(number);
+            }
+
+            // Negative integer -1-0x00..-1-0x17 (-1..-24)
+            case 0x20:
+            case 0x21:
+            case 0x22:
+            case 0x23:
+            case 0x24:
+            case 0x25:
+            case 0x26:
+            case 0x27:
+            case 0x28:
+            case 0x29:
+            case 0x2A:
+            case 0x2B:
+            case 0x2C:
+            case 0x2D:
+            case 0x2E:
+            case 0x2F:
+            case 0x30:
+            case 0x31:
+            case 0x32:
+            case 0x33:
+            case 0x34:
+            case 0x35:
+            case 0x36:
+            case 0x37:
+                return sax->number_integer(static_cast<std::int8_t>(0x20 - 1 - current));
+
+            case 0x38: // Negative integer (one-byte uint8_t follows)
+            {
+                std::uint8_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);
+            }
+
+            case 0x39: // Negative integer -1-n (two-byte uint16_t follows)
+            {
+                std::uint16_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);
+            }
+
+            case 0x3A: // Negative integer -1-n (four-byte uint32_t follows)
+            {
+                std::uint32_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1) - number);
+            }
+
+            case 0x3B: // Negative integer -1-n (eight-byte uint64_t follows)
+            {
+                std::uint64_t number{};
+                return get_number(input_format_t::cbor, number) && sax->number_integer(static_cast<number_integer_t>(-1)
+                        - static_cast<number_integer_t>(number));
+            }
+
+            // Binary data (0x00..0x17 bytes follow)
+            case 0x40:
+            case 0x41:
+            case 0x42:
+            case 0x43:
+            case 0x44:
+            case 0x45:
+            case 0x46:
+            case 0x47:
+            case 0x48:
+            case 0x49:
+            case 0x4A:
+            case 0x4B:
+            case 0x4C:
+            case 0x4D:
+            case 0x4E:
+            case 0x4F:
+            case 0x50:
+            case 0x51:
+            case 0x52:
+            case 0x53:
+            case 0x54:
+            case 0x55:
+            case 0x56:
+            case 0x57:
+            case 0x58: // Binary data (one-byte uint8_t for n follows)
+            case 0x59: // Binary data (two-byte uint16_t for n follow)
+            case 0x5A: // Binary data (four-byte uint32_t for n follow)
+            case 0x5B: // Binary data (eight-byte uint64_t for n follow)
+            case 0x5F: // Binary data (indefinite length)
+            {
+                binary_t b;
+                return get_cbor_binary(b) && sax->binary(b);
+            }
+
+            // UTF-8 string (0x00..0x17 bytes follow)
+            case 0x60:
+            case 0x61:
+            case 0x62:
+            case 0x63:
+            case 0x64:
+            case 0x65:
+            case 0x66:
+            case 0x67:
+            case 0x68:
+            case 0x69:
+            case 0x6A:
+            case 0x6B:
+            case 0x6C:
+            case 0x6D:
+            case 0x6E:
+            case 0x6F:
+            case 0x70:
+            case 0x71:
+            case 0x72:
+            case 0x73:
+            case 0x74:
+            case 0x75:
+            case 0x76:
+            case 0x77:
+            case 0x78: // UTF-8 string (one-byte uint8_t for n follows)
+            case 0x79: // UTF-8 string (two-byte uint16_t for n follow)
+            case 0x7A: // UTF-8 string (four-byte uint32_t for n follow)
+            case 0x7B: // UTF-8 string (eight-byte uint64_t for n follow)
+            case 0x7F: // UTF-8 string (indefinite length)
+            {
+                string_t s;
+                return get_cbor_string(s) && sax->string(s);
+            }
+
+            // array (0x00..0x17 data items follow)
+            case 0x80:
+            case 0x81:
+            case 0x82:
+            case 0x83:
+            case 0x84:
+            case 0x85:
+            case 0x86:
+            case 0x87:
+            case 0x88:
+            case 0x89:
+            case 0x8A:
+            case 0x8B:
+            case 0x8C:
+            case 0x8D:
+            case 0x8E:
+            case 0x8F:
+            case 0x90:
+            case 0x91:
+            case 0x92:
+            case 0x93:
+            case 0x94:
+            case 0x95:
+            case 0x96:
+            case 0x97:
+                return get_cbor_array(
+                           conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x1Fu), tag_handler);
+
+            case 0x98: // array (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x99: // array (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x9A: // array (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x9B: // array (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_array(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0x9F: // array (indefinite length)
+                return get_cbor_array(detail::unknown_size(), tag_handler);
+
+            // map (0x00..0x17 pairs of data items follow)
+            case 0xA0:
+            case 0xA1:
+            case 0xA2:
+            case 0xA3:
+            case 0xA4:
+            case 0xA5:
+            case 0xA6:
+            case 0xA7:
+            case 0xA8:
+            case 0xA9:
+            case 0xAA:
+            case 0xAB:
+            case 0xAC:
+            case 0xAD:
+            case 0xAE:
+            case 0xAF:
+            case 0xB0:
+            case 0xB1:
+            case 0xB2:
+            case 0xB3:
+            case 0xB4:
+            case 0xB5:
+            case 0xB6:
+            case 0xB7:
+                return get_cbor_object(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x1Fu), tag_handler);
+
+            case 0xB8: // map (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xB9: // map (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xBA: // map (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xBB: // map (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) && get_cbor_object(conditional_static_cast<std::size_t>(len), tag_handler);
+            }
+
+            case 0xBF: // map (indefinite length)
+                return get_cbor_object(detail::unknown_size(), tag_handler);
+
+            case 0xC6: // tagged item
+            case 0xC7:
+            case 0xC8:
+            case 0xC9:
+            case 0xCA:
+            case 0xCB:
+            case 0xCC:
+            case 0xCD:
+            case 0xCE:
+            case 0xCF:
+            case 0xD0:
+            case 0xD1:
+            case 0xD2:
+            case 0xD3:
+            case 0xD4:
+            case 0xD8: // tagged item (1 bytes follow)
+            case 0xD9: // tagged item (2 bytes follow)
+            case 0xDA: // tagged item (4 bytes follow)
+            case 0xDB: // tagged item (8 bytes follow)
+            {
+                switch (tag_handler)
+                {
+                    case cbor_tag_handler_t::error:
+                    {
+                        auto last_token = get_token_string();
+                        return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                                exception_message(input_format_t::cbor, concat("invalid byte: 0x", last_token), "value"), nullptr));
+                    }
+
+                    case cbor_tag_handler_t::ignore:
+                    {
+                        // ignore binary subtype
+                        switch (current)
+                        {
+                            case 0xD8:
+                            {
+                                std::uint8_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            case 0xD9:
+                            {
+                                std::uint16_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            case 0xDA:
+                            {
+                                std::uint32_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            case 0xDB:
+                            {
+                                std::uint64_t subtype_to_ignore{};
+                                get_number(input_format_t::cbor, subtype_to_ignore);
+                                break;
+                            }
+                            default:
+                                break;
+                        }
+                        return parse_cbor_internal(true, tag_handler);
+                    }
+
+                    case cbor_tag_handler_t::store:
+                    {
+                        binary_t b;
+                        // use binary subtype and store in binary container
+                        switch (current)
+                        {
+                            case 0xD8:
+                            {
+                                std::uint8_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            case 0xD9:
+                            {
+                                std::uint16_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            case 0xDA:
+                            {
+                                std::uint32_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            case 0xDB:
+                            {
+                                std::uint64_t subtype{};
+                                get_number(input_format_t::cbor, subtype);
+                                b.set_subtype(detail::conditional_static_cast<typename binary_t::subtype_type>(subtype));
+                                break;
+                            }
+                            default:
+                                return parse_cbor_internal(true, tag_handler);
+                        }
+                        get();
+                        return get_cbor_binary(b) && sax->binary(b);
+                    }
+
+                    default:                 // LCOV_EXCL_LINE
+                        JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+                        return false;        // LCOV_EXCL_LINE
+                }
+            }
+
+            case 0xF4: // false
+                return sax->boolean(false);
+
+            case 0xF5: // true
+                return sax->boolean(true);
+
+            case 0xF6: // null
+                return sax->null();
+
+            case 0xF9: // Half-Precision Float (two-byte IEEE 754)
+            {
+                const auto byte1_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "number")))
+                {
+                    return false;
+                }
+                const auto byte2_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "number")))
+                {
+                    return false;
+                }
+
+                const auto byte1 = static_cast<unsigned char>(byte1_raw);
+                const auto byte2 = static_cast<unsigned char>(byte2_raw);
+
+                // code from RFC 7049, Appendix D, Figure 3:
+                // As half-precision floating-point numbers were only added
+                // to IEEE 754 in 2008, today's programming platforms often
+                // still only have limited support for them. It is very
+                // easy to include at least decoding support for them even
+                // without such support. An example of a small decoder for
+                // half-precision floating-point numbers in the C language
+                // is shown in Fig. 3.
+                const auto half = static_cast<unsigned int>((byte1 << 8u) + byte2);
+                const double val = [&half]
+                {
+                    const int exp = (half >> 10u) & 0x1Fu;
+                    const unsigned int mant = half & 0x3FFu;
+                    JSON_ASSERT(0 <= exp&& exp <= 32);
+                    JSON_ASSERT(mant <= 1024);
+                    switch (exp)
+                    {
+                        case 0:
+                            return std::ldexp(mant, -24);
+                        case 31:
+                            return (mant == 0)
+                            ? std::numeric_limits<double>::infinity()
+                            : std::numeric_limits<double>::quiet_NaN();
+                        default:
+                            return std::ldexp(mant + 1024, exp - 25);
+                    }
+                }();
+                return sax->number_float((half & 0x8000u) != 0
+                                         ? static_cast<number_float_t>(-val)
+                                         : static_cast<number_float_t>(val), "");
+            }
+
+            case 0xFA: // Single-Precision Float (four-byte IEEE 754)
+            {
+                float number{};
+                return get_number(input_format_t::cbor, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0xFB: // Double-Precision Float (eight-byte IEEE 754)
+            {
+                double number{};
+                return get_number(input_format_t::cbor, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            default: // anything else (0xFF is handled inside the other types)
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format_t::cbor, concat("invalid byte: 0x", last_token), "value"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a CBOR string
+
+    This function first reads starting bytes to determine the expected
+    string length and then copies this number of bytes into a string.
+    Additionally, CBOR's strings with indefinite lengths are supported.
+
+    @param[out] result  created string
+
+    @return whether string creation completed
+    */
+    bool get_cbor_string(string_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "string")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            // UTF-8 string (0x00..0x17 bytes follow)
+            case 0x60:
+            case 0x61:
+            case 0x62:
+            case 0x63:
+            case 0x64:
+            case 0x65:
+            case 0x66:
+            case 0x67:
+            case 0x68:
+            case 0x69:
+            case 0x6A:
+            case 0x6B:
+            case 0x6C:
+            case 0x6D:
+            case 0x6E:
+            case 0x6F:
+            case 0x70:
+            case 0x71:
+            case 0x72:
+            case 0x73:
+            case 0x74:
+            case 0x75:
+            case 0x76:
+            case 0x77:
+            {
+                return get_string(input_format_t::cbor, static_cast<unsigned int>(current) & 0x1Fu, result);
+            }
+
+            case 0x78: // UTF-8 string (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x79: // UTF-8 string (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x7A: // UTF-8 string (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x7B: // UTF-8 string (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) && get_string(input_format_t::cbor, len, result);
+            }
+
+            case 0x7F: // UTF-8 string (indefinite length)
+            {
+                while (get() != 0xFF)
+                {
+                    string_t chunk;
+                    if (!get_cbor_string(chunk))
+                    {
+                        return false;
+                    }
+                    result.append(chunk);
+                }
+                return true;
+            }
+
+            default:
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                        exception_message(input_format_t::cbor, concat("expected length specification (0x60-0x7B) or indefinite string type (0x7F); last byte: 0x", last_token), "string"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a CBOR byte array
+
+    This function first reads starting bytes to determine the expected
+    byte array length and then copies this number of bytes into the byte array.
+    Additionally, CBOR's byte arrays with indefinite lengths are supported.
+
+    @param[out] result  created byte array
+
+    @return whether byte array creation completed
+    */
+    bool get_cbor_binary(binary_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::cbor, "binary")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            // Binary data (0x00..0x17 bytes follow)
+            case 0x40:
+            case 0x41:
+            case 0x42:
+            case 0x43:
+            case 0x44:
+            case 0x45:
+            case 0x46:
+            case 0x47:
+            case 0x48:
+            case 0x49:
+            case 0x4A:
+            case 0x4B:
+            case 0x4C:
+            case 0x4D:
+            case 0x4E:
+            case 0x4F:
+            case 0x50:
+            case 0x51:
+            case 0x52:
+            case 0x53:
+            case 0x54:
+            case 0x55:
+            case 0x56:
+            case 0x57:
+            {
+                return get_binary(input_format_t::cbor, static_cast<unsigned int>(current) & 0x1Fu, result);
+            }
+
+            case 0x58: // Binary data (one-byte uint8_t for n follows)
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x59: // Binary data (two-byte uint16_t for n follow)
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x5A: // Binary data (four-byte uint32_t for n follow)
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x5B: // Binary data (eight-byte uint64_t for n follow)
+            {
+                std::uint64_t len{};
+                return get_number(input_format_t::cbor, len) &&
+                       get_binary(input_format_t::cbor, len, result);
+            }
+
+            case 0x5F: // Binary data (indefinite length)
+            {
+                while (get() != 0xFF)
+                {
+                    binary_t chunk;
+                    if (!get_cbor_binary(chunk))
+                    {
+                        return false;
+                    }
+                    result.insert(result.end(), chunk.begin(), chunk.end());
+                }
+                return true;
+            }
+
+            default:
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                        exception_message(input_format_t::cbor, concat("expected length specification (0x40-0x5B) or indefinite binary array type (0x5F); last byte: 0x", last_token), "binary"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @param[in] len  the length of the array or detail::unknown_size() for an
+                    array of indefinite size
+    @param[in] tag_handler how CBOR tags should be treated
+    @return whether array creation completed
+    */
+    bool get_cbor_array(const std::size_t len,
+                        const cbor_tag_handler_t tag_handler)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(len)))
+        {
+            return false;
+        }
+
+        if (len != detail::unknown_size())
+        {
+            for (std::size_t i = 0; i < len; ++i)
+            {
+                if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))
+                {
+                    return false;
+                }
+            }
+        }
+        else
+        {
+            while (get() != 0xFF)
+            {
+                if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(false, tag_handler)))
+                {
+                    return false;
+                }
+            }
+        }
+
+        return sax->end_array();
+    }
+
+    /*!
+    @param[in] len  the length of the object or detail::unknown_size() for an
+                    object of indefinite size
+    @param[in] tag_handler how CBOR tags should be treated
+    @return whether object creation completed
+    */
+    bool get_cbor_object(const std::size_t len,
+                         const cbor_tag_handler_t tag_handler)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(len)))
+        {
+            return false;
+        }
+
+        if (len != 0)
+        {
+            string_t key;
+            if (len != detail::unknown_size())
+            {
+                for (std::size_t i = 0; i < len; ++i)
+                {
+                    get();
+                    if (JSON_HEDLEY_UNLIKELY(!get_cbor_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+
+                    if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+            else
+            {
+                while (get() != 0xFF)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_cbor_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+
+                    if (JSON_HEDLEY_UNLIKELY(!parse_cbor_internal(true, tag_handler)))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+        }
+
+        return sax->end_object();
+    }
+
+    /////////////
+    // MsgPack //
+    /////////////
+
+    /*!
+    @return whether a valid MessagePack value was passed to the SAX parser
+    */
+    bool parse_msgpack_internal()
+    {
+        switch (get())
+        {
+            // EOF
+            case char_traits<char_type>::eof():
+                return unexpect_eof(input_format_t::msgpack, "value");
+
+            // positive fixint
+            case 0x00:
+            case 0x01:
+            case 0x02:
+            case 0x03:
+            case 0x04:
+            case 0x05:
+            case 0x06:
+            case 0x07:
+            case 0x08:
+            case 0x09:
+            case 0x0A:
+            case 0x0B:
+            case 0x0C:
+            case 0x0D:
+            case 0x0E:
+            case 0x0F:
+            case 0x10:
+            case 0x11:
+            case 0x12:
+            case 0x13:
+            case 0x14:
+            case 0x15:
+            case 0x16:
+            case 0x17:
+            case 0x18:
+            case 0x19:
+            case 0x1A:
+            case 0x1B:
+            case 0x1C:
+            case 0x1D:
+            case 0x1E:
+            case 0x1F:
+            case 0x20:
+            case 0x21:
+            case 0x22:
+            case 0x23:
+            case 0x24:
+            case 0x25:
+            case 0x26:
+            case 0x27:
+            case 0x28:
+            case 0x29:
+            case 0x2A:
+            case 0x2B:
+            case 0x2C:
+            case 0x2D:
+            case 0x2E:
+            case 0x2F:
+            case 0x30:
+            case 0x31:
+            case 0x32:
+            case 0x33:
+            case 0x34:
+            case 0x35:
+            case 0x36:
+            case 0x37:
+            case 0x38:
+            case 0x39:
+            case 0x3A:
+            case 0x3B:
+            case 0x3C:
+            case 0x3D:
+            case 0x3E:
+            case 0x3F:
+            case 0x40:
+            case 0x41:
+            case 0x42:
+            case 0x43:
+            case 0x44:
+            case 0x45:
+            case 0x46:
+            case 0x47:
+            case 0x48:
+            case 0x49:
+            case 0x4A:
+            case 0x4B:
+            case 0x4C:
+            case 0x4D:
+            case 0x4E:
+            case 0x4F:
+            case 0x50:
+            case 0x51:
+            case 0x52:
+            case 0x53:
+            case 0x54:
+            case 0x55:
+            case 0x56:
+            case 0x57:
+            case 0x58:
+            case 0x59:
+            case 0x5A:
+            case 0x5B:
+            case 0x5C:
+            case 0x5D:
+            case 0x5E:
+            case 0x5F:
+            case 0x60:
+            case 0x61:
+            case 0x62:
+            case 0x63:
+            case 0x64:
+            case 0x65:
+            case 0x66:
+            case 0x67:
+            case 0x68:
+            case 0x69:
+            case 0x6A:
+            case 0x6B:
+            case 0x6C:
+            case 0x6D:
+            case 0x6E:
+            case 0x6F:
+            case 0x70:
+            case 0x71:
+            case 0x72:
+            case 0x73:
+            case 0x74:
+            case 0x75:
+            case 0x76:
+            case 0x77:
+            case 0x78:
+            case 0x79:
+            case 0x7A:
+            case 0x7B:
+            case 0x7C:
+            case 0x7D:
+            case 0x7E:
+            case 0x7F:
+                return sax->number_unsigned(static_cast<number_unsigned_t>(current));
+
+            // fixmap
+            case 0x80:
+            case 0x81:
+            case 0x82:
+            case 0x83:
+            case 0x84:
+            case 0x85:
+            case 0x86:
+            case 0x87:
+            case 0x88:
+            case 0x89:
+            case 0x8A:
+            case 0x8B:
+            case 0x8C:
+            case 0x8D:
+            case 0x8E:
+            case 0x8F:
+                return get_msgpack_object(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x0Fu));
+
+            // fixarray
+            case 0x90:
+            case 0x91:
+            case 0x92:
+            case 0x93:
+            case 0x94:
+            case 0x95:
+            case 0x96:
+            case 0x97:
+            case 0x98:
+            case 0x99:
+            case 0x9A:
+            case 0x9B:
+            case 0x9C:
+            case 0x9D:
+            case 0x9E:
+            case 0x9F:
+                return get_msgpack_array(conditional_static_cast<std::size_t>(static_cast<unsigned int>(current) & 0x0Fu));
+
+            // fixstr
+            case 0xA0:
+            case 0xA1:
+            case 0xA2:
+            case 0xA3:
+            case 0xA4:
+            case 0xA5:
+            case 0xA6:
+            case 0xA7:
+            case 0xA8:
+            case 0xA9:
+            case 0xAA:
+            case 0xAB:
+            case 0xAC:
+            case 0xAD:
+            case 0xAE:
+            case 0xAF:
+            case 0xB0:
+            case 0xB1:
+            case 0xB2:
+            case 0xB3:
+            case 0xB4:
+            case 0xB5:
+            case 0xB6:
+            case 0xB7:
+            case 0xB8:
+            case 0xB9:
+            case 0xBA:
+            case 0xBB:
+            case 0xBC:
+            case 0xBD:
+            case 0xBE:
+            case 0xBF:
+            case 0xD9: // str 8
+            case 0xDA: // str 16
+            case 0xDB: // str 32
+            {
+                string_t s;
+                return get_msgpack_string(s) && sax->string(s);
+            }
+
+            case 0xC0: // nil
+                return sax->null();
+
+            case 0xC2: // false
+                return sax->boolean(false);
+
+            case 0xC3: // true
+                return sax->boolean(true);
+
+            case 0xC4: // bin 8
+            case 0xC5: // bin 16
+            case 0xC6: // bin 32
+            case 0xC7: // ext 8
+            case 0xC8: // ext 16
+            case 0xC9: // ext 32
+            case 0xD4: // fixext 1
+            case 0xD5: // fixext 2
+            case 0xD6: // fixext 4
+            case 0xD7: // fixext 8
+            case 0xD8: // fixext 16
+            {
+                binary_t b;
+                return get_msgpack_binary(b) && sax->binary(b);
+            }
+
+            case 0xCA: // float 32
+            {
+                float number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0xCB: // float 64
+            {
+                double number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 0xCC: // uint 8
+            {
+                std::uint8_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xCD: // uint 16
+            {
+                std::uint16_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xCE: // uint 32
+            {
+                std::uint32_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xCF: // uint 64
+            {
+                std::uint64_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_unsigned(number);
+            }
+
+            case 0xD0: // int 8
+            {
+                std::int8_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xD1: // int 16
+            {
+                std::int16_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xD2: // int 32
+            {
+                std::int32_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xD3: // int 64
+            {
+                std::int64_t number{};
+                return get_number(input_format_t::msgpack, number) && sax->number_integer(number);
+            }
+
+            case 0xDC: // array 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_array(static_cast<std::size_t>(len));
+            }
+
+            case 0xDD: // array 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_array(conditional_static_cast<std::size_t>(len));
+            }
+
+            case 0xDE: // map 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_object(static_cast<std::size_t>(len));
+            }
+
+            case 0xDF: // map 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) && get_msgpack_object(conditional_static_cast<std::size_t>(len));
+            }
+
+            // negative fixint
+            case 0xE0:
+            case 0xE1:
+            case 0xE2:
+            case 0xE3:
+            case 0xE4:
+            case 0xE5:
+            case 0xE6:
+            case 0xE7:
+            case 0xE8:
+            case 0xE9:
+            case 0xEA:
+            case 0xEB:
+            case 0xEC:
+            case 0xED:
+            case 0xEE:
+            case 0xEF:
+            case 0xF0:
+            case 0xF1:
+            case 0xF2:
+            case 0xF3:
+            case 0xF4:
+            case 0xF5:
+            case 0xF6:
+            case 0xF7:
+            case 0xF8:
+            case 0xF9:
+            case 0xFA:
+            case 0xFB:
+            case 0xFC:
+            case 0xFD:
+            case 0xFE:
+            case 0xFF:
+                return sax->number_integer(static_cast<std::int8_t>(current));
+
+            default: // anything else
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format_t::msgpack, concat("invalid byte: 0x", last_token), "value"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a MessagePack string
+
+    This function first reads starting bytes to determine the expected
+    string length and then copies this number of bytes into a string.
+
+    @param[out] result  created string
+
+    @return whether string creation completed
+    */
+    bool get_msgpack_string(string_t& result)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format_t::msgpack, "string")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            // fixstr
+            case 0xA0:
+            case 0xA1:
+            case 0xA2:
+            case 0xA3:
+            case 0xA4:
+            case 0xA5:
+            case 0xA6:
+            case 0xA7:
+            case 0xA8:
+            case 0xA9:
+            case 0xAA:
+            case 0xAB:
+            case 0xAC:
+            case 0xAD:
+            case 0xAE:
+            case 0xAF:
+            case 0xB0:
+            case 0xB1:
+            case 0xB2:
+            case 0xB3:
+            case 0xB4:
+            case 0xB5:
+            case 0xB6:
+            case 0xB7:
+            case 0xB8:
+            case 0xB9:
+            case 0xBA:
+            case 0xBB:
+            case 0xBC:
+            case 0xBD:
+            case 0xBE:
+            case 0xBF:
+            {
+                return get_string(input_format_t::msgpack, static_cast<unsigned int>(current) & 0x1Fu, result);
+            }
+
+            case 0xD9: // str 8
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);
+            }
+
+            case 0xDA: // str 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);
+            }
+
+            case 0xDB: // str 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) && get_string(input_format_t::msgpack, len, result);
+            }
+
+            default:
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                        exception_message(input_format_t::msgpack, concat("expected length specification (0xA0-0xBF, 0xD9-0xDB); last byte: 0x", last_token), "string"), nullptr));
+            }
+        }
+    }
+
+    /*!
+    @brief reads a MessagePack byte array
+
+    This function first reads starting bytes to determine the expected
+    byte array length and then copies this number of bytes into a byte array.
+
+    @param[out] result  created byte array
+
+    @return whether byte array creation completed
+    */
+    bool get_msgpack_binary(binary_t& result)
+    {
+        // helper function to set the subtype
+        auto assign_and_return_true = [&result](std::int8_t subtype)
+        {
+            result.set_subtype(static_cast<std::uint8_t>(subtype));
+            return true;
+        };
+
+        switch (current)
+        {
+            case 0xC4: // bin 8
+            {
+                std::uint8_t len{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_binary(input_format_t::msgpack, len, result);
+            }
+
+            case 0xC5: // bin 16
+            {
+                std::uint16_t len{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_binary(input_format_t::msgpack, len, result);
+            }
+
+            case 0xC6: // bin 32
+            {
+                std::uint32_t len{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_binary(input_format_t::msgpack, len, result);
+            }
+
+            case 0xC7: // ext 8
+            {
+                std::uint8_t len{};
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, len, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xC8: // ext 16
+            {
+                std::uint16_t len{};
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, len, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xC9: // ext 32
+            {
+                std::uint32_t len{};
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, len) &&
+                       get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, len, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD4: // fixext 1
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 1, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD5: // fixext 2
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 2, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD6: // fixext 4
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 4, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD7: // fixext 8
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 8, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            case 0xD8: // fixext 16
+            {
+                std::int8_t subtype{};
+                return get_number(input_format_t::msgpack, subtype) &&
+                       get_binary(input_format_t::msgpack, 16, result) &&
+                       assign_and_return_true(subtype);
+            }
+
+            default:           // LCOV_EXCL_LINE
+                return false;  // LCOV_EXCL_LINE
+        }
+    }
+
+    /*!
+    @param[in] len  the length of the array
+    @return whether array creation completed
+    */
+    bool get_msgpack_array(const std::size_t len)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(len)))
+        {
+            return false;
+        }
+
+        for (std::size_t i = 0; i < len; ++i)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!parse_msgpack_internal()))
+            {
+                return false;
+            }
+        }
+
+        return sax->end_array();
+    }
+
+    /*!
+    @param[in] len  the length of the object
+    @return whether object creation completed
+    */
+    bool get_msgpack_object(const std::size_t len)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(len)))
+        {
+            return false;
+        }
+
+        string_t key;
+        for (std::size_t i = 0; i < len; ++i)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!get_msgpack_string(key) || !sax->key(key)))
+            {
+                return false;
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(!parse_msgpack_internal()))
+            {
+                return false;
+            }
+            key.clear();
+        }
+
+        return sax->end_object();
+    }
+
+    ////////////
+    // UBJSON //
+    ////////////
+
+    /*!
+    @param[in] get_char  whether a new character should be retrieved from the
+                         input (true, default) or whether the last read
+                         character should be considered instead
+
+    @return whether a valid UBJSON value was passed to the SAX parser
+    */
+    bool parse_ubjson_internal(const bool get_char = true)
+    {
+        return get_ubjson_value(get_char ? get_ignore_noop() : current);
+    }
+
+    /*!
+    @brief reads a UBJSON string
+
+    This function is either called after reading the 'S' byte explicitly
+    indicating a string, or in case of an object key where the 'S' byte can be
+    left out.
+
+    @param[out] result   created string
+    @param[in] get_char  whether a new character should be retrieved from the
+                         input (true, default) or whether the last read
+                         character should be considered instead
+
+    @return whether string creation completed
+    */
+    bool get_ubjson_string(string_t& result, const bool get_char = true)
+    {
+        if (get_char)
+        {
+            get();  // TODO(niels): may we ignore N here?
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "value")))
+        {
+            return false;
+        }
+
+        switch (current)
+        {
+            case 'U':
+            {
+                std::uint8_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'i':
+            {
+                std::int8_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'I':
+            {
+                std::int16_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'l':
+            {
+                std::int32_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'L':
+            {
+                std::int64_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'u':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint16_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'm':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint32_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            case 'M':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint64_t len{};
+                return get_number(input_format, len) && get_string(input_format, len, result);
+            }
+
+            default:
+                break;
+        }
+        auto last_token = get_token_string();
+        std::string message;
+
+        if (input_format != input_format_t::bjdata)
+        {
+            message = "expected length type specification (U, i, I, l, L); last byte: 0x" + last_token;
+        }
+        else
+        {
+            message = "expected length type specification (U, i, u, I, m, l, M, L); last byte: 0x" + last_token;
+        }
+        return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read, exception_message(input_format, message, "string"), nullptr));
+    }
+
+    /*!
+    @param[out] dim  an integer vector storing the ND array dimensions
+    @return whether reading ND array size vector is successful
+    */
+    bool get_ubjson_ndarray_size(std::vector<size_t>& dim)
+    {
+        std::pair<std::size_t, char_int_type> size_and_type;
+        size_t dimlen = 0;
+        bool no_ndarray = true;
+
+        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type, no_ndarray)))
+        {
+            return false;
+        }
+
+        if (size_and_type.first != npos)
+        {
+            if (size_and_type.second != 0)
+            {
+                if (size_and_type.second != 'N')
+                {
+                    for (std::size_t i = 0; i < size_and_type.first; ++i)
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray, size_and_type.second)))
+                        {
+                            return false;
+                        }
+                        dim.push_back(dimlen);
+                    }
+                }
+            }
+            else
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray)))
+                    {
+                        return false;
+                    }
+                    dim.push_back(dimlen);
+                }
+            }
+        }
+        else
+        {
+            while (current != ']')
+            {
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_value(dimlen, no_ndarray, current)))
+                {
+                    return false;
+                }
+                dim.push_back(dimlen);
+                get_ignore_noop();
+            }
+        }
+        return true;
+    }
+
+    /*!
+    @param[out] result  determined size
+    @param[in,out] is_ndarray  for input, `true` means already inside an ndarray vector
+                               or ndarray dimension is not allowed; `false` means ndarray
+                               is allowed; for output, `true` means an ndarray is found;
+                               is_ndarray can only return `true` when its initial value
+                               is `false`
+    @param[in] prefix  type marker if already read, otherwise set to 0
+
+    @return whether size determination completed
+    */
+    bool get_ubjson_size_value(std::size_t& result, bool& is_ndarray, char_int_type prefix = 0)
+    {
+        if (prefix == 0)
+        {
+            prefix = get_ignore_noop();
+        }
+
+        switch (prefix)
+        {
+            case 'U':
+            {
+                std::uint8_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'i':
+            {
+                std::int8_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number); // NOLINT(bugprone-signed-char-misuse,cert-str34-c): number is not a char
+                return true;
+            }
+
+            case 'I':
+            {
+                std::int16_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'l':
+            {
+                std::int32_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'L':
+            {
+                std::int64_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (number < 0)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read,
+                                            exception_message(input_format, "count in an optimized container must be positive", "size"), nullptr));
+                }
+                if (!value_in_range_of<std::size_t>(number))
+                {
+                    return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408,
+                                            exception_message(input_format, "integer value overflow", "size"), nullptr));
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'u':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint16_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                result = static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'm':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint32_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                result = conditional_static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case 'M':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint64_t number{};
+                if (JSON_HEDLEY_UNLIKELY(!get_number(input_format, number)))
+                {
+                    return false;
+                }
+                if (!value_in_range_of<std::size_t>(number))
+                {
+                    return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408,
+                                            exception_message(input_format, "integer value overflow", "size"), nullptr));
+                }
+                result = detail::conditional_static_cast<std::size_t>(number);
+                return true;
+            }
+
+            case '[':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                if (is_ndarray) // ndarray dimensional vector can only contain integers, and can not embed another array
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(113, chars_read, exception_message(input_format, "ndarray dimensional vector is not allowed", "size"), nullptr));
+                }
+                std::vector<size_t> dim;
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_ndarray_size(dim)))
+                {
+                    return false;
+                }
+                if (dim.size() == 1 || (dim.size() == 2 && dim.at(0) == 1)) // return normal array size if 1D row vector
+                {
+                    result = dim.at(dim.size() - 1);
+                    return true;
+                }
+                if (!dim.empty())  // if ndarray, convert to an object in JData annotated array format
+                {
+                    for (auto i : dim) // test if any dimension in an ndarray is 0, if so, return a 1D empty container
+                    {
+                        if ( i == 0 )
+                        {
+                            result = 0;
+                            return true;
+                        }
+                    }
+
+                    string_t key = "_ArraySize_";
+                    if (JSON_HEDLEY_UNLIKELY(!sax->start_object(3) || !sax->key(key) || !sax->start_array(dim.size())))
+                    {
+                        return false;
+                    }
+                    result = 1;
+                    for (auto i : dim)
+                    {
+                        result *= i;
+                        if (result == 0 || result == npos) // because dim elements shall not have zeros, result = 0 means overflow happened; it also can't be npos as it is used to initialize size in get_ubjson_size_type()
+                        {
+                            return sax->parse_error(chars_read, get_token_string(), out_of_range::create(408, exception_message(input_format, "excessive ndarray size caused overflow", "size"), nullptr));
+                        }
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_unsigned(static_cast<number_unsigned_t>(i))))
+                        {
+                            return false;
+                        }
+                    }
+                    is_ndarray = true;
+                    return sax->end_array();
+                }
+                result = 0;
+                return true;
+            }
+
+            default:
+                break;
+        }
+        auto last_token = get_token_string();
+        std::string message;
+
+        if (input_format != input_format_t::bjdata)
+        {
+            message = "expected length type specification (U, i, I, l, L) after '#'; last byte: 0x" + last_token;
+        }
+        else
+        {
+            message = "expected length type specification (U, i, u, I, m, l, M, L) after '#'; last byte: 0x" + last_token;
+        }
+        return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read, exception_message(input_format, message, "size"), nullptr));
+    }
+
+    /*!
+    @brief determine the type and size for a container
+
+    In the optimized UBJSON format, a type and a size can be provided to allow
+    for a more compact representation.
+
+    @param[out] result  pair of the size and the type
+    @param[in] inside_ndarray  whether the parser is parsing an ND array dimensional vector
+
+    @return whether pair creation completed
+    */
+    bool get_ubjson_size_type(std::pair<std::size_t, char_int_type>& result, bool inside_ndarray = false)
+    {
+        result.first = npos; // size
+        result.second = 0; // type
+        bool is_ndarray = false;
+
+        get_ignore_noop();
+
+        if (current == '$')
+        {
+            result.second = get();  // must not ignore 'N', because 'N' maybe the type
+            if (input_format == input_format_t::bjdata
+                    && JSON_HEDLEY_UNLIKELY(std::binary_search(bjd_optimized_type_markers.begin(), bjd_optimized_type_markers.end(), result.second)))
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format, concat("marker 0x", last_token, " is not a permitted optimized array type"), "type"), nullptr));
+            }
+
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "type")))
+            {
+                return false;
+            }
+
+            get_ignore_noop();
+            if (JSON_HEDLEY_UNLIKELY(current != '#'))
+            {
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "value")))
+                {
+                    return false;
+                }
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format, concat("expected '#' after type information; last byte: 0x", last_token), "size"), nullptr));
+            }
+
+            const bool is_error = get_ubjson_size_value(result.first, is_ndarray);
+            if (input_format == input_format_t::bjdata && is_ndarray)
+            {
+                if (inside_ndarray)
+                {
+                    return sax->parse_error(chars_read, get_token_string(), parse_error::create(112, chars_read,
+                                            exception_message(input_format, "ndarray can not be recursive", "size"), nullptr));
+                }
+                result.second |= (1 << 8); // use bit 8 to indicate ndarray, all UBJSON and BJData markers should be ASCII letters
+            }
+            return is_error;
+        }
+
+        if (current == '#')
+        {
+            const bool is_error = get_ubjson_size_value(result.first, is_ndarray);
+            if (input_format == input_format_t::bjdata && is_ndarray)
+            {
+                return sax->parse_error(chars_read, get_token_string(), parse_error::create(112, chars_read,
+                                        exception_message(input_format, "ndarray requires both type and size", "size"), nullptr));
+            }
+            return is_error;
+        }
+
+        return true;
+    }
+
+    /*!
+    @param prefix  the previously read or set type prefix
+    @return whether value creation completed
+    */
+    bool get_ubjson_value(const char_int_type prefix)
+    {
+        switch (prefix)
+        {
+            case char_traits<char_type>::eof():  // EOF
+                return unexpect_eof(input_format, "value");
+
+            case 'T':  // true
+                return sax->boolean(true);
+            case 'F':  // false
+                return sax->boolean(false);
+
+            case 'Z':  // null
+                return sax->null();
+
+            case 'B':  // byte
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint8_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'U':
+            {
+                std::uint8_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'i':
+            {
+                std::int8_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'I':
+            {
+                std::int16_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'l':
+            {
+                std::int32_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'L':
+            {
+                std::int64_t number{};
+                return get_number(input_format, number) && sax->number_integer(number);
+            }
+
+            case 'u':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint16_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'm':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint32_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'M':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                std::uint64_t number{};
+                return get_number(input_format, number) && sax->number_unsigned(number);
+            }
+
+            case 'h':
+            {
+                if (input_format != input_format_t::bjdata)
+                {
+                    break;
+                }
+                const auto byte1_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "number")))
+                {
+                    return false;
+                }
+                const auto byte2_raw = get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "number")))
+                {
+                    return false;
+                }
+
+                const auto byte1 = static_cast<unsigned char>(byte1_raw);
+                const auto byte2 = static_cast<unsigned char>(byte2_raw);
+
+                // code from RFC 7049, Appendix D, Figure 3:
+                // As half-precision floating-point numbers were only added
+                // to IEEE 754 in 2008, today's programming platforms often
+                // still only have limited support for them. It is very
+                // easy to include at least decoding support for them even
+                // without such support. An example of a small decoder for
+                // half-precision floating-point numbers in the C language
+                // is shown in Fig. 3.
+                const auto half = static_cast<unsigned int>((byte2 << 8u) + byte1);
+                const double val = [&half]
+                {
+                    const int exp = (half >> 10u) & 0x1Fu;
+                    const unsigned int mant = half & 0x3FFu;
+                    JSON_ASSERT(0 <= exp&& exp <= 32);
+                    JSON_ASSERT(mant <= 1024);
+                    switch (exp)
+                    {
+                        case 0:
+                            return std::ldexp(mant, -24);
+                        case 31:
+                            return (mant == 0)
+                            ? std::numeric_limits<double>::infinity()
+                            : std::numeric_limits<double>::quiet_NaN();
+                        default:
+                            return std::ldexp(mant + 1024, exp - 25);
+                    }
+                }();
+                return sax->number_float((half & 0x8000u) != 0
+                                         ? static_cast<number_float_t>(-val)
+                                         : static_cast<number_float_t>(val), "");
+            }
+
+            case 'd':
+            {
+                float number{};
+                return get_number(input_format, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 'D':
+            {
+                double number{};
+                return get_number(input_format, number) && sax->number_float(static_cast<number_float_t>(number), "");
+            }
+
+            case 'H':
+            {
+                return get_ubjson_high_precision_number();
+            }
+
+            case 'C':  // char
+            {
+                get();
+                if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "char")))
+                {
+                    return false;
+                }
+                if (JSON_HEDLEY_UNLIKELY(current > 127))
+                {
+                    auto last_token = get_token_string();
+                    return sax->parse_error(chars_read, last_token, parse_error::create(113, chars_read,
+                                            exception_message(input_format, concat("byte after 'C' must be in range 0x00..0x7F; last byte: 0x", last_token), "char"), nullptr));
+                }
+                string_t s(1, static_cast<typename string_t::value_type>(current));
+                return sax->string(s);
+            }
+
+            case 'S':  // string
+            {
+                string_t s;
+                return get_ubjson_string(s) && sax->string(s);
+            }
+
+            case '[':  // array
+                return get_ubjson_array();
+
+            case '{':  // object
+                return get_ubjson_object();
+
+            default: // anything else
+                break;
+        }
+        auto last_token = get_token_string();
+        return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read, exception_message(input_format, "invalid byte: 0x" + last_token, "value"), nullptr));
+    }
+
+    /*!
+    @return whether array creation completed
+    */
+    bool get_ubjson_array()
+    {
+        std::pair<std::size_t, char_int_type> size_and_type;
+        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type)))
+        {
+            return false;
+        }
+
+        // if bit-8 of size_and_type.second is set to 1, encode bjdata ndarray as an object in JData annotated array format (https://github.com/NeuroJSON/jdata):
+        // {"_ArrayType_" : "typeid", "_ArraySize_" : [n1, n2, ...], "_ArrayData_" : [v1, v2, ...]}
+
+        if (input_format == input_format_t::bjdata && size_and_type.first != npos && (size_and_type.second & (1 << 8)) != 0)
+        {
+            size_and_type.second &= ~(static_cast<char_int_type>(1) << 8);  // use bit 8 to indicate ndarray, here we remove the bit to restore the type marker
+            auto it = std::lower_bound(bjd_types_map.begin(), bjd_types_map.end(), size_and_type.second, [](const bjd_type & p, char_int_type t)
+            {
+                return p.first < t;
+            });
+            string_t key = "_ArrayType_";
+            if (JSON_HEDLEY_UNLIKELY(it == bjd_types_map.end() || it->first != size_and_type.second))
+            {
+                auto last_token = get_token_string();
+                return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                        exception_message(input_format, "invalid byte: 0x" + last_token, "type"), nullptr));
+            }
+
+            string_t type = it->second; // sax->string() takes a reference
+            if (JSON_HEDLEY_UNLIKELY(!sax->key(key) || !sax->string(type)))
+            {
+                return false;
+            }
+
+            if (size_and_type.second == 'C' || size_and_type.second == 'B')
+            {
+                size_and_type.second = 'U';
+            }
+
+            key = "_ArrayData_";
+            if (JSON_HEDLEY_UNLIKELY(!sax->key(key) || !sax->start_array(size_and_type.first) ))
+            {
+                return false;
+            }
+
+            for (std::size_t i = 0; i < size_and_type.first; ++i)
+            {
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))
+                {
+                    return false;
+                }
+            }
+
+            return (sax->end_array() && sax->end_object());
+        }
+
+        // If BJData type marker is 'B' decode as binary
+        if (input_format == input_format_t::bjdata && size_and_type.first != npos && size_and_type.second == 'B')
+        {
+            binary_t result;
+            return get_binary(input_format, size_and_type.first, result) && sax->binary(result);
+        }
+
+        if (size_and_type.first != npos)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_array(size_and_type.first)))
+            {
+                return false;
+            }
+
+            if (size_and_type.second != 0)
+            {
+                if (size_and_type.second != 'N')
+                {
+                    for (std::size_t i = 0; i < size_and_type.first; ++i)
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))
+                        {
+                            return false;
+                        }
+                    }
+                }
+            }
+            else
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))
+                    {
+                        return false;
+                    }
+                }
+            }
+        }
+        else
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_array(detail::unknown_size())))
+            {
+                return false;
+            }
+
+            while (current != ']')
+            {
+                if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal(false)))
+                {
+                    return false;
+                }
+                get_ignore_noop();
+            }
+        }
+
+        return sax->end_array();
+    }
+
+    /*!
+    @return whether object creation completed
+    */
+    bool get_ubjson_object()
+    {
+        std::pair<std::size_t, char_int_type> size_and_type;
+        if (JSON_HEDLEY_UNLIKELY(!get_ubjson_size_type(size_and_type)))
+        {
+            return false;
+        }
+
+        // do not accept ND-array size in objects in BJData
+        if (input_format == input_format_t::bjdata && size_and_type.first != npos && (size_and_type.second & (1 << 8)) != 0)
+        {
+            auto last_token = get_token_string();
+            return sax->parse_error(chars_read, last_token, parse_error::create(112, chars_read,
+                                    exception_message(input_format, "BJData object does not support ND-array size in optimized format", "object"), nullptr));
+        }
+
+        string_t key;
+        if (size_and_type.first != npos)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_object(size_and_type.first)))
+            {
+                return false;
+            }
+
+            if (size_and_type.second != 0)
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_value(size_and_type.second)))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+            else
+            {
+                for (std::size_t i = 0; i < size_and_type.first; ++i)
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key) || !sax->key(key)))
+                    {
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))
+                    {
+                        return false;
+                    }
+                    key.clear();
+                }
+            }
+        }
+        else
+        {
+            if (JSON_HEDLEY_UNLIKELY(!sax->start_object(detail::unknown_size())))
+            {
+                return false;
+            }
+
+            while (current != '}')
+            {
+                if (JSON_HEDLEY_UNLIKELY(!get_ubjson_string(key, false) || !sax->key(key)))
+                {
+                    return false;
+                }
+                if (JSON_HEDLEY_UNLIKELY(!parse_ubjson_internal()))
+                {
+                    return false;
+                }
+                get_ignore_noop();
+                key.clear();
+            }
+        }
+
+        return sax->end_object();
+    }
+
+    // Note, no reader for UBJSON binary types is implemented because they do
+    // not exist
+
+    bool get_ubjson_high_precision_number()
+    {
+        // get size of following number string
+        std::size_t size{};
+        bool no_ndarray = true;
+        auto res = get_ubjson_size_value(size, no_ndarray);
+        if (JSON_HEDLEY_UNLIKELY(!res))
+        {
+            return res;
+        }
+
+        // get number string
+        std::vector<char> number_vector;
+        for (std::size_t i = 0; i < size; ++i)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(input_format, "number")))
+            {
+                return false;
+            }
+            number_vector.push_back(static_cast<char>(current));
+        }
+
+        // parse number string
+        using ia_type = decltype(detail::input_adapter(number_vector));
+        auto number_lexer = detail::lexer<BasicJsonType, ia_type>(detail::input_adapter(number_vector), false);
+        const auto result_number = number_lexer.scan();
+        const auto number_string = number_lexer.get_token_string();
+        const auto result_remainder = number_lexer.scan();
+
+        using token_type = typename detail::lexer_base<BasicJsonType>::token_type;
+
+        if (JSON_HEDLEY_UNLIKELY(result_remainder != token_type::end_of_input))
+        {
+            return sax->parse_error(chars_read, number_string, parse_error::create(115, chars_read,
+                                    exception_message(input_format, concat("invalid number text: ", number_lexer.get_token_string()), "high-precision number"), nullptr));
+        }
+
+        switch (result_number)
+        {
+            case token_type::value_integer:
+                return sax->number_integer(number_lexer.get_number_integer());
+            case token_type::value_unsigned:
+                return sax->number_unsigned(number_lexer.get_number_unsigned());
+            case token_type::value_float:
+                return sax->number_float(number_lexer.get_number_float(), std::move(number_string));
+            case token_type::uninitialized:
+            case token_type::literal_true:
+            case token_type::literal_false:
+            case token_type::literal_null:
+            case token_type::value_string:
+            case token_type::begin_array:
+            case token_type::begin_object:
+            case token_type::end_array:
+            case token_type::end_object:
+            case token_type::name_separator:
+            case token_type::value_separator:
+            case token_type::parse_error:
+            case token_type::end_of_input:
+            case token_type::literal_or_value:
+            default:
+                return sax->parse_error(chars_read, number_string, parse_error::create(115, chars_read,
+                                        exception_message(input_format, concat("invalid number text: ", number_lexer.get_token_string()), "high-precision number"), nullptr));
+        }
+    }
+
+    ///////////////////////
+    // Utility functions //
+    ///////////////////////
+
+    /*!
+    @brief get next character from the input
+
+    This function provides the interface to the used input adapter. It does
+    not throw in case the input reached EOF, but returns a -'ve valued
+    `char_traits<char_type>::eof()` in that case.
+
+    @return character read from the input
+    */
+    char_int_type get()
+    {
+        ++chars_read;
+        return current = ia.get_character();
+    }
+
+    /*!
+    @brief get_to read into a primitive type
+
+    This function provides the interface to the used input adapter. It does
+    not throw in case the input reached EOF, but returns false instead
+
+    @return bool, whether the read was successful
+    */
+    template<class T>
+    bool get_to(T& dest, const input_format_t format, const char* context)
+    {
+        auto new_chars_read = ia.get_elements(&dest);
+        chars_read += new_chars_read;
+        if (JSON_HEDLEY_UNLIKELY(new_chars_read < sizeof(T)))
+        {
+            // in case of failure, advance position by 1 to report failing location
+            ++chars_read;
+            sax->parse_error(chars_read, "<end of file>", parse_error::create(110, chars_read, exception_message(format, "unexpected end of input", context), nullptr));
+            return false;
+        }
+        return true;
+    }
+
+    /*!
+    @return character read from the input after ignoring all 'N' entries
+    */
+    char_int_type get_ignore_noop()
+    {
+        do
+        {
+            get();
+        }
+        while (current == 'N');
+
+        return current;
+    }
+
+    template<class NumberType>
+    static void byte_swap(NumberType& number)
+    {
+        constexpr std::size_t sz = sizeof(number);
+#ifdef __cpp_lib_byteswap
+        if constexpr (sz == 1)
+        {
+            return;
+        }
+        if constexpr(std::is_integral_v<NumberType>)
+        {
+            number = std::byteswap(number);
+            return;
+        }
+#endif
+        auto* ptr = reinterpret_cast<std::uint8_t*>(&number);
+        for (std::size_t i = 0; i < sz / 2; ++i)
+        {
+            std::swap(ptr[i], ptr[sz - i - 1]);
+        }
+    }
+
+    /*
+    @brief read a number from the input
+
+    @tparam NumberType the type of the number
+    @param[in] format   the current format (for diagnostics)
+    @param[out] result  number of type @a NumberType
+
+    @return whether conversion completed
+
+    @note This function needs to respect the system's endianness, because
+          bytes in CBOR, MessagePack, and UBJSON are stored in network order
+          (big endian) and therefore need reordering on little endian systems.
+          On the other hand, BSON and BJData use little endian and should reorder
+          on big endian systems.
+    */
+    template<typename NumberType, bool InputIsLittleEndian = false>
+    bool get_number(const input_format_t format, NumberType& result)
+    {
+        // read in the original format
+
+        if (JSON_HEDLEY_UNLIKELY(!get_to(result, format, "number")))
+        {
+            return false;
+        }
+        if (is_little_endian != (InputIsLittleEndian || format == input_format_t::bjdata))
+        {
+            byte_swap(result);
+        }
+        return true;
+    }
+
+    /*!
+    @brief create a string by reading characters from the input
+
+    @tparam NumberType the type of the number
+    @param[in] format the current format (for diagnostics)
+    @param[in] len number of characters to read
+    @param[out] result string created by reading @a len bytes
+
+    @return whether string creation completed
+
+    @note We can not reserve @a len bytes for the result, because @a len
+          may be too large. Usually, @ref unexpect_eof() detects the end of
+          the input before we run out of string memory.
+    */
+    template<typename NumberType>
+    bool get_string(const input_format_t format,
+                    const NumberType len,
+                    string_t& result)
+    {
+        bool success = true;
+        for (NumberType i = 0; i < len; i++)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, "string")))
+            {
+                success = false;
+                break;
+            }
+            result.push_back(static_cast<typename string_t::value_type>(current));
+        }
+        return success;
+    }
+
+    /*!
+    @brief create a byte array by reading bytes from the input
+
+    @tparam NumberType the type of the number
+    @param[in] format the current format (for diagnostics)
+    @param[in] len number of bytes to read
+    @param[out] result byte array created by reading @a len bytes
+
+    @return whether byte array creation completed
+
+    @note We can not reserve @a len bytes for the result, because @a len
+          may be too large. Usually, @ref unexpect_eof() detects the end of
+          the input before we run out of memory.
+    */
+    template<typename NumberType>
+    bool get_binary(const input_format_t format,
+                    const NumberType len,
+                    binary_t& result)
+    {
+        bool success = true;
+        for (NumberType i = 0; i < len; i++)
+        {
+            get();
+            if (JSON_HEDLEY_UNLIKELY(!unexpect_eof(format, "binary")))
+            {
+                success = false;
+                break;
+            }
+            result.push_back(static_cast<std::uint8_t>(current));
+        }
+        return success;
+    }
+
+    /*!
+    @param[in] format   the current format (for diagnostics)
+    @param[in] context  further context information (for diagnostics)
+    @return whether the last read character is not EOF
+    */
+    JSON_HEDLEY_NON_NULL(3)
+    bool unexpect_eof(const input_format_t format, const char* context) const
+    {
+        if (JSON_HEDLEY_UNLIKELY(current == char_traits<char_type>::eof()))
+        {
+            return sax->parse_error(chars_read, "<end of file>",
+                                    parse_error::create(110, chars_read, exception_message(format, "unexpected end of input", context), nullptr));
+        }
+        return true;
+    }
+
+    /*!
+    @return a string representation of the last read byte
+    */
+    std::string get_token_string() const
+    {
+        std::array<char, 3> cr{{}};
+        static_cast<void>((std::snprintf)(cr.data(), cr.size(), "%.2hhX", static_cast<unsigned char>(current))); // NOLINT(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+        return std::string{cr.data()};
+    }
+
+    /*!
+    @param[in] format   the current format
+    @param[in] detail   a detailed error message
+    @param[in] context  further context information
+    @return a message string to use in the parse_error exceptions
+    */
+    std::string exception_message(const input_format_t format,
+                                  const std::string& detail,
+                                  const std::string& context) const
+    {
+        std::string error_msg = "syntax error while parsing ";
+
+        switch (format)
+        {
+            case input_format_t::cbor:
+                error_msg += "CBOR";
+                break;
+
+            case input_format_t::msgpack:
+                error_msg += "MessagePack";
+                break;
+
+            case input_format_t::ubjson:
+                error_msg += "UBJSON";
+                break;
+
+            case input_format_t::bson:
+                error_msg += "BSON";
+                break;
+
+            case input_format_t::bjdata:
+                error_msg += "BJData";
+                break;
+
+            case input_format_t::json: // LCOV_EXCL_LINE
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+
+        return concat(error_msg, ' ', context, ": ", detail);
+    }
+
+  private:
+    static JSON_INLINE_VARIABLE constexpr std::size_t npos = detail::unknown_size();
+
+    /// input adapter
+    InputAdapterType ia;
+
+    /// the current character
+    char_int_type current = char_traits<char_type>::eof();
+
+    /// the number of characters read
+    std::size_t chars_read = 0;
+
+    /// whether we can assume little endianness
+    const bool is_little_endian = little_endianness();
+
+    /// input format
+    const input_format_t input_format = input_format_t::json;
+
+    /// the SAX parser
+    json_sax_t* sax = nullptr;
+
+    // excluded markers in bjdata optimized type
+#define JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_ \
+    make_array<char_int_type>('F', 'H', 'N', 'S', 'T', 'Z', '[', '{')
+
+#define JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_ \
+    make_array<bjd_type>(                      \
+    bjd_type{'B', "byte"},                     \
+    bjd_type{'C', "char"},                     \
+    bjd_type{'D', "double"},                   \
+    bjd_type{'I', "int16"},                    \
+    bjd_type{'L', "int64"},                    \
+    bjd_type{'M', "uint64"},                   \
+    bjd_type{'U', "uint8"},                    \
+    bjd_type{'d', "single"},                   \
+    bjd_type{'i', "int8"},                     \
+    bjd_type{'l', "int32"},                    \
+    bjd_type{'m', "uint32"},                   \
+    bjd_type{'u', "uint16"})
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    // lookup tables
+    // NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
+    const decltype(JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_) bjd_optimized_type_markers =
+        JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_;
+
+    using bjd_type = std::pair<char_int_type, string_t>;
+    // NOLINTNEXTLINE(cppcoreguidelines-non-private-member-variables-in-classes)
+    const decltype(JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_) bjd_types_map =
+        JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_;
+
+#undef JSON_BINARY_READER_MAKE_BJD_OPTIMIZED_TYPE_MARKERS_
+#undef JSON_BINARY_READER_MAKE_BJD_TYPES_MAP_
+};
+
+#ifndef JSON_HAS_CPP_17
+    template<typename BasicJsonType, typename InputAdapterType, typename SAX>
+    constexpr std::size_t binary_reader<BasicJsonType, InputAdapterType, SAX>::npos;
+#endif
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+
+// #include <nlohmann/detail/input/lexer.hpp>
+
+// #include <nlohmann/detail/input/parser.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cmath> // isfinite
+#include <cstdint> // uint8_t
+#include <functional> // function
+#include <string> // string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/input/input_adapters.hpp>
+
+// #include <nlohmann/detail/input/json_sax.hpp>
+
+// #include <nlohmann/detail/input/lexer.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/is_sax.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+////////////
+// parser //
+////////////
+
+enum class parse_event_t : std::uint8_t
+{
+    /// the parser read `{` and started to process a JSON object
+    object_start,
+    /// the parser read `}` and finished processing a JSON object
+    object_end,
+    /// the parser read `[` and started to process a JSON array
+    array_start,
+    /// the parser read `]` and finished processing a JSON array
+    array_end,
+    /// the parser read a key of a value in an object
+    key,
+    /// the parser finished reading a JSON value
+    value
+};
+
+template<typename BasicJsonType>
+using parser_callback_t =
+    std::function<bool(int /*depth*/, parse_event_t /*event*/, BasicJsonType& /*parsed*/)>;
+
+/*!
+@brief syntax analysis
+
+This class implements a recursive descent parser.
+*/
+template<typename BasicJsonType, typename InputAdapterType>
+class parser
+{
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using string_t = typename BasicJsonType::string_t;
+    using lexer_t = lexer<BasicJsonType, InputAdapterType>;
+    using token_type = typename lexer_t::token_type;
+
+  public:
+    /// a parser reading from an input adapter
+    explicit parser(InputAdapterType&& adapter,
+                    parser_callback_t<BasicJsonType> cb = nullptr,
+                    const bool allow_exceptions_ = true,
+                    const bool skip_comments = false)
+        : callback(std::move(cb))
+        , m_lexer(std::move(adapter), skip_comments)
+        , allow_exceptions(allow_exceptions_)
+    {
+        // read first token
+        get_token();
+    }
+
+    /*!
+    @brief public parser interface
+
+    @param[in] strict      whether to expect the last token to be EOF
+    @param[in,out] result  parsed JSON value
+
+    @throw parse_error.101 in case of an unexpected token
+    @throw parse_error.102 if to_unicode fails or surrogate error
+    @throw parse_error.103 if to_unicode fails
+    */
+    void parse(const bool strict, BasicJsonType& result)
+    {
+        if (callback)
+        {
+            json_sax_dom_callback_parser<BasicJsonType, InputAdapterType> sdp(result, callback, allow_exceptions, &m_lexer);
+            sax_parse_internal(&sdp);
+
+            // in strict mode, input must be completely read
+            if (strict && (get_token() != token_type::end_of_input))
+            {
+                sdp.parse_error(m_lexer.get_position(),
+                                m_lexer.get_token_string(),
+                                parse_error::create(101, m_lexer.get_position(),
+                                                    exception_message(token_type::end_of_input, "value"), nullptr));
+            }
+
+            // in case of an error, return discarded value
+            if (sdp.is_errored())
+            {
+                result = value_t::discarded;
+                return;
+            }
+
+            // set top-level value to null if it was discarded by the callback
+            // function
+            if (result.is_discarded())
+            {
+                result = nullptr;
+            }
+        }
+        else
+        {
+            json_sax_dom_parser<BasicJsonType, InputAdapterType> sdp(result, allow_exceptions, &m_lexer);
+            sax_parse_internal(&sdp);
+
+            // in strict mode, input must be completely read
+            if (strict && (get_token() != token_type::end_of_input))
+            {
+                sdp.parse_error(m_lexer.get_position(),
+                                m_lexer.get_token_string(),
+                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_of_input, "value"), nullptr));
+            }
+
+            // in case of an error, return discarded value
+            if (sdp.is_errored())
+            {
+                result = value_t::discarded;
+                return;
+            }
+        }
+
+        result.assert_invariant();
+    }
+
+    /*!
+    @brief public accept interface
+
+    @param[in] strict  whether to expect the last token to be EOF
+    @return whether the input is a proper JSON text
+    */
+    bool accept(const bool strict = true)
+    {
+        json_sax_acceptor<BasicJsonType> sax_acceptor;
+        return sax_parse(&sax_acceptor, strict);
+    }
+
+    template<typename SAX>
+    JSON_HEDLEY_NON_NULL(2)
+    bool sax_parse(SAX* sax, const bool strict = true)
+    {
+        (void)detail::is_sax_static_asserts<SAX, BasicJsonType> {};
+        const bool result = sax_parse_internal(sax);
+
+        // strict mode: next byte must be EOF
+        if (result && strict && (get_token() != token_type::end_of_input))
+        {
+            return sax->parse_error(m_lexer.get_position(),
+                                    m_lexer.get_token_string(),
+                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_of_input, "value"), nullptr));
+        }
+
+        return result;
+    }
+
+  private:
+    template<typename SAX>
+    JSON_HEDLEY_NON_NULL(2)
+    bool sax_parse_internal(SAX* sax)
+    {
+        // stack to remember the hierarchy of structured values we are parsing
+        // true = array; false = object
+        std::vector<bool> states;
+        // value to avoid a goto (see comment where set to true)
+        bool skip_to_state_evaluation = false;
+
+        while (true)
+        {
+            if (!skip_to_state_evaluation)
+            {
+                // invariant: get_token() was called before each iteration
+                switch (last_token)
+                {
+                    case token_type::begin_object:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->start_object(detail::unknown_size())))
+                        {
+                            return false;
+                        }
+
+                        // closing } -> we are done
+                        if (get_token() == token_type::end_object)
+                        {
+                            if (JSON_HEDLEY_UNLIKELY(!sax->end_object()))
+                            {
+                                return false;
+                            }
+                            break;
+                        }
+
+                        // parse key
+                        if (JSON_HEDLEY_UNLIKELY(last_token != token_type::value_string))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::value_string, "object key"), nullptr));
+                        }
+                        if (JSON_HEDLEY_UNLIKELY(!sax->key(m_lexer.get_string())))
+                        {
+                            return false;
+                        }
+
+                        // parse separator (:)
+                        if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::name_separator))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::name_separator, "object separator"), nullptr));
+                        }
+
+                        // remember we are now inside an object
+                        states.push_back(false);
+
+                        // parse values
+                        get_token();
+                        continue;
+                    }
+
+                    case token_type::begin_array:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->start_array(detail::unknown_size())))
+                        {
+                            return false;
+                        }
+
+                        // closing ] -> we are done
+                        if (get_token() == token_type::end_array)
+                        {
+                            if (JSON_HEDLEY_UNLIKELY(!sax->end_array()))
+                            {
+                                return false;
+                            }
+                            break;
+                        }
+
+                        // remember we are now inside an array
+                        states.push_back(true);
+
+                        // parse values (no need to call get_token)
+                        continue;
+                    }
+
+                    case token_type::value_float:
+                    {
+                        const auto res = m_lexer.get_number_float();
+
+                        if (JSON_HEDLEY_UNLIKELY(!std::isfinite(res)))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    out_of_range::create(406, concat("number overflow parsing '", m_lexer.get_token_string(), '\''), nullptr));
+                        }
+
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_float(res, m_lexer.get_string())))
+                        {
+                            return false;
+                        }
+
+                        break;
+                    }
+
+                    case token_type::literal_false:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->boolean(false)))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::literal_null:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->null()))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::literal_true:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->boolean(true)))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::value_integer:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_integer(m_lexer.get_number_integer())))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::value_string:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->string(m_lexer.get_string())))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::value_unsigned:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!sax->number_unsigned(m_lexer.get_number_unsigned())))
+                        {
+                            return false;
+                        }
+                        break;
+                    }
+
+                    case token_type::parse_error:
+                    {
+                        // using "uninitialized" to avoid "expected" message
+                        return sax->parse_error(m_lexer.get_position(),
+                                                m_lexer.get_token_string(),
+                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::uninitialized, "value"), nullptr));
+                    }
+                    case token_type::end_of_input:
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(m_lexer.get_position().chars_read_total == 1))
+                        {
+                            return sax->parse_error(m_lexer.get_position(),
+                                                    m_lexer.get_token_string(),
+                                                    parse_error::create(101, m_lexer.get_position(),
+                                                            "attempting to parse an empty input; check that your input string or stream contains the expected JSON", nullptr));
+                        }
+
+                        return sax->parse_error(m_lexer.get_position(),
+                                                m_lexer.get_token_string(),
+                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::literal_or_value, "value"), nullptr));
+                    }
+                    case token_type::uninitialized:
+                    case token_type::end_array:
+                    case token_type::end_object:
+                    case token_type::name_separator:
+                    case token_type::value_separator:
+                    case token_type::literal_or_value:
+                    default: // the last token was unexpected
+                    {
+                        return sax->parse_error(m_lexer.get_position(),
+                                                m_lexer.get_token_string(),
+                                                parse_error::create(101, m_lexer.get_position(), exception_message(token_type::literal_or_value, "value"), nullptr));
+                    }
+                }
+            }
+            else
+            {
+                skip_to_state_evaluation = false;
+            }
+
+            // we reached this line after we successfully parsed a value
+            if (states.empty())
+            {
+                // empty stack: we reached the end of the hierarchy: done
+                return true;
+            }
+
+            if (states.back())  // array
+            {
+                // comma -> next value
+                if (get_token() == token_type::value_separator)
+                {
+                    // parse a new value
+                    get_token();
+                    continue;
+                }
+
+                // closing ]
+                if (JSON_HEDLEY_LIKELY(last_token == token_type::end_array))
+                {
+                    if (JSON_HEDLEY_UNLIKELY(!sax->end_array()))
+                    {
+                        return false;
+                    }
+
+                    // We are done with this array. Before we can parse a
+                    // new value, we need to evaluate the new state first.
+                    // By setting skip_to_state_evaluation to false, we
+                    // are effectively jumping to the beginning of this if.
+                    JSON_ASSERT(!states.empty());
+                    states.pop_back();
+                    skip_to_state_evaluation = true;
+                    continue;
+                }
+
+                return sax->parse_error(m_lexer.get_position(),
+                                        m_lexer.get_token_string(),
+                                        parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_array, "array"), nullptr));
+            }
+
+            // states.back() is false -> object
+
+            // comma -> next value
+            if (get_token() == token_type::value_separator)
+            {
+                // parse key
+                if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::value_string))
+                {
+                    return sax->parse_error(m_lexer.get_position(),
+                                            m_lexer.get_token_string(),
+                                            parse_error::create(101, m_lexer.get_position(), exception_message(token_type::value_string, "object key"), nullptr));
+                }
+
+                if (JSON_HEDLEY_UNLIKELY(!sax->key(m_lexer.get_string())))
+                {
+                    return false;
+                }
+
+                // parse separator (:)
+                if (JSON_HEDLEY_UNLIKELY(get_token() != token_type::name_separator))
+                {
+                    return sax->parse_error(m_lexer.get_position(),
+                                            m_lexer.get_token_string(),
+                                            parse_error::create(101, m_lexer.get_position(), exception_message(token_type::name_separator, "object separator"), nullptr));
+                }
+
+                // parse values
+                get_token();
+                continue;
+            }
+
+            // closing }
+            if (JSON_HEDLEY_LIKELY(last_token == token_type::end_object))
+            {
+                if (JSON_HEDLEY_UNLIKELY(!sax->end_object()))
+                {
+                    return false;
+                }
+
+                // We are done with this object. Before we can parse a
+                // new value, we need to evaluate the new state first.
+                // By setting skip_to_state_evaluation to false, we
+                // are effectively jumping to the beginning of this if.
+                JSON_ASSERT(!states.empty());
+                states.pop_back();
+                skip_to_state_evaluation = true;
+                continue;
+            }
+
+            return sax->parse_error(m_lexer.get_position(),
+                                    m_lexer.get_token_string(),
+                                    parse_error::create(101, m_lexer.get_position(), exception_message(token_type::end_object, "object"), nullptr));
+        }
+    }
+
+    /// get next token from lexer
+    token_type get_token()
+    {
+        return last_token = m_lexer.scan();
+    }
+
+    std::string exception_message(const token_type expected, const std::string& context)
+    {
+        std::string error_msg = "syntax error ";
+
+        if (!context.empty())
+        {
+            error_msg += concat("while parsing ", context, ' ');
+        }
+
+        error_msg += "- ";
+
+        if (last_token == token_type::parse_error)
+        {
+            error_msg += concat(m_lexer.get_error_message(), "; last read: '",
+                                m_lexer.get_token_string(), '\'');
+        }
+        else
+        {
+            error_msg += concat("unexpected ", lexer_t::token_type_name(last_token));
+        }
+
+        if (expected != token_type::uninitialized)
+        {
+            error_msg += concat("; expected ", lexer_t::token_type_name(expected));
+        }
+
+        return error_msg;
+    }
+
+  private:
+    /// callback function
+    const parser_callback_t<BasicJsonType> callback = nullptr;
+    /// the type of the last read token
+    token_type last_token = token_type::uninitialized;
+    /// the lexer
+    lexer_t m_lexer;
+    /// whether to throw exceptions in case of errors
+    const bool allow_exceptions = true;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/internal_iterator.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/iterators/primitive_iterator.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // ptrdiff_t
+#include <limits>  // numeric_limits
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*
+@brief an iterator for primitive JSON types
+
+This class models an iterator for primitive JSON types (boolean, number,
+string). It's only purpose is to allow the iterator/const_iterator classes
+to "iterate" over primitive values. Internally, the iterator is modeled by
+a `difference_type` variable. Value begin_value (`0`) models the begin,
+end_value (`1`) models past the end.
+*/
+class primitive_iterator_t
+{
+  private:
+    using difference_type = std::ptrdiff_t;
+    static constexpr difference_type begin_value = 0;
+    static constexpr difference_type end_value = begin_value + 1;
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /// iterator as signed integer type
+    difference_type m_it = (std::numeric_limits<std::ptrdiff_t>::min)();
+
+  public:
+    constexpr difference_type get_value() const noexcept
+    {
+        return m_it;
+    }
+
+    /// set iterator to a defined beginning
+    void set_begin() noexcept
+    {
+        m_it = begin_value;
+    }
+
+    /// set iterator to a defined past the end
+    void set_end() noexcept
+    {
+        m_it = end_value;
+    }
+
+    /// return whether the iterator can be dereferenced
+    constexpr bool is_begin() const noexcept
+    {
+        return m_it == begin_value;
+    }
+
+    /// return whether the iterator is at end
+    constexpr bool is_end() const noexcept
+    {
+        return m_it == end_value;
+    }
+
+    friend constexpr bool operator==(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept
+    {
+        return lhs.m_it == rhs.m_it;
+    }
+
+    friend constexpr bool operator<(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept
+    {
+        return lhs.m_it < rhs.m_it;
+    }
+
+    primitive_iterator_t operator+(difference_type n) noexcept
+    {
+        auto result = *this;
+        result += n;
+        return result;
+    }
+
+    friend constexpr difference_type operator-(primitive_iterator_t lhs, primitive_iterator_t rhs) noexcept
+    {
+        return lhs.m_it - rhs.m_it;
+    }
+
+    primitive_iterator_t& operator++() noexcept
+    {
+        ++m_it;
+        return *this;
+    }
+
+    primitive_iterator_t operator++(int)& noexcept // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        ++m_it;
+        return result;
+    }
+
+    primitive_iterator_t& operator--() noexcept
+    {
+        --m_it;
+        return *this;
+    }
+
+    primitive_iterator_t operator--(int)& noexcept // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        --m_it;
+        return result;
+    }
+
+    primitive_iterator_t& operator+=(difference_type n) noexcept
+    {
+        m_it += n;
+        return *this;
+    }
+
+    primitive_iterator_t& operator-=(difference_type n) noexcept
+    {
+        m_it -= n;
+        return *this;
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief an iterator value
+
+@note This structure could easily be a union, but MSVC currently does not allow
+unions members with complex constructors, see https://github.com/nlohmann/json/pull/105.
+*/
+template<typename BasicJsonType> struct internal_iterator
+{
+    /// iterator for JSON objects
+    typename BasicJsonType::object_t::iterator object_iterator {};
+    /// iterator for JSON arrays
+    typename BasicJsonType::array_t::iterator array_iterator {};
+    /// generic iterator for all other types
+    primitive_iterator_t primitive_iterator {};
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/iter_impl.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <iterator> // iterator, random_access_iterator_tag, bidirectional_iterator_tag, advance, next
+#include <type_traits> // conditional, is_const, remove_const
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/iterators/internal_iterator.hpp>
+
+// #include <nlohmann/detail/iterators/primitive_iterator.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+// forward declare, to be able to friend it later on
+template<typename IteratorType> class iteration_proxy;
+template<typename IteratorType> class iteration_proxy_value;
+
+/*!
+@brief a template for a bidirectional iterator for the @ref basic_json class
+This class implements a both iterators (iterator and const_iterator) for the
+@ref basic_json class.
+@note An iterator is called *initialized* when a pointer to a JSON value has
+      been set (e.g., by a constructor or a copy assignment). If the iterator is
+      default-constructed, it is *uninitialized* and most methods are undefined.
+      **The library uses assertions to detect calls on uninitialized iterators.**
+@requirement The class satisfies the following concept requirements:
+-
+[BidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator):
+  The iterator that can be moved can be moved in both directions (i.e.
+  incremented and decremented).
+@since version 1.0.0, simplified in version 2.0.9, change to bidirectional
+       iterators in version 3.0.0 (see https://github.com/nlohmann/json/issues/593)
+*/
+template<typename BasicJsonType>
+class iter_impl // NOLINT(cppcoreguidelines-special-member-functions,hicpp-special-member-functions)
+{
+    /// the iterator with BasicJsonType of different const-ness
+    using other_iter_impl = iter_impl<typename std::conditional<std::is_const<BasicJsonType>::value, typename std::remove_const<BasicJsonType>::type, const BasicJsonType>::type>;
+    /// allow basic_json to access private members
+    friend other_iter_impl;
+    friend BasicJsonType;
+    friend iteration_proxy<iter_impl>;
+    friend iteration_proxy_value<iter_impl>;
+
+    using object_t = typename BasicJsonType::object_t;
+    using array_t = typename BasicJsonType::array_t;
+    // make sure BasicJsonType is basic_json or const basic_json
+    static_assert(is_basic_json<typename std::remove_const<BasicJsonType>::type>::value,
+                  "iter_impl only accepts (const) basic_json");
+    // superficial check for the LegacyBidirectionalIterator named requirement
+    static_assert(std::is_base_of<std::bidirectional_iterator_tag, std::bidirectional_iterator_tag>::value
+                  &&  std::is_base_of<std::bidirectional_iterator_tag, typename std::iterator_traits<typename array_t::iterator>::iterator_category>::value,
+                  "basic_json iterator assumes array and object type iterators satisfy the LegacyBidirectionalIterator named requirement.");
+
+  public:
+    /// The std::iterator class template (used as a base class to provide typedefs) is deprecated in C++17.
+    /// The C++ Standard has never required user-defined iterators to derive from std::iterator.
+    /// A user-defined iterator should provide publicly accessible typedefs named
+    /// iterator_category, value_type, difference_type, pointer, and reference.
+    /// Note that value_type is required to be non-const, even for constant iterators.
+    using iterator_category = std::bidirectional_iterator_tag;
+
+    /// the type of the values when the iterator is dereferenced
+    using value_type = typename BasicJsonType::value_type;
+    /// a type to represent differences between iterators
+    using difference_type = typename BasicJsonType::difference_type;
+    /// defines a pointer to the type iterated over (value_type)
+    using pointer = typename std::conditional<std::is_const<BasicJsonType>::value,
+          typename BasicJsonType::const_pointer,
+          typename BasicJsonType::pointer>::type;
+    /// defines a reference to the type iterated over (value_type)
+    using reference =
+        typename std::conditional<std::is_const<BasicJsonType>::value,
+        typename BasicJsonType::const_reference,
+        typename BasicJsonType::reference>::type;
+
+    iter_impl() = default;
+    ~iter_impl() = default;
+    iter_impl(iter_impl&&) noexcept = default;
+    iter_impl& operator=(iter_impl&&) noexcept = default;
+
+    /*!
+    @brief constructor for a given JSON instance
+    @param[in] object  pointer to a JSON object for this iterator
+    @pre object != nullptr
+    @post The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    explicit iter_impl(pointer object) noexcept : m_object(object)
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_it.object_iterator = typename object_t::iterator();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_it.array_iterator = typename array_t::iterator();
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator = primitive_iterator_t();
+                break;
+            }
+        }
+    }
+
+    /*!
+    @note The conventional copy constructor and copy assignment are implicitly
+          defined. Combined with the following converting constructor and
+          assignment, they support: (1) copy from iterator to iterator, (2)
+          copy from const iterator to const iterator, and (3) conversion from
+          iterator to const iterator. However conversion from const iterator
+          to iterator is not defined.
+    */
+
+    /*!
+    @brief const copy constructor
+    @param[in] other const iterator to copy from
+    @note This copy constructor had to be defined explicitly to circumvent a bug
+          occurring on msvc v19.0 compiler (VS 2015) debug build. For more
+          information refer to: https://github.com/nlohmann/json/issues/1608
+    */
+    iter_impl(const iter_impl<const BasicJsonType>& other) noexcept
+        : m_object(other.m_object), m_it(other.m_it)
+    {}
+
+    /*!
+    @brief converting assignment
+    @param[in] other const iterator to copy from
+    @return const/non-const iterator
+    @note It is not checked whether @a other is initialized.
+    */
+    iter_impl& operator=(const iter_impl<const BasicJsonType>& other) noexcept
+    {
+        if (&other != this)
+        {
+            m_object = other.m_object;
+            m_it = other.m_it;
+        }
+        return *this;
+    }
+
+    /*!
+    @brief converting constructor
+    @param[in] other  non-const iterator to copy from
+    @note It is not checked whether @a other is initialized.
+    */
+    iter_impl(const iter_impl<typename std::remove_const<BasicJsonType>::type>& other) noexcept
+        : m_object(other.m_object), m_it(other.m_it)
+    {}
+
+    /*!
+    @brief converting assignment
+    @param[in] other  non-const iterator to copy from
+    @return const/non-const iterator
+    @note It is not checked whether @a other is initialized.
+    */
+    iter_impl& operator=(const iter_impl<typename std::remove_const<BasicJsonType>::type>& other) noexcept // NOLINT(cert-oop54-cpp)
+    {
+        m_object = other.m_object;
+        m_it = other.m_it;
+        return *this;
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /*!
+    @brief set the iterator to the first value
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    void set_begin() noexcept
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_it.object_iterator = m_object->m_data.m_value.object->begin();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_it.array_iterator = m_object->m_data.m_value.array->begin();
+                break;
+            }
+
+            case value_t::null:
+            {
+                // set to end so begin()==end() is true: null is empty
+                m_it.primitive_iterator.set_end();
+                break;
+            }
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator.set_begin();
+                break;
+            }
+        }
+    }
+
+    /*!
+    @brief set the iterator past the last value
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    void set_end() noexcept
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_it.object_iterator = m_object->m_data.m_value.object->end();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_it.array_iterator = m_object->m_data.m_value.array->end();
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator.set_end();
+                break;
+            }
+        }
+    }
+
+  public:
+    /*!
+    @brief return a reference to the value pointed to by the iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    reference operator*() const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                JSON_ASSERT(m_it.object_iterator != m_object->m_data.m_value.object->end());
+                return m_it.object_iterator->second;
+            }
+
+            case value_t::array:
+            {
+                JSON_ASSERT(m_it.array_iterator != m_object->m_data.m_value.array->end());
+                return *m_it.array_iterator;
+            }
+
+            case value_t::null:
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.is_begin()))
+                {
+                    return *m_object;
+                }
+
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+            }
+        }
+    }
+
+    /*!
+    @brief dereference the iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    pointer operator->() const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                JSON_ASSERT(m_it.object_iterator != m_object->m_data.m_value.object->end());
+                return &(m_it.object_iterator->second);
+            }
+
+            case value_t::array:
+            {
+                JSON_ASSERT(m_it.array_iterator != m_object->m_data.m_value.array->end());
+                return &*m_it.array_iterator;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.is_begin()))
+                {
+                    return m_object;
+                }
+
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+            }
+        }
+    }
+
+    /*!
+    @brief post-increment (it++)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator++(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        ++(*this);
+        return result;
+    }
+
+    /*!
+    @brief pre-increment (++it)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator++()
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                std::advance(m_it.object_iterator, 1);
+                break;
+            }
+
+            case value_t::array:
+            {
+                std::advance(m_it.array_iterator, 1);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                ++m_it.primitive_iterator;
+                break;
+            }
+        }
+
+        return *this;
+    }
+
+    /*!
+    @brief post-decrement (it--)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator--(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        auto result = *this;
+        --(*this);
+        return result;
+    }
+
+    /*!
+    @brief pre-decrement (--it)
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator--()
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+            {
+                std::advance(m_it.object_iterator, -1);
+                break;
+            }
+
+            case value_t::array:
+            {
+                std::advance(m_it.array_iterator, -1);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                --m_it.primitive_iterator;
+                break;
+            }
+        }
+
+        return *this;
+    }
+
+    /*!
+    @brief comparison: equal
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    template < typename IterImpl, detail::enable_if_t < (std::is_same<IterImpl, iter_impl>::value || std::is_same<IterImpl, other_iter_impl>::value), std::nullptr_t > = nullptr >
+    bool operator==(const IterImpl& other) const
+    {
+        // if objects are not the same, the comparison is undefined
+        if (JSON_HEDLEY_UNLIKELY(m_object != other.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(212, "cannot compare iterators of different containers", m_object));
+        }
+
+        // value-initialized forward iterators can be compared, and must compare equal to other value-initialized iterators of the same type #4493
+        if (m_object == nullptr)
+        {
+            return true;
+        }
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                return (m_it.object_iterator == other.m_it.object_iterator);
+
+            case value_t::array:
+                return (m_it.array_iterator == other.m_it.array_iterator);
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return (m_it.primitive_iterator == other.m_it.primitive_iterator);
+        }
+    }
+
+    /*!
+    @brief comparison: not equal
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    template < typename IterImpl, detail::enable_if_t < (std::is_same<IterImpl, iter_impl>::value || std::is_same<IterImpl, other_iter_impl>::value), std::nullptr_t > = nullptr >
+    bool operator!=(const IterImpl& other) const
+    {
+        return !operator==(other);
+    }
+
+    /*!
+    @brief comparison: smaller
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    bool operator<(const iter_impl& other) const
+    {
+        // if objects are not the same, the comparison is undefined
+        if (JSON_HEDLEY_UNLIKELY(m_object != other.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(212, "cannot compare iterators of different containers", m_object));
+        }
+
+        // value-initialized forward iterators can be compared, and must compare equal to other value-initialized iterators of the same type #4493
+        if (m_object == nullptr)
+        {
+            // the iterators are both value-initialized and are to be considered equal, but this function checks for smaller, so we return false
+            return false;
+        }
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(213, "cannot compare order of object iterators", m_object));
+
+            case value_t::array:
+                return (m_it.array_iterator < other.m_it.array_iterator);
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return (m_it.primitive_iterator < other.m_it.primitive_iterator);
+        }
+    }
+
+    /*!
+    @brief comparison: less than or equal
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    bool operator<=(const iter_impl& other) const
+    {
+        return !other.operator < (*this);
+    }
+
+    /*!
+    @brief comparison: greater than
+    @pre (1) Both iterators are initialized to point to the same object, or (2) both iterators are value-initialized.
+    */
+    bool operator>(const iter_impl& other) const
+    {
+        return !operator<=(other);
+    }
+
+    /*!
+    @brief comparison: greater than or equal
+    @pre (1) The iterator is initialized; i.e. `m_object != nullptr`, or (2) both iterators are value-initialized.
+    */
+    bool operator>=(const iter_impl& other) const
+    {
+        return !operator<(other);
+    }
+
+    /*!
+    @brief add to iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator+=(difference_type i)
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(209, "cannot use offsets with object iterators", m_object));
+
+            case value_t::array:
+            {
+                std::advance(m_it.array_iterator, i);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                m_it.primitive_iterator += i;
+                break;
+            }
+        }
+
+        return *this;
+    }
+
+    /*!
+    @brief subtract from iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl& operator-=(difference_type i)
+    {
+        return operator+=(-i);
+    }
+
+    /*!
+    @brief add to iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator+(difference_type i) const
+    {
+        auto result = *this;
+        result += i;
+        return result;
+    }
+
+    /*!
+    @brief addition of distance and iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    friend iter_impl operator+(difference_type i, const iter_impl& it)
+    {
+        auto result = it;
+        result += i;
+        return result;
+    }
+
+    /*!
+    @brief subtract from iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    iter_impl operator-(difference_type i) const
+    {
+        auto result = *this;
+        result -= i;
+        return result;
+    }
+
+    /*!
+    @brief return difference
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    difference_type operator-(const iter_impl& other) const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(209, "cannot use offsets with object iterators", m_object));
+
+            case value_t::array:
+                return m_it.array_iterator - other.m_it.array_iterator;
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                return m_it.primitive_iterator - other.m_it.primitive_iterator;
+        }
+    }
+
+    /*!
+    @brief access to successor
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    reference operator[](difference_type n) const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        switch (m_object->m_data.m_type)
+        {
+            case value_t::object:
+                JSON_THROW(invalid_iterator::create(208, "cannot use operator[] for object iterators", m_object));
+
+            case value_t::array:
+                return *std::next(m_it.array_iterator, n);
+
+            case value_t::null:
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                if (JSON_HEDLEY_LIKELY(m_it.primitive_iterator.get_value() == -n))
+                {
+                    return *m_object;
+                }
+
+                JSON_THROW(invalid_iterator::create(214, "cannot get value", m_object));
+            }
+        }
+    }
+
+    /*!
+    @brief return the key of an object iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    const typename object_t::key_type& key() const
+    {
+        JSON_ASSERT(m_object != nullptr);
+
+        if (JSON_HEDLEY_LIKELY(m_object->is_object()))
+        {
+            return m_it.object_iterator->first;
+        }
+
+        JSON_THROW(invalid_iterator::create(207, "cannot use key() for non-object iterators", m_object));
+    }
+
+    /*!
+    @brief return the value of an iterator
+    @pre The iterator is initialized; i.e. `m_object != nullptr`.
+    */
+    reference value() const
+    {
+        return operator*();
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /// associated JSON instance
+    pointer m_object = nullptr;
+    /// the actual iterator of the associated instance
+    internal_iterator<typename std::remove_const<BasicJsonType>::type> m_it {};
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/iteration_proxy.hpp>
+
+// #include <nlohmann/detail/iterators/json_reverse_iterator.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <cstddef> // ptrdiff_t
+#include <iterator> // reverse_iterator
+#include <utility> // declval
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+//////////////////////
+// reverse_iterator //
+//////////////////////
+
+/*!
+@brief a template for a reverse iterator class
+
+@tparam Base the base iterator type to reverse. Valid types are @ref
+iterator (to create @ref reverse_iterator) and @ref const_iterator (to
+create @ref const_reverse_iterator).
+
+@requirement The class satisfies the following concept requirements:
+-
+[BidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator):
+  The iterator that can be moved can be moved in both directions (i.e.
+  incremented and decremented).
+- [OutputIterator](https://en.cppreference.com/w/cpp/named_req/OutputIterator):
+  It is possible to write to the pointed-to element (only if @a Base is
+  @ref iterator).
+
+@since version 1.0.0
+*/
+template<typename Base>
+class json_reverse_iterator : public std::reverse_iterator<Base>
+{
+  public:
+    using difference_type = std::ptrdiff_t;
+    /// shortcut to the reverse iterator adapter
+    using base_iterator = std::reverse_iterator<Base>;
+    /// the reference type for the pointed-to element
+    using reference = typename Base::reference;
+
+    /// create reverse iterator from iterator
+    explicit json_reverse_iterator(const typename base_iterator::iterator_type& it) noexcept
+        : base_iterator(it) {}
+
+    /// create reverse iterator from base class
+    explicit json_reverse_iterator(const base_iterator& it) noexcept : base_iterator(it) {}
+
+    /// post-increment (it++)
+    json_reverse_iterator operator++(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator++(1));
+    }
+
+    /// pre-increment (++it)
+    json_reverse_iterator& operator++()
+    {
+        return static_cast<json_reverse_iterator&>(base_iterator::operator++());
+    }
+
+    /// post-decrement (it--)
+    json_reverse_iterator operator--(int)& // NOLINT(cert-dcl21-cpp)
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator--(1));
+    }
+
+    /// pre-decrement (--it)
+    json_reverse_iterator& operator--()
+    {
+        return static_cast<json_reverse_iterator&>(base_iterator::operator--());
+    }
+
+    /// add to iterator
+    json_reverse_iterator& operator+=(difference_type i)
+    {
+        return static_cast<json_reverse_iterator&>(base_iterator::operator+=(i));
+    }
+
+    /// add to iterator
+    json_reverse_iterator operator+(difference_type i) const
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator+(i));
+    }
+
+    /// subtract from iterator
+    json_reverse_iterator operator-(difference_type i) const
+    {
+        return static_cast<json_reverse_iterator>(base_iterator::operator-(i));
+    }
+
+    /// return difference
+    difference_type operator-(const json_reverse_iterator& other) const
+    {
+        return base_iterator(*this) - base_iterator(other);
+    }
+
+    /// access to successor
+    reference operator[](difference_type n) const
+    {
+        return *(this->operator+(n));
+    }
+
+    /// return the key of an object iterator
+    auto key() const -> decltype(std::declval<Base>().key())
+    {
+        auto it = --this->base();
+        return it.key();
+    }
+
+    /// return the value of an iterator
+    reference value() const
+    {
+        auto it = --this->base();
+        return it.operator * ();
+    }
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/iterators/primitive_iterator.hpp>
+
+// #include <nlohmann/detail/json_custom_base_class.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <type_traits> // conditional, is_same
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief Default base class of the @ref basic_json class.
+
+So that the correct implementations of the copy / move ctors / assign operators
+of @ref basic_json do not require complex case distinctions
+(no base class / custom base class used as customization point),
+@ref basic_json always has a base class.
+By default, this class is used because it is empty and thus has no effect
+on the behavior of @ref basic_json.
+*/
+struct json_default_base {};
+
+template<class T>
+using json_base_class = typename std::conditional <
+                        std::is_same<T, void>::value,
+                        json_default_base,
+                        T
+                        >::type;
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/json_pointer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // all_of
+#include <cctype> // isdigit
+#include <cerrno> // errno, ERANGE
+#include <cstdlib> // strtoull
+#ifndef JSON_NO_IO
+    #include <iosfwd> // ostream
+#endif  // JSON_NO_IO
+#include <limits> // max
+#include <numeric> // accumulate
+#include <string> // string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/string_escape.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// @brief JSON Pointer defines a string syntax for identifying a specific value within a JSON document
+/// @sa https://json.nlohmann.me/api/json_pointer/
+template<typename RefStringType>
+class json_pointer
+{
+    // allow basic_json to access private members
+    NLOHMANN_BASIC_JSON_TPL_DECLARATION
+    friend class basic_json;
+
+    template<typename>
+    friend class json_pointer;
+
+    template<typename T>
+    struct string_t_helper
+    {
+        using type = T;
+    };
+
+    NLOHMANN_BASIC_JSON_TPL_DECLARATION
+    struct string_t_helper<NLOHMANN_BASIC_JSON_TPL>
+    {
+        using type = StringType;
+    };
+
+  public:
+    // for backwards compatibility accept BasicJsonType
+    using string_t = typename string_t_helper<RefStringType>::type;
+
+    /// @brief create JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/json_pointer/
+    explicit json_pointer(const string_t& s = "")
+        : reference_tokens(split(s))
+    {}
+
+    /// @brief return a string representation of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/to_string/
+    string_t to_string() const
+    {
+        return std::accumulate(reference_tokens.begin(), reference_tokens.end(),
+                               string_t{},
+                               [](const string_t& a, const string_t& b)
+        {
+            return detail::concat(a, '/', detail::escape(b));
+        });
+    }
+
+    /// @brief return a string representation of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_string/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, to_string())
+    operator string_t() const
+    {
+        return to_string();
+    }
+
+#ifndef JSON_NO_IO
+    /// @brief write string representation of the JSON pointer to stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/
+    friend std::ostream& operator<<(std::ostream& o, const json_pointer& ptr)
+    {
+        o << ptr.to_string();
+        return o;
+    }
+#endif
+
+    /// @brief append another JSON pointer at the end of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/
+    json_pointer& operator/=(const json_pointer& ptr)
+    {
+        reference_tokens.insert(reference_tokens.end(),
+                                ptr.reference_tokens.begin(),
+                                ptr.reference_tokens.end());
+        return *this;
+    }
+
+    /// @brief append an unescaped reference token at the end of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/
+    json_pointer& operator/=(string_t token)
+    {
+        push_back(std::move(token));
+        return *this;
+    }
+
+    /// @brief append an array index at the end of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slasheq/
+    json_pointer& operator/=(std::size_t array_idx)
+    {
+        return *this /= std::to_string(array_idx);
+    }
+
+    /// @brief create a new JSON pointer by appending the right JSON pointer at the end of the left JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/
+    friend json_pointer operator/(const json_pointer& lhs,
+                                  const json_pointer& rhs)
+    {
+        return json_pointer(lhs) /= rhs;
+    }
+
+    /// @brief create a new JSON pointer by appending the unescaped token at the end of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/
+    friend json_pointer operator/(const json_pointer& lhs, string_t token) // NOLINT(performance-unnecessary-value-param)
+    {
+        return json_pointer(lhs) /= std::move(token);
+    }
+
+    /// @brief create a new JSON pointer by appending the array-index-token at the end of the JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_slash/
+    friend json_pointer operator/(const json_pointer& lhs, std::size_t array_idx)
+    {
+        return json_pointer(lhs) /= array_idx;
+    }
+
+    /// @brief returns the parent of this JSON pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/parent_pointer/
+    json_pointer parent_pointer() const
+    {
+        if (empty())
+        {
+            return *this;
+        }
+
+        json_pointer res = *this;
+        res.pop_back();
+        return res;
+    }
+
+    /// @brief remove last reference token
+    /// @sa https://json.nlohmann.me/api/json_pointer/pop_back/
+    void pop_back()
+    {
+        if (JSON_HEDLEY_UNLIKELY(empty()))
+        {
+            JSON_THROW(detail::out_of_range::create(405, "JSON pointer has no parent", nullptr));
+        }
+
+        reference_tokens.pop_back();
+    }
+
+    /// @brief return last reference token
+    /// @sa https://json.nlohmann.me/api/json_pointer/back/
+    const string_t& back() const
+    {
+        if (JSON_HEDLEY_UNLIKELY(empty()))
+        {
+            JSON_THROW(detail::out_of_range::create(405, "JSON pointer has no parent", nullptr));
+        }
+
+        return reference_tokens.back();
+    }
+
+    /// @brief append an unescaped token at the end of the reference pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/push_back/
+    void push_back(const string_t& token)
+    {
+        reference_tokens.push_back(token);
+    }
+
+    /// @brief append an unescaped token at the end of the reference pointer
+    /// @sa https://json.nlohmann.me/api/json_pointer/push_back/
+    void push_back(string_t&& token)
+    {
+        reference_tokens.push_back(std::move(token));
+    }
+
+    /// @brief return whether pointer points to the root document
+    /// @sa https://json.nlohmann.me/api/json_pointer/empty/
+    bool empty() const noexcept
+    {
+        return reference_tokens.empty();
+    }
+
+  private:
+    /*!
+    @param[in] s  reference token to be converted into an array index
+
+    @return integer representation of @a s
+
+    @throw parse_error.106  if an array index begins with '0'
+    @throw parse_error.109  if an array index begins not with a digit
+    @throw out_of_range.404 if string @a s could not be converted to an integer
+    @throw out_of_range.410 if an array index exceeds size_type
+    */
+    template<typename BasicJsonType>
+    static typename BasicJsonType::size_type array_index(const string_t& s)
+    {
+        using size_type = typename BasicJsonType::size_type;
+
+        // error condition (cf. RFC 6901, Sect. 4)
+        if (JSON_HEDLEY_UNLIKELY(s.size() > 1 && s[0] == '0'))
+        {
+            JSON_THROW(detail::parse_error::create(106, 0, detail::concat("array index '", s, "' must not begin with '0'"), nullptr));
+        }
+
+        // error condition (cf. RFC 6901, Sect. 4)
+        if (JSON_HEDLEY_UNLIKELY(s.size() > 1 && !(s[0] >= '1' && s[0] <= '9')))
+        {
+            JSON_THROW(detail::parse_error::create(109, 0, detail::concat("array index '", s, "' is not a number"), nullptr));
+        }
+
+        const char* p = s.c_str();
+        char* p_end = nullptr; // NOLINT(misc-const-correctness)
+        errno = 0; // strtoull doesn't reset errno
+        const unsigned long long res = std::strtoull(p, &p_end, 10); // NOLINT(runtime/int)
+        if (p == p_end // invalid input or empty string
+                || errno == ERANGE // out of range
+                || JSON_HEDLEY_UNLIKELY(static_cast<std::size_t>(p_end - p) != s.size())) // incomplete read
+        {
+            JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", s, "'"), nullptr));
+        }
+
+        // only triggered on special platforms (like 32bit), see also
+        // https://github.com/nlohmann/json/pull/2203
+        if (res >= static_cast<unsigned long long>((std::numeric_limits<size_type>::max)()))  // NOLINT(runtime/int)
+        {
+            JSON_THROW(detail::out_of_range::create(410, detail::concat("array index ", s, " exceeds size_type"), nullptr));   // LCOV_EXCL_LINE
+        }
+
+        return static_cast<size_type>(res);
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    json_pointer top() const
+    {
+        if (JSON_HEDLEY_UNLIKELY(empty()))
+        {
+            JSON_THROW(detail::out_of_range::create(405, "JSON pointer has no parent", nullptr));
+        }
+
+        json_pointer result = *this;
+        result.reference_tokens = {reference_tokens[0]};
+        return result;
+    }
+
+  private:
+    /*!
+    @brief create and return a reference to the pointed to value
+
+    @complexity Linear in the number of reference tokens.
+
+    @throw parse_error.109 if array index is not a number
+    @throw type_error.313 if value cannot be unflattened
+    */
+    template<typename BasicJsonType>
+    BasicJsonType& get_and_create(BasicJsonType& j) const
+    {
+        auto* result = &j;
+
+        // in case no reference tokens exist, return a reference to the JSON value
+        // j which will be overwritten by a primitive value
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (result->type())
+            {
+                case detail::value_t::null:
+                {
+                    if (reference_token == "0")
+                    {
+                        // start a new array if reference token is 0
+                        result = &result->operator[](0);
+                    }
+                    else
+                    {
+                        // start a new object otherwise
+                        result = &result->operator[](reference_token);
+                    }
+                    break;
+                }
+
+                case detail::value_t::object:
+                {
+                    // create an entry in the object
+                    result = &result->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    // create an entry in the array
+                    result = &result->operator[](array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                /*
+                The following code is only reached if there exists a reference
+                token _and_ the current value is primitive. In this case, we have
+                an error situation, because primitive values may only occur as
+                single value; that is, with an empty list of reference tokens.
+                */
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::type_error::create(313, "invalid value to unflatten", &j));
+            }
+        }
+
+        return *result;
+    }
+
+    /*!
+    @brief return a reference to the pointed to value
+
+    @note This version does not throw if a value is not present, but tries to
+          create nested values instead. For instance, calling this function
+          with pointer `"/this/that"` on a null value is equivalent to calling
+          `operator[]("this").operator[]("that")` on that value, effectively
+          changing the null value to an object.
+
+    @param[in] ptr  a JSON value
+
+    @return reference to the JSON value pointed to by the JSON pointer
+
+    @complexity Linear in the length of the JSON pointer.
+
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    BasicJsonType& get_unchecked(BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            // convert null values to arrays or objects before continuing
+            if (ptr->is_null())
+            {
+                // check if reference token is a number
+                const bool nums =
+                    std::all_of(reference_token.begin(), reference_token.end(),
+                                [](const unsigned char x)
+                {
+                    return std::isdigit(x);
+                });
+
+                // change value to array for numbers or "-" or to object otherwise
+                *ptr = (nums || reference_token == "-")
+                       ? detail::value_t::array
+                       : detail::value_t::object;
+            }
+
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // use unchecked object access
+                    ptr = &ptr->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (reference_token == "-")
+                    {
+                        // explicitly treat "-" as index beyond the end
+                        ptr = &ptr->operator[](ptr->m_data.m_value.array->size());
+                    }
+                    else
+                    {
+                        // convert array index to number; unchecked access
+                        ptr = &ptr->operator[](array_index<BasicJsonType>(reference_token));
+                    }
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.402  if the array index '-' is used
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    BasicJsonType& get_checked(BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // note: at performs range check
+                    ptr = &ptr->at(reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" always fails the range check
+                        JSON_THROW(detail::out_of_range::create(402, detail::concat(
+                                "array index '-' (", std::to_string(ptr->m_data.m_value.array->size()),
+                                ") is out of range"), ptr));
+                    }
+
+                    // note: at performs range check
+                    ptr = &ptr->at(array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @brief return a const reference to the pointed to value
+
+    @param[in] ptr  a JSON value
+
+    @return const reference to the JSON value pointed to by the JSON
+    pointer
+
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.402  if the array index '-' is used
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    const BasicJsonType& get_unchecked(const BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // use unchecked object access
+                    ptr = &ptr->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" cannot be used for const access
+                        JSON_THROW(detail::out_of_range::create(402, detail::concat("array index '-' (", std::to_string(ptr->m_data.m_value.array->size()), ") is out of range"), ptr));
+                    }
+
+                    // use unchecked array access
+                    ptr = &ptr->operator[](array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    @throw out_of_range.402  if the array index '-' is used
+    @throw out_of_range.404  if the JSON pointer can not be resolved
+    */
+    template<typename BasicJsonType>
+    const BasicJsonType& get_checked(const BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    // note: at performs range check
+                    ptr = &ptr->at(reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" always fails the range check
+                        JSON_THROW(detail::out_of_range::create(402, detail::concat(
+                                "array index '-' (", std::to_string(ptr->m_data.m_value.array->size()),
+                                ") is out of range"), ptr));
+                    }
+
+                    // note: at performs range check
+                    ptr = &ptr->at(array_index<BasicJsonType>(reference_token));
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                    JSON_THROW(detail::out_of_range::create(404, detail::concat("unresolved reference token '", reference_token, "'"), ptr));
+            }
+        }
+
+        return *ptr;
+    }
+
+    /*!
+    @throw parse_error.106   if an array index begins with '0'
+    @throw parse_error.109   if an array index was not a number
+    */
+    template<typename BasicJsonType>
+    bool contains(const BasicJsonType* ptr) const
+    {
+        for (const auto& reference_token : reference_tokens)
+        {
+            switch (ptr->type())
+            {
+                case detail::value_t::object:
+                {
+                    if (!ptr->contains(reference_token))
+                    {
+                        // we did not find the key in the object
+                        return false;
+                    }
+
+                    ptr = &ptr->operator[](reference_token);
+                    break;
+                }
+
+                case detail::value_t::array:
+                {
+                    if (JSON_HEDLEY_UNLIKELY(reference_token == "-"))
+                    {
+                        // "-" always fails the range check
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(reference_token.size() == 1 && !("0" <= reference_token && reference_token <= "9")))
+                    {
+                        // invalid char
+                        return false;
+                    }
+                    if (JSON_HEDLEY_UNLIKELY(reference_token.size() > 1))
+                    {
+                        if (JSON_HEDLEY_UNLIKELY(!('1' <= reference_token[0] && reference_token[0] <= '9')))
+                        {
+                            // first char should be between '1' and '9'
+                            return false;
+                        }
+                        for (std::size_t i = 1; i < reference_token.size(); i++)
+                        {
+                            if (JSON_HEDLEY_UNLIKELY(!('0' <= reference_token[i] && reference_token[i] <= '9')))
+                            {
+                                // other char should be between '0' and '9'
+                                return false;
+                            }
+                        }
+                    }
+
+                    const auto idx = array_index<BasicJsonType>(reference_token);
+                    if (idx >= ptr->size())
+                    {
+                        // index out of range
+                        return false;
+                    }
+
+                    ptr = &ptr->operator[](idx);
+                    break;
+                }
+
+                case detail::value_t::null:
+                case detail::value_t::string:
+                case detail::value_t::boolean:
+                case detail::value_t::number_integer:
+                case detail::value_t::number_unsigned:
+                case detail::value_t::number_float:
+                case detail::value_t::binary:
+                case detail::value_t::discarded:
+                default:
+                {
+                    // we do not expect primitive values if there is still a
+                    // reference token to process
+                    return false;
+                }
+            }
+        }
+
+        // no reference token left means we found a primitive value
+        return true;
+    }
+
+    /*!
+    @brief split the string input to reference tokens
+
+    @note This function is only called by the json_pointer constructor.
+          All exceptions below are documented there.
+
+    @throw parse_error.107  if the pointer is not empty or begins with '/'
+    @throw parse_error.108  if character '~' is not followed by '0' or '1'
+    */
+    static std::vector<string_t> split(const string_t& reference_string)
+    {
+        std::vector<string_t> result;
+
+        // special case: empty reference string -> no reference tokens
+        if (reference_string.empty())
+        {
+            return result;
+        }
+
+        // check if nonempty reference string begins with slash
+        if (JSON_HEDLEY_UNLIKELY(reference_string[0] != '/'))
+        {
+            JSON_THROW(detail::parse_error::create(107, 1, detail::concat("JSON pointer must be empty or begin with '/' - was: '", reference_string, "'"), nullptr));
+        }
+
+        // extract the reference tokens:
+        // - slash: position of the last read slash (or end of string)
+        // - start: position after the previous slash
+        for (
+            // search for the first slash after the first character
+            std::size_t slash = reference_string.find_first_of('/', 1),
+            // set the beginning of the first reference token
+            start = 1;
+            // we can stop if start == 0 (if slash == string_t::npos)
+            start != 0;
+            // set the beginning of the next reference token
+            // (will eventually be 0 if slash == string_t::npos)
+            start = (slash == string_t::npos) ? 0 : slash + 1,
+            // find next slash
+            slash = reference_string.find_first_of('/', start))
+        {
+            // use the text between the beginning of the reference token
+            // (start) and the last slash (slash).
+            auto reference_token = reference_string.substr(start, slash - start);
+
+            // check reference tokens are properly escaped
+            for (std::size_t pos = reference_token.find_first_of('~');
+                    pos != string_t::npos;
+                    pos = reference_token.find_first_of('~', pos + 1))
+            {
+                JSON_ASSERT(reference_token[pos] == '~');
+
+                // ~ must be followed by 0 or 1
+                if (JSON_HEDLEY_UNLIKELY(pos == reference_token.size() - 1 ||
+                                         (reference_token[pos + 1] != '0' &&
+                                          reference_token[pos + 1] != '1')))
+                {
+                    JSON_THROW(detail::parse_error::create(108, 0, "escape character '~' must be followed with '0' or '1'", nullptr));
+                }
+            }
+
+            // finally, store the reference token
+            detail::unescape(reference_token);
+            result.push_back(reference_token);
+        }
+
+        return result;
+    }
+
+  private:
+    /*!
+    @param[in] reference_string  the reference string to the current value
+    @param[in] value             the value to consider
+    @param[in,out] result        the result object to insert values to
+
+    @note Empty objects or arrays are flattened to `null`.
+    */
+    template<typename BasicJsonType>
+    static void flatten(const string_t& reference_string,
+                        const BasicJsonType& value,
+                        BasicJsonType& result)
+    {
+        switch (value.type())
+        {
+            case detail::value_t::array:
+            {
+                if (value.m_data.m_value.array->empty())
+                {
+                    // flatten empty array as null
+                    result[reference_string] = nullptr;
+                }
+                else
+                {
+                    // iterate array and use index as reference string
+                    for (std::size_t i = 0; i < value.m_data.m_value.array->size(); ++i)
+                    {
+                        flatten(detail::concat<string_t>(reference_string, '/', std::to_string(i)),
+                                value.m_data.m_value.array->operator[](i), result);
+                    }
+                }
+                break;
+            }
+
+            case detail::value_t::object:
+            {
+                if (value.m_data.m_value.object->empty())
+                {
+                    // flatten empty object as null
+                    result[reference_string] = nullptr;
+                }
+                else
+                {
+                    // iterate object and use keys as reference string
+                    for (const auto& element : *value.m_data.m_value.object)
+                    {
+                        flatten(detail::concat<string_t>(reference_string, '/', detail::escape(element.first)), element.second, result);
+                    }
+                }
+                break;
+            }
+
+            case detail::value_t::null:
+            case detail::value_t::string:
+            case detail::value_t::boolean:
+            case detail::value_t::number_integer:
+            case detail::value_t::number_unsigned:
+            case detail::value_t::number_float:
+            case detail::value_t::binary:
+            case detail::value_t::discarded:
+            default:
+            {
+                // add primitive value with its reference string
+                result[reference_string] = value;
+                break;
+            }
+        }
+    }
+
+    /*!
+    @param[in] value  flattened JSON
+
+    @return unflattened JSON
+
+    @throw parse_error.109 if array index is not a number
+    @throw type_error.314  if value is not an object
+    @throw type_error.315  if object values are not primitive
+    @throw type_error.313  if value cannot be unflattened
+    */
+    template<typename BasicJsonType>
+    static BasicJsonType
+    unflatten(const BasicJsonType& value)
+    {
+        if (JSON_HEDLEY_UNLIKELY(!value.is_object()))
+        {
+            JSON_THROW(detail::type_error::create(314, "only objects can be unflattened", &value));
+        }
+
+        BasicJsonType result;
+
+        // iterate the JSON object values
+        for (const auto& element : *value.m_data.m_value.object)
+        {
+            if (JSON_HEDLEY_UNLIKELY(!element.second.is_primitive()))
+            {
+                JSON_THROW(detail::type_error::create(315, "values in object must be primitive", &element.second));
+            }
+
+            // assign value to reference pointed to by JSON pointer; Note that if
+            // the JSON pointer is "" (i.e., points to the whole value), function
+            // get_and_create returns a reference to result itself. An assignment
+            // will then create a primitive value.
+            json_pointer(element.first).get_and_create(result) = element.second;
+        }
+
+        return result;
+    }
+
+    // can't use conversion operator because of ambiguity
+    json_pointer<string_t> convert() const&
+    {
+        json_pointer<string_t> result;
+        result.reference_tokens = reference_tokens;
+        return result;
+    }
+
+    json_pointer<string_t> convert()&&
+    {
+        json_pointer<string_t> result;
+        result.reference_tokens = std::move(reference_tokens);
+        return result;
+    }
+
+  public:
+#if JSON_HAS_THREE_WAY_COMPARISON
+    /// @brief compares two JSON pointers for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeRhs>
+    bool operator==(const json_pointer<RefStringTypeRhs>& rhs) const noexcept
+    {
+        return reference_tokens == rhs.reference_tokens;
+    }
+
+    /// @brief compares JSON pointer and string for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer))
+    bool operator==(const string_t& rhs) const
+    {
+        return *this == json_pointer(rhs);
+    }
+
+    /// @brief 3-way compares two JSON pointers
+    template<typename RefStringTypeRhs>
+    std::strong_ordering operator<=>(const json_pointer<RefStringTypeRhs>& rhs) const noexcept // *NOPAD*
+    {
+        return  reference_tokens <=> rhs.reference_tokens; // *NOPAD*
+    }
+#else
+    /// @brief compares two JSON pointers for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs) noexcept;
+
+    /// @brief compares JSON pointer and string for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeLhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                           const StringType& rhs);
+
+    /// @brief compares string and JSON pointer for equality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_eq/
+    template<typename RefStringTypeRhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator==(const StringType& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs);
+
+    /// @brief compares two JSON pointers for inequality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/
+    template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs) noexcept;
+
+    /// @brief compares JSON pointer and string for inequality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/
+    template<typename RefStringTypeLhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                           const StringType& rhs);
+
+    /// @brief compares string and JSON pointer for inequality
+    /// @sa https://json.nlohmann.me/api/json_pointer/operator_ne/
+    template<typename RefStringTypeRhs, typename StringType>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator!=(const StringType& lhs,
+                           const json_pointer<RefStringTypeRhs>& rhs);
+
+    /// @brief compares two JSON pointer for less-than
+    template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+    // NOLINTNEXTLINE(readability-redundant-declaration)
+    friend bool operator<(const json_pointer<RefStringTypeLhs>& lhs,
+                          const json_pointer<RefStringTypeRhs>& rhs) noexcept;
+#endif
+
+  private:
+    /// the reference tokens
+    std::vector<string_t> reference_tokens;
+};
+
+#if !JSON_HAS_THREE_WAY_COMPARISON
+// functions cannot be defined inside class due to ODR violations
+template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+inline bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs) noexcept
+{
+    return lhs.reference_tokens == rhs.reference_tokens;
+}
+
+template<typename RefStringTypeLhs,
+         typename StringType = typename json_pointer<RefStringTypeLhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer, json_pointer))
+inline bool operator==(const json_pointer<RefStringTypeLhs>& lhs,
+                       const StringType& rhs)
+{
+    return lhs == json_pointer<RefStringTypeLhs>(rhs);
+}
+
+template<typename RefStringTypeRhs,
+         typename StringType = typename json_pointer<RefStringTypeRhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator==(json_pointer, json_pointer))
+inline bool operator==(const StringType& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs)
+{
+    return json_pointer<RefStringTypeRhs>(lhs) == rhs;
+}
+
+template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+inline bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs) noexcept
+{
+    return !(lhs == rhs);
+}
+
+template<typename RefStringTypeLhs,
+         typename StringType = typename json_pointer<RefStringTypeLhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator!=(json_pointer, json_pointer))
+inline bool operator!=(const json_pointer<RefStringTypeLhs>& lhs,
+                       const StringType& rhs)
+{
+    return !(lhs == rhs);
+}
+
+template<typename RefStringTypeRhs,
+         typename StringType = typename json_pointer<RefStringTypeRhs>::string_t>
+JSON_HEDLEY_DEPRECATED_FOR(3.11.2, operator!=(json_pointer, json_pointer))
+inline bool operator!=(const StringType& lhs,
+                       const json_pointer<RefStringTypeRhs>& rhs)
+{
+    return !(lhs == rhs);
+}
+
+template<typename RefStringTypeLhs, typename RefStringTypeRhs>
+inline bool operator<(const json_pointer<RefStringTypeLhs>& lhs,
+                      const json_pointer<RefStringTypeRhs>& rhs) noexcept
+{
+    return lhs.reference_tokens < rhs.reference_tokens;
+}
+#endif
+
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/json_ref.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <initializer_list>
+#include <utility>
+
+// #include <nlohmann/detail/abi_macros.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+template<typename BasicJsonType>
+class json_ref
+{
+  public:
+    using value_type = BasicJsonType;
+
+    json_ref(value_type&& value)
+        : owned_value(std::move(value))
+    {}
+
+    json_ref(const value_type& value)
+        : value_ref(&value)
+    {}
+
+    json_ref(std::initializer_list<json_ref> init)
+        : owned_value(init)
+    {}
+
+    template <
+        class... Args,
+        enable_if_t<std::is_constructible<value_type, Args...>::value, int> = 0 >
+    json_ref(Args && ... args)
+        : owned_value(std::forward<Args>(args)...)
+    {}
+
+    // class should be movable only
+    json_ref(json_ref&&) noexcept = default;
+    json_ref(const json_ref&) = delete;
+    json_ref& operator=(const json_ref&) = delete;
+    json_ref& operator=(json_ref&&) = delete;
+    ~json_ref() = default;
+
+    value_type moved_or_copied() const
+    {
+        if (value_ref == nullptr)
+        {
+            return std::move(owned_value);
+        }
+        return *value_ref;
+    }
+
+    value_type const& operator*() const
+    {
+        return value_ref ? *value_ref : owned_value;
+    }
+
+    value_type const* operator->() const
+    {
+        return &** this;
+    }
+
+  private:
+    mutable value_type owned_value = nullptr;
+    value_type const* value_ref = nullptr;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/string_escape.hpp>
+
+// #include <nlohmann/detail/string_utils.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+// #include <nlohmann/detail/output/binary_writer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // reverse
+#include <array> // array
+#include <map> // map
+#include <cmath> // isnan, isinf
+#include <cstdint> // uint8_t, uint16_t, uint32_t, uint64_t
+#include <cstring> // memcpy
+#include <limits> // numeric_limits
+#include <string> // string
+#include <utility> // move
+#include <vector> // vector
+
+// #include <nlohmann/detail/input/binary_reader.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/output/output_adapters.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // copy
+#include <cstddef> // size_t
+#include <iterator> // back_inserter
+#include <memory> // shared_ptr, make_shared
+#include <string> // basic_string
+#include <vector> // vector
+
+#ifndef JSON_NO_IO
+    #include <ios>      // streamsize
+    #include <ostream>  // basic_ostream
+#endif  // JSON_NO_IO
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// abstract output adapter interface
+template<typename CharType> struct output_adapter_protocol
+{
+    virtual void write_character(CharType c) = 0;
+    virtual void write_characters(const CharType* s, std::size_t length) = 0;
+    virtual ~output_adapter_protocol() = default;
+
+    output_adapter_protocol() = default;
+    output_adapter_protocol(const output_adapter_protocol&) = default;
+    output_adapter_protocol(output_adapter_protocol&&) noexcept = default;
+    output_adapter_protocol& operator=(const output_adapter_protocol&) = default;
+    output_adapter_protocol& operator=(output_adapter_protocol&&) noexcept = default;
+};
+
+/// a type to simplify interfaces
+template<typename CharType>
+using output_adapter_t = std::shared_ptr<output_adapter_protocol<CharType>>;
+
+/// output adapter for byte vectors
+template<typename CharType, typename AllocatorType = std::allocator<CharType>>
+class output_vector_adapter : public output_adapter_protocol<CharType>
+{
+  public:
+    explicit output_vector_adapter(std::vector<CharType, AllocatorType>& vec) noexcept
+        : v(vec)
+    {}
+
+    void write_character(CharType c) override
+    {
+        v.push_back(c);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    void write_characters(const CharType* s, std::size_t length) override
+    {
+        v.insert(v.end(), s, s + length);
+    }
+
+  private:
+    std::vector<CharType, AllocatorType>& v;
+};
+
+#ifndef JSON_NO_IO
+/// output adapter for output streams
+template<typename CharType>
+class output_stream_adapter : public output_adapter_protocol<CharType>
+{
+  public:
+    explicit output_stream_adapter(std::basic_ostream<CharType>& s) noexcept
+        : stream(s)
+    {}
+
+    void write_character(CharType c) override
+    {
+        stream.put(c);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    void write_characters(const CharType* s, std::size_t length) override
+    {
+        stream.write(s, static_cast<std::streamsize>(length));
+    }
+
+  private:
+    std::basic_ostream<CharType>& stream;
+};
+#endif  // JSON_NO_IO
+
+/// output adapter for basic_string
+template<typename CharType, typename StringType = std::basic_string<CharType>>
+class output_string_adapter : public output_adapter_protocol<CharType>
+{
+  public:
+    explicit output_string_adapter(StringType& s) noexcept
+        : str(s)
+    {}
+
+    void write_character(CharType c) override
+    {
+        str.push_back(c);
+    }
+
+    JSON_HEDLEY_NON_NULL(2)
+    void write_characters(const CharType* s, std::size_t length) override
+    {
+        str.append(s, length);
+    }
+
+  private:
+    StringType& str;
+};
+
+template<typename CharType, typename StringType = std::basic_string<CharType>>
+class output_adapter
+{
+  public:
+    template<typename AllocatorType = std::allocator<CharType>>
+    output_adapter(std::vector<CharType, AllocatorType>& vec)
+        : oa(std::make_shared<output_vector_adapter<CharType, AllocatorType>>(vec)) {}
+
+#ifndef JSON_NO_IO
+    output_adapter(std::basic_ostream<CharType>& s)
+        : oa(std::make_shared<output_stream_adapter<CharType>>(s)) {}
+#endif  // JSON_NO_IO
+
+    output_adapter(StringType& s)
+        : oa(std::make_shared<output_string_adapter<CharType, StringType>>(s)) {}
+
+    operator output_adapter_t<CharType>()
+    {
+        return oa;
+    }
+
+  private:
+    output_adapter_t<CharType> oa = nullptr;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/// how to encode BJData
+enum class bjdata_version_t
+{
+    draft2,
+    draft3,
+};
+
+///////////////////
+// binary writer //
+///////////////////
+
+/*!
+@brief serialization to CBOR and MessagePack values
+*/
+template<typename BasicJsonType, typename CharType>
+class binary_writer
+{
+    using string_t = typename BasicJsonType::string_t;
+    using binary_t = typename BasicJsonType::binary_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+
+  public:
+    /*!
+    @brief create a binary writer
+
+    @param[in] adapter  output adapter to write to
+    */
+    explicit binary_writer(output_adapter_t<CharType> adapter) : oa(std::move(adapter))
+    {
+        JSON_ASSERT(oa);
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    @pre       j.type() == value_t::object
+    */
+    void write_bson(const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::object:
+            {
+                write_bson_object(*j.m_data.m_value.object);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::array:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                JSON_THROW(type_error::create(317, concat("to serialize to BSON, top-level type must be object, but is ", j.type_name()), &j));
+            }
+        }
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    */
+    void write_cbor(const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::null:
+            {
+                oa->write_character(to_char_type(0xF6));
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                oa->write_character(j.m_data.m_value.boolean
+                                    ? to_char_type(0xF5)
+                                    : to_char_type(0xF4));
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                if (j.m_data.m_value.number_integer >= 0)
+                {
+                    // CBOR does not differentiate between positive signed
+                    // integers and unsigned integers. Therefore, we used the
+                    // code from the value_t::number_unsigned case here.
+                    if (j.m_data.m_value.number_integer <= 0x17)
+                    {
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x18));
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x19));
+                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x1A));
+                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));
+                    }
+                    else
+                    {
+                        oa->write_character(to_char_type(0x1B));
+                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));
+                    }
+                }
+                else
+                {
+                    // The conversions below encode the sign in the first
+                    // byte, and the value is converted to a positive number.
+                    const auto positive_number = -1 - j.m_data.m_value.number_integer;
+                    if (j.m_data.m_value.number_integer >= -24)
+                    {
+                        write_number(static_cast<std::uint8_t>(0x20 + positive_number));
+                    }
+                    else if (positive_number <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x38));
+                        write_number(static_cast<std::uint8_t>(positive_number));
+                    }
+                    else if (positive_number <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x39));
+                        write_number(static_cast<std::uint16_t>(positive_number));
+                    }
+                    else if (positive_number <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        oa->write_character(to_char_type(0x3A));
+                        write_number(static_cast<std::uint32_t>(positive_number));
+                    }
+                    else
+                    {
+                        oa->write_character(to_char_type(0x3B));
+                        write_number(static_cast<std::uint64_t>(positive_number));
+                    }
+                }
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                if (j.m_data.m_value.number_unsigned <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_unsigned));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x18));
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_unsigned));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x19));
+                    write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_unsigned));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x1A));
+                    write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_unsigned));
+                }
+                else
+                {
+                    oa->write_character(to_char_type(0x1B));
+                    write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_unsigned));
+                }
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                if (std::isnan(j.m_data.m_value.number_float))
+                {
+                    // NaN is 0xf97e00 in CBOR
+                    oa->write_character(to_char_type(0xF9));
+                    oa->write_character(to_char_type(0x7E));
+                    oa->write_character(to_char_type(0x00));
+                }
+                else if (std::isinf(j.m_data.m_value.number_float))
+                {
+                    // Infinity is 0xf97c00, -Infinity is 0xf9fc00
+                    oa->write_character(to_char_type(0xf9));
+                    oa->write_character(j.m_data.m_value.number_float > 0 ? to_char_type(0x7C) : to_char_type(0xFC));
+                    oa->write_character(to_char_type(0x00));
+                }
+                else
+                {
+                    write_compact_float(j.m_data.m_value.number_float, detail::input_format_t::cbor);
+                }
+                break;
+            }
+
+            case value_t::string:
+            {
+                // step 1: write control byte and the string length
+                const auto N = j.m_data.m_value.string->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0x60 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x78));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x79));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x7A));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x7B));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write the string
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),
+                    j.m_data.m_value.string->size());
+                break;
+            }
+
+            case value_t::array:
+            {
+                // step 1: write control byte and the array size
+                const auto N = j.m_data.m_value.array->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0x80 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x98));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x99));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x9A));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x9B));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.array)
+                {
+                    write_cbor(el);
+                }
+                break;
+            }
+
+            case value_t::binary:
+            {
+                if (j.m_data.m_value.binary->has_subtype())
+                {
+                    if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xd8));
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xd9));
+                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xda));
+                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                    else if (j.m_data.m_value.binary->subtype() <= (std::numeric_limits<std::uint64_t>::max)())
+                    {
+                        write_number(static_cast<std::uint8_t>(0xdb));
+                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.binary->subtype()));
+                    }
+                }
+
+                // step 1: write control byte and the binary array size
+                const auto N = j.m_data.m_value.binary->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0x40 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x58));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x59));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x5A));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0x5B));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write each element
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),
+                    N);
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                // step 1: write control byte and the object size
+                const auto N = j.m_data.m_value.object->size();
+                if (N <= 0x17)
+                {
+                    write_number(static_cast<std::uint8_t>(0xA0 + N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xB8));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xB9));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xBA));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+                // LCOV_EXCL_START
+                else if (N <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    oa->write_character(to_char_type(0xBB));
+                    write_number(static_cast<std::uint64_t>(N));
+                }
+                // LCOV_EXCL_STOP
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.object)
+                {
+                    write_cbor(el.first);
+                    write_cbor(el.second);
+                }
+                break;
+            }
+
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    */
+    void write_msgpack(const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::null: // nil
+            {
+                oa->write_character(to_char_type(0xC0));
+                break;
+            }
+
+            case value_t::boolean: // true and false
+            {
+                oa->write_character(j.m_data.m_value.boolean
+                                    ? to_char_type(0xC3)
+                                    : to_char_type(0xC2));
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                if (j.m_data.m_value.number_integer >= 0)
+                {
+                    // MessagePack does not differentiate between positive
+                    // signed integers and unsigned integers. Therefore, we used
+                    // the code from the value_t::number_unsigned case here.
+                    if (j.m_data.m_value.number_unsigned < 128)
+                    {
+                        // positive fixnum
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())
+                    {
+                        // uint 8
+                        oa->write_character(to_char_type(0xCC));
+                        write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())
+                    {
+                        // uint 16
+                        oa->write_character(to_char_type(0xCD));
+                        write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())
+                    {
+                        // uint 32
+                        oa->write_character(to_char_type(0xCE));
+                        write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())
+                    {
+                        // uint 64
+                        oa->write_character(to_char_type(0xCF));
+                        write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));
+                    }
+                }
+                else
+                {
+                    if (j.m_data.m_value.number_integer >= -32)
+                    {
+                        // negative fixnum
+                        write_number(static_cast<std::int8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int8_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int8_t>::max)())
+                    {
+                        // int 8
+                        oa->write_character(to_char_type(0xD0));
+                        write_number(static_cast<std::int8_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int16_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int16_t>::max)())
+                    {
+                        // int 16
+                        oa->write_character(to_char_type(0xD1));
+                        write_number(static_cast<std::int16_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int32_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int32_t>::max)())
+                    {
+                        // int 32
+                        oa->write_character(to_char_type(0xD2));
+                        write_number(static_cast<std::int32_t>(j.m_data.m_value.number_integer));
+                    }
+                    else if (j.m_data.m_value.number_integer >= (std::numeric_limits<std::int64_t>::min)() &&
+                             j.m_data.m_value.number_integer <= (std::numeric_limits<std::int64_t>::max)())
+                    {
+                        // int 64
+                        oa->write_character(to_char_type(0xD3));
+                        write_number(static_cast<std::int64_t>(j.m_data.m_value.number_integer));
+                    }
+                }
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                if (j.m_data.m_value.number_unsigned < 128)
+                {
+                    // positive fixnum
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    // uint 8
+                    oa->write_character(to_char_type(0xCC));
+                    write_number(static_cast<std::uint8_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // uint 16
+                    oa->write_character(to_char_type(0xCD));
+                    write_number(static_cast<std::uint16_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // uint 32
+                    oa->write_character(to_char_type(0xCE));
+                    write_number(static_cast<std::uint32_t>(j.m_data.m_value.number_integer));
+                }
+                else if (j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    // uint 64
+                    oa->write_character(to_char_type(0xCF));
+                    write_number(static_cast<std::uint64_t>(j.m_data.m_value.number_integer));
+                }
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                write_compact_float(j.m_data.m_value.number_float, detail::input_format_t::msgpack);
+                break;
+            }
+
+            case value_t::string:
+            {
+                // step 1: write control byte and the string length
+                const auto N = j.m_data.m_value.string->size();
+                if (N <= 31)
+                {
+                    // fixstr
+                    write_number(static_cast<std::uint8_t>(0xA0 | N));
+                }
+                else if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    // str 8
+                    oa->write_character(to_char_type(0xD9));
+                    write_number(static_cast<std::uint8_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // str 16
+                    oa->write_character(to_char_type(0xDA));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // str 32
+                    oa->write_character(to_char_type(0xDB));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 2: write the string
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),
+                    j.m_data.m_value.string->size());
+                break;
+            }
+
+            case value_t::array:
+            {
+                // step 1: write control byte and the array size
+                const auto N = j.m_data.m_value.array->size();
+                if (N <= 15)
+                {
+                    // fixarray
+                    write_number(static_cast<std::uint8_t>(0x90 | N));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // array 16
+                    oa->write_character(to_char_type(0xDC));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // array 32
+                    oa->write_character(to_char_type(0xDD));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.array)
+                {
+                    write_msgpack(el);
+                }
+                break;
+            }
+
+            case value_t::binary:
+            {
+                // step 0: determine if the binary type has a set subtype to
+                // determine whether to use the ext or fixext types
+                const bool use_ext = j.m_data.m_value.binary->has_subtype();
+
+                // step 1: write control byte and the byte string length
+                const auto N = j.m_data.m_value.binary->size();
+                if (N <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    std::uint8_t output_type{};
+                    bool fixed = true;
+                    if (use_ext)
+                    {
+                        switch (N)
+                        {
+                            case 1:
+                                output_type = 0xD4; // fixext 1
+                                break;
+                            case 2:
+                                output_type = 0xD5; // fixext 2
+                                break;
+                            case 4:
+                                output_type = 0xD6; // fixext 4
+                                break;
+                            case 8:
+                                output_type = 0xD7; // fixext 8
+                                break;
+                            case 16:
+                                output_type = 0xD8; // fixext 16
+                                break;
+                            default:
+                                output_type = 0xC7; // ext 8
+                                fixed = false;
+                                break;
+                        }
+
+                    }
+                    else
+                    {
+                        output_type = 0xC4; // bin 8
+                        fixed = false;
+                    }
+
+                    oa->write_character(to_char_type(output_type));
+                    if (!fixed)
+                    {
+                        write_number(static_cast<std::uint8_t>(N));
+                    }
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    const std::uint8_t output_type = use_ext
+                                                     ? 0xC8 // ext 16
+                                                     : 0xC5; // bin 16
+
+                    oa->write_character(to_char_type(output_type));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    const std::uint8_t output_type = use_ext
+                                                     ? 0xC9 // ext 32
+                                                     : 0xC6; // bin 32
+
+                    oa->write_character(to_char_type(output_type));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 1.5: if this is an ext type, write the subtype
+                if (use_ext)
+                {
+                    write_number(static_cast<std::int8_t>(j.m_data.m_value.binary->subtype()));
+                }
+
+                // step 2: write the byte string
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),
+                    N);
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                // step 1: write control byte and the object size
+                const auto N = j.m_data.m_value.object->size();
+                if (N <= 15)
+                {
+                    // fixmap
+                    write_number(static_cast<std::uint8_t>(0x80 | (N & 0xF)));
+                }
+                else if (N <= (std::numeric_limits<std::uint16_t>::max)())
+                {
+                    // map 16
+                    oa->write_character(to_char_type(0xDE));
+                    write_number(static_cast<std::uint16_t>(N));
+                }
+                else if (N <= (std::numeric_limits<std::uint32_t>::max)())
+                {
+                    // map 32
+                    oa->write_character(to_char_type(0xDF));
+                    write_number(static_cast<std::uint32_t>(N));
+                }
+
+                // step 2: write each element
+                for (const auto& el : *j.m_data.m_value.object)
+                {
+                    write_msgpack(el.first);
+                    write_msgpack(el.second);
+                }
+                break;
+            }
+
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+    /*!
+    @param[in] j  JSON value to serialize
+    @param[in] use_count   whether to use '#' prefixes (optimized format)
+    @param[in] use_type    whether to use '$' prefixes (optimized format)
+    @param[in] add_prefix  whether prefixes need to be used for this value
+    @param[in] use_bjdata  whether write in BJData format, default is false
+    @param[in] bjdata_version  which BJData version to use, default is draft2
+    */
+    void write_ubjson(const BasicJsonType& j, const bool use_count,
+                      const bool use_type, const bool add_prefix = true,
+                      const bool use_bjdata = false, const bjdata_version_t bjdata_version = bjdata_version_t::draft2)
+    {
+        const bool bjdata_draft3 = use_bjdata && bjdata_version == bjdata_version_t::draft3;
+
+        switch (j.type())
+        {
+            case value_t::null:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('Z'));
+                }
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(j.m_data.m_value.boolean
+                                        ? to_char_type('T')
+                                        : to_char_type('F'));
+                }
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                write_number_with_ubjson_prefix(j.m_data.m_value.number_integer, add_prefix, use_bjdata);
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                write_number_with_ubjson_prefix(j.m_data.m_value.number_unsigned, add_prefix, use_bjdata);
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                write_number_with_ubjson_prefix(j.m_data.m_value.number_float, add_prefix, use_bjdata);
+                break;
+            }
+
+            case value_t::string:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('S'));
+                }
+                write_number_with_ubjson_prefix(j.m_data.m_value.string->size(), true, use_bjdata);
+                oa->write_characters(
+                    reinterpret_cast<const CharType*>(j.m_data.m_value.string->c_str()),
+                    j.m_data.m_value.string->size());
+                break;
+            }
+
+            case value_t::array:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('['));
+                }
+
+                bool prefix_required = true;
+                if (use_type && !j.m_data.m_value.array->empty())
+                {
+                    JSON_ASSERT(use_count);
+                    const CharType first_prefix = ubjson_prefix(j.front(), use_bjdata);
+                    const bool same_prefix = std::all_of(j.begin() + 1, j.end(),
+                                                         [this, first_prefix, use_bjdata](const BasicJsonType & v)
+                    {
+                        return ubjson_prefix(v, use_bjdata) == first_prefix;
+                    });
+
+                    std::vector<CharType> bjdx = {'[', '{', 'S', 'H', 'T', 'F', 'N', 'Z'}; // excluded markers in bjdata optimized type
+
+                    if (same_prefix && !(use_bjdata && std::find(bjdx.begin(), bjdx.end(), first_prefix) != bjdx.end()))
+                    {
+                        prefix_required = false;
+                        oa->write_character(to_char_type('$'));
+                        oa->write_character(first_prefix);
+                    }
+                }
+
+                if (use_count)
+                {
+                    oa->write_character(to_char_type('#'));
+                    write_number_with_ubjson_prefix(j.m_data.m_value.array->size(), true, use_bjdata);
+                }
+
+                for (const auto& el : *j.m_data.m_value.array)
+                {
+                    write_ubjson(el, use_count, use_type, prefix_required, use_bjdata, bjdata_version);
+                }
+
+                if (!use_count)
+                {
+                    oa->write_character(to_char_type(']'));
+                }
+
+                break;
+            }
+
+            case value_t::binary:
+            {
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('['));
+                }
+
+                if (use_type && (bjdata_draft3 || !j.m_data.m_value.binary->empty()))
+                {
+                    JSON_ASSERT(use_count);
+                    oa->write_character(to_char_type('$'));
+                    oa->write_character(bjdata_draft3 ? 'B' : 'U');
+                }
+
+                if (use_count)
+                {
+                    oa->write_character(to_char_type('#'));
+                    write_number_with_ubjson_prefix(j.m_data.m_value.binary->size(), true, use_bjdata);
+                }
+
+                if (use_type)
+                {
+                    oa->write_characters(
+                        reinterpret_cast<const CharType*>(j.m_data.m_value.binary->data()),
+                        j.m_data.m_value.binary->size());
+                }
+                else
+                {
+                    for (size_t i = 0; i < j.m_data.m_value.binary->size(); ++i)
+                    {
+                        oa->write_character(to_char_type(bjdata_draft3 ? 'B' : 'U'));
+                        oa->write_character(j.m_data.m_value.binary->data()[i]);
+                    }
+                }
+
+                if (!use_count)
+                {
+                    oa->write_character(to_char_type(']'));
+                }
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                if (use_bjdata && j.m_data.m_value.object->size() == 3 && j.m_data.m_value.object->find("_ArrayType_") != j.m_data.m_value.object->end() && j.m_data.m_value.object->find("_ArraySize_") != j.m_data.m_value.object->end() && j.m_data.m_value.object->find("_ArrayData_") != j.m_data.m_value.object->end())
+                {
+                    if (!write_bjdata_ndarray(*j.m_data.m_value.object, use_count, use_type, bjdata_version))  // decode bjdata ndarray in the JData format (https://github.com/NeuroJSON/jdata)
+                    {
+                        break;
+                    }
+                }
+
+                if (add_prefix)
+                {
+                    oa->write_character(to_char_type('{'));
+                }
+
+                bool prefix_required = true;
+                if (use_type && !j.m_data.m_value.object->empty())
+                {
+                    JSON_ASSERT(use_count);
+                    const CharType first_prefix = ubjson_prefix(j.front(), use_bjdata);
+                    const bool same_prefix = std::all_of(j.begin(), j.end(),
+                                                         [this, first_prefix, use_bjdata](const BasicJsonType & v)
+                    {
+                        return ubjson_prefix(v, use_bjdata) == first_prefix;
+                    });
+
+                    std::vector<CharType> bjdx = {'[', '{', 'S', 'H', 'T', 'F', 'N', 'Z'}; // excluded markers in bjdata optimized type
+
+                    if (same_prefix && !(use_bjdata && std::find(bjdx.begin(), bjdx.end(), first_prefix) != bjdx.end()))
+                    {
+                        prefix_required = false;
+                        oa->write_character(to_char_type('$'));
+                        oa->write_character(first_prefix);
+                    }
+                }
+
+                if (use_count)
+                {
+                    oa->write_character(to_char_type('#'));
+                    write_number_with_ubjson_prefix(j.m_data.m_value.object->size(), true, use_bjdata);
+                }
+
+                for (const auto& el : *j.m_data.m_value.object)
+                {
+                    write_number_with_ubjson_prefix(el.first.size(), true, use_bjdata);
+                    oa->write_characters(
+                        reinterpret_cast<const CharType*>(el.first.c_str()),
+                        el.first.size());
+                    write_ubjson(el.second, use_count, use_type, prefix_required, use_bjdata, bjdata_version);
+                }
+
+                if (!use_count)
+                {
+                    oa->write_character(to_char_type('}'));
+                }
+
+                break;
+            }
+
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+  private:
+    //////////
+    // BSON //
+    //////////
+
+    /*!
+    @return The size of a BSON document entry header, including the id marker
+            and the entry name size (and its null-terminator).
+    */
+    static std::size_t calc_bson_entry_header_size(const string_t& name, const BasicJsonType& j)
+    {
+        const auto it = name.find(static_cast<typename string_t::value_type>(0));
+        if (JSON_HEDLEY_UNLIKELY(it != BasicJsonType::string_t::npos))
+        {
+            JSON_THROW(out_of_range::create(409, concat("BSON key cannot contain code point U+0000 (at byte ", std::to_string(it), ")"), &j));
+            static_cast<void>(j);
+        }
+
+        return /*id*/ 1ul + name.size() + /*zero-terminator*/1u;
+    }
+
+    /*!
+    @brief Writes the given @a element_type and @a name to the output adapter
+    */
+    void write_bson_entry_header(const string_t& name,
+                                 const std::uint8_t element_type)
+    {
+        oa->write_character(to_char_type(element_type)); // boolean
+        oa->write_characters(
+            reinterpret_cast<const CharType*>(name.c_str()),
+            name.size() + 1u);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and boolean value @a value
+    */
+    void write_bson_boolean(const string_t& name,
+                            const bool value)
+    {
+        write_bson_entry_header(name, 0x08);
+        oa->write_character(value ? to_char_type(0x01) : to_char_type(0x00));
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and double value @a value
+    */
+    void write_bson_double(const string_t& name,
+                           const double value)
+    {
+        write_bson_entry_header(name, 0x01);
+        write_number<double>(value, true);
+    }
+
+    /*!
+    @return The size of the BSON-encoded string in @a value
+    */
+    static std::size_t calc_bson_string_size(const string_t& value)
+    {
+        return sizeof(std::int32_t) + value.size() + 1ul;
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and string value @a value
+    */
+    void write_bson_string(const string_t& name,
+                           const string_t& value)
+    {
+        write_bson_entry_header(name, 0x02);
+
+        write_number<std::int32_t>(static_cast<std::int32_t>(value.size() + 1ul), true);
+        oa->write_characters(
+            reinterpret_cast<const CharType*>(value.c_str()),
+            value.size() + 1);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and null value
+    */
+    void write_bson_null(const string_t& name)
+    {
+        write_bson_entry_header(name, 0x0A);
+    }
+
+    /*!
+    @return The size of the BSON-encoded integer @a value
+    */
+    static std::size_t calc_bson_integer_size(const std::int64_t value)
+    {
+        return (std::numeric_limits<std::int32_t>::min)() <= value && value <= (std::numeric_limits<std::int32_t>::max)()
+               ? sizeof(std::int32_t)
+               : sizeof(std::int64_t);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and integer @a value
+    */
+    void write_bson_integer(const string_t& name,
+                            const std::int64_t value)
+    {
+        if ((std::numeric_limits<std::int32_t>::min)() <= value && value <= (std::numeric_limits<std::int32_t>::max)())
+        {
+            write_bson_entry_header(name, 0x10); // int32
+            write_number<std::int32_t>(static_cast<std::int32_t>(value), true);
+        }
+        else
+        {
+            write_bson_entry_header(name, 0x12); // int64
+            write_number<std::int64_t>(static_cast<std::int64_t>(value), true);
+        }
+    }
+
+    /*!
+    @return The size of the BSON-encoded unsigned integer in @a j
+    */
+    static constexpr std::size_t calc_bson_unsigned_size(const std::uint64_t value) noexcept
+    {
+        return (value <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+               ? sizeof(std::int32_t)
+               : sizeof(std::int64_t);
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and unsigned @a value
+    */
+    void write_bson_unsigned(const string_t& name,
+                             const BasicJsonType& j)
+    {
+        if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+        {
+            write_bson_entry_header(name, 0x10 /* int32 */);
+            write_number<std::int32_t>(static_cast<std::int32_t>(j.m_data.m_value.number_unsigned), true);
+        }
+        else if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))
+        {
+            write_bson_entry_header(name, 0x12 /* int64 */);
+            write_number<std::int64_t>(static_cast<std::int64_t>(j.m_data.m_value.number_unsigned), true);
+        }
+        else
+        {
+            write_bson_entry_header(name, 0x11 /* uint64 */);
+            write_number<std::uint64_t>(static_cast<std::uint64_t>(j.m_data.m_value.number_unsigned), true);
+        }
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and object @a value
+    */
+    void write_bson_object_entry(const string_t& name,
+                                 const typename BasicJsonType::object_t& value)
+    {
+        write_bson_entry_header(name, 0x03); // object
+        write_bson_object(value);
+    }
+
+    /*!
+    @return The size of the BSON-encoded array @a value
+    */
+    static std::size_t calc_bson_array_size(const typename BasicJsonType::array_t& value)
+    {
+        std::size_t array_index = 0ul;
+
+        const std::size_t embedded_document_size = std::accumulate(std::begin(value), std::end(value), static_cast<std::size_t>(0), [&array_index](std::size_t result, const typename BasicJsonType::array_t::value_type & el)
+        {
+            return result + calc_bson_element_size(std::to_string(array_index++), el);
+        });
+
+        return sizeof(std::int32_t) + embedded_document_size + 1ul;
+    }
+
+    /*!
+    @return The size of the BSON-encoded binary array @a value
+    */
+    static std::size_t calc_bson_binary_size(const typename BasicJsonType::binary_t& value)
+    {
+        return sizeof(std::int32_t) + value.size() + 1ul;
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and array @a value
+    */
+    void write_bson_array(const string_t& name,
+                          const typename BasicJsonType::array_t& value)
+    {
+        write_bson_entry_header(name, 0x04); // array
+        write_number<std::int32_t>(static_cast<std::int32_t>(calc_bson_array_size(value)), true);
+
+        std::size_t array_index = 0ul;
+
+        for (const auto& el : value)
+        {
+            write_bson_element(std::to_string(array_index++), el);
+        }
+
+        oa->write_character(to_char_type(0x00));
+    }
+
+    /*!
+    @brief Writes a BSON element with key @a name and binary value @a value
+    */
+    void write_bson_binary(const string_t& name,
+                           const binary_t& value)
+    {
+        write_bson_entry_header(name, 0x05);
+
+        write_number<std::int32_t>(static_cast<std::int32_t>(value.size()), true);
+        write_number(value.has_subtype() ? static_cast<std::uint8_t>(value.subtype()) : static_cast<std::uint8_t>(0x00));
+
+        oa->write_characters(reinterpret_cast<const CharType*>(value.data()), value.size());
+    }
+
+    /*!
+    @brief Calculates the size necessary to serialize the JSON value @a j with its @a name
+    @return The calculated size for the BSON document entry for @a j with the given @a name.
+    */
+    static std::size_t calc_bson_element_size(const string_t& name,
+            const BasicJsonType& j)
+    {
+        const auto header_size = calc_bson_entry_header_size(name, j);
+        switch (j.type())
+        {
+            case value_t::object:
+                return header_size + calc_bson_object_size(*j.m_data.m_value.object);
+
+            case value_t::array:
+                return header_size + calc_bson_array_size(*j.m_data.m_value.array);
+
+            case value_t::binary:
+                return header_size + calc_bson_binary_size(*j.m_data.m_value.binary);
+
+            case value_t::boolean:
+                return header_size + 1ul;
+
+            case value_t::number_float:
+                return header_size + 8ul;
+
+            case value_t::number_integer:
+                return header_size + calc_bson_integer_size(j.m_data.m_value.number_integer);
+
+            case value_t::number_unsigned:
+                return header_size + calc_bson_unsigned_size(j.m_data.m_value.number_unsigned);
+
+            case value_t::string:
+                return header_size + calc_bson_string_size(*j.m_data.m_value.string);
+
+            case value_t::null:
+                return header_size + 0ul;
+
+            // LCOV_EXCL_START
+            case value_t::discarded:
+            default:
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
+                return 0ul;
+                // LCOV_EXCL_STOP
+        }
+    }
+
+    /*!
+    @brief Serializes the JSON value @a j to BSON and associates it with the
+           key @a name.
+    @param name The name to associate with the JSON entity @a j within the
+                current BSON document
+    */
+    void write_bson_element(const string_t& name,
+                            const BasicJsonType& j)
+    {
+        switch (j.type())
+        {
+            case value_t::object:
+                return write_bson_object_entry(name, *j.m_data.m_value.object);
+
+            case value_t::array:
+                return write_bson_array(name, *j.m_data.m_value.array);
+
+            case value_t::binary:
+                return write_bson_binary(name, *j.m_data.m_value.binary);
+
+            case value_t::boolean:
+                return write_bson_boolean(name, j.m_data.m_value.boolean);
+
+            case value_t::number_float:
+                return write_bson_double(name, j.m_data.m_value.number_float);
+
+            case value_t::number_integer:
+                return write_bson_integer(name, j.m_data.m_value.number_integer);
+
+            case value_t::number_unsigned:
+                return write_bson_unsigned(name, j);
+
+            case value_t::string:
+                return write_bson_string(name, *j.m_data.m_value.string);
+
+            case value_t::null:
+                return write_bson_null(name);
+
+            // LCOV_EXCL_START
+            case value_t::discarded:
+            default:
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert)
+                return;
+                // LCOV_EXCL_STOP
+        }
+    }
+
+    /*!
+    @brief Calculates the size of the BSON serialization of the given
+           JSON-object @a j.
+    @param[in] value  JSON value to serialize
+    @pre       value.type() == value_t::object
+    */
+    static std::size_t calc_bson_object_size(const typename BasicJsonType::object_t& value)
+    {
+        const std::size_t document_size = std::accumulate(value.begin(), value.end(), static_cast<std::size_t>(0),
+                                          [](size_t result, const typename BasicJsonType::object_t::value_type & el)
+        {
+            return result += calc_bson_element_size(el.first, el.second);
+        });
+
+        return sizeof(std::int32_t) + document_size + 1ul;
+    }
+
+    /*!
+    @param[in] value  JSON value to serialize
+    @pre       value.type() == value_t::object
+    */
+    void write_bson_object(const typename BasicJsonType::object_t& value)
+    {
+        write_number<std::int32_t>(static_cast<std::int32_t>(calc_bson_object_size(value)), true);
+
+        for (const auto& el : value)
+        {
+            write_bson_element(el.first, el.second);
+        }
+
+        oa->write_character(to_char_type(0x00));
+    }
+
+    //////////
+    // CBOR //
+    //////////
+
+    static constexpr CharType get_cbor_float_prefix(float /*unused*/)
+    {
+        return to_char_type(0xFA);  // Single-Precision Float
+    }
+
+    static constexpr CharType get_cbor_float_prefix(double /*unused*/)
+    {
+        return to_char_type(0xFB);  // Double-Precision Float
+    }
+
+    /////////////
+    // MsgPack //
+    /////////////
+
+    static constexpr CharType get_msgpack_float_prefix(float /*unused*/)
+    {
+        return to_char_type(0xCA);  // float 32
+    }
+
+    static constexpr CharType get_msgpack_float_prefix(double /*unused*/)
+    {
+        return to_char_type(0xCB);  // float 64
+    }
+
+    ////////////
+    // UBJSON //
+    ////////////
+
+    // UBJSON: write number (floating point)
+    template<typename NumberType, typename std::enable_if<
+                 std::is_floating_point<NumberType>::value, int>::type = 0>
+    void write_number_with_ubjson_prefix(const NumberType n,
+                                         const bool add_prefix,
+                                         const bool use_bjdata)
+    {
+        if (add_prefix)
+        {
+            oa->write_character(get_ubjson_float_prefix(n));
+        }
+        write_number(n, use_bjdata);
+    }
+
+    // UBJSON: write number (unsigned integer)
+    template<typename NumberType, typename std::enable_if<
+                 std::is_unsigned<NumberType>::value, int>::type = 0>
+    void write_number_with_ubjson_prefix(const NumberType n,
+                                         const bool add_prefix,
+                                         const bool use_bjdata)
+    {
+        if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int8_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('i'));  // int8
+            }
+            write_number(static_cast<std::uint8_t>(n), use_bjdata);
+        }
+        else if (n <= (std::numeric_limits<std::uint8_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('U'));  // uint8
+            }
+            write_number(static_cast<std::uint8_t>(n), use_bjdata);
+        }
+        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int16_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('I'));  // int16
+            }
+            write_number(static_cast<std::int16_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && n <= static_cast<uint64_t>((std::numeric_limits<uint16_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('u'));  // uint16 - bjdata only
+            }
+            write_number(static_cast<std::uint16_t>(n), use_bjdata);
+        }
+        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('l'));  // int32
+            }
+            write_number(static_cast<std::int32_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && n <= static_cast<uint64_t>((std::numeric_limits<uint32_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('m'));  // uint32 - bjdata only
+            }
+            write_number(static_cast<std::uint32_t>(n), use_bjdata);
+        }
+        else if (n <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('L'));  // int64
+            }
+            write_number(static_cast<std::int64_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && n <= (std::numeric_limits<uint64_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('M'));  // uint64 - bjdata only
+            }
+            write_number(static_cast<std::uint64_t>(n), use_bjdata);
+        }
+        else
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('H'));  // high-precision number
+            }
+
+            const auto number = BasicJsonType(n).dump();
+            write_number_with_ubjson_prefix(number.size(), true, use_bjdata);
+            for (std::size_t i = 0; i < number.size(); ++i)
+            {
+                oa->write_character(to_char_type(static_cast<std::uint8_t>(number[i])));
+            }
+        }
+    }
+
+    // UBJSON: write number (signed integer)
+    template < typename NumberType, typename std::enable_if <
+                   std::is_signed<NumberType>::value&&
+                   !std::is_floating_point<NumberType>::value, int >::type = 0 >
+    void write_number_with_ubjson_prefix(const NumberType n,
+                                         const bool add_prefix,
+                                         const bool use_bjdata)
+    {
+        if ((std::numeric_limits<std::int8_t>::min)() <= n && n <= (std::numeric_limits<std::int8_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('i'));  // int8
+            }
+            write_number(static_cast<std::int8_t>(n), use_bjdata);
+        }
+        else if (static_cast<std::int64_t>((std::numeric_limits<std::uint8_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint8_t>::max)()))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('U'));  // uint8
+            }
+            write_number(static_cast<std::uint8_t>(n), use_bjdata);
+        }
+        else if ((std::numeric_limits<std::int16_t>::min)() <= n && n <= (std::numeric_limits<std::int16_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('I'));  // int16
+            }
+            write_number(static_cast<std::int16_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && (static_cast<std::int64_t>((std::numeric_limits<std::uint16_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint16_t>::max)())))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('u'));  // uint16 - bjdata only
+            }
+            write_number(static_cast<uint16_t>(n), use_bjdata);
+        }
+        else if ((std::numeric_limits<std::int32_t>::min)() <= n && n <= (std::numeric_limits<std::int32_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('l'));  // int32
+            }
+            write_number(static_cast<std::int32_t>(n), use_bjdata);
+        }
+        else if (use_bjdata && (static_cast<std::int64_t>((std::numeric_limits<std::uint32_t>::min)()) <= n && n <= static_cast<std::int64_t>((std::numeric_limits<std::uint32_t>::max)())))
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('m'));  // uint32 - bjdata only
+            }
+            write_number(static_cast<uint32_t>(n), use_bjdata);
+        }
+        else if ((std::numeric_limits<std::int64_t>::min)() <= n && n <= (std::numeric_limits<std::int64_t>::max)())
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('L'));  // int64
+            }
+            write_number(static_cast<std::int64_t>(n), use_bjdata);
+        }
+        // LCOV_EXCL_START
+        else
+        {
+            if (add_prefix)
+            {
+                oa->write_character(to_char_type('H'));  // high-precision number
+            }
+
+            const auto number = BasicJsonType(n).dump();
+            write_number_with_ubjson_prefix(number.size(), true, use_bjdata);
+            for (std::size_t i = 0; i < number.size(); ++i)
+            {
+                oa->write_character(to_char_type(static_cast<std::uint8_t>(number[i])));
+            }
+        }
+        // LCOV_EXCL_STOP
+    }
+
+    /*!
+    @brief determine the type prefix of container values
+    */
+    CharType ubjson_prefix(const BasicJsonType& j, const bool use_bjdata) const noexcept
+    {
+        switch (j.type())
+        {
+            case value_t::null:
+                return 'Z';
+
+            case value_t::boolean:
+                return j.m_data.m_value.boolean ? 'T' : 'F';
+
+            case value_t::number_integer:
+            {
+                if ((std::numeric_limits<std::int8_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int8_t>::max)())
+                {
+                    return 'i';
+                }
+                if ((std::numeric_limits<std::uint8_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint8_t>::max)())
+                {
+                    return 'U';
+                }
+                if ((std::numeric_limits<std::int16_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int16_t>::max)())
+                {
+                    return 'I';
+                }
+                if (use_bjdata && ((std::numeric_limits<std::uint16_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint16_t>::max)()))
+                {
+                    return 'u';
+                }
+                if ((std::numeric_limits<std::int32_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int32_t>::max)())
+                {
+                    return 'l';
+                }
+                if (use_bjdata && ((std::numeric_limits<std::uint32_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::uint32_t>::max)()))
+                {
+                    return 'm';
+                }
+                if ((std::numeric_limits<std::int64_t>::min)() <= j.m_data.m_value.number_integer && j.m_data.m_value.number_integer <= (std::numeric_limits<std::int64_t>::max)())
+                {
+                    return 'L';
+                }
+                // anything else is treated as high-precision number
+                return 'H'; // LCOV_EXCL_LINE
+            }
+
+            case value_t::number_unsigned:
+            {
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int8_t>::max)()))
+                {
+                    return 'i';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint8_t>::max)()))
+                {
+                    return 'U';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int16_t>::max)()))
+                {
+                    return 'I';
+                }
+                if (use_bjdata && j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint16_t>::max)()))
+                {
+                    return 'u';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int32_t>::max)()))
+                {
+                    return 'l';
+                }
+                if (use_bjdata && j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::uint32_t>::max)()))
+                {
+                    return 'm';
+                }
+                if (j.m_data.m_value.number_unsigned <= static_cast<std::uint64_t>((std::numeric_limits<std::int64_t>::max)()))
+                {
+                    return 'L';
+                }
+                if (use_bjdata && j.m_data.m_value.number_unsigned <= (std::numeric_limits<std::uint64_t>::max)())
+                {
+                    return 'M';
+                }
+                // anything else is treated as high-precision number
+                return 'H'; // LCOV_EXCL_LINE
+            }
+
+            case value_t::number_float:
+                return get_ubjson_float_prefix(j.m_data.m_value.number_float);
+
+            case value_t::string:
+                return 'S';
+
+            case value_t::array: // fallthrough
+            case value_t::binary:
+                return '[';
+
+            case value_t::object:
+                return '{';
+
+            case value_t::discarded:
+            default:  // discarded values
+                return 'N';
+        }
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(float /*unused*/)
+    {
+        return 'd';  // float 32
+    }
+
+    static constexpr CharType get_ubjson_float_prefix(double /*unused*/)
+    {
+        return 'D';  // float 64
+    }
+
+    /*!
+    @return false if the object is successfully converted to a bjdata ndarray, true if the type or size is invalid
+    */
+    bool write_bjdata_ndarray(const typename BasicJsonType::object_t& value, const bool use_count, const bool use_type, const bjdata_version_t bjdata_version)
+    {
+        std::map<string_t, CharType> bjdtype = {{"uint8", 'U'},  {"int8", 'i'},  {"uint16", 'u'}, {"int16", 'I'},
+            {"uint32", 'm'}, {"int32", 'l'}, {"uint64", 'M'}, {"int64", 'L'}, {"single", 'd'}, {"double", 'D'},
+            {"char", 'C'}, {"byte", 'B'}
+        };
+
+        string_t key = "_ArrayType_";
+        auto it = bjdtype.find(static_cast<string_t>(value.at(key)));
+        if (it == bjdtype.end())
+        {
+            return true;
+        }
+        CharType dtype = it->second;
+
+        key = "_ArraySize_";
+        std::size_t len = (value.at(key).empty() ? 0 : 1);
+        for (const auto& el : value.at(key))
+        {
+            len *= static_cast<std::size_t>(el.m_data.m_value.number_unsigned);
+        }
+
+        key = "_ArrayData_";
+        if (value.at(key).size() != len)
+        {
+            return true;
+        }
+
+        oa->write_character('[');
+        oa->write_character('$');
+        oa->write_character(dtype);
+        oa->write_character('#');
+
+        key = "_ArraySize_";
+        write_ubjson(value.at(key), use_count, use_type, true,  true, bjdata_version);
+
+        key = "_ArrayData_";
+        if (dtype == 'U' || dtype == 'C' || dtype == 'B')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint8_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'i')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int8_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'u')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint16_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'I')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int16_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'm')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint32_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'l')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int32_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'M')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::uint64_t>(el.m_data.m_value.number_unsigned), true);
+            }
+        }
+        else if (dtype == 'L')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<std::int64_t>(el.m_data.m_value.number_integer), true);
+            }
+        }
+        else if (dtype == 'd')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<float>(el.m_data.m_value.number_float), true);
+            }
+        }
+        else if (dtype == 'D')
+        {
+            for (const auto& el : value.at(key))
+            {
+                write_number(static_cast<double>(el.m_data.m_value.number_float), true);
+            }
+        }
+        return false;
+    }
+
+    ///////////////////////
+    // Utility functions //
+    ///////////////////////
+
+    /*
+    @brief write a number to output input
+    @param[in] n number of type @a NumberType
+    @param[in] OutputIsLittleEndian Set to true if output data is
+                                 required to be little endian
+    @tparam NumberType the type of the number
+
+    @note This function needs to respect the system's endianness, because bytes
+          in CBOR, MessagePack, and UBJSON are stored in network order (big
+          endian) and therefore need reordering on little endian systems.
+          On the other hand, BSON and BJData use little endian and should reorder
+          on big endian systems.
+    */
+    template<typename NumberType>
+    void write_number(const NumberType n, const bool OutputIsLittleEndian = false)
+    {
+        // step 1: write number to array of length NumberType
+        std::array<CharType, sizeof(NumberType)> vec{};
+        std::memcpy(vec.data(), &n, sizeof(NumberType));
+
+        // step 2: write array to output (with possible reordering)
+        if (is_little_endian != OutputIsLittleEndian)
+        {
+            // reverse byte order prior to conversion if necessary
+            std::reverse(vec.begin(), vec.end());
+        }
+
+        oa->write_characters(vec.data(), sizeof(NumberType));
+    }
+
+    void write_compact_float(const number_float_t n, detail::input_format_t format)
+    {
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+        if (static_cast<double>(n) >= static_cast<double>(std::numeric_limits<float>::lowest()) &&
+                static_cast<double>(n) <= static_cast<double>((std::numeric_limits<float>::max)()) &&
+                static_cast<double>(static_cast<float>(n)) == static_cast<double>(n))
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(static_cast<float>(n))
+                                : get_msgpack_float_prefix(static_cast<float>(n)));
+            write_number(static_cast<float>(n));
+        }
+        else
+        {
+            oa->write_character(format == detail::input_format_t::cbor
+                                ? get_cbor_float_prefix(n)
+                                : get_msgpack_float_prefix(n));
+            write_number(n);
+        }
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+    }
+
+  public:
+    // The following to_char_type functions are implement the conversion
+    // between uint8_t and CharType. In case CharType is not unsigned,
+    // such a conversion is required to allow values greater than 128.
+    // See <https://github.com/nlohmann/json/issues/1286> for a discussion.
+    template < typename C = CharType,
+               enable_if_t < std::is_signed<C>::value && std::is_signed<char>::value > * = nullptr >
+    static constexpr CharType to_char_type(std::uint8_t x) noexcept
+    {
+        return *reinterpret_cast<char*>(&x);
+    }
+
+    template < typename C = CharType,
+               enable_if_t < std::is_signed<C>::value && std::is_unsigned<char>::value > * = nullptr >
+    static CharType to_char_type(std::uint8_t x) noexcept
+    {
+        static_assert(sizeof(std::uint8_t) == sizeof(CharType), "size of CharType must be equal to std::uint8_t");
+        static_assert(std::is_trivial<CharType>::value, "CharType must be trivial");
+        CharType result;
+        std::memcpy(&result, &x, sizeof(x));
+        return result;
+    }
+
+    template<typename C = CharType,
+             enable_if_t<std::is_unsigned<C>::value>* = nullptr>
+    static constexpr CharType to_char_type(std::uint8_t x) noexcept
+    {
+        return x;
+    }
+
+    template < typename InputCharType, typename C = CharType,
+               enable_if_t <
+                   std::is_signed<C>::value &&
+                   std::is_signed<char>::value &&
+                   std::is_same<char, typename std::remove_cv<InputCharType>::type>::value
+                   > * = nullptr >
+    static constexpr CharType to_char_type(InputCharType x) noexcept
+    {
+        return x;
+    }
+
+  private:
+    /// whether we can assume little endianness
+    const bool is_little_endian = little_endianness();
+
+    /// the output
+    output_adapter_t<CharType> oa = nullptr;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/output/output_adapters.hpp>
+
+// #include <nlohmann/detail/output/serializer.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2008 - 2009 Björn Hoehrmann <bjoern@hoehrmann.de>
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <algorithm> // reverse, remove, fill, find, none_of
+#include <array> // array
+#include <clocale> // localeconv, lconv
+#include <cmath> // labs, isfinite, isnan, signbit
+#include <cstddef> // size_t, ptrdiff_t
+#include <cstdint> // uint8_t
+#include <cstdio> // snprintf
+#include <limits> // numeric_limits
+#include <string> // string, char_traits
+#include <iomanip> // setfill, setw
+#include <type_traits> // is_same
+#include <utility> // move
+
+// #include <nlohmann/detail/conversions/to_chars.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2009 Florian Loitsch <https://florian.loitsch.com/>
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <array> // array
+#include <cmath>   // signbit, isfinite
+#include <cstdint> // intN_t, uintN_t
+#include <cstring> // memcpy, memmove
+#include <limits> // numeric_limits
+#include <type_traits> // conditional
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+/*!
+@brief implements the Grisu2 algorithm for binary to decimal floating-point
+conversion.
+
+This implementation is a slightly modified version of the reference
+implementation which may be obtained from
+http://florian.loitsch.com/publications (bench.tar.gz).
+
+The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch.
+
+For a detailed description of the algorithm see:
+
+[1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with
+    Integers", Proceedings of the ACM SIGPLAN 2010 Conference on Programming
+    Language Design and Implementation, PLDI 2010
+[2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately",
+    Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language
+    Design and Implementation, PLDI 1996
+*/
+namespace dtoa_impl
+{
+
+template<typename Target, typename Source>
+Target reinterpret_bits(const Source source)
+{
+    static_assert(sizeof(Target) == sizeof(Source), "size mismatch");
+
+    Target target;
+    std::memcpy(&target, &source, sizeof(Source));
+    return target;
+}
+
+struct diyfp // f * 2^e
+{
+    static constexpr int kPrecision = 64; // = q
+
+    std::uint64_t f = 0;
+    int e = 0;
+
+    constexpr diyfp(std::uint64_t f_, int e_) noexcept : f(f_), e(e_) {}
+
+    /*!
+    @brief returns x - y
+    @pre x.e == y.e and x.f >= y.f
+    */
+    static diyfp sub(const diyfp& x, const diyfp& y) noexcept
+    {
+        JSON_ASSERT(x.e == y.e);
+        JSON_ASSERT(x.f >= y.f);
+
+        return {x.f - y.f, x.e};
+    }
+
+    /*!
+    @brief returns x * y
+    @note The result is rounded. (Only the upper q bits are returned.)
+    */
+    static diyfp mul(const diyfp& x, const diyfp& y) noexcept
+    {
+        static_assert(kPrecision == 64, "internal error");
+
+        // Computes:
+        //  f = round((x.f * y.f) / 2^q)
+        //  e = x.e + y.e + q
+
+        // Emulate the 64-bit * 64-bit multiplication:
+        //
+        // p = u * v
+        //   = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi)
+        //   = (u_lo v_lo         ) + 2^32 ((u_lo v_hi         ) + (u_hi v_lo         )) + 2^64 (u_hi v_hi         )
+        //   = (p0                ) + 2^32 ((p1                ) + (p2                )) + 2^64 (p3                )
+        //   = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3                )
+        //   = (p0_lo             ) + 2^32 (p0_hi + p1_lo + p2_lo                      ) + 2^64 (p1_hi + p2_hi + p3)
+        //   = (p0_lo             ) + 2^32 (Q                                          ) + 2^64 (H                 )
+        //   = (p0_lo             ) + 2^32 (Q_lo + 2^32 Q_hi                           ) + 2^64 (H                 )
+        //
+        // (Since Q might be larger than 2^32 - 1)
+        //
+        //   = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H)
+        //
+        // (Q_hi + H does not overflow a 64-bit int)
+        //
+        //   = p_lo + 2^64 p_hi
+
+        const std::uint64_t u_lo = x.f & 0xFFFFFFFFu;
+        const std::uint64_t u_hi = x.f >> 32u;
+        const std::uint64_t v_lo = y.f & 0xFFFFFFFFu;
+        const std::uint64_t v_hi = y.f >> 32u;
+
+        const std::uint64_t p0 = u_lo * v_lo;
+        const std::uint64_t p1 = u_lo * v_hi;
+        const std::uint64_t p2 = u_hi * v_lo;
+        const std::uint64_t p3 = u_hi * v_hi;
+
+        const std::uint64_t p0_hi = p0 >> 32u;
+        const std::uint64_t p1_lo = p1 & 0xFFFFFFFFu;
+        const std::uint64_t p1_hi = p1 >> 32u;
+        const std::uint64_t p2_lo = p2 & 0xFFFFFFFFu;
+        const std::uint64_t p2_hi = p2 >> 32u;
+
+        std::uint64_t Q = p0_hi + p1_lo + p2_lo;
+
+        // The full product might now be computed as
+        //
+        // p_hi = p3 + p2_hi + p1_hi + (Q >> 32)
+        // p_lo = p0_lo + (Q << 32)
+        //
+        // But in this particular case here, the full p_lo is not required.
+        // Effectively we only need to add the highest bit in p_lo to p_hi (and
+        // Q_hi + 1 does not overflow).
+
+        Q += std::uint64_t{1} << (64u - 32u - 1u); // round, ties up
+
+        const std::uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32u);
+
+        return {h, x.e + y.e + 64};
+    }
+
+    /*!
+    @brief normalize x such that the significand is >= 2^(q-1)
+    @pre x.f != 0
+    */
+    static diyfp normalize(diyfp x) noexcept
+    {
+        JSON_ASSERT(x.f != 0);
+
+        while ((x.f >> 63u) == 0)
+        {
+            x.f <<= 1u;
+            x.e--;
+        }
+
+        return x;
+    }
+
+    /*!
+    @brief normalize x such that the result has the exponent E
+    @pre e >= x.e and the upper e - x.e bits of x.f must be zero.
+    */
+    static diyfp normalize_to(const diyfp& x, const int target_exponent) noexcept
+    {
+        const int delta = x.e - target_exponent;
+
+        JSON_ASSERT(delta >= 0);
+        JSON_ASSERT(((x.f << delta) >> delta) == x.f);
+
+        return {x.f << delta, target_exponent};
+    }
+};
+
+struct boundaries
+{
+    diyfp w;
+    diyfp minus;
+    diyfp plus;
+};
+
+/*!
+Compute the (normalized) diyfp representing the input number 'value' and its
+boundaries.
+
+@pre value must be finite and positive
+*/
+template<typename FloatType>
+boundaries compute_boundaries(FloatType value)
+{
+    JSON_ASSERT(std::isfinite(value));
+    JSON_ASSERT(value > 0);
+
+    // Convert the IEEE representation into a diyfp.
+    //
+    // If v is denormal:
+    //      value = 0.F * 2^(1 - bias) = (          F) * 2^(1 - bias - (p-1))
+    // If v is normalized:
+    //      value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1))
+
+    static_assert(std::numeric_limits<FloatType>::is_iec559,
+                  "internal error: dtoa_short requires an IEEE-754 floating-point implementation");
+
+    constexpr int      kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit)
+    constexpr int      kBias      = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1);
+    constexpr int      kMinExp    = 1 - kBias;
+    constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1)
+
+    using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t >::type;
+
+    const auto bits = static_cast<std::uint64_t>(reinterpret_bits<bits_type>(value));
+    const std::uint64_t E = bits >> (kPrecision - 1);
+    const std::uint64_t F = bits & (kHiddenBit - 1);
+
+    const bool is_denormal = E == 0;
+    const diyfp v = is_denormal
+                    ? diyfp(F, kMinExp)
+                    : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias);
+
+    // Compute the boundaries m- and m+ of the floating-point value
+    // v = f * 2^e.
+    //
+    // Determine v- and v+, the floating-point predecessor and successor if v,
+    // respectively.
+    //
+    //      v- = v - 2^e        if f != 2^(p-1) or e == e_min                (A)
+    //         = v - 2^(e-1)    if f == 2^(p-1) and e > e_min                (B)
+    //
+    //      v+ = v + 2^e
+    //
+    // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_
+    // between m- and m+ round to v, regardless of how the input rounding
+    // algorithm breaks ties.
+    //
+    //      ---+-------------+-------------+-------------+-------------+---  (A)
+    //         v-            m-            v             m+            v+
+    //
+    //      -----------------+------+------+-------------+-------------+---  (B)
+    //                       v-     m-     v             m+            v+
+
+    const bool lower_boundary_is_closer = F == 0 && E > 1;
+    const diyfp m_plus = diyfp((2 * v.f) + 1, v.e - 1);
+    const diyfp m_minus = lower_boundary_is_closer
+                          ? diyfp((4 * v.f) - 1, v.e - 2)  // (B)
+                          : diyfp((2 * v.f) - 1, v.e - 1); // (A)
+
+    // Determine the normalized w+ = m+.
+    const diyfp w_plus = diyfp::normalize(m_plus);
+
+    // Determine w- = m- such that e_(w-) = e_(w+).
+    const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e);
+
+    return {diyfp::normalize(v), w_minus, w_plus};
+}
+
+// Given normalized diyfp w, Grisu needs to find a (normalized) cached
+// power-of-ten c, such that the exponent of the product c * w = f * 2^e lies
+// within a certain range [alpha, gamma] (Definition 3.2 from [1])
+//
+//      alpha <= e = e_c + e_w + q <= gamma
+//
+// or
+//
+//      f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q
+//                          <= f_c * f_w * 2^gamma
+//
+// Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies
+//
+//      2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma
+//
+// or
+//
+//      2^(q - 2 + alpha) <= c * w < 2^(q + gamma)
+//
+// The choice of (alpha,gamma) determines the size of the table and the form of
+// the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well
+// in practice:
+//
+// The idea is to cut the number c * w = f * 2^e into two parts, which can be
+// processed independently: An integral part p1, and a fractional part p2:
+//
+//      f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e
+//              = (f div 2^-e) + (f mod 2^-e) * 2^e
+//              = p1 + p2 * 2^e
+//
+// The conversion of p1 into decimal form requires a series of divisions and
+// modulos by (a power of) 10. These operations are faster for 32-bit than for
+// 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be
+// achieved by choosing
+//
+//      -e >= 32   or   e <= -32 := gamma
+//
+// In order to convert the fractional part
+//
+//      p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ...
+//
+// into decimal form, the fraction is repeatedly multiplied by 10 and the digits
+// d[-i] are extracted in order:
+//
+//      (10 * p2) div 2^-e = d[-1]
+//      (10 * p2) mod 2^-e = d[-2] / 10^1 + ...
+//
+// The multiplication by 10 must not overflow. It is sufficient to choose
+//
+//      10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64.
+//
+// Since p2 = f mod 2^-e < 2^-e,
+//
+//      -e <= 60   or   e >= -60 := alpha
+
+constexpr int kAlpha = -60;
+constexpr int kGamma = -32;
+
+struct cached_power // c = f * 2^e ~= 10^k
+{
+    std::uint64_t f;
+    int e;
+    int k;
+};
+
+/*!
+For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached
+power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c
+satisfies (Definition 3.2 from [1])
+
+     alpha <= e_c + e + q <= gamma.
+*/
+inline cached_power get_cached_power_for_binary_exponent(int e)
+{
+    // Now
+    //
+    //      alpha <= e_c + e + q <= gamma                                    (1)
+    //      ==> f_c * 2^alpha <= c * 2^e * 2^q
+    //
+    // and since the c's are normalized, 2^(q-1) <= f_c,
+    //
+    //      ==> 2^(q - 1 + alpha) <= c * 2^(e + q)
+    //      ==> 2^(alpha - e - 1) <= c
+    //
+    // If c were an exact power of ten, i.e. c = 10^k, one may determine k as
+    //
+    //      k = ceil( log_10( 2^(alpha - e - 1) ) )
+    //        = ceil( (alpha - e - 1) * log_10(2) )
+    //
+    // From the paper:
+    // "In theory the result of the procedure could be wrong since c is rounded,
+    //  and the computation itself is approximated [...]. In practice, however,
+    //  this simple function is sufficient."
+    //
+    // For IEEE double precision floating-point numbers converted into
+    // normalized diyfp's w = f * 2^e, with q = 64,
+    //
+    //      e >= -1022      (min IEEE exponent)
+    //           -52        (p - 1)
+    //           -52        (p - 1, possibly normalize denormal IEEE numbers)
+    //           -11        (normalize the diyfp)
+    //         = -1137
+    //
+    // and
+    //
+    //      e <= +1023      (max IEEE exponent)
+    //           -52        (p - 1)
+    //           -11        (normalize the diyfp)
+    //         = 960
+    //
+    // This binary exponent range [-1137,960] results in a decimal exponent
+    // range [-307,324]. One does not need to store a cached power for each
+    // k in this range. For each such k it suffices to find a cached power
+    // such that the exponent of the product lies in [alpha,gamma].
+    // This implies that the difference of the decimal exponents of adjacent
+    // table entries must be less than or equal to
+    //
+    //      floor( (gamma - alpha) * log_10(2) ) = 8.
+    //
+    // (A smaller distance gamma-alpha would require a larger table.)
+
+    // NB:
+    // Actually this function returns c, such that -60 <= e_c + e + 64 <= -34.
+
+    constexpr int kCachedPowersMinDecExp = -300;
+    constexpr int kCachedPowersDecStep = 8;
+
+    static constexpr std::array<cached_power, 79> kCachedPowers =
+    {
+        {
+            { 0xAB70FE17C79AC6CA, -1060, -300 },
+            { 0xFF77B1FCBEBCDC4F, -1034, -292 },
+            { 0xBE5691EF416BD60C, -1007, -284 },
+            { 0x8DD01FAD907FFC3C,  -980, -276 },
+            { 0xD3515C2831559A83,  -954, -268 },
+            { 0x9D71AC8FADA6C9B5,  -927, -260 },
+            { 0xEA9C227723EE8BCB,  -901, -252 },
+            { 0xAECC49914078536D,  -874, -244 },
+            { 0x823C12795DB6CE57,  -847, -236 },
+            { 0xC21094364DFB5637,  -821, -228 },
+            { 0x9096EA6F3848984F,  -794, -220 },
+            { 0xD77485CB25823AC7,  -768, -212 },
+            { 0xA086CFCD97BF97F4,  -741, -204 },
+            { 0xEF340A98172AACE5,  -715, -196 },
+            { 0xB23867FB2A35B28E,  -688, -188 },
+            { 0x84C8D4DFD2C63F3B,  -661, -180 },
+            { 0xC5DD44271AD3CDBA,  -635, -172 },
+            { 0x936B9FCEBB25C996,  -608, -164 },
+            { 0xDBAC6C247D62A584,  -582, -156 },
+            { 0xA3AB66580D5FDAF6,  -555, -148 },
+            { 0xF3E2F893DEC3F126,  -529, -140 },
+            { 0xB5B5ADA8AAFF80B8,  -502, -132 },
+            { 0x87625F056C7C4A8B,  -475, -124 },
+            { 0xC9BCFF6034C13053,  -449, -116 },
+            { 0x964E858C91BA2655,  -422, -108 },
+            { 0xDFF9772470297EBD,  -396, -100 },
+            { 0xA6DFBD9FB8E5B88F,  -369,  -92 },
+            { 0xF8A95FCF88747D94,  -343,  -84 },
+            { 0xB94470938FA89BCF,  -316,  -76 },
+            { 0x8A08F0F8BF0F156B,  -289,  -68 },
+            { 0xCDB02555653131B6,  -263,  -60 },
+            { 0x993FE2C6D07B7FAC,  -236,  -52 },
+            { 0xE45C10C42A2B3B06,  -210,  -44 },
+            { 0xAA242499697392D3,  -183,  -36 },
+            { 0xFD87B5F28300CA0E,  -157,  -28 },
+            { 0xBCE5086492111AEB,  -130,  -20 },
+            { 0x8CBCCC096F5088CC,  -103,  -12 },
+            { 0xD1B71758E219652C,   -77,   -4 },
+            { 0x9C40000000000000,   -50,    4 },
+            { 0xE8D4A51000000000,   -24,   12 },
+            { 0xAD78EBC5AC620000,     3,   20 },
+            { 0x813F3978F8940984,    30,   28 },
+            { 0xC097CE7BC90715B3,    56,   36 },
+            { 0x8F7E32CE7BEA5C70,    83,   44 },
+            { 0xD5D238A4ABE98068,   109,   52 },
+            { 0x9F4F2726179A2245,   136,   60 },
+            { 0xED63A231D4C4FB27,   162,   68 },
+            { 0xB0DE65388CC8ADA8,   189,   76 },
+            { 0x83C7088E1AAB65DB,   216,   84 },
+            { 0xC45D1DF942711D9A,   242,   92 },
+            { 0x924D692CA61BE758,   269,  100 },
+            { 0xDA01EE641A708DEA,   295,  108 },
+            { 0xA26DA3999AEF774A,   322,  116 },
+            { 0xF209787BB47D6B85,   348,  124 },
+            { 0xB454E4A179DD1877,   375,  132 },
+            { 0x865B86925B9BC5C2,   402,  140 },
+            { 0xC83553C5C8965D3D,   428,  148 },
+            { 0x952AB45CFA97A0B3,   455,  156 },
+            { 0xDE469FBD99A05FE3,   481,  164 },
+            { 0xA59BC234DB398C25,   508,  172 },
+            { 0xF6C69A72A3989F5C,   534,  180 },
+            { 0xB7DCBF5354E9BECE,   561,  188 },
+            { 0x88FCF317F22241E2,   588,  196 },
+            { 0xCC20CE9BD35C78A5,   614,  204 },
+            { 0x98165AF37B2153DF,   641,  212 },
+            { 0xE2A0B5DC971F303A,   667,  220 },
+            { 0xA8D9D1535CE3B396,   694,  228 },
+            { 0xFB9B7CD9A4A7443C,   720,  236 },
+            { 0xBB764C4CA7A44410,   747,  244 },
+            { 0x8BAB8EEFB6409C1A,   774,  252 },
+            { 0xD01FEF10A657842C,   800,  260 },
+            { 0x9B10A4E5E9913129,   827,  268 },
+            { 0xE7109BFBA19C0C9D,   853,  276 },
+            { 0xAC2820D9623BF429,   880,  284 },
+            { 0x80444B5E7AA7CF85,   907,  292 },
+            { 0xBF21E44003ACDD2D,   933,  300 },
+            { 0x8E679C2F5E44FF8F,   960,  308 },
+            { 0xD433179D9C8CB841,   986,  316 },
+            { 0x9E19DB92B4E31BA9,  1013,  324 },
+        }
+    };
+
+    // This computation gives exactly the same results for k as
+    //      k = ceil((kAlpha - e - 1) * 0.30102999566398114)
+    // for |e| <= 1500, but doesn't require floating-point operations.
+    // NB: log_10(2) ~= 78913 / 2^18
+    JSON_ASSERT(e >= -1500);
+    JSON_ASSERT(e <=  1500);
+    const int f = kAlpha - e - 1;
+    const int k = ((f * 78913) / (1 << 18)) + static_cast<int>(f > 0);
+
+    const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep;
+    JSON_ASSERT(index >= 0);
+    JSON_ASSERT(static_cast<std::size_t>(index) < kCachedPowers.size());
+
+    const cached_power cached = kCachedPowers[static_cast<std::size_t>(index)];
+    JSON_ASSERT(kAlpha <= cached.e + e + 64);
+    JSON_ASSERT(kGamma >= cached.e + e + 64);
+
+    return cached;
+}
+
+/*!
+For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k.
+For n == 0, returns 1 and sets pow10 := 1.
+*/
+inline int find_largest_pow10(const std::uint32_t n, std::uint32_t& pow10)
+{
+    // LCOV_EXCL_START
+    if (n >= 1000000000)
+    {
+        pow10 = 1000000000;
+        return 10;
+    }
+    // LCOV_EXCL_STOP
+    if (n >= 100000000)
+    {
+        pow10 = 100000000;
+        return  9;
+    }
+    if (n >= 10000000)
+    {
+        pow10 = 10000000;
+        return  8;
+    }
+    if (n >= 1000000)
+    {
+        pow10 = 1000000;
+        return  7;
+    }
+    if (n >= 100000)
+    {
+        pow10 = 100000;
+        return  6;
+    }
+    if (n >= 10000)
+    {
+        pow10 = 10000;
+        return  5;
+    }
+    if (n >= 1000)
+    {
+        pow10 = 1000;
+        return  4;
+    }
+    if (n >= 100)
+    {
+        pow10 = 100;
+        return  3;
+    }
+    if (n >= 10)
+    {
+        pow10 = 10;
+        return  2;
+    }
+
+    pow10 = 1;
+    return 1;
+}
+
+inline void grisu2_round(char* buf, int len, std::uint64_t dist, std::uint64_t delta,
+                         std::uint64_t rest, std::uint64_t ten_k)
+{
+    JSON_ASSERT(len >= 1);
+    JSON_ASSERT(dist <= delta);
+    JSON_ASSERT(rest <= delta);
+    JSON_ASSERT(ten_k > 0);
+
+    //               <--------------------------- delta ---->
+    //                                  <---- dist --------->
+    // --------------[------------------+-------------------]--------------
+    //               M-                 w                   M+
+    //
+    //                                  ten_k
+    //                                <------>
+    //                                       <---- rest ---->
+    // --------------[------------------+----+--------------]--------------
+    //                                  w    V
+    //                                       = buf * 10^k
+    //
+    // ten_k represents a unit-in-the-last-place in the decimal representation
+    // stored in buf.
+    // Decrement buf by ten_k while this takes buf closer to w.
+
+    // The tests are written in this order to avoid overflow in unsigned
+    // integer arithmetic.
+
+    while (rest < dist
+            && delta - rest >= ten_k
+            && (rest + ten_k < dist || dist - rest > rest + ten_k - dist))
+    {
+        JSON_ASSERT(buf[len - 1] != '0');
+        buf[len - 1]--;
+        rest += ten_k;
+    }
+}
+
+/*!
+Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+.
+M- and M+ must be normalized and share the same exponent -60 <= e <= -32.
+*/
+inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent,
+                             diyfp M_minus, diyfp w, diyfp M_plus)
+{
+    static_assert(kAlpha >= -60, "internal error");
+    static_assert(kGamma <= -32, "internal error");
+
+    // Generates the digits (and the exponent) of a decimal floating-point
+    // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's
+    // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma.
+    //
+    //               <--------------------------- delta ---->
+    //                                  <---- dist --------->
+    // --------------[------------------+-------------------]--------------
+    //               M-                 w                   M+
+    //
+    // Grisu2 generates the digits of M+ from left to right and stops as soon as
+    // V is in [M-,M+].
+
+    JSON_ASSERT(M_plus.e >= kAlpha);
+    JSON_ASSERT(M_plus.e <= kGamma);
+
+    std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e)
+    std::uint64_t dist  = diyfp::sub(M_plus, w      ).f; // (significand of (M+ - w ), implicit exponent is e)
+
+    // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0):
+    //
+    //      M+ = f * 2^e
+    //         = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e
+    //         = ((p1        ) * 2^-e + (p2        )) * 2^e
+    //         = p1 + p2 * 2^e
+
+    const diyfp one(std::uint64_t{1} << -M_plus.e, M_plus.e);
+
+    auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.)
+    std::uint64_t p2 = M_plus.f & (one.f - 1);                    // p2 = f mod 2^-e
+
+    // 1)
+    //
+    // Generate the digits of the integral part p1 = d[n-1]...d[1]d[0]
+
+    JSON_ASSERT(p1 > 0);
+
+    std::uint32_t pow10{};
+    const int k = find_largest_pow10(p1, pow10);
+
+    //      10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1)
+    //
+    //      p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1))
+    //         = (d[k-1]         ) * 10^(k-1) + (p1 mod 10^(k-1))
+    //
+    //      M+ = p1                                             + p2 * 2^e
+    //         = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1))          + p2 * 2^e
+    //         = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e
+    //         = d[k-1] * 10^(k-1) + (                         rest) * 2^e
+    //
+    // Now generate the digits d[n] of p1 from left to right (n = k-1,...,0)
+    //
+    //      p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0]
+    //
+    // but stop as soon as
+    //
+    //      rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e
+
+    int n = k;
+    while (n > 0)
+    {
+        // Invariants:
+        //      M+ = buffer * 10^n + (p1 + p2 * 2^e)    (buffer = 0 for n = k)
+        //      pow10 = 10^(n-1) <= p1 < 10^n
+        //
+        const std::uint32_t d = p1 / pow10;  // d = p1 div 10^(n-1)
+        const std::uint32_t r = p1 % pow10;  // r = p1 mod 10^(n-1)
+        //
+        //      M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e
+        //         = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e)
+        //
+        JSON_ASSERT(d <= 9);
+        buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
+        //
+        //      M+ = buffer * 10^(n-1) + (r + p2 * 2^e)
+        //
+        p1 = r;
+        n--;
+        //
+        //      M+ = buffer * 10^n + (p1 + p2 * 2^e)
+        //      pow10 = 10^n
+        //
+
+        // Now check if enough digits have been generated.
+        // Compute
+        //
+        //      p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e
+        //
+        // Note:
+        // Since rest and delta share the same exponent e, it suffices to
+        // compare the significands.
+        const std::uint64_t rest = (std::uint64_t{p1} << -one.e) + p2;
+        if (rest <= delta)
+        {
+            // V = buffer * 10^n, with M- <= V <= M+.
+
+            decimal_exponent += n;
+
+            // We may now just stop. But instead look if the buffer could be
+            // decremented to bring V closer to w.
+            //
+            // pow10 = 10^n is now 1 ulp in the decimal representation V.
+            // The rounding procedure works with diyfp's with an implicit
+            // exponent of e.
+            //
+            //      10^n = (10^n * 2^-e) * 2^e = ulp * 2^e
+            //
+            const std::uint64_t ten_n = std::uint64_t{pow10} << -one.e;
+            grisu2_round(buffer, length, dist, delta, rest, ten_n);
+
+            return;
+        }
+
+        pow10 /= 10;
+        //
+        //      pow10 = 10^(n-1) <= p1 < 10^n
+        // Invariants restored.
+    }
+
+    // 2)
+    //
+    // The digits of the integral part have been generated:
+    //
+    //      M+ = d[k-1]...d[1]d[0] + p2 * 2^e
+    //         = buffer            + p2 * 2^e
+    //
+    // Now generate the digits of the fractional part p2 * 2^e.
+    //
+    // Note:
+    // No decimal point is generated: the exponent is adjusted instead.
+    //
+    // p2 actually represents the fraction
+    //
+    //      p2 * 2^e
+    //          = p2 / 2^-e
+    //          = d[-1] / 10^1 + d[-2] / 10^2 + ...
+    //
+    // Now generate the digits d[-m] of p1 from left to right (m = 1,2,...)
+    //
+    //      p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m
+    //                      + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...)
+    //
+    // using
+    //
+    //      10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e)
+    //                = (                   d) * 2^-e + (                   r)
+    //
+    // or
+    //      10^m * p2 * 2^e = d + r * 2^e
+    //
+    // i.e.
+    //
+    //      M+ = buffer + p2 * 2^e
+    //         = buffer + 10^-m * (d + r * 2^e)
+    //         = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e
+    //
+    // and stop as soon as 10^-m * r * 2^e <= delta * 2^e
+
+    JSON_ASSERT(p2 > delta);
+
+    int m = 0;
+    for (;;)
+    {
+        // Invariant:
+        //      M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e
+        //         = buffer * 10^-m + 10^-m * (p2                                 ) * 2^e
+        //         = buffer * 10^-m + 10^-m * (1/10 * (10 * p2)                   ) * 2^e
+        //         = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e
+        //
+        JSON_ASSERT(p2 <= (std::numeric_limits<std::uint64_t>::max)() / 10);
+        p2 *= 10;
+        const std::uint64_t d = p2 >> -one.e;     // d = (10 * p2) div 2^-e
+        const std::uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e
+        //
+        //      M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e
+        //         = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e))
+        //         = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e
+        //
+        JSON_ASSERT(d <= 9);
+        buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d
+        //
+        //      M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e
+        //
+        p2 = r;
+        m++;
+        //
+        //      M+ = buffer * 10^-m + 10^-m * p2 * 2^e
+        // Invariant restored.
+
+        // Check if enough digits have been generated.
+        //
+        //      10^-m * p2 * 2^e <= delta * 2^e
+        //              p2 * 2^e <= 10^m * delta * 2^e
+        //                    p2 <= 10^m * delta
+        delta *= 10;
+        dist  *= 10;
+        if (p2 <= delta)
+        {
+            break;
+        }
+    }
+
+    // V = buffer * 10^-m, with M- <= V <= M+.
+
+    decimal_exponent -= m;
+
+    // 1 ulp in the decimal representation is now 10^-m.
+    // Since delta and dist are now scaled by 10^m, we need to do the
+    // same with ulp in order to keep the units in sync.
+    //
+    //      10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e
+    //
+    const std::uint64_t ten_m = one.f;
+    grisu2_round(buffer, length, dist, delta, p2, ten_m);
+
+    // By construction this algorithm generates the shortest possible decimal
+    // number (Loitsch, Theorem 6.2) which rounds back to w.
+    // For an input number of precision p, at least
+    //
+    //      N = 1 + ceil(p * log_10(2))
+    //
+    // decimal digits are sufficient to identify all binary floating-point
+    // numbers (Matula, "In-and-Out conversions").
+    // This implies that the algorithm does not produce more than N decimal
+    // digits.
+    //
+    //      N = 17 for p = 53 (IEEE double precision)
+    //      N = 9  for p = 24 (IEEE single precision)
+}
+
+/*!
+v = buf * 10^decimal_exponent
+len is the length of the buffer (number of decimal digits)
+The buffer must be large enough, i.e. >= max_digits10.
+*/
+JSON_HEDLEY_NON_NULL(1)
+inline void grisu2(char* buf, int& len, int& decimal_exponent,
+                   diyfp m_minus, diyfp v, diyfp m_plus)
+{
+    JSON_ASSERT(m_plus.e == m_minus.e);
+    JSON_ASSERT(m_plus.e == v.e);
+
+    //  --------(-----------------------+-----------------------)--------    (A)
+    //          m-                      v                       m+
+    //
+    //  --------------------(-----------+-----------------------)--------    (B)
+    //                      m-          v                       m+
+    //
+    // First scale v (and m- and m+) such that the exponent is in the range
+    // [alpha, gamma].
+
+    const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e);
+
+    const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k
+
+    // The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma]
+    const diyfp w       = diyfp::mul(v,       c_minus_k);
+    const diyfp w_minus = diyfp::mul(m_minus, c_minus_k);
+    const diyfp w_plus  = diyfp::mul(m_plus,  c_minus_k);
+
+    //  ----(---+---)---------------(---+---)---------------(---+---)----
+    //          w-                      w                       w+
+    //          = c*m-                  = c*v                   = c*m+
+    //
+    // diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and
+    // w+ are now off by a small amount.
+    // In fact:
+    //
+    //      w - v * 10^k < 1 ulp
+    //
+    // To account for this inaccuracy, add resp. subtract 1 ulp.
+    //
+    //  --------+---[---------------(---+---)---------------]---+--------
+    //          w-  M-                  w                   M+  w+
+    //
+    // Now any number in [M-, M+] (bounds included) will round to w when input,
+    // regardless of how the input rounding algorithm breaks ties.
+    //
+    // And digit_gen generates the shortest possible such number in [M-, M+].
+    // Note that this does not mean that Grisu2 always generates the shortest
+    // possible number in the interval (m-, m+).
+    const diyfp M_minus(w_minus.f + 1, w_minus.e);
+    const diyfp M_plus (w_plus.f  - 1, w_plus.e );
+
+    decimal_exponent = -cached.k; // = -(-k) = k
+
+    grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus);
+}
+
+/*!
+v = buf * 10^decimal_exponent
+len is the length of the buffer (number of decimal digits)
+The buffer must be large enough, i.e. >= max_digits10.
+*/
+template<typename FloatType>
+JSON_HEDLEY_NON_NULL(1)
+void grisu2(char* buf, int& len, int& decimal_exponent, FloatType value)
+{
+    static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3,
+                  "internal error: not enough precision");
+
+    JSON_ASSERT(std::isfinite(value));
+    JSON_ASSERT(value > 0);
+
+    // If the neighbors (and boundaries) of 'value' are always computed for double-precision
+    // numbers, all float's can be recovered using strtod (and strtof). However, the resulting
+    // decimal representations are not exactly "short".
+    //
+    // The documentation for 'std::to_chars' (https://en.cppreference.com/w/cpp/utility/to_chars)
+    // says "value is converted to a string as if by std::sprintf in the default ("C") locale"
+    // and since sprintf promotes floats to doubles, I think this is exactly what 'std::to_chars'
+    // does.
+    // On the other hand, the documentation for 'std::to_chars' requires that "parsing the
+    // representation using the corresponding std::from_chars function recovers value exactly". That
+    // indicates that single precision floating-point numbers should be recovered using
+    // 'std::strtof'.
+    //
+    // NB: If the neighbors are computed for single-precision numbers, there is a single float
+    //     (7.0385307e-26f) which can't be recovered using strtod. The resulting double precision
+    //     value is off by 1 ulp.
+#if 0 // NOLINT(readability-avoid-unconditional-preprocessor-if)
+    const boundaries w = compute_boundaries(static_cast<double>(value));
+#else
+    const boundaries w = compute_boundaries(value);
+#endif
+
+    grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus);
+}
+
+/*!
+@brief appends a decimal representation of e to buf
+@return a pointer to the element following the exponent.
+@pre -1000 < e < 1000
+*/
+JSON_HEDLEY_NON_NULL(1)
+JSON_HEDLEY_RETURNS_NON_NULL
+inline char* append_exponent(char* buf, int e)
+{
+    JSON_ASSERT(e > -1000);
+    JSON_ASSERT(e <  1000);
+
+    if (e < 0)
+    {
+        e = -e;
+        *buf++ = '-';
+    }
+    else
+    {
+        *buf++ = '+';
+    }
+
+    auto k = static_cast<std::uint32_t>(e);
+    if (k < 10)
+    {
+        // Always print at least two digits in the exponent.
+        // This is for compatibility with printf("%g").
+        *buf++ = '0';
+        *buf++ = static_cast<char>('0' + k);
+    }
+    else if (k < 100)
+    {
+        *buf++ = static_cast<char>('0' + (k / 10));
+        k %= 10;
+        *buf++ = static_cast<char>('0' + k);
+    }
+    else
+    {
+        *buf++ = static_cast<char>('0' + (k / 100));
+        k %= 100;
+        *buf++ = static_cast<char>('0' + (k / 10));
+        k %= 10;
+        *buf++ = static_cast<char>('0' + k);
+    }
+
+    return buf;
+}
+
+/*!
+@brief prettify v = buf * 10^decimal_exponent
+
+If v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point
+notation. Otherwise it will be printed in exponential notation.
+
+@pre min_exp < 0
+@pre max_exp > 0
+*/
+JSON_HEDLEY_NON_NULL(1)
+JSON_HEDLEY_RETURNS_NON_NULL
+inline char* format_buffer(char* buf, int len, int decimal_exponent,
+                           int min_exp, int max_exp)
+{
+    JSON_ASSERT(min_exp < 0);
+    JSON_ASSERT(max_exp > 0);
+
+    const int k = len;
+    const int n = len + decimal_exponent;
+
+    // v = buf * 10^(n-k)
+    // k is the length of the buffer (number of decimal digits)
+    // n is the position of the decimal point relative to the start of the buffer.
+
+    if (k <= n && n <= max_exp)
+    {
+        // digits[000]
+        // len <= max_exp + 2
+
+        std::memset(buf + k, '0', static_cast<size_t>(n) - static_cast<size_t>(k));
+        // Make it look like a floating-point number (#362, #378)
+        buf[n + 0] = '.';
+        buf[n + 1] = '0';
+        return buf + (static_cast<size_t>(n) + 2);
+    }
+
+    if (0 < n && n <= max_exp)
+    {
+        // dig.its
+        // len <= max_digits10 + 1
+
+        JSON_ASSERT(k > n);
+
+        std::memmove(buf + (static_cast<size_t>(n) + 1), buf + n, static_cast<size_t>(k) - static_cast<size_t>(n));
+        buf[n] = '.';
+        return buf + (static_cast<size_t>(k) + 1U);
+    }
+
+    if (min_exp < n && n <= 0)
+    {
+        // 0.[000]digits
+        // len <= 2 + (-min_exp - 1) + max_digits10
+
+        std::memmove(buf + (2 + static_cast<size_t>(-n)), buf, static_cast<size_t>(k));
+        buf[0] = '0';
+        buf[1] = '.';
+        std::memset(buf + 2, '0', static_cast<size_t>(-n));
+        return buf + (2U + static_cast<size_t>(-n) + static_cast<size_t>(k));
+    }
+
+    if (k == 1)
+    {
+        // dE+123
+        // len <= 1 + 5
+
+        buf += 1;
+    }
+    else
+    {
+        // d.igitsE+123
+        // len <= max_digits10 + 1 + 5
+
+        std::memmove(buf + 2, buf + 1, static_cast<size_t>(k) - 1);
+        buf[1] = '.';
+        buf += 1 + static_cast<size_t>(k);
+    }
+
+    *buf++ = 'e';
+    return append_exponent(buf, n - 1);
+}
+
+}  // namespace dtoa_impl
+
+/*!
+@brief generates a decimal representation of the floating-point number value in [first, last).
+
+The format of the resulting decimal representation is similar to printf's %g
+format. Returns an iterator pointing past-the-end of the decimal representation.
+
+@note The input number must be finite, i.e. NaN's and Inf's are not supported.
+@note The buffer must be large enough.
+@note The result is NOT null-terminated.
+*/
+template<typename FloatType>
+JSON_HEDLEY_NON_NULL(1, 2)
+JSON_HEDLEY_RETURNS_NON_NULL
+char* to_chars(char* first, const char* last, FloatType value)
+{
+    static_cast<void>(last); // maybe unused - fix warning
+    JSON_ASSERT(std::isfinite(value));
+
+    // Use signbit(value) instead of (value < 0) since signbit works for -0.
+    if (std::signbit(value))
+    {
+        value = -value;
+        *first++ = '-';
+    }
+
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+    if (value == 0) // +-0
+    {
+        *first++ = '0';
+        // Make it look like a floating-point number (#362, #378)
+        *first++ = '.';
+        *first++ = '0';
+        return first;
+    }
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+
+    JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10);
+
+    // Compute v = buffer * 10^decimal_exponent.
+    // The decimal digits are stored in the buffer, which needs to be interpreted
+    // as an unsigned decimal integer.
+    // len is the length of the buffer, i.e. the number of decimal digits.
+    int len = 0;
+    int decimal_exponent = 0;
+    dtoa_impl::grisu2(first, len, decimal_exponent, value);
+
+    JSON_ASSERT(len <= std::numeric_limits<FloatType>::max_digits10);
+
+    // Format the buffer like printf("%.*g", prec, value)
+    constexpr int kMinExp = -4;
+    // Use digits10 here to increase compatibility with version 2.
+    constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10;
+
+    JSON_ASSERT(last - first >= kMaxExp + 2);
+    JSON_ASSERT(last - first >= 2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10);
+    JSON_ASSERT(last - first >= std::numeric_limits<FloatType>::max_digits10 + 6);
+
+    return dtoa_impl::format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp);
+}
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/exceptions.hpp>
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/cpp_future.hpp>
+
+// #include <nlohmann/detail/output/binary_writer.hpp>
+
+// #include <nlohmann/detail/output/output_adapters.hpp>
+
+// #include <nlohmann/detail/string_concat.hpp>
+
+// #include <nlohmann/detail/value_t.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+namespace detail
+{
+
+///////////////////
+// serialization //
+///////////////////
+
+/// how to treat decoding errors
+enum class error_handler_t
+{
+    strict,  ///< throw a type_error exception in case of invalid UTF-8
+    replace, ///< replace invalid UTF-8 sequences with U+FFFD
+    ignore   ///< ignore invalid UTF-8 sequences
+};
+
+template<typename BasicJsonType>
+class serializer
+{
+    using string_t = typename BasicJsonType::string_t;
+    using number_float_t = typename BasicJsonType::number_float_t;
+    using number_integer_t = typename BasicJsonType::number_integer_t;
+    using number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+    using binary_char_t = typename BasicJsonType::binary_t::value_type;
+    static constexpr std::uint8_t UTF8_ACCEPT = 0;
+    static constexpr std::uint8_t UTF8_REJECT = 1;
+
+  public:
+    /*!
+    @param[in] s  output stream to serialize to
+    @param[in] ichar  indentation character to use
+    @param[in] error_handler_  how to react on decoding errors
+    */
+    serializer(output_adapter_t<char> s, const char ichar,
+               error_handler_t error_handler_ = error_handler_t::strict)
+        : o(std::move(s))
+        , loc(std::localeconv())
+        , thousands_sep(loc->thousands_sep == nullptr ? '\0' : std::char_traits<char>::to_char_type(* (loc->thousands_sep)))
+        , decimal_point(loc->decimal_point == nullptr ? '\0' : std::char_traits<char>::to_char_type(* (loc->decimal_point)))
+        , indent_char(ichar)
+        , indent_string(512, indent_char)
+        , error_handler(error_handler_)
+    {}
+
+    // delete because of pointer members
+    serializer(const serializer&) = delete;
+    serializer& operator=(const serializer&) = delete;
+    serializer(serializer&&) = delete;
+    serializer& operator=(serializer&&) = delete;
+    ~serializer() = default;
+
+    /*!
+    @brief internal implementation of the serialization function
+
+    This function is called by the public member function dump and organizes
+    the serialization internally. The indentation level is propagated as
+    additional parameter. In case of arrays and objects, the function is
+    called recursively.
+
+    - strings and object keys are escaped using `escape_string()`
+    - integer numbers are converted implicitly via `operator<<`
+    - floating-point numbers are converted to a string using `"%g"` format
+    - binary values are serialized as objects containing the subtype and the
+      byte array
+
+    @param[in] val               value to serialize
+    @param[in] pretty_print      whether the output shall be pretty-printed
+    @param[in] ensure_ascii If @a ensure_ascii is true, all non-ASCII characters
+    in the output are escaped with `\uXXXX` sequences, and the result consists
+    of ASCII characters only.
+    @param[in] indent_step       the indent level
+    @param[in] current_indent    the current indent level (only used internally)
+    */
+    void dump(const BasicJsonType& val,
+              const bool pretty_print,
+              const bool ensure_ascii,
+              const unsigned int indent_step,
+              const unsigned int current_indent = 0)
+    {
+        switch (val.m_data.m_type)
+        {
+            case value_t::object:
+            {
+                if (val.m_data.m_value.object->empty())
+                {
+                    o->write_characters("{}", 2);
+                    return;
+                }
+
+                if (pretty_print)
+                {
+                    o->write_characters("{\n", 2);
+
+                    // variable to hold indentation for recursive calls
+                    const auto new_indent = current_indent + indent_step;
+                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))
+                    {
+                        indent_string.resize(indent_string.size() * 2, ' ');
+                    }
+
+                    // first n-1 elements
+                    auto i = val.m_data.m_value.object->cbegin();
+                    for (std::size_t cnt = 0; cnt < val.m_data.m_value.object->size() - 1; ++cnt, ++i)
+                    {
+                        o->write_characters(indent_string.c_str(), new_indent);
+                        o->write_character('\"');
+                        dump_escaped(i->first, ensure_ascii);
+                        o->write_characters("\": ", 3);
+                        dump(i->second, true, ensure_ascii, indent_step, new_indent);
+                        o->write_characters(",\n", 2);
+                    }
+
+                    // last element
+                    JSON_ASSERT(i != val.m_data.m_value.object->cend());
+                    JSON_ASSERT(std::next(i) == val.m_data.m_value.object->cend());
+                    o->write_characters(indent_string.c_str(), new_indent);
+                    o->write_character('\"');
+                    dump_escaped(i->first, ensure_ascii);
+                    o->write_characters("\": ", 3);
+                    dump(i->second, true, ensure_ascii, indent_step, new_indent);
+
+                    o->write_character('\n');
+                    o->write_characters(indent_string.c_str(), current_indent);
+                    o->write_character('}');
+                }
+                else
+                {
+                    o->write_character('{');
+
+                    // first n-1 elements
+                    auto i = val.m_data.m_value.object->cbegin();
+                    for (std::size_t cnt = 0; cnt < val.m_data.m_value.object->size() - 1; ++cnt, ++i)
+                    {
+                        o->write_character('\"');
+                        dump_escaped(i->first, ensure_ascii);
+                        o->write_characters("\":", 2);
+                        dump(i->second, false, ensure_ascii, indent_step, current_indent);
+                        o->write_character(',');
+                    }
+
+                    // last element
+                    JSON_ASSERT(i != val.m_data.m_value.object->cend());
+                    JSON_ASSERT(std::next(i) == val.m_data.m_value.object->cend());
+                    o->write_character('\"');
+                    dump_escaped(i->first, ensure_ascii);
+                    o->write_characters("\":", 2);
+                    dump(i->second, false, ensure_ascii, indent_step, current_indent);
+
+                    o->write_character('}');
+                }
+
+                return;
+            }
+
+            case value_t::array:
+            {
+                if (val.m_data.m_value.array->empty())
+                {
+                    o->write_characters("[]", 2);
+                    return;
+                }
+
+                if (pretty_print)
+                {
+                    o->write_characters("[\n", 2);
+
+                    // variable to hold indentation for recursive calls
+                    const auto new_indent = current_indent + indent_step;
+                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))
+                    {
+                        indent_string.resize(indent_string.size() * 2, ' ');
+                    }
+
+                    // first n-1 elements
+                    for (auto i = val.m_data.m_value.array->cbegin();
+                            i != val.m_data.m_value.array->cend() - 1; ++i)
+                    {
+                        o->write_characters(indent_string.c_str(), new_indent);
+                        dump(*i, true, ensure_ascii, indent_step, new_indent);
+                        o->write_characters(",\n", 2);
+                    }
+
+                    // last element
+                    JSON_ASSERT(!val.m_data.m_value.array->empty());
+                    o->write_characters(indent_string.c_str(), new_indent);
+                    dump(val.m_data.m_value.array->back(), true, ensure_ascii, indent_step, new_indent);
+
+                    o->write_character('\n');
+                    o->write_characters(indent_string.c_str(), current_indent);
+                    o->write_character(']');
+                }
+                else
+                {
+                    o->write_character('[');
+
+                    // first n-1 elements
+                    for (auto i = val.m_data.m_value.array->cbegin();
+                            i != val.m_data.m_value.array->cend() - 1; ++i)
+                    {
+                        dump(*i, false, ensure_ascii, indent_step, current_indent);
+                        o->write_character(',');
+                    }
+
+                    // last element
+                    JSON_ASSERT(!val.m_data.m_value.array->empty());
+                    dump(val.m_data.m_value.array->back(), false, ensure_ascii, indent_step, current_indent);
+
+                    o->write_character(']');
+                }
+
+                return;
+            }
+
+            case value_t::string:
+            {
+                o->write_character('\"');
+                dump_escaped(*val.m_data.m_value.string, ensure_ascii);
+                o->write_character('\"');
+                return;
+            }
+
+            case value_t::binary:
+            {
+                if (pretty_print)
+                {
+                    o->write_characters("{\n", 2);
+
+                    // variable to hold indentation for recursive calls
+                    const auto new_indent = current_indent + indent_step;
+                    if (JSON_HEDLEY_UNLIKELY(indent_string.size() < new_indent))
+                    {
+                        indent_string.resize(indent_string.size() * 2, ' ');
+                    }
+
+                    o->write_characters(indent_string.c_str(), new_indent);
+
+                    o->write_characters("\"bytes\": [", 10);
+
+                    if (!val.m_data.m_value.binary->empty())
+                    {
+                        for (auto i = val.m_data.m_value.binary->cbegin();
+                                i != val.m_data.m_value.binary->cend() - 1; ++i)
+                        {
+                            dump_integer(*i);
+                            o->write_characters(", ", 2);
+                        }
+                        dump_integer(val.m_data.m_value.binary->back());
+                    }
+
+                    o->write_characters("],\n", 3);
+                    o->write_characters(indent_string.c_str(), new_indent);
+
+                    o->write_characters("\"subtype\": ", 11);
+                    if (val.m_data.m_value.binary->has_subtype())
+                    {
+                        dump_integer(val.m_data.m_value.binary->subtype());
+                    }
+                    else
+                    {
+                        o->write_characters("null", 4);
+                    }
+                    o->write_character('\n');
+                    o->write_characters(indent_string.c_str(), current_indent);
+                    o->write_character('}');
+                }
+                else
+                {
+                    o->write_characters("{\"bytes\":[", 10);
+
+                    if (!val.m_data.m_value.binary->empty())
+                    {
+                        for (auto i = val.m_data.m_value.binary->cbegin();
+                                i != val.m_data.m_value.binary->cend() - 1; ++i)
+                        {
+                            dump_integer(*i);
+                            o->write_character(',');
+                        }
+                        dump_integer(val.m_data.m_value.binary->back());
+                    }
+
+                    o->write_characters("],\"subtype\":", 12);
+                    if (val.m_data.m_value.binary->has_subtype())
+                    {
+                        dump_integer(val.m_data.m_value.binary->subtype());
+                        o->write_character('}');
+                    }
+                    else
+                    {
+                        o->write_characters("null}", 5);
+                    }
+                }
+                return;
+            }
+
+            case value_t::boolean:
+            {
+                if (val.m_data.m_value.boolean)
+                {
+                    o->write_characters("true", 4);
+                }
+                else
+                {
+                    o->write_characters("false", 5);
+                }
+                return;
+            }
+
+            case value_t::number_integer:
+            {
+                dump_integer(val.m_data.m_value.number_integer);
+                return;
+            }
+
+            case value_t::number_unsigned:
+            {
+                dump_integer(val.m_data.m_value.number_unsigned);
+                return;
+            }
+
+            case value_t::number_float:
+            {
+                dump_float(val.m_data.m_value.number_float);
+                return;
+            }
+
+            case value_t::discarded:
+            {
+                o->write_characters("<discarded>", 11);
+                return;
+            }
+
+            case value_t::null:
+            {
+                o->write_characters("null", 4);
+                return;
+            }
+
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /*!
+    @brief dump escaped string
+
+    Escape a string by replacing certain special characters by a sequence of an
+    escape character (backslash) and another character and other control
+    characters by a sequence of "\u" followed by a four-digit hex
+    representation. The escaped string is written to output stream @a o.
+
+    @param[in] s  the string to escape
+    @param[in] ensure_ascii  whether to escape non-ASCII characters with
+                             \uXXXX sequences
+
+    @complexity Linear in the length of string @a s.
+    */
+    void dump_escaped(const string_t& s, const bool ensure_ascii)
+    {
+        std::uint32_t codepoint{};
+        std::uint8_t state = UTF8_ACCEPT;
+        std::size_t bytes = 0;  // number of bytes written to string_buffer
+
+        // number of bytes written at the point of the last valid byte
+        std::size_t bytes_after_last_accept = 0;
+        std::size_t undumped_chars = 0;
+
+        for (std::size_t i = 0; i < s.size(); ++i)
+        {
+            const auto byte = static_cast<std::uint8_t>(s[i]);
+
+            switch (decode(state, codepoint, byte))
+            {
+                case UTF8_ACCEPT:  // decode found a new code point
+                {
+                    switch (codepoint)
+                    {
+                        case 0x08: // backspace
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'b';
+                            break;
+                        }
+
+                        case 0x09: // horizontal tab
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 't';
+                            break;
+                        }
+
+                        case 0x0A: // newline
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'n';
+                            break;
+                        }
+
+                        case 0x0C: // formfeed
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'f';
+                            break;
+                        }
+
+                        case 0x0D: // carriage return
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = 'r';
+                            break;
+                        }
+
+                        case 0x22: // quotation mark
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = '\"';
+                            break;
+                        }
+
+                        case 0x5C: // reverse solidus
+                        {
+                            string_buffer[bytes++] = '\\';
+                            string_buffer[bytes++] = '\\';
+                            break;
+                        }
+
+                        default:
+                        {
+                            // escape control characters (0x00..0x1F) or, if
+                            // ensure_ascii parameter is used, non-ASCII characters
+                            if ((codepoint <= 0x1F) || (ensure_ascii && (codepoint >= 0x7F)))
+                            {
+                                if (codepoint <= 0xFFFF)
+                                {
+                                    // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                                    static_cast<void>((std::snprintf)(string_buffer.data() + bytes, 7, "\\u%04x",
+                                                                      static_cast<std::uint16_t>(codepoint)));
+                                    bytes += 6;
+                                }
+                                else
+                                {
+                                    // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+                                    static_cast<void>((std::snprintf)(string_buffer.data() + bytes, 13, "\\u%04x\\u%04x",
+                                                                      static_cast<std::uint16_t>(0xD7C0u + (codepoint >> 10u)),
+                                                                      static_cast<std::uint16_t>(0xDC00u + (codepoint & 0x3FFu))));
+                                    bytes += 12;
+                                }
+                            }
+                            else
+                            {
+                                // copy byte to buffer (all previous bytes
+                                // been copied have in default case above)
+                                string_buffer[bytes++] = s[i];
+                            }
+                            break;
+                        }
+                    }
+
+                    // write buffer and reset index; there must be 13 bytes
+                    // left, as this is the maximal number of bytes to be
+                    // written ("\uxxxx\uxxxx\0") for one code point
+                    if (string_buffer.size() - bytes < 13)
+                    {
+                        o->write_characters(string_buffer.data(), bytes);
+                        bytes = 0;
+                    }
+
+                    // remember the byte position of this accept
+                    bytes_after_last_accept = bytes;
+                    undumped_chars = 0;
+                    break;
+                }
+
+                case UTF8_REJECT:  // decode found invalid UTF-8 byte
+                {
+                    switch (error_handler)
+                    {
+                        case error_handler_t::strict:
+                        {
+                            JSON_THROW(type_error::create(316, concat("invalid UTF-8 byte at index ", std::to_string(i), ": 0x", hex_bytes(byte | 0)), nullptr));
+                        }
+
+                        case error_handler_t::ignore:
+                        case error_handler_t::replace:
+                        {
+                            // in case we saw this character the first time, we
+                            // would like to read it again, because the byte
+                            // may be OK for itself, but just not OK for the
+                            // previous sequence
+                            if (undumped_chars > 0)
+                            {
+                                --i;
+                            }
+
+                            // reset length buffer to the last accepted index;
+                            // thus removing/ignoring the invalid characters
+                            bytes = bytes_after_last_accept;
+
+                            if (error_handler == error_handler_t::replace)
+                            {
+                                // add a replacement character
+                                if (ensure_ascii)
+                                {
+                                    string_buffer[bytes++] = '\\';
+                                    string_buffer[bytes++] = 'u';
+                                    string_buffer[bytes++] = 'f';
+                                    string_buffer[bytes++] = 'f';
+                                    string_buffer[bytes++] = 'f';
+                                    string_buffer[bytes++] = 'd';
+                                }
+                                else
+                                {
+                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\xEF');
+                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\xBF');
+                                    string_buffer[bytes++] = detail::binary_writer<BasicJsonType, char>::to_char_type('\xBD');
+                                }
+
+                                // write buffer and reset index; there must be 13 bytes
+                                // left, as this is the maximal number of bytes to be
+                                // written ("\uxxxx\uxxxx\0") for one code point
+                                if (string_buffer.size() - bytes < 13)
+                                {
+                                    o->write_characters(string_buffer.data(), bytes);
+                                    bytes = 0;
+                                }
+
+                                bytes_after_last_accept = bytes;
+                            }
+
+                            undumped_chars = 0;
+
+                            // continue processing the string
+                            state = UTF8_ACCEPT;
+                            break;
+                        }
+
+                        default:            // LCOV_EXCL_LINE
+                            JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+                    }
+                    break;
+                }
+
+                default:  // decode found yet incomplete multi-byte code point
+                {
+                    if (!ensure_ascii)
+                    {
+                        // code point will not be escaped - copy byte to buffer
+                        string_buffer[bytes++] = s[i];
+                    }
+                    ++undumped_chars;
+                    break;
+                }
+            }
+        }
+
+        // we finished processing the string
+        if (JSON_HEDLEY_LIKELY(state == UTF8_ACCEPT))
+        {
+            // write buffer
+            if (bytes > 0)
+            {
+                o->write_characters(string_buffer.data(), bytes);
+            }
+        }
+        else
+        {
+            // we finish reading, but do not accept: string was incomplete
+            switch (error_handler)
+            {
+                case error_handler_t::strict:
+                {
+                    JSON_THROW(type_error::create(316, concat("incomplete UTF-8 string; last byte: 0x", hex_bytes(static_cast<std::uint8_t>(s.back() | 0))), nullptr));
+                }
+
+                case error_handler_t::ignore:
+                {
+                    // write all accepted bytes
+                    o->write_characters(string_buffer.data(), bytes_after_last_accept);
+                    break;
+                }
+
+                case error_handler_t::replace:
+                {
+                    // write all accepted bytes
+                    o->write_characters(string_buffer.data(), bytes_after_last_accept);
+                    // add a replacement character
+                    if (ensure_ascii)
+                    {
+                        o->write_characters("\\ufffd", 6);
+                    }
+                    else
+                    {
+                        o->write_characters("\xEF\xBF\xBD", 3);
+                    }
+                    break;
+                }
+
+                default:            // LCOV_EXCL_LINE
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+            }
+        }
+    }
+
+  private:
+    /*!
+    @brief count digits
+
+    Count the number of decimal (base 10) digits for an input unsigned integer.
+
+    @param[in] x  unsigned integer number to count its digits
+    @return    number of decimal digits
+    */
+    unsigned int count_digits(number_unsigned_t x) noexcept
+    {
+        unsigned int n_digits = 1;
+        for (;;)
+        {
+            if (x < 10)
+            {
+                return n_digits;
+            }
+            if (x < 100)
+            {
+                return n_digits + 1;
+            }
+            if (x < 1000)
+            {
+                return n_digits + 2;
+            }
+            if (x < 10000)
+            {
+                return n_digits + 3;
+            }
+            x = x / 10000u;
+            n_digits += 4;
+        }
+    }
+
+    /*!
+     * @brief convert a byte to a uppercase hex representation
+     * @param[in] byte byte to represent
+     * @return representation ("00".."FF")
+     */
+    static std::string hex_bytes(std::uint8_t byte)
+    {
+        std::string result = "FF";
+        constexpr const char* nibble_to_hex = "0123456789ABCDEF";
+        result[0] = nibble_to_hex[byte / 16];
+        result[1] = nibble_to_hex[byte % 16];
+        return result;
+    }
+
+    // templates to avoid warnings about useless casts
+    template <typename NumberType, enable_if_t<std::is_signed<NumberType>::value, int> = 0>
+    bool is_negative_number(NumberType x)
+    {
+        return x < 0;
+    }
+
+    template < typename NumberType, enable_if_t <std::is_unsigned<NumberType>::value, int > = 0 >
+    bool is_negative_number(NumberType /*unused*/)
+    {
+        return false;
+    }
+
+    /*!
+    @brief dump an integer
+
+    Dump a given integer to output stream @a o. Works internally with
+    @a number_buffer.
+
+    @param[in] x  integer number (signed or unsigned) to dump
+    @tparam NumberType either @a number_integer_t or @a number_unsigned_t
+    */
+    template < typename NumberType, detail::enable_if_t <
+                   std::is_integral<NumberType>::value ||
+                   std::is_same<NumberType, number_unsigned_t>::value ||
+                   std::is_same<NumberType, number_integer_t>::value ||
+                   std::is_same<NumberType, binary_char_t>::value,
+                   int > = 0 >
+    void dump_integer(NumberType x)
+    {
+        static constexpr std::array<std::array<char, 2>, 100> digits_to_99
+        {
+            {
+                {{'0', '0'}}, {{'0', '1'}}, {{'0', '2'}}, {{'0', '3'}}, {{'0', '4'}}, {{'0', '5'}}, {{'0', '6'}}, {{'0', '7'}}, {{'0', '8'}}, {{'0', '9'}},
+                {{'1', '0'}}, {{'1', '1'}}, {{'1', '2'}}, {{'1', '3'}}, {{'1', '4'}}, {{'1', '5'}}, {{'1', '6'}}, {{'1', '7'}}, {{'1', '8'}}, {{'1', '9'}},
+                {{'2', '0'}}, {{'2', '1'}}, {{'2', '2'}}, {{'2', '3'}}, {{'2', '4'}}, {{'2', '5'}}, {{'2', '6'}}, {{'2', '7'}}, {{'2', '8'}}, {{'2', '9'}},
+                {{'3', '0'}}, {{'3', '1'}}, {{'3', '2'}}, {{'3', '3'}}, {{'3', '4'}}, {{'3', '5'}}, {{'3', '6'}}, {{'3', '7'}}, {{'3', '8'}}, {{'3', '9'}},
+                {{'4', '0'}}, {{'4', '1'}}, {{'4', '2'}}, {{'4', '3'}}, {{'4', '4'}}, {{'4', '5'}}, {{'4', '6'}}, {{'4', '7'}}, {{'4', '8'}}, {{'4', '9'}},
+                {{'5', '0'}}, {{'5', '1'}}, {{'5', '2'}}, {{'5', '3'}}, {{'5', '4'}}, {{'5', '5'}}, {{'5', '6'}}, {{'5', '7'}}, {{'5', '8'}}, {{'5', '9'}},
+                {{'6', '0'}}, {{'6', '1'}}, {{'6', '2'}}, {{'6', '3'}}, {{'6', '4'}}, {{'6', '5'}}, {{'6', '6'}}, {{'6', '7'}}, {{'6', '8'}}, {{'6', '9'}},
+                {{'7', '0'}}, {{'7', '1'}}, {{'7', '2'}}, {{'7', '3'}}, {{'7', '4'}}, {{'7', '5'}}, {{'7', '6'}}, {{'7', '7'}}, {{'7', '8'}}, {{'7', '9'}},
+                {{'8', '0'}}, {{'8', '1'}}, {{'8', '2'}}, {{'8', '3'}}, {{'8', '4'}}, {{'8', '5'}}, {{'8', '6'}}, {{'8', '7'}}, {{'8', '8'}}, {{'8', '9'}},
+                {{'9', '0'}}, {{'9', '1'}}, {{'9', '2'}}, {{'9', '3'}}, {{'9', '4'}}, {{'9', '5'}}, {{'9', '6'}}, {{'9', '7'}}, {{'9', '8'}}, {{'9', '9'}},
+            }
+        };
+
+        // special case for "0"
+        if (x == 0)
+        {
+            o->write_character('0');
+            return;
+        }
+
+        // use a pointer to fill the buffer
+        auto buffer_ptr = number_buffer.begin(); // NOLINT(llvm-qualified-auto,readability-qualified-auto,cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+
+        number_unsigned_t abs_value;
+
+        unsigned int n_chars{};
+
+        if (is_negative_number(x))
+        {
+            *buffer_ptr = '-';
+            abs_value = remove_sign(static_cast<number_integer_t>(x));
+
+            // account one more byte for the minus sign
+            n_chars = 1 + count_digits(abs_value);
+        }
+        else
+        {
+            abs_value = static_cast<number_unsigned_t>(x);
+            n_chars = count_digits(abs_value);
+        }
+
+        // spare 1 byte for '\0'
+        JSON_ASSERT(n_chars < number_buffer.size() - 1);
+
+        // jump to the end to generate the string from backward,
+        // so we later avoid reversing the result
+        buffer_ptr += n_chars;
+
+        // Fast int2ascii implementation inspired by "Fastware" talk by Andrei Alexandrescu
+        // See: https://www.youtube.com/watch?v=o4-CwDo2zpg
+        while (abs_value >= 100)
+        {
+            const auto digits_index = static_cast<unsigned>((abs_value % 100));
+            abs_value /= 100;
+            *(--buffer_ptr) = digits_to_99[digits_index][1];
+            *(--buffer_ptr) = digits_to_99[digits_index][0];
+        }
+
+        if (abs_value >= 10)
+        {
+            const auto digits_index = static_cast<unsigned>(abs_value);
+            *(--buffer_ptr) = digits_to_99[digits_index][1];
+            *(--buffer_ptr) = digits_to_99[digits_index][0];
+        }
+        else
+        {
+            *(--buffer_ptr) = static_cast<char>('0' + abs_value);
+        }
+
+        o->write_characters(number_buffer.data(), n_chars);
+    }
+
+    /*!
+    @brief dump a floating-point number
+
+    Dump a given floating-point number to output stream @a o. Works internally
+    with @a number_buffer.
+
+    @param[in] x  floating-point number to dump
+    */
+    void dump_float(number_float_t x)
+    {
+        // NaN / inf
+        if (!std::isfinite(x))
+        {
+            o->write_characters("null", 4);
+            return;
+        }
+
+        // If number_float_t is an IEEE-754 single or double precision number,
+        // use the Grisu2 algorithm to produce short numbers which are
+        // guaranteed to round-trip, using strtof and strtod, resp.
+        //
+        // NB: The test below works if <long double> == <double>.
+        static constexpr bool is_ieee_single_or_double
+            = (std::numeric_limits<number_float_t>::is_iec559 && std::numeric_limits<number_float_t>::digits == 24 && std::numeric_limits<number_float_t>::max_exponent == 128) ||
+              (std::numeric_limits<number_float_t>::is_iec559 && std::numeric_limits<number_float_t>::digits == 53 && std::numeric_limits<number_float_t>::max_exponent == 1024);
+
+        dump_float(x, std::integral_constant<bool, is_ieee_single_or_double>());
+    }
+
+    void dump_float(number_float_t x, std::true_type /*is_ieee_single_or_double*/)
+    {
+        auto* begin = number_buffer.data();
+        auto* end = ::nlohmann::detail::to_chars(begin, begin + number_buffer.size(), x);
+
+        o->write_characters(begin, static_cast<size_t>(end - begin));
+    }
+
+    void dump_float(number_float_t x, std::false_type /*is_ieee_single_or_double*/)
+    {
+        // get number of digits for a float -> text -> float round-trip
+        static constexpr auto d = std::numeric_limits<number_float_t>::max_digits10;
+
+        // the actual conversion
+        // NOLINTNEXTLINE(cppcoreguidelines-pro-type-vararg,hicpp-vararg)
+        std::ptrdiff_t len = (std::snprintf)(number_buffer.data(), number_buffer.size(), "%.*g", d, x);
+
+        // negative value indicates an error
+        JSON_ASSERT(len > 0);
+        // check if buffer was large enough
+        JSON_ASSERT(static_cast<std::size_t>(len) < number_buffer.size());
+
+        // erase thousands separator
+        if (thousands_sep != '\0')
+        {
+            // NOLINTNEXTLINE(readability-qualified-auto,llvm-qualified-auto): std::remove returns an iterator, see https://github.com/nlohmann/json/issues/3081
+            const auto end = std::remove(number_buffer.begin(), number_buffer.begin() + len, thousands_sep);
+            std::fill(end, number_buffer.end(), '\0');
+            JSON_ASSERT((end - number_buffer.begin()) <= len);
+            len = (end - number_buffer.begin());
+        }
+
+        // convert decimal point to '.'
+        if (decimal_point != '\0' && decimal_point != '.')
+        {
+            // NOLINTNEXTLINE(readability-qualified-auto,llvm-qualified-auto): std::find returns an iterator, see https://github.com/nlohmann/json/issues/3081
+            const auto dec_pos = std::find(number_buffer.begin(), number_buffer.end(), decimal_point);
+            if (dec_pos != number_buffer.end())
+            {
+                *dec_pos = '.';
+            }
+        }
+
+        o->write_characters(number_buffer.data(), static_cast<std::size_t>(len));
+
+        // determine if we need to append ".0"
+        const bool value_is_int_like =
+            std::none_of(number_buffer.begin(), number_buffer.begin() + len + 1,
+                         [](char c)
+        {
+            return c == '.' || c == 'e';
+        });
+
+        if (value_is_int_like)
+        {
+            o->write_characters(".0", 2);
+        }
+    }
+
+    /*!
+    @brief check whether a string is UTF-8 encoded
+
+    The function checks each byte of a string whether it is UTF-8 encoded. The
+    result of the check is stored in the @a state parameter. The function must
+    be called initially with state 0 (accept). State 1 means the string must
+    be rejected, because the current byte is not allowed. If the string is
+    completely processed, but the state is non-zero, the string ended
+    prematurely; that is, the last byte indicated more bytes should have
+    followed.
+
+    @param[in,out] state  the state of the decoding
+    @param[in,out] codep  codepoint (valid only if resulting state is UTF8_ACCEPT)
+    @param[in] byte       next byte to decode
+    @return               new state
+
+    @note The function has been edited: a std::array is used.
+
+    @copyright Copyright (c) 2008-2009 Bjoern Hoehrmann <bjoern@hoehrmann.de>
+    @sa http://bjoern.hoehrmann.de/utf-8/decoder/dfa/
+    */
+    static std::uint8_t decode(std::uint8_t& state, std::uint32_t& codep, const std::uint8_t byte) noexcept
+    {
+        static const std::array<std::uint8_t, 400> utf8d =
+        {
+            {
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 00..1F
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 20..3F
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 40..5F
+                0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 60..7F
+                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, // 80..9F
+                7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, // A0..BF
+                8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // C0..DF
+                0xA, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x3, 0x4, 0x3, 0x3, // E0..EF
+                0xB, 0x6, 0x6, 0x6, 0x5, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, 0x8, // F0..FF
+                0x0, 0x1, 0x2, 0x3, 0x5, 0x8, 0x7, 0x1, 0x1, 0x1, 0x4, 0x6, 0x1, 0x1, 0x1, 0x1, // s0..s0
+                1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, // s1..s2
+                1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, // s3..s4
+                1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, // s5..s6
+                1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 // s7..s8
+            }
+        };
+
+        JSON_ASSERT(byte < utf8d.size());
+        const std::uint8_t type = utf8d[byte];
+
+        codep = (state != UTF8_ACCEPT)
+                ? (byte & 0x3fu) | (codep << 6u)
+                : (0xFFu >> type) & (byte);
+
+        const std::size_t index = 256u + (static_cast<size_t>(state) * 16u) + static_cast<size_t>(type);
+        JSON_ASSERT(index < utf8d.size());
+        state = utf8d[index];
+        return state;
+    }
+
+    /*
+     * Overload to make the compiler happy while it is instantiating
+     * dump_integer for number_unsigned_t.
+     * Must never be called.
+     */
+    number_unsigned_t remove_sign(number_unsigned_t x)
+    {
+        JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        return x; // LCOV_EXCL_LINE
+    }
+
+    /*
+     * Helper function for dump_integer
+     *
+     * This function takes a negative signed integer and returns its absolute
+     * value as unsigned integer. The plus/minus shuffling is necessary as we can
+     * not directly remove the sign of an arbitrary signed integer as the
+     * absolute values of INT_MIN and INT_MAX are usually not the same. See
+     * #1708 for details.
+     */
+    number_unsigned_t remove_sign(number_integer_t x) noexcept
+    {
+        JSON_ASSERT(x < 0 && x < (std::numeric_limits<number_integer_t>::max)()); // NOLINT(misc-redundant-expression)
+        return static_cast<number_unsigned_t>(-(x + 1)) + 1;
+    }
+
+  private:
+    /// the output of the serializer
+    output_adapter_t<char> o = nullptr;
+
+    /// a (hopefully) large enough character buffer
+    std::array<char, 64> number_buffer{{}};
+
+    /// the locale
+    const std::lconv* loc = nullptr;
+    /// the locale's thousand separator character
+    const char thousands_sep = '\0';
+    /// the locale's decimal point character
+    const char decimal_point = '\0';
+
+    /// string buffer
+    std::array<char, 512> string_buffer{{}};
+
+    /// the indentation character
+    const char indent_char;
+    /// the indentation string
+    string_t indent_string;
+
+    /// error_handler how to react on decoding errors
+    const error_handler_t error_handler;
+};
+
+}  // namespace detail
+NLOHMANN_JSON_NAMESPACE_END
+
+// #include <nlohmann/detail/value_t.hpp>
+
+// #include <nlohmann/json_fwd.hpp>
+
+// #include <nlohmann/ordered_map.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#include <functional> // equal_to, less
+#include <initializer_list> // initializer_list
+#include <iterator> // input_iterator_tag, iterator_traits
+#include <memory> // allocator
+#include <stdexcept> // for out_of_range
+#include <type_traits> // enable_if, is_convertible
+#include <utility> // pair
+#include <vector> // vector
+
+// #include <nlohmann/detail/macro_scope.hpp>
+
+// #include <nlohmann/detail/meta/type_traits.hpp>
+
+
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/// ordered_map: a minimal map-like container that preserves insertion order
+/// for use within nlohmann::basic_json<ordered_map>
+template <class Key, class T, class IgnoredLess = std::less<Key>,
+          class Allocator = std::allocator<std::pair<const Key, T>>>
+              struct ordered_map : std::vector<std::pair<const Key, T>, Allocator>
+{
+    using key_type = Key;
+    using mapped_type = T;
+    using Container = std::vector<std::pair<const Key, T>, Allocator>;
+    using iterator = typename Container::iterator;
+    using const_iterator = typename Container::const_iterator;
+    using size_type = typename Container::size_type;
+    using value_type = typename Container::value_type;
+#ifdef JSON_HAS_CPP_14
+    using key_compare = std::equal_to<>;
+#else
+    using key_compare = std::equal_to<Key>;
+#endif
+
+    // Explicit constructors instead of `using Container::Container`
+    // otherwise older compilers choke on it (GCC <= 5.5, xcode <= 9.4)
+    ordered_map() noexcept(noexcept(Container())) : Container{} {}
+    explicit ordered_map(const Allocator& alloc) noexcept(noexcept(Container(alloc))) : Container{alloc} {}
+    template <class It>
+    ordered_map(It first, It last, const Allocator& alloc = Allocator())
+        : Container{first, last, alloc} {}
+    ordered_map(std::initializer_list<value_type> init, const Allocator& alloc = Allocator() )
+        : Container{init, alloc} {}
+
+    std::pair<iterator, bool> emplace(const key_type& key, T&& t)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return {it, false};
+            }
+        }
+        Container::emplace_back(key, std::forward<T>(t));
+        return {std::prev(this->end()), true};
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    std::pair<iterator, bool> emplace(KeyType && key, T && t)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return {it, false};
+            }
+        }
+        Container::emplace_back(std::forward<KeyType>(key), std::forward<T>(t));
+        return {std::prev(this->end()), true};
+    }
+
+    T& operator[](const key_type& key)
+    {
+        return emplace(key, T{}).first->second;
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    T & operator[](KeyType && key)
+    {
+        return emplace(std::forward<KeyType>(key), T{}).first->second;
+    }
+
+    const T& operator[](const key_type& key) const
+    {
+        return at(key);
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    const T & operator[](KeyType && key) const
+    {
+        return at(std::forward<KeyType>(key));
+    }
+
+    T& at(const key_type& key)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    T & at(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    const T& at(const key_type& key) const
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    const T & at(KeyType && key) const // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it->second;
+            }
+        }
+
+        JSON_THROW(std::out_of_range("key not found"));
+    }
+
+    size_type erase(const key_type& key)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                // Since we cannot move const Keys, re-construct them in place
+                for (auto next = it; ++next != this->end(); ++it)
+                {
+                    it->~value_type(); // Destroy but keep allocation
+                    new (&*it) value_type{std::move(*next)};
+                }
+                Container::pop_back();
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    size_type erase(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                // Since we cannot move const Keys, re-construct them in place
+                for (auto next = it; ++next != this->end(); ++it)
+                {
+                    it->~value_type(); // Destroy but keep allocation
+                    new (&*it) value_type{std::move(*next)};
+                }
+                Container::pop_back();
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    iterator erase(iterator pos)
+    {
+        return erase(pos, std::next(pos));
+    }
+
+    iterator erase(iterator first, iterator last)
+    {
+        if (first == last)
+        {
+            return first;
+        }
+
+        const auto elements_affected = std::distance(first, last);
+        const auto offset = std::distance(Container::begin(), first);
+
+        // This is the start situation. We need to delete elements_affected
+        // elements (3 in this example: e, f, g), and need to return an
+        // iterator past the last deleted element (h in this example).
+        // Note that offset is the distance from the start of the vector
+        // to first. We will need this later.
+
+        // [ a, b, c, d, e, f, g, h, i, j ]
+        //               ^        ^
+        //             first    last
+
+        // Since we cannot move const Keys, we re-construct them in place.
+        // We start at first and re-construct (viz. copy) the elements from
+        // the back of the vector. Example for first iteration:
+
+        //               ,--------.
+        //               v        |   destroy e and re-construct with h
+        // [ a, b, c, d, e, f, g, h, i, j ]
+        //               ^        ^
+        //               it       it + elements_affected
+
+        for (auto it = first; std::next(it, elements_affected) != Container::end(); ++it)
+        {
+            it->~value_type(); // destroy but keep allocation
+            new (&*it) value_type{std::move(*std::next(it, elements_affected))}; // "move" next element to it
+        }
+
+        // [ a, b, c, d, h, i, j, h, i, j ]
+        //               ^        ^
+        //             first    last
+
+        // remove the unneeded elements at the end of the vector
+        Container::resize(this->size() - static_cast<size_type>(elements_affected));
+
+        // [ a, b, c, d, h, i, j ]
+        //               ^        ^
+        //             first    last
+
+        // first is now pointing past the last deleted element, but we cannot
+        // use this iterator, because it may have been invalidated by the
+        // resize call. Instead, we can return begin() + offset.
+        return Container::begin() + offset;
+    }
+
+    size_type count(const key_type& key) const
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    size_type count(KeyType && key) const // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return 1;
+            }
+        }
+        return 0;
+    }
+
+    iterator find(const key_type& key)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it;
+            }
+        }
+        return Container::end();
+    }
+
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_key_type<key_compare, key_type, KeyType>::value, int> = 0>
+    iterator find(KeyType && key) // NOLINT(cppcoreguidelines-missing-std-forward)
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it;
+            }
+        }
+        return Container::end();
+    }
+
+    const_iterator find(const key_type& key) const
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, key))
+            {
+                return it;
+            }
+        }
+        return Container::end();
+    }
+
+    std::pair<iterator, bool> insert( value_type&& value )
+    {
+        return emplace(value.first, std::move(value.second));
+    }
+
+    std::pair<iterator, bool> insert( const value_type& value )
+    {
+        for (auto it = this->begin(); it != this->end(); ++it)
+        {
+            if (m_compare(it->first, value.first))
+            {
+                return {it, false};
+            }
+        }
+        Container::push_back(value);
+        return {--this->end(), true};
+    }
+
+    template<typename InputIt>
+    using require_input_iter = typename std::enable_if<std::is_convertible<typename std::iterator_traits<InputIt>::iterator_category,
+        std::input_iterator_tag>::value>::type;
+
+    template<typename InputIt, typename = require_input_iter<InputIt>>
+    void insert(InputIt first, InputIt last)
+    {
+        for (auto it = first; it != last; ++it)
+        {
+            insert(*it);
+        }
+    }
+
+private:
+    JSON_NO_UNIQUE_ADDRESS key_compare m_compare = key_compare();
+};
+
+NLOHMANN_JSON_NAMESPACE_END
+
+
+#if defined(JSON_HAS_CPP_17)
+    #if JSON_HAS_STATIC_RTTI
+        #include <any>
+    #endif
+    #include <string_view>
+#endif
+
+/*!
+@brief namespace for Niels Lohmann
+@see https://github.com/nlohmann
+@since version 1.0.0
+*/
+NLOHMANN_JSON_NAMESPACE_BEGIN
+
+/*!
+@brief a class to store JSON values
+
+@internal
+@invariant The member variables @a m_value and @a m_type have the following
+relationship:
+- If `m_type == value_t::object`, then `m_value.object != nullptr`.
+- If `m_type == value_t::array`, then `m_value.array != nullptr`.
+- If `m_type == value_t::string`, then `m_value.string != nullptr`.
+The invariants are checked by member function assert_invariant().
+
+@note ObjectType trick from https://stackoverflow.com/a/9860911
+@endinternal
+
+@since version 1.0.0
+
+@nosubgrouping
+*/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+class basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-special-member-functions)
+    : public ::nlohmann::detail::json_base_class<CustomBaseClass>
+{
+  private:
+    template<detail::value_t> friend struct detail::external_constructor;
+
+    template<typename>
+    friend class ::nlohmann::json_pointer;
+    // can be restored when json_pointer backwards compatibility is removed
+    // friend ::nlohmann::json_pointer<StringType>;
+
+    template<typename BasicJsonType, typename InputType>
+    friend class ::nlohmann::detail::parser;
+    friend ::nlohmann::detail::serializer<basic_json>;
+    template<typename BasicJsonType>
+    friend class ::nlohmann::detail::iter_impl;
+    template<typename BasicJsonType, typename CharType>
+    friend class ::nlohmann::detail::binary_writer;
+    template<typename BasicJsonType, typename InputType, typename SAX>
+    friend class ::nlohmann::detail::binary_reader;
+    template<typename BasicJsonType, typename InputAdapterType>
+    friend class ::nlohmann::detail::json_sax_dom_parser;
+    template<typename BasicJsonType, typename InputAdapterType>
+    friend class ::nlohmann::detail::json_sax_dom_callback_parser;
+    friend class ::nlohmann::detail::exception;
+
+    /// workaround type for MSVC
+    using basic_json_t = NLOHMANN_BASIC_JSON_TPL;
+    using json_base_class_t = ::nlohmann::detail::json_base_class<CustomBaseClass>;
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    // convenience aliases for types residing in namespace detail;
+    using lexer = ::nlohmann::detail::lexer_base<basic_json>;
+
+    template<typename InputAdapterType>
+    static ::nlohmann::detail::parser<basic_json, InputAdapterType> parser(
+        InputAdapterType adapter,
+        detail::parser_callback_t<basic_json>cb = nullptr,
+        const bool allow_exceptions = true,
+        const bool ignore_comments = false
+                                 )
+    {
+        return ::nlohmann::detail::parser<basic_json, InputAdapterType>(std::move(adapter),
+            std::move(cb), allow_exceptions, ignore_comments);
+    }
+
+  private:
+    using primitive_iterator_t = ::nlohmann::detail::primitive_iterator_t;
+    template<typename BasicJsonType>
+    using internal_iterator = ::nlohmann::detail::internal_iterator<BasicJsonType>;
+    template<typename BasicJsonType>
+    using iter_impl = ::nlohmann::detail::iter_impl<BasicJsonType>;
+    template<typename Iterator>
+    using iteration_proxy = ::nlohmann::detail::iteration_proxy<Iterator>;
+    template<typename Base> using json_reverse_iterator = ::nlohmann::detail::json_reverse_iterator<Base>;
+
+    template<typename CharType>
+    using output_adapter_t = ::nlohmann::detail::output_adapter_t<CharType>;
+
+    template<typename InputType>
+    using binary_reader = ::nlohmann::detail::binary_reader<basic_json, InputType>;
+    template<typename CharType> using binary_writer = ::nlohmann::detail::binary_writer<basic_json, CharType>;
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    using serializer = ::nlohmann::detail::serializer<basic_json>;
+
+  public:
+    using value_t = detail::value_t;
+    /// JSON Pointer, see @ref nlohmann::json_pointer
+    using json_pointer = ::nlohmann::json_pointer<StringType>;
+    template<typename T, typename SFINAE>
+    using json_serializer = JSONSerializer<T, SFINAE>;
+    /// how to treat decoding errors
+    using error_handler_t = detail::error_handler_t;
+    /// how to treat CBOR tags
+    using cbor_tag_handler_t = detail::cbor_tag_handler_t;
+    /// how to encode BJData
+    using bjdata_version_t = detail::bjdata_version_t;
+    /// helper type for initializer lists of basic_json values
+    using initializer_list_t = std::initializer_list<detail::json_ref<basic_json>>;
+
+    using input_format_t = detail::input_format_t;
+    /// SAX interface type, see @ref nlohmann::json_sax
+    using json_sax_t = json_sax<basic_json>;
+
+    ////////////////
+    // exceptions //
+    ////////////////
+
+    /// @name exceptions
+    /// Classes to implement user-defined exceptions.
+    /// @{
+
+    using exception = detail::exception;
+    using parse_error = detail::parse_error;
+    using invalid_iterator = detail::invalid_iterator;
+    using type_error = detail::type_error;
+    using out_of_range = detail::out_of_range;
+    using other_error = detail::other_error;
+
+    /// @}
+
+    /////////////////////
+    // container types //
+    /////////////////////
+
+    /// @name container types
+    /// The canonic container types to use @ref basic_json like any other STL
+    /// container.
+    /// @{
+
+    /// the type of elements in a basic_json container
+    using value_type = basic_json;
+
+    /// the type of an element reference
+    using reference = value_type&;
+    /// the type of an element const reference
+    using const_reference = const value_type&;
+
+    /// a type to represent differences between iterators
+    using difference_type = std::ptrdiff_t;
+    /// a type to represent container sizes
+    using size_type = std::size_t;
+
+    /// the allocator type
+    using allocator_type = AllocatorType<basic_json>;
+
+    /// the type of an element pointer
+    using pointer = typename std::allocator_traits<allocator_type>::pointer;
+    /// the type of an element const pointer
+    using const_pointer = typename std::allocator_traits<allocator_type>::const_pointer;
+
+    /// an iterator for a basic_json container
+    using iterator = iter_impl<basic_json>;
+    /// a const iterator for a basic_json container
+    using const_iterator = iter_impl<const basic_json>;
+    /// a reverse iterator for a basic_json container
+    using reverse_iterator = json_reverse_iterator<typename basic_json::iterator>;
+    /// a const reverse iterator for a basic_json container
+    using const_reverse_iterator = json_reverse_iterator<typename basic_json::const_iterator>;
+
+    /// @}
+
+    /// @brief returns the allocator associated with the container
+    /// @sa https://json.nlohmann.me/api/basic_json/get_allocator/
+    static allocator_type get_allocator()
+    {
+        return allocator_type();
+    }
+
+    /// @brief returns version information on the library
+    /// @sa https://json.nlohmann.me/api/basic_json/meta/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json meta()
+    {
+        basic_json result;
+
+        result["copyright"] = "(C) 2013-2025 Niels Lohmann";
+        result["name"] = "JSON for Modern C++";
+        result["url"] = "https://github.com/nlohmann/json";
+        result["version"]["string"] =
+            detail::concat(std::to_string(NLOHMANN_JSON_VERSION_MAJOR), '.',
+                           std::to_string(NLOHMANN_JSON_VERSION_MINOR), '.',
+                           std::to_string(NLOHMANN_JSON_VERSION_PATCH));
+        result["version"]["major"] = NLOHMANN_JSON_VERSION_MAJOR;
+        result["version"]["minor"] = NLOHMANN_JSON_VERSION_MINOR;
+        result["version"]["patch"] = NLOHMANN_JSON_VERSION_PATCH;
+
+#ifdef _WIN32
+        result["platform"] = "win32";
+#elif defined __linux__
+        result["platform"] = "linux";
+#elif defined __APPLE__
+        result["platform"] = "apple";
+#elif defined __unix__
+        result["platform"] = "unix";
+#else
+        result["platform"] = "unknown";
+#endif
+
+#if defined(__ICC) || defined(__INTEL_COMPILER)
+        result["compiler"] = {{"family", "icc"}, {"version", __INTEL_COMPILER}};
+#elif defined(__clang__)
+        result["compiler"] = {{"family", "clang"}, {"version", __clang_version__}};
+#elif defined(__GNUC__) || defined(__GNUG__)
+        result["compiler"] = {{"family", "gcc"}, {"version", detail::concat(
+                    std::to_string(__GNUC__), '.',
+                    std::to_string(__GNUC_MINOR__), '.',
+                    std::to_string(__GNUC_PATCHLEVEL__))
+            }
+        };
+#elif defined(__HP_cc) || defined(__HP_aCC)
+        result["compiler"] = "hp"
+#elif defined(__IBMCPP__)
+        result["compiler"] = {{"family", "ilecpp"}, {"version", __IBMCPP__}};
+#elif defined(_MSC_VER)
+        result["compiler"] = {{"family", "msvc"}, {"version", _MSC_VER}};
+#elif defined(__PGI)
+        result["compiler"] = {{"family", "pgcpp"}, {"version", __PGI}};
+#elif defined(__SUNPRO_CC)
+        result["compiler"] = {{"family", "sunpro"}, {"version", __SUNPRO_CC}};
+#else
+        result["compiler"] = {{"family", "unknown"}, {"version", "unknown"}};
+#endif
+
+#if defined(_MSVC_LANG)
+        result["compiler"]["c++"] = std::to_string(_MSVC_LANG);
+#elif defined(__cplusplus)
+        result["compiler"]["c++"] = std::to_string(__cplusplus);
+#else
+        result["compiler"]["c++"] = "unknown";
+#endif
+        return result;
+    }
+
+    ///////////////////////////
+    // JSON value data types //
+    ///////////////////////////
+
+    /// @name JSON value data types
+    /// The data types to store a JSON value. These types are derived from
+    /// the template arguments passed to class @ref basic_json.
+    /// @{
+
+    /// @brief default object key comparator type
+    /// The actual object key comparator type (@ref object_comparator_t) may be
+    /// different.
+    /// @sa https://json.nlohmann.me/api/basic_json/default_object_comparator_t/
+#if defined(JSON_HAS_CPP_14)
+    // use of transparent comparator avoids unnecessary repeated construction of temporaries
+    // in functions involving lookup by key with types other than object_t::key_type (aka. StringType)
+    using default_object_comparator_t = std::less<>;
+#else
+    using default_object_comparator_t = std::less<StringType>;
+#endif
+
+    /// @brief a type for an object
+    /// @sa https://json.nlohmann.me/api/basic_json/object_t/
+    using object_t = ObjectType<StringType,
+          basic_json,
+          default_object_comparator_t,
+          AllocatorType<std::pair<const StringType,
+          basic_json>>>;
+
+    /// @brief a type for an array
+    /// @sa https://json.nlohmann.me/api/basic_json/array_t/
+    using array_t = ArrayType<basic_json, AllocatorType<basic_json>>;
+
+    /// @brief a type for a string
+    /// @sa https://json.nlohmann.me/api/basic_json/string_t/
+    using string_t = StringType;
+
+    /// @brief a type for a boolean
+    /// @sa https://json.nlohmann.me/api/basic_json/boolean_t/
+    using boolean_t = BooleanType;
+
+    /// @brief a type for a number (integer)
+    /// @sa https://json.nlohmann.me/api/basic_json/number_integer_t/
+    using number_integer_t = NumberIntegerType;
+
+    /// @brief a type for a number (unsigned)
+    /// @sa https://json.nlohmann.me/api/basic_json/number_unsigned_t/
+    using number_unsigned_t = NumberUnsignedType;
+
+    /// @brief a type for a number (floating-point)
+    /// @sa https://json.nlohmann.me/api/basic_json/number_float_t/
+    using number_float_t = NumberFloatType;
+
+    /// @brief a type for a packed binary type
+    /// @sa https://json.nlohmann.me/api/basic_json/binary_t/
+    using binary_t = nlohmann::byte_container_with_subtype<BinaryType>;
+
+    /// @brief object key comparator type
+    /// @sa https://json.nlohmann.me/api/basic_json/object_comparator_t/
+    using object_comparator_t = detail::actual_object_comparator_t<basic_json>;
+
+    /// @}
+
+  private:
+
+    /// helper for exception-safe object creation
+    template<typename T, typename... Args>
+    JSON_HEDLEY_RETURNS_NON_NULL
+    static T* create(Args&& ... args)
+    {
+        AllocatorType<T> alloc;
+        using AllocatorTraits = std::allocator_traits<AllocatorType<T>>;
+
+        auto deleter = [&](T * obj)
+        {
+            AllocatorTraits::deallocate(alloc, obj, 1);
+        };
+        std::unique_ptr<T, decltype(deleter)> obj(AllocatorTraits::allocate(alloc, 1), deleter);
+        AllocatorTraits::construct(alloc, obj.get(), std::forward<Args>(args)...);
+        JSON_ASSERT(obj != nullptr);
+        return obj.release();
+    }
+
+    ////////////////////////
+    // JSON value storage //
+    ////////////////////////
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    /*!
+    @brief a JSON value
+
+    The actual storage for a JSON value of the @ref basic_json class. This
+    union combines the different storage types for the JSON value types
+    defined in @ref value_t.
+
+    JSON type | value_t type    | used type
+    --------- | --------------- | ------------------------
+    object    | object          | pointer to @ref object_t
+    array     | array           | pointer to @ref array_t
+    string    | string          | pointer to @ref string_t
+    boolean   | boolean         | @ref boolean_t
+    number    | number_integer  | @ref number_integer_t
+    number    | number_unsigned | @ref number_unsigned_t
+    number    | number_float    | @ref number_float_t
+    binary    | binary          | pointer to @ref binary_t
+    null      | null            | *no value is stored*
+
+    @note Variable-length types (objects, arrays, and strings) are stored as
+    pointers. The size of the union should not exceed 64 bits if the default
+    value types are used.
+
+    @since version 1.0.0
+    */
+    union json_value
+    {
+        /// object (stored with pointer to save storage)
+        object_t* object;
+        /// array (stored with pointer to save storage)
+        array_t* array;
+        /// string (stored with pointer to save storage)
+        string_t* string;
+        /// binary (stored with pointer to save storage)
+        binary_t* binary;
+        /// boolean
+        boolean_t boolean;
+        /// number (integer)
+        number_integer_t number_integer;
+        /// number (unsigned integer)
+        number_unsigned_t number_unsigned;
+        /// number (floating-point)
+        number_float_t number_float;
+
+        /// default constructor (for null values)
+        json_value() = default;
+        /// constructor for booleans
+        json_value(boolean_t v) noexcept : boolean(v) {}
+        /// constructor for numbers (integer)
+        json_value(number_integer_t v) noexcept : number_integer(v) {}
+        /// constructor for numbers (unsigned)
+        json_value(number_unsigned_t v) noexcept : number_unsigned(v) {}
+        /// constructor for numbers (floating-point)
+        json_value(number_float_t v) noexcept : number_float(v) {}
+        /// constructor for empty values of a given type
+        json_value(value_t t)
+        {
+            switch (t)
+            {
+                case value_t::object:
+                {
+                    object = create<object_t>();
+                    break;
+                }
+
+                case value_t::array:
+                {
+                    array = create<array_t>();
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    string = create<string_t>("");
+                    break;
+                }
+
+                case value_t::binary:
+                {
+                    binary = create<binary_t>();
+                    break;
+                }
+
+                case value_t::boolean:
+                {
+                    boolean = static_cast<boolean_t>(false);
+                    break;
+                }
+
+                case value_t::number_integer:
+                {
+                    number_integer = static_cast<number_integer_t>(0);
+                    break;
+                }
+
+                case value_t::number_unsigned:
+                {
+                    number_unsigned = static_cast<number_unsigned_t>(0);
+                    break;
+                }
+
+                case value_t::number_float:
+                {
+                    number_float = static_cast<number_float_t>(0.0);
+                    break;
+                }
+
+                case value_t::null:
+                {
+                    object = nullptr;  // silence warning, see #821
+                    break;
+                }
+
+                case value_t::discarded:
+                default:
+                {
+                    object = nullptr;  // silence warning, see #821
+                    if (JSON_HEDLEY_UNLIKELY(t == value_t::null))
+                    {
+                        JSON_THROW(other_error::create(500, "961c151d2e87f2686a955a9be24d316f1362bf21 3.12.0", nullptr)); // LCOV_EXCL_LINE
+                    }
+                    break;
+                }
+            }
+        }
+
+        /// constructor for strings
+        json_value(const string_t& value) : string(create<string_t>(value)) {}
+
+        /// constructor for rvalue strings
+        json_value(string_t&& value) : string(create<string_t>(std::move(value))) {}
+
+        /// constructor for objects
+        json_value(const object_t& value) : object(create<object_t>(value)) {}
+
+        /// constructor for rvalue objects
+        json_value(object_t&& value) : object(create<object_t>(std::move(value))) {}
+
+        /// constructor for arrays
+        json_value(const array_t& value) : array(create<array_t>(value)) {}
+
+        /// constructor for rvalue arrays
+        json_value(array_t&& value) : array(create<array_t>(std::move(value))) {}
+
+        /// constructor for binary arrays
+        json_value(const typename binary_t::container_type& value) : binary(create<binary_t>(value)) {}
+
+        /// constructor for rvalue binary arrays
+        json_value(typename binary_t::container_type&& value) : binary(create<binary_t>(std::move(value))) {}
+
+        /// constructor for binary arrays (internal type)
+        json_value(const binary_t& value) : binary(create<binary_t>(value)) {}
+
+        /// constructor for rvalue binary arrays (internal type)
+        json_value(binary_t&& value) : binary(create<binary_t>(std::move(value))) {}
+
+        void destroy(value_t t)
+        {
+            if (
+                (t == value_t::object && object == nullptr) ||
+                (t == value_t::array && array == nullptr) ||
+                (t == value_t::string && string == nullptr) ||
+                (t == value_t::binary && binary == nullptr)
+            )
+            {
+                //not initialized (e.g. due to exception in the ctor)
+                return;
+            }
+            if (t == value_t::array || t == value_t::object)
+            {
+                // flatten the current json_value to a heap-allocated stack
+                std::vector<basic_json> stack;
+
+                // move the top-level items to stack
+                if (t == value_t::array)
+                {
+                    stack.reserve(array->size());
+                    std::move(array->begin(), array->end(), std::back_inserter(stack));
+                }
+                else
+                {
+                    stack.reserve(object->size());
+                    for (auto&& it : *object)
+                    {
+                        stack.push_back(std::move(it.second));
+                    }
+                }
+
+                while (!stack.empty())
+                {
+                    // move the last item to local variable to be processed
+                    basic_json current_item(std::move(stack.back()));
+                    stack.pop_back();
+
+                    // if current_item is array/object, move
+                    // its children to the stack to be processed later
+                    if (current_item.is_array())
+                    {
+                        std::move(current_item.m_data.m_value.array->begin(), current_item.m_data.m_value.array->end(), std::back_inserter(stack));
+
+                        current_item.m_data.m_value.array->clear();
+                    }
+                    else if (current_item.is_object())
+                    {
+                        for (auto&& it : *current_item.m_data.m_value.object)
+                        {
+                            stack.push_back(std::move(it.second));
+                        }
+
+                        current_item.m_data.m_value.object->clear();
+                    }
+
+                    // it's now safe that current_item get destructed
+                    // since it doesn't have any children
+                }
+            }
+
+            switch (t)
+            {
+                case value_t::object:
+                {
+                    AllocatorType<object_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, object);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, object, 1);
+                    break;
+                }
+
+                case value_t::array:
+                {
+                    AllocatorType<array_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, array);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, array, 1);
+                    break;
+                }
+
+                case value_t::string:
+                {
+                    AllocatorType<string_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, string);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, string, 1);
+                    break;
+                }
+
+                case value_t::binary:
+                {
+                    AllocatorType<binary_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, binary);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, binary, 1);
+                    break;
+                }
+
+                case value_t::null:
+                case value_t::boolean:
+                case value_t::number_integer:
+                case value_t::number_unsigned:
+                case value_t::number_float:
+                case value_t::discarded:
+                default:
+                {
+                    break;
+                }
+            }
+        }
+    };
+
+  private:
+    /*!
+    @brief checks the class invariants
+
+    This function asserts the class invariants. It needs to be called at the
+    end of every constructor to make sure that created objects respect the
+    invariant. Furthermore, it has to be called each time the type of a JSON
+    value is changed, because the invariant expresses a relationship between
+    @a m_type and @a m_value.
+
+    Furthermore, the parent relation is checked for arrays and objects: If
+    @a check_parents true and the value is an array or object, then the
+    container's elements must have the current value as parent.
+
+    @param[in] check_parents  whether the parent relation should be checked.
+               The value is true by default and should only be set to false
+               during destruction of objects when the invariant does not
+               need to hold.
+    */
+    void assert_invariant(bool check_parents = true) const noexcept
+    {
+        JSON_ASSERT(m_data.m_type != value_t::object || m_data.m_value.object != nullptr);
+        JSON_ASSERT(m_data.m_type != value_t::array || m_data.m_value.array != nullptr);
+        JSON_ASSERT(m_data.m_type != value_t::string || m_data.m_value.string != nullptr);
+        JSON_ASSERT(m_data.m_type != value_t::binary || m_data.m_value.binary != nullptr);
+
+#if JSON_DIAGNOSTICS
+        JSON_TRY
+        {
+            // cppcheck-suppress assertWithSideEffect
+            JSON_ASSERT(!check_parents || !is_structured() || std::all_of(begin(), end(), [this](const basic_json & j)
+            {
+                return j.m_parent == this;
+            }));
+        }
+        JSON_CATCH(...) {} // LCOV_EXCL_LINE
+#endif
+        static_cast<void>(check_parents);
+    }
+
+    void set_parents()
+    {
+#if JSON_DIAGNOSTICS
+        switch (m_data.m_type)
+        {
+            case value_t::array:
+            {
+                for (auto& element : *m_data.m_value.array)
+                {
+                    element.m_parent = this;
+                }
+                break;
+            }
+
+            case value_t::object:
+            {
+                for (auto& element : *m_data.m_value.object)
+                {
+                    element.second.m_parent = this;
+                }
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                break;
+        }
+#endif
+    }
+
+    iterator set_parents(iterator it, typename iterator::difference_type count_set_parents)
+    {
+#if JSON_DIAGNOSTICS
+        for (typename iterator::difference_type i = 0; i < count_set_parents; ++i)
+        {
+            (it + i)->m_parent = this;
+        }
+#else
+        static_cast<void>(count_set_parents);
+#endif
+        return it;
+    }
+
+    reference set_parent(reference j, std::size_t old_capacity = detail::unknown_size())
+    {
+#if JSON_DIAGNOSTICS
+        if (old_capacity != detail::unknown_size())
+        {
+            // see https://github.com/nlohmann/json/issues/2838
+            JSON_ASSERT(type() == value_t::array);
+            if (JSON_HEDLEY_UNLIKELY(m_data.m_value.array->capacity() != old_capacity))
+            {
+                // capacity has changed: update all parents
+                set_parents();
+                return j;
+            }
+        }
+
+        // ordered_json uses a vector internally, so pointers could have
+        // been invalidated; see https://github.com/nlohmann/json/issues/2962
+#ifdef JSON_HEDLEY_MSVC_VERSION
+#pragma warning(push )
+#pragma warning(disable : 4127) // ignore warning to replace if with if constexpr
+#endif
+        if (detail::is_ordered_map<object_t>::value)
+        {
+            set_parents();
+            return j;
+        }
+#ifdef JSON_HEDLEY_MSVC_VERSION
+#pragma warning( pop )
+#endif
+
+        j.m_parent = this;
+#else
+        static_cast<void>(j);
+        static_cast<void>(old_capacity);
+#endif
+        return j;
+    }
+
+  public:
+    //////////////////////////
+    // JSON parser callback //
+    //////////////////////////
+
+    /// @brief parser event types
+    /// @sa https://json.nlohmann.me/api/basic_json/parse_event_t/
+    using parse_event_t = detail::parse_event_t;
+
+    /// @brief per-element parser callback type
+    /// @sa https://json.nlohmann.me/api/basic_json/parser_callback_t/
+    using parser_callback_t = detail::parser_callback_t<basic_json>;
+
+    //////////////////
+    // constructors //
+    //////////////////
+
+    /// @name constructors and destructors
+    /// Constructors of class @ref basic_json, copy/move constructor, copy
+    /// assignment, static functions creating objects, and the destructor.
+    /// @{
+
+    /// @brief create an empty value with a given type
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(const value_t v)
+        : m_data(v)
+    {
+        assert_invariant();
+    }
+
+    /// @brief create a null object
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(std::nullptr_t = nullptr) noexcept // NOLINT(bugprone-exception-escape)
+        : basic_json(value_t::null)
+    {
+        assert_invariant();
+    }
+
+    /// @brief create a JSON value from compatible types
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    template < typename CompatibleType,
+               typename U = detail::uncvref_t<CompatibleType>,
+               detail::enable_if_t <
+                   !detail::is_basic_json<U>::value && detail::is_compatible_type<basic_json_t, U>::value, int > = 0 >
+    basic_json(CompatibleType && val) noexcept(noexcept( // NOLINT(bugprone-forwarding-reference-overload,bugprone-exception-escape)
+            JSONSerializer<U>::to_json(std::declval<basic_json_t&>(),
+                                       std::forward<CompatibleType>(val))))
+    {
+        JSONSerializer<U>::to_json(*this, std::forward<CompatibleType>(val));
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief create a JSON value from an existing one
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    template < typename BasicJsonType,
+               detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value&& !std::is_same<basic_json, BasicJsonType>::value, int > = 0 >
+    basic_json(const BasicJsonType& val)
+#if JSON_DIAGNOSTIC_POSITIONS
+        : start_position(val.start_pos()),
+          end_position(val.end_pos())
+#endif
+    {
+        using other_boolean_t = typename BasicJsonType::boolean_t;
+        using other_number_float_t = typename BasicJsonType::number_float_t;
+        using other_number_integer_t = typename BasicJsonType::number_integer_t;
+        using other_number_unsigned_t = typename BasicJsonType::number_unsigned_t;
+        using other_string_t = typename BasicJsonType::string_t;
+        using other_object_t = typename BasicJsonType::object_t;
+        using other_array_t = typename BasicJsonType::array_t;
+        using other_binary_t = typename BasicJsonType::binary_t;
+
+        switch (val.type())
+        {
+            case value_t::boolean:
+                JSONSerializer<other_boolean_t>::to_json(*this, val.template get<other_boolean_t>());
+                break;
+            case value_t::number_float:
+                JSONSerializer<other_number_float_t>::to_json(*this, val.template get<other_number_float_t>());
+                break;
+            case value_t::number_integer:
+                JSONSerializer<other_number_integer_t>::to_json(*this, val.template get<other_number_integer_t>());
+                break;
+            case value_t::number_unsigned:
+                JSONSerializer<other_number_unsigned_t>::to_json(*this, val.template get<other_number_unsigned_t>());
+                break;
+            case value_t::string:
+                JSONSerializer<other_string_t>::to_json(*this, val.template get_ref<const other_string_t&>());
+                break;
+            case value_t::object:
+                JSONSerializer<other_object_t>::to_json(*this, val.template get_ref<const other_object_t&>());
+                break;
+            case value_t::array:
+                JSONSerializer<other_array_t>::to_json(*this, val.template get_ref<const other_array_t&>());
+                break;
+            case value_t::binary:
+                JSONSerializer<other_binary_t>::to_json(*this, val.template get_ref<const other_binary_t&>());
+                break;
+            case value_t::null:
+                *this = nullptr;
+                break;
+            case value_t::discarded:
+                m_data.m_type = value_t::discarded;
+                break;
+            default:            // LCOV_EXCL_LINE
+                JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+        }
+        JSON_ASSERT(m_data.m_type == val.type());
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief create a container (array or object) from an initializer list
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(initializer_list_t init,
+               bool type_deduction = true,
+               value_t manual_type = value_t::array)
+    {
+        // check if each element is an array with two elements whose first
+        // element is a string
+        bool is_an_object = std::all_of(init.begin(), init.end(),
+                                        [](const detail::json_ref<basic_json>& element_ref)
+        {
+            // The cast is to ensure op[size_type] is called, bearing in mind size_type may not be int;
+            // (many string types can be constructed from 0 via its null-pointer guise, so we get a
+            // broken call to op[key_type], the wrong semantics and a 4804 warning on Windows)
+            return element_ref->is_array() && element_ref->size() == 2 && (*element_ref)[static_cast<size_type>(0)].is_string();
+        });
+
+        // adjust type if type deduction is not wanted
+        if (!type_deduction)
+        {
+            // if array is wanted, do not create an object though possible
+            if (manual_type == value_t::array)
+            {
+                is_an_object = false;
+            }
+
+            // if object is wanted but impossible, throw an exception
+            if (JSON_HEDLEY_UNLIKELY(manual_type == value_t::object && !is_an_object))
+            {
+                JSON_THROW(type_error::create(301, "cannot create object from initializer list", nullptr));
+            }
+        }
+
+        if (is_an_object)
+        {
+            // the initializer list is a list of pairs -> create object
+            m_data.m_type = value_t::object;
+            m_data.m_value = value_t::object;
+
+            for (auto& element_ref : init)
+            {
+                auto element = element_ref.moved_or_copied();
+                m_data.m_value.object->emplace(
+                    std::move(*((*element.m_data.m_value.array)[0].m_data.m_value.string)),
+                    std::move((*element.m_data.m_value.array)[1]));
+            }
+        }
+        else
+        {
+            // the initializer list describes an array -> create array
+            m_data.m_type = value_t::array;
+            m_data.m_value.array = create<array_t>(init.begin(), init.end());
+        }
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief explicitly create a binary array (without subtype)
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(const typename binary_t::container_type& init)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = init;
+        return res;
+    }
+
+    /// @brief explicitly create a binary array (with subtype)
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(const typename binary_t::container_type& init, typename binary_t::subtype_type subtype)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = binary_t(init, subtype);
+        return res;
+    }
+
+    /// @brief explicitly create a binary array
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(typename binary_t::container_type&& init)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = std::move(init);
+        return res;
+    }
+
+    /// @brief explicitly create a binary array (with subtype)
+    /// @sa https://json.nlohmann.me/api/basic_json/binary/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json binary(typename binary_t::container_type&& init, typename binary_t::subtype_type subtype)
+    {
+        auto res = basic_json();
+        res.m_data.m_type = value_t::binary;
+        res.m_data.m_value = binary_t(std::move(init), subtype);
+        return res;
+    }
+
+    /// @brief explicitly create an array from an initializer list
+    /// @sa https://json.nlohmann.me/api/basic_json/array/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json array(initializer_list_t init = {})
+    {
+        return basic_json(init, false, value_t::array);
+    }
+
+    /// @brief explicitly create an object from an initializer list
+    /// @sa https://json.nlohmann.me/api/basic_json/object/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json object(initializer_list_t init = {})
+    {
+        return basic_json(init, false, value_t::object);
+    }
+
+    /// @brief construct an array with count copies of given value
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(size_type cnt, const basic_json& val):
+        m_data{cnt, val}
+    {
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief construct a JSON container given an iterator range
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    template < class InputIT, typename std::enable_if <
+                   std::is_same<InputIT, typename basic_json_t::iterator>::value ||
+                   std::is_same<InputIT, typename basic_json_t::const_iterator>::value, int >::type = 0 >
+    basic_json(InputIT first, InputIT last) // NOLINT(performance-unnecessary-value-param)
+    {
+        JSON_ASSERT(first.m_object != nullptr);
+        JSON_ASSERT(last.m_object != nullptr);
+
+        // make sure iterator fits the current value
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(201, "iterators are not compatible", nullptr));
+        }
+
+        // copy type from first iterator
+        m_data.m_type = first.m_object->m_data.m_type;
+
+        // check if iterator range is complete for primitive values
+        switch (m_data.m_type)
+        {
+            case value_t::boolean:
+            case value_t::number_float:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::string:
+            {
+                if (JSON_HEDLEY_UNLIKELY(!first.m_it.primitive_iterator.is_begin()
+                                         || !last.m_it.primitive_iterator.is_end()))
+                {
+                    JSON_THROW(invalid_iterator::create(204, "iterators out of range", first.m_object));
+                }
+                break;
+            }
+
+            case value_t::null:
+            case value_t::object:
+            case value_t::array:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+                break;
+        }
+
+        switch (m_data.m_type)
+        {
+            case value_t::number_integer:
+            {
+                m_data.m_value.number_integer = first.m_object->m_data.m_value.number_integer;
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                m_data.m_value.number_unsigned = first.m_object->m_data.m_value.number_unsigned;
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                m_data.m_value.number_float = first.m_object->m_data.m_value.number_float;
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                m_data.m_value.boolean = first.m_object->m_data.m_value.boolean;
+                break;
+            }
+
+            case value_t::string:
+            {
+                m_data.m_value = *first.m_object->m_data.m_value.string;
+                break;
+            }
+
+            case value_t::object:
+            {
+                m_data.m_value.object = create<object_t>(first.m_it.object_iterator,
+                                        last.m_it.object_iterator);
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_data.m_value.array = create<array_t>(first.m_it.array_iterator,
+                                                       last.m_it.array_iterator);
+                break;
+            }
+
+            case value_t::binary:
+            {
+                m_data.m_value = *first.m_object->m_data.m_value.binary;
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                JSON_THROW(invalid_iterator::create(206, detail::concat("cannot construct with iterators from ", first.m_object->type_name()), first.m_object));
+        }
+
+        set_parents();
+        assert_invariant();
+    }
+
+    ///////////////////////////////////////
+    // other constructors and destructor //
+    ///////////////////////////////////////
+
+    template<typename JsonRef,
+             detail::enable_if_t<detail::conjunction<detail::is_json_ref<JsonRef>,
+                                 std::is_same<typename JsonRef::value_type, basic_json>>::value, int> = 0 >
+    basic_json(const JsonRef& ref) : basic_json(ref.moved_or_copied()) {}
+
+    /// @brief copy constructor
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(const basic_json& other)
+        : json_base_class_t(other)
+#if JSON_DIAGNOSTIC_POSITIONS
+        , start_position(other.start_position)
+        , end_position(other.end_position)
+#endif
+    {
+        m_data.m_type = other.m_data.m_type;
+        // check of passed value is valid
+        other.assert_invariant();
+
+        switch (m_data.m_type)
+        {
+            case value_t::object:
+            {
+                m_data.m_value = *other.m_data.m_value.object;
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_data.m_value = *other.m_data.m_value.array;
+                break;
+            }
+
+            case value_t::string:
+            {
+                m_data.m_value = *other.m_data.m_value.string;
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                m_data.m_value = other.m_data.m_value.boolean;
+                break;
+            }
+
+            case value_t::number_integer:
+            {
+                m_data.m_value = other.m_data.m_value.number_integer;
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                m_data.m_value = other.m_data.m_value.number_unsigned;
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                m_data.m_value = other.m_data.m_value.number_float;
+                break;
+            }
+
+            case value_t::binary:
+            {
+                m_data.m_value = *other.m_data.m_value.binary;
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                break;
+        }
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief move constructor
+    /// @sa https://json.nlohmann.me/api/basic_json/basic_json/
+    basic_json(basic_json&& other) noexcept
+        : json_base_class_t(std::forward<json_base_class_t>(other)),
+          m_data(std::move(other.m_data)) // cppcheck-suppress[accessForwarded] TODO check
+#if JSON_DIAGNOSTIC_POSITIONS
+        , start_position(other.start_position) // cppcheck-suppress[accessForwarded] TODO check
+        , end_position(other.end_position) // cppcheck-suppress[accessForwarded] TODO check
+#endif
+    {
+        // check that passed value is valid
+        other.assert_invariant(false); // cppcheck-suppress[accessForwarded]
+
+        // invalidate payload
+        other.m_data.m_type = value_t::null;
+        other.m_data.m_value = {};
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        other.start_position = std::string::npos;
+        other.end_position = std::string::npos;
+#endif
+
+        set_parents();
+        assert_invariant();
+    }
+
+    /// @brief copy assignment
+    /// @sa https://json.nlohmann.me/api/basic_json/operator=/
+    basic_json& operator=(basic_json other) noexcept (
+        std::is_nothrow_move_constructible<value_t>::value&&
+        std::is_nothrow_move_assignable<value_t>::value&&
+        std::is_nothrow_move_constructible<json_value>::value&&
+        std::is_nothrow_move_assignable<json_value>::value&&
+        std::is_nothrow_move_assignable<json_base_class_t>::value
+    )
+    {
+        // check that passed value is valid
+        other.assert_invariant();
+
+        using std::swap;
+        swap(m_data.m_type, other.m_data.m_type);
+        swap(m_data.m_value, other.m_data.m_value);
+
+#if JSON_DIAGNOSTIC_POSITIONS
+        swap(start_position, other.start_position);
+        swap(end_position, other.end_position);
+#endif
+
+        json_base_class_t::operator=(std::move(other));
+
+        set_parents();
+        assert_invariant();
+        return *this;
+    }
+
+    /// @brief destructor
+    /// @sa https://json.nlohmann.me/api/basic_json/~basic_json/
+    ~basic_json() noexcept
+    {
+        assert_invariant(false);
+    }
+
+    /// @}
+
+  public:
+    ///////////////////////
+    // object inspection //
+    ///////////////////////
+
+    /// @name object inspection
+    /// Functions to inspect the type of a JSON value.
+    /// @{
+
+    /// @brief serialization
+    /// @sa https://json.nlohmann.me/api/basic_json/dump/
+    string_t dump(const int indent = -1,
+                  const char indent_char = ' ',
+                  const bool ensure_ascii = false,
+                  const error_handler_t error_handler = error_handler_t::strict) const
+    {
+        string_t result;
+        serializer s(detail::output_adapter<char, string_t>(result), indent_char, error_handler);
+
+        if (indent >= 0)
+        {
+            s.dump(*this, true, ensure_ascii, static_cast<unsigned int>(indent));
+        }
+        else
+        {
+            s.dump(*this, false, ensure_ascii, 0);
+        }
+
+        return result;
+    }
+
+    /// @brief return the type of the JSON value (explicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/type/
+    constexpr value_t type() const noexcept
+    {
+        return m_data.m_type;
+    }
+
+    /// @brief return whether type is primitive
+    /// @sa https://json.nlohmann.me/api/basic_json/is_primitive/
+    constexpr bool is_primitive() const noexcept
+    {
+        return is_null() || is_string() || is_boolean() || is_number() || is_binary();
+    }
+
+    /// @brief return whether type is structured
+    /// @sa https://json.nlohmann.me/api/basic_json/is_structured/
+    constexpr bool is_structured() const noexcept
+    {
+        return is_array() || is_object();
+    }
+
+    /// @brief return whether value is null
+    /// @sa https://json.nlohmann.me/api/basic_json/is_null/
+    constexpr bool is_null() const noexcept
+    {
+        return m_data.m_type == value_t::null;
+    }
+
+    /// @brief return whether value is a boolean
+    /// @sa https://json.nlohmann.me/api/basic_json/is_boolean/
+    constexpr bool is_boolean() const noexcept
+    {
+        return m_data.m_type == value_t::boolean;
+    }
+
+    /// @brief return whether value is a number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number/
+    constexpr bool is_number() const noexcept
+    {
+        return is_number_integer() || is_number_float();
+    }
+
+    /// @brief return whether value is an integer number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number_integer/
+    constexpr bool is_number_integer() const noexcept
+    {
+        return m_data.m_type == value_t::number_integer || m_data.m_type == value_t::number_unsigned;
+    }
+
+    /// @brief return whether value is an unsigned integer number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number_unsigned/
+    constexpr bool is_number_unsigned() const noexcept
+    {
+        return m_data.m_type == value_t::number_unsigned;
+    }
+
+    /// @brief return whether value is a floating-point number
+    /// @sa https://json.nlohmann.me/api/basic_json/is_number_float/
+    constexpr bool is_number_float() const noexcept
+    {
+        return m_data.m_type == value_t::number_float;
+    }
+
+    /// @brief return whether value is an object
+    /// @sa https://json.nlohmann.me/api/basic_json/is_object/
+    constexpr bool is_object() const noexcept
+    {
+        return m_data.m_type == value_t::object;
+    }
+
+    /// @brief return whether value is an array
+    /// @sa https://json.nlohmann.me/api/basic_json/is_array/
+    constexpr bool is_array() const noexcept
+    {
+        return m_data.m_type == value_t::array;
+    }
+
+    /// @brief return whether value is a string
+    /// @sa https://json.nlohmann.me/api/basic_json/is_string/
+    constexpr bool is_string() const noexcept
+    {
+        return m_data.m_type == value_t::string;
+    }
+
+    /// @brief return whether value is a binary array
+    /// @sa https://json.nlohmann.me/api/basic_json/is_binary/
+    constexpr bool is_binary() const noexcept
+    {
+        return m_data.m_type == value_t::binary;
+    }
+
+    /// @brief return whether value is discarded
+    /// @sa https://json.nlohmann.me/api/basic_json/is_discarded/
+    constexpr bool is_discarded() const noexcept
+    {
+        return m_data.m_type == value_t::discarded;
+    }
+
+    /// @brief return the type of the JSON value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_value_t/
+    constexpr operator value_t() const noexcept
+    {
+        return m_data.m_type;
+    }
+
+    /// @}
+
+  private:
+    //////////////////
+    // value access //
+    //////////////////
+
+    /// get a boolean (explicit)
+    boolean_t get_impl(boolean_t* /*unused*/) const
+    {
+        if (JSON_HEDLEY_LIKELY(is_boolean()))
+        {
+            return m_data.m_value.boolean;
+        }
+
+        JSON_THROW(type_error::create(302, detail::concat("type must be boolean, but is ", type_name()), this));
+    }
+
+    /// get a pointer to the value (object)
+    object_t* get_impl_ptr(object_t* /*unused*/) noexcept
+    {
+        return is_object() ? m_data.m_value.object : nullptr;
+    }
+
+    /// get a pointer to the value (object)
+    constexpr const object_t* get_impl_ptr(const object_t* /*unused*/) const noexcept
+    {
+        return is_object() ? m_data.m_value.object : nullptr;
+    }
+
+    /// get a pointer to the value (array)
+    array_t* get_impl_ptr(array_t* /*unused*/) noexcept
+    {
+        return is_array() ? m_data.m_value.array : nullptr;
+    }
+
+    /// get a pointer to the value (array)
+    constexpr const array_t* get_impl_ptr(const array_t* /*unused*/) const noexcept
+    {
+        return is_array() ? m_data.m_value.array : nullptr;
+    }
+
+    /// get a pointer to the value (string)
+    string_t* get_impl_ptr(string_t* /*unused*/) noexcept
+    {
+        return is_string() ? m_data.m_value.string : nullptr;
+    }
+
+    /// get a pointer to the value (string)
+    constexpr const string_t* get_impl_ptr(const string_t* /*unused*/) const noexcept
+    {
+        return is_string() ? m_data.m_value.string : nullptr;
+    }
+
+    /// get a pointer to the value (boolean)
+    boolean_t* get_impl_ptr(boolean_t* /*unused*/) noexcept
+    {
+        return is_boolean() ? &m_data.m_value.boolean : nullptr;
+    }
+
+    /// get a pointer to the value (boolean)
+    constexpr const boolean_t* get_impl_ptr(const boolean_t* /*unused*/) const noexcept
+    {
+        return is_boolean() ? &m_data.m_value.boolean : nullptr;
+    }
+
+    /// get a pointer to the value (integer number)
+    number_integer_t* get_impl_ptr(number_integer_t* /*unused*/) noexcept
+    {
+        return m_data.m_type == value_t::number_integer ? &m_data.m_value.number_integer : nullptr;
+    }
+
+    /// get a pointer to the value (integer number)
+    constexpr const number_integer_t* get_impl_ptr(const number_integer_t* /*unused*/) const noexcept
+    {
+        return m_data.m_type == value_t::number_integer ? &m_data.m_value.number_integer : nullptr;
+    }
+
+    /// get a pointer to the value (unsigned number)
+    number_unsigned_t* get_impl_ptr(number_unsigned_t* /*unused*/) noexcept
+    {
+        return is_number_unsigned() ? &m_data.m_value.number_unsigned : nullptr;
+    }
+
+    /// get a pointer to the value (unsigned number)
+    constexpr const number_unsigned_t* get_impl_ptr(const number_unsigned_t* /*unused*/) const noexcept
+    {
+        return is_number_unsigned() ? &m_data.m_value.number_unsigned : nullptr;
+    }
+
+    /// get a pointer to the value (floating-point number)
+    number_float_t* get_impl_ptr(number_float_t* /*unused*/) noexcept
+    {
+        return is_number_float() ? &m_data.m_value.number_float : nullptr;
+    }
+
+    /// get a pointer to the value (floating-point number)
+    constexpr const number_float_t* get_impl_ptr(const number_float_t* /*unused*/) const noexcept
+    {
+        return is_number_float() ? &m_data.m_value.number_float : nullptr;
+    }
+
+    /// get a pointer to the value (binary)
+    binary_t* get_impl_ptr(binary_t* /*unused*/) noexcept
+    {
+        return is_binary() ? m_data.m_value.binary : nullptr;
+    }
+
+    /// get a pointer to the value (binary)
+    constexpr const binary_t* get_impl_ptr(const binary_t* /*unused*/) const noexcept
+    {
+        return is_binary() ? m_data.m_value.binary : nullptr;
+    }
+
+    /*!
+    @brief helper function to implement get_ref()
+
+    This function helps to implement get_ref() without code duplication for
+    const and non-const overloads
+
+    @tparam ThisType will be deduced as `basic_json` or `const basic_json`
+
+    @throw type_error.303 if ReferenceType does not match underlying value
+    type of the current JSON
+    */
+    template<typename ReferenceType, typename ThisType>
+    static ReferenceType get_ref_impl(ThisType& obj)
+    {
+        // delegate the call to get_ptr<>()
+        auto* ptr = obj.template get_ptr<typename std::add_pointer<ReferenceType>::type>();
+
+        if (JSON_HEDLEY_LIKELY(ptr != nullptr))
+        {
+            return *ptr;
+        }
+
+        JSON_THROW(type_error::create(303, detail::concat("incompatible ReferenceType for get_ref, actual type is ", obj.type_name()), &obj));
+    }
+
+  public:
+    /// @name value access
+    /// Direct access to the stored value of a JSON value.
+    /// @{
+
+    /// @brief get a pointer value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ptr/
+    template<typename PointerType, typename std::enable_if<
+                 std::is_pointer<PointerType>::value, int>::type = 0>
+    auto get_ptr() noexcept -> decltype(std::declval<basic_json_t&>().get_impl_ptr(std::declval<PointerType>()))
+    {
+        // delegate the call to get_impl_ptr<>()
+        return get_impl_ptr(static_cast<PointerType>(nullptr));
+    }
+
+    /// @brief get a pointer value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ptr/
+    template < typename PointerType, typename std::enable_if <
+                   std::is_pointer<PointerType>::value&&
+                   std::is_const<typename std::remove_pointer<PointerType>::type>::value, int >::type = 0 >
+    constexpr auto get_ptr() const noexcept -> decltype(std::declval<const basic_json_t&>().get_impl_ptr(std::declval<PointerType>()))
+    {
+        // delegate the call to get_impl_ptr<>() const
+        return get_impl_ptr(static_cast<PointerType>(nullptr));
+    }
+
+  private:
+    /*!
+    @brief get a value (explicit)
+
+    Explicit type conversion between the JSON value and a compatible value
+    which is [CopyConstructible](https://en.cppreference.com/w/cpp/named_req/CopyConstructible)
+    and [DefaultConstructible](https://en.cppreference.com/w/cpp/named_req/DefaultConstructible).
+    The value is converted by calling the @ref json_serializer<ValueType>
+    `from_json()` method.
+
+    The function is equivalent to executing
+    @code {.cpp}
+    ValueType ret;
+    JSONSerializer<ValueType>::from_json(*this, ret);
+    return ret;
+    @endcode
+
+    This overloads is chosen if:
+    - @a ValueType is not @ref basic_json,
+    - @ref json_serializer<ValueType> has a `from_json()` method of the form
+      `void from_json(const basic_json&, ValueType&)`, and
+    - @ref json_serializer<ValueType> does not have a `from_json()` method of
+      the form `ValueType from_json(const basic_json&)`
+
+    @tparam ValueType the returned value type
+
+    @return copy of the JSON value, converted to @a ValueType
+
+    @throw what @ref json_serializer<ValueType> `from_json()` method throws
+
+    @liveexample{The example below shows several conversions from JSON values
+    to other types. There a few things to note: (1) Floating-point numbers can
+    be converted to integers\, (2) A JSON array can be converted to a standard
+    `std::vector<short>`\, (3) A JSON object can be converted to C++
+    associative containers such as `std::unordered_map<std::string\,
+    json>`.,get__ValueType_const}
+
+    @since version 2.1.0
+    */
+    template < typename ValueType,
+               detail::enable_if_t <
+                   detail::is_default_constructible<ValueType>::value&&
+                   detail::has_from_json<basic_json_t, ValueType>::value,
+                   int > = 0 >
+    ValueType get_impl(detail::priority_tag<0> /*unused*/) const noexcept(noexcept(
+            JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>(), std::declval<ValueType&>())))
+    {
+        auto ret = ValueType();
+        JSONSerializer<ValueType>::from_json(*this, ret);
+        return ret;
+    }
+
+    /*!
+    @brief get a value (explicit); special case
+
+    Explicit type conversion between the JSON value and a compatible value
+    which is **not** [CopyConstructible](https://en.cppreference.com/w/cpp/named_req/CopyConstructible)
+    and **not** [DefaultConstructible](https://en.cppreference.com/w/cpp/named_req/DefaultConstructible).
+    The value is converted by calling the @ref json_serializer<ValueType>
+    `from_json()` method.
+
+    The function is equivalent to executing
+    @code {.cpp}
+    return JSONSerializer<ValueType>::from_json(*this);
+    @endcode
+
+    This overloads is chosen if:
+    - @a ValueType is not @ref basic_json and
+    - @ref json_serializer<ValueType> has a `from_json()` method of the form
+      `ValueType from_json(const basic_json&)`
+
+    @note If @ref json_serializer<ValueType> has both overloads of
+    `from_json()`, this one is chosen.
+
+    @tparam ValueType the returned value type
+
+    @return copy of the JSON value, converted to @a ValueType
+
+    @throw what @ref json_serializer<ValueType> `from_json()` method throws
+
+    @since version 2.1.0
+    */
+    template < typename ValueType,
+               detail::enable_if_t <
+                   detail::has_non_default_from_json<basic_json_t, ValueType>::value,
+                   int > = 0 >
+    ValueType get_impl(detail::priority_tag<1> /*unused*/) const noexcept(noexcept(
+            JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>())))
+    {
+        return JSONSerializer<ValueType>::from_json(*this);
+    }
+
+    /*!
+    @brief get special-case overload
+
+    This overloads converts the current @ref basic_json in a different
+    @ref basic_json type
+
+    @tparam BasicJsonType == @ref basic_json
+
+    @return a copy of *this, converted into @a BasicJsonType
+
+    @complexity Depending on the implementation of the called `from_json()`
+                method.
+
+    @since version 3.2.0
+    */
+    template < typename BasicJsonType,
+               detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value,
+                   int > = 0 >
+    BasicJsonType get_impl(detail::priority_tag<2> /*unused*/) const
+    {
+        return *this;
+    }
+
+    /*!
+    @brief get special-case overload
+
+    This overloads avoids a lot of template boilerplate, it can be seen as the
+    identity method
+
+    @tparam BasicJsonType == @ref basic_json
+
+    @return a copy of *this
+
+    @complexity Constant.
+
+    @since version 2.1.0
+    */
+    template<typename BasicJsonType,
+             detail::enable_if_t<
+                 std::is_same<BasicJsonType, basic_json_t>::value,
+                 int> = 0>
+    basic_json get_impl(detail::priority_tag<3> /*unused*/) const
+    {
+        return *this;
+    }
+
+    /*!
+    @brief get a pointer value (explicit)
+    @copydoc get()
+    */
+    template<typename PointerType,
+             detail::enable_if_t<
+                 std::is_pointer<PointerType>::value,
+                 int> = 0>
+    constexpr auto get_impl(detail::priority_tag<4> /*unused*/) const noexcept
+    -> decltype(std::declval<const basic_json_t&>().template get_ptr<PointerType>())
+    {
+        // delegate the call to get_ptr
+        return get_ptr<PointerType>();
+    }
+
+  public:
+    /*!
+    @brief get a (pointer) value (explicit)
+
+    Performs explicit type conversion between the JSON value and a compatible value if required.
+
+    - If the requested type is a pointer to the internally stored JSON value that pointer is returned.
+    No copies are made.
+
+    - If the requested type is the current @ref basic_json, or a different @ref basic_json convertible
+    from the current @ref basic_json.
+
+    - Otherwise the value is converted by calling the @ref json_serializer<ValueType> `from_json()`
+    method.
+
+    @tparam ValueTypeCV the provided value type
+    @tparam ValueType the returned value type
+
+    @return copy of the JSON value, converted to @tparam ValueType if necessary
+
+    @throw what @ref json_serializer<ValueType> `from_json()` method throws if conversion is required
+
+    @since version 2.1.0
+    */
+    template < typename ValueTypeCV, typename ValueType = detail::uncvref_t<ValueTypeCV>>
+#if defined(JSON_HAS_CPP_14)
+    constexpr
+#endif
+    auto get() const noexcept(
+    noexcept(std::declval<const basic_json_t&>().template get_impl<ValueType>(detail::priority_tag<4> {})))
+    -> decltype(std::declval<const basic_json_t&>().template get_impl<ValueType>(detail::priority_tag<4> {}))
+    {
+        // we cannot static_assert on ValueTypeCV being non-const, because
+        // there is support for get<const basic_json_t>(), which is why we
+        // still need the uncvref
+        static_assert(!std::is_reference<ValueTypeCV>::value,
+                      "get() cannot be used with reference types, you might want to use get_ref()");
+        return get_impl<ValueType>(detail::priority_tag<4> {});
+    }
+
+    /*!
+    @brief get a pointer value (explicit)
+
+    Explicit pointer access to the internally stored JSON value. No copies are
+    made.
+
+    @warning The pointer becomes invalid if the underlying JSON object
+    changes.
+
+    @tparam PointerType pointer type; must be a pointer to @ref array_t, @ref
+    object_t, @ref string_t, @ref boolean_t, @ref number_integer_t,
+    @ref number_unsigned_t, or @ref number_float_t.
+
+    @return pointer to the internally stored JSON value if the requested
+    pointer type @a PointerType fits to the JSON value; `nullptr` otherwise
+
+    @complexity Constant.
+
+    @liveexample{The example below shows how pointers to internal values of a
+    JSON value can be requested. Note that no type conversions are made and a
+    `nullptr` is returned if the value and the requested pointer type does not
+    match.,get__PointerType}
+
+    @sa see @ref get_ptr() for explicit pointer-member access
+
+    @since version 1.0.0
+    */
+    template<typename PointerType, typename std::enable_if<
+                 std::is_pointer<PointerType>::value, int>::type = 0>
+    auto get() noexcept -> decltype(std::declval<basic_json_t&>().template get_ptr<PointerType>())
+    {
+        // delegate the call to get_ptr
+        return get_ptr<PointerType>();
+    }
+
+    /// @brief get a value (explicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_to/
+    template < typename ValueType,
+               detail::enable_if_t <
+                   !detail::is_basic_json<ValueType>::value&&
+                   detail::has_from_json<basic_json_t, ValueType>::value,
+                   int > = 0 >
+    ValueType & get_to(ValueType& v) const noexcept(noexcept(
+            JSONSerializer<ValueType>::from_json(std::declval<const basic_json_t&>(), v)))
+    {
+        JSONSerializer<ValueType>::from_json(*this, v);
+        return v;
+    }
+
+    // specialization to allow calling get_to with a basic_json value
+    // see https://github.com/nlohmann/json/issues/2175
+    template<typename ValueType,
+             detail::enable_if_t <
+                 detail::is_basic_json<ValueType>::value,
+                 int> = 0>
+    ValueType & get_to(ValueType& v) const
+    {
+        v = *this;
+        return v;
+    }
+
+    template <
+        typename T, std::size_t N,
+        typename Array = T (&)[N], // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+        detail::enable_if_t <
+            detail::has_from_json<basic_json_t, Array>::value, int > = 0 >
+    Array get_to(T (&v)[N]) const // NOLINT(cppcoreguidelines-avoid-c-arrays,hicpp-avoid-c-arrays,modernize-avoid-c-arrays)
+    noexcept(noexcept(JSONSerializer<Array>::from_json(
+                          std::declval<const basic_json_t&>(), v)))
+    {
+        JSONSerializer<Array>::from_json(*this, v);
+        return v;
+    }
+
+    /// @brief get a reference value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ref/
+    template<typename ReferenceType, typename std::enable_if<
+                 std::is_reference<ReferenceType>::value, int>::type = 0>
+    ReferenceType get_ref()
+    {
+        // delegate call to get_ref_impl
+        return get_ref_impl<ReferenceType>(*this);
+    }
+
+    /// @brief get a reference value (implicit)
+    /// @sa https://json.nlohmann.me/api/basic_json/get_ref/
+    template < typename ReferenceType, typename std::enable_if <
+                   std::is_reference<ReferenceType>::value&&
+                   std::is_const<typename std::remove_reference<ReferenceType>::type>::value, int >::type = 0 >
+    ReferenceType get_ref() const
+    {
+        // delegate call to get_ref_impl
+        return get_ref_impl<ReferenceType>(*this);
+    }
+
+    /*!
+    @brief get a value (implicit)
+
+    Implicit type conversion between the JSON value and a compatible value.
+    The call is realized by calling @ref get() const.
+
+    @tparam ValueType non-pointer type compatible to the JSON value, for
+    instance `int` for JSON integer numbers, `bool` for JSON booleans, or
+    `std::vector` types for JSON arrays. The character type of @ref string_t
+    as well as an initializer list of this type is excluded to avoid
+    ambiguities as these types implicitly convert to `std::string`.
+
+    @return copy of the JSON value, converted to type @a ValueType
+
+    @throw type_error.302 in case passed type @a ValueType is incompatible
+    to the JSON value type (e.g., the JSON value is of type boolean, but a
+    string is requested); see example below
+
+    @complexity Linear in the size of the JSON value.
+
+    @liveexample{The example below shows several conversions from JSON values
+    to other types. There a few things to note: (1) Floating-point numbers can
+    be converted to integers\, (2) A JSON array can be converted to a standard
+    `std::vector<short>`\, (3) A JSON object can be converted to C++
+    associative containers such as `std::unordered_map<std::string\,
+    json>`.,operator__ValueType}
+
+    @since version 1.0.0
+    */
+    template < typename ValueType, typename std::enable_if <
+                   detail::conjunction <
+                       detail::negation<std::is_pointer<ValueType>>,
+                       detail::negation<std::is_same<ValueType, std::nullptr_t>>,
+                       detail::negation<std::is_same<ValueType, detail::json_ref<basic_json>>>,
+                                        detail::negation<std::is_same<ValueType, typename string_t::value_type>>,
+                                        detail::negation<detail::is_basic_json<ValueType>>,
+                                        detail::negation<std::is_same<ValueType, std::initializer_list<typename string_t::value_type>>>,
+#if defined(JSON_HAS_CPP_17) && (defined(__GNUC__) || (defined(_MSC_VER) && _MSC_VER >= 1910 && _MSC_VER <= 1914))
+                                                detail::negation<std::is_same<ValueType, std::string_view>>,
+#endif
+#if defined(JSON_HAS_CPP_17) && JSON_HAS_STATIC_RTTI
+                                                detail::negation<std::is_same<ValueType, std::any>>,
+#endif
+                                                detail::is_detected_lazy<detail::get_template_function, const basic_json_t&, ValueType>
+                                                >::value, int >::type = 0 >
+                                        JSON_EXPLICIT operator ValueType() const
+    {
+        // delegate the call to get<>() const
+        return get<ValueType>();
+    }
+
+    /// @brief get a binary value
+    /// @sa https://json.nlohmann.me/api/basic_json/get_binary/
+    binary_t& get_binary()
+    {
+        if (!is_binary())
+        {
+            JSON_THROW(type_error::create(302, detail::concat("type must be binary, but is ", type_name()), this));
+        }
+
+        return *get_ptr<binary_t*>();
+    }
+
+    /// @brief get a binary value
+    /// @sa https://json.nlohmann.me/api/basic_json/get_binary/
+    const binary_t& get_binary() const
+    {
+        if (!is_binary())
+        {
+            JSON_THROW(type_error::create(302, detail::concat("type must be binary, but is ", type_name()), this));
+        }
+
+        return *get_ptr<const binary_t*>();
+    }
+
+    /// @}
+
+    ////////////////////
+    // element access //
+    ////////////////////
+
+    /// @name element access
+    /// Access to the JSON value.
+    /// @{
+
+    /// @brief access specified array element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    reference at(size_type idx)
+    {
+        // at only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            JSON_TRY
+            {
+                return set_parent(m_data.m_value.array->at(idx));
+            }
+            JSON_CATCH (std::out_of_range&)
+            {
+                // create better exception explanation
+                JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), this));
+            } // cppcheck-suppress[missingReturn]
+        }
+        else
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+    }
+
+    /// @brief access specified array element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    const_reference at(size_type idx) const
+    {
+        // at only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            JSON_TRY
+            {
+                return m_data.m_value.array->at(idx);
+            }
+            JSON_CATCH (std::out_of_range&)
+            {
+                // create better exception explanation
+                JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), this));
+            } // cppcheck-suppress[missingReturn]
+        }
+        else
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    reference at(const typename object_t::key_type& key)
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(key);
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", key, "' not found"), this));
+        }
+        return set_parent(it->second);
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    reference at(KeyType && key)
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", string_t(std::forward<KeyType>(key)), "' not found"), this));
+        }
+        return set_parent(it->second);
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    const_reference at(const typename object_t::key_type& key) const
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(key);
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", key, "' not found"), this));
+        }
+        return it->second;
+    }
+
+    /// @brief access specified object element with bounds checking
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    const_reference at(KeyType && key) const
+    {
+        // at only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(304, detail::concat("cannot use at() with ", type_name()), this));
+        }
+
+        auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+        if (it == m_data.m_value.object->end())
+        {
+            JSON_THROW(out_of_range::create(403, detail::concat("key '", string_t(std::forward<KeyType>(key)), "' not found"), this));
+        }
+        return it->second;
+    }
+
+    /// @brief access specified array element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    reference operator[](size_type idx)
+    {
+        // implicitly convert null value to an empty array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value.array = create<array_t>();
+            assert_invariant();
+        }
+
+        // operator[] only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            // fill up array with null values if given idx is outside range
+            if (idx >= m_data.m_value.array->size())
+            {
+#if JSON_DIAGNOSTICS
+                // remember array size & capacity before resizing
+                const auto old_size = m_data.m_value.array->size();
+                const auto old_capacity = m_data.m_value.array->capacity();
+#endif
+                m_data.m_value.array->resize(idx + 1);
+
+#if JSON_DIAGNOSTICS
+                if (JSON_HEDLEY_UNLIKELY(m_data.m_value.array->capacity() != old_capacity))
+                {
+                    // capacity has changed: update all parents
+                    set_parents();
+                }
+                else
+                {
+                    // set parent for values added above
+                    set_parents(begin() + static_cast<typename iterator::difference_type>(old_size), static_cast<typename iterator::difference_type>(idx + 1 - old_size));
+                }
+#endif
+                assert_invariant();
+            }
+
+            return m_data.m_value.array->operator[](idx);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a numeric argument with ", type_name()), this));
+    }
+
+    /// @brief access specified array element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    const_reference operator[](size_type idx) const
+    {
+        // const operator[] only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            return m_data.m_value.array->operator[](idx);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a numeric argument with ", type_name()), this));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    reference operator[](typename object_t::key_type key) // NOLINT(performance-unnecessary-value-param)
+    {
+        // implicitly convert null value to an empty object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value.object = create<object_t>();
+            assert_invariant();
+        }
+
+        // operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto result = m_data.m_value.object->emplace(std::move(key), nullptr);
+            return set_parent(result.first->second);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    const_reference operator[](const typename object_t::key_type& key) const
+    {
+        // const operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto it = m_data.m_value.object->find(key);
+            JSON_ASSERT(it != m_data.m_value.object->end());
+            return it->second;
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+    // these two functions resolve a (const) char * ambiguity affecting Clang and MSVC
+    // (they seemingly cannot be constrained to resolve the ambiguity)
+    template<typename T>
+    reference operator[](T* key)
+    {
+        return operator[](typename object_t::key_type(key));
+    }
+
+    template<typename T>
+    const_reference operator[](T* key) const
+    {
+        return operator[](typename object_t::key_type(key));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    reference operator[](KeyType && key)
+    {
+        // implicitly convert null value to an empty object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value.object = create<object_t>();
+            assert_invariant();
+        }
+
+        // operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto result = m_data.m_value.object->emplace(std::forward<KeyType>(key), nullptr);
+            return set_parent(result.first->second);
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+    /// @brief access specified object element
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    const_reference operator[](KeyType && key) const
+    {
+        // const operator[] only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+            JSON_ASSERT(it != m_data.m_value.object->end());
+            return it->second;
+        }
+
+        JSON_THROW(type_error::create(305, detail::concat("cannot use operator[] with a string argument with ", type_name()), this));
+    }
+
+  private:
+    template<typename KeyType>
+    using is_comparable_with_object_key = detail::is_comparable <
+        object_comparator_t, const typename object_t::key_type&, KeyType >;
+
+    template<typename ValueType>
+    using value_return_type = std::conditional <
+        detail::is_c_string_uncvref<ValueType>::value,
+        string_t, typename std::decay<ValueType>::type >;
+
+  public:
+    /// @brief access specified object element with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, detail::enable_if_t <
+                   !detail::is_transparent<object_comparator_t>::value
+                   && detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ValueType value(const typename object_t::key_type& key, const ValueType& default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(key);
+            if (it != end())
+            {
+                return it->template get<ValueType>();
+            }
+
+            return default_value;
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   !detail::is_transparent<object_comparator_t>::value
+                   && detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ReturnType value(const typename object_t::key_type& key, ValueType && default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(key);
+            if (it != end())
+            {
+                return it->template get<ReturnType>();
+            }
+
+            return std::forward<ValueType>(default_value);
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class KeyType, detail::enable_if_t <
+                   detail::is_transparent<object_comparator_t>::value
+                   && !detail::is_json_pointer<KeyType>::value
+                   && is_comparable_with_object_key<KeyType>::value
+                   && detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ValueType value(KeyType && key, const ValueType& default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(std::forward<KeyType>(key));
+            if (it != end())
+            {
+                return it->template get<ValueType>();
+            }
+
+            return default_value;
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element via JSON Pointer with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class KeyType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   detail::is_transparent<object_comparator_t>::value
+                   && !detail::is_json_pointer<KeyType>::value
+                   && is_comparable_with_object_key<KeyType>::value
+                   && detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ReturnType value(KeyType && key, ValueType && default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if key is found, return value and given default value otherwise
+            const auto it = find(std::forward<KeyType>(key));
+            if (it != end())
+            {
+                return it->template get<ReturnType>();
+            }
+
+            return std::forward<ValueType>(default_value);
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element via JSON Pointer with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, detail::enable_if_t <
+                   detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ValueType value(const json_pointer& ptr, const ValueType& default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if pointer resolves a value, return it or use default value
+            JSON_TRY
+            {
+                return ptr.get_checked(this).template get<ValueType>();
+            }
+            JSON_INTERNAL_CATCH (out_of_range&)
+            {
+                return default_value;
+            }
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    /// @brief access specified object element via JSON Pointer with default value
+    /// @sa https://json.nlohmann.me/api/basic_json/value/
+    template < class ValueType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    ReturnType value(const json_pointer& ptr, ValueType && default_value) const
+    {
+        // value only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            // if pointer resolves a value, return it or use default value
+            JSON_TRY
+            {
+                return ptr.get_checked(this).template get<ReturnType>();
+            }
+            JSON_INTERNAL_CATCH (out_of_range&)
+            {
+                return std::forward<ValueType>(default_value);
+            }
+        }
+
+        JSON_THROW(type_error::create(306, detail::concat("cannot use value() with ", type_name()), this));
+    }
+
+    template < class ValueType, class BasicJsonType, detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value
+                   && detail::is_getable<basic_json_t, ValueType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    ValueType value(const ::nlohmann::json_pointer<BasicJsonType>& ptr, const ValueType& default_value) const
+    {
+        return value(ptr.convert(), default_value);
+    }
+
+    template < class ValueType, class BasicJsonType, class ReturnType = typename value_return_type<ValueType>::type,
+               detail::enable_if_t <
+                   detail::is_basic_json<BasicJsonType>::value
+                   && detail::is_getable<basic_json_t, ReturnType>::value
+                   && !std::is_same<value_t, detail::uncvref_t<ValueType>>::value, int > = 0 >
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    ReturnType value(const ::nlohmann::json_pointer<BasicJsonType>& ptr, ValueType && default_value) const
+    {
+        return value(ptr.convert(), std::forward<ValueType>(default_value));
+    }
+
+    /// @brief access the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/front/
+    reference front()
+    {
+        return *begin();
+    }
+
+    /// @brief access the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/front/
+    const_reference front() const
+    {
+        return *cbegin();
+    }
+
+    /// @brief access the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/back/
+    reference back()
+    {
+        auto tmp = end();
+        --tmp;
+        return *tmp;
+    }
+
+    /// @brief access the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/back/
+    const_reference back() const
+    {
+        auto tmp = cend();
+        --tmp;
+        return *tmp;
+    }
+
+    /// @brief remove element given an iterator
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    template < class IteratorType, detail::enable_if_t <
+                   std::is_same<IteratorType, typename basic_json_t::iterator>::value ||
+                   std::is_same<IteratorType, typename basic_json_t::const_iterator>::value, int > = 0 >
+    IteratorType erase(IteratorType pos) // NOLINT(performance-unnecessary-value-param)
+    {
+        // make sure iterator fits the current value
+        if (JSON_HEDLEY_UNLIKELY(this != pos.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+        }
+
+        IteratorType result = end();
+
+        switch (m_data.m_type)
+        {
+            case value_t::boolean:
+            case value_t::number_float:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::string:
+            case value_t::binary:
+            {
+                if (JSON_HEDLEY_UNLIKELY(!pos.m_it.primitive_iterator.is_begin()))
+                {
+                    JSON_THROW(invalid_iterator::create(205, "iterator out of range", this));
+                }
+
+                if (is_string())
+                {
+                    AllocatorType<string_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.string);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.string, 1);
+                    m_data.m_value.string = nullptr;
+                }
+                else if (is_binary())
+                {
+                    AllocatorType<binary_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.binary);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.binary, 1);
+                    m_data.m_value.binary = nullptr;
+                }
+
+                m_data.m_type = value_t::null;
+                assert_invariant();
+                break;
+            }
+
+            case value_t::object:
+            {
+                result.m_it.object_iterator = m_data.m_value.object->erase(pos.m_it.object_iterator);
+                break;
+            }
+
+            case value_t::array:
+            {
+                result.m_it.array_iterator = m_data.m_value.array->erase(pos.m_it.array_iterator);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        return result;
+    }
+
+    /// @brief remove elements given an iterator range
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    template < class IteratorType, detail::enable_if_t <
+                   std::is_same<IteratorType, typename basic_json_t::iterator>::value ||
+                   std::is_same<IteratorType, typename basic_json_t::const_iterator>::value, int > = 0 >
+    IteratorType erase(IteratorType first, IteratorType last) // NOLINT(performance-unnecessary-value-param)
+    {
+        // make sure iterator fits the current value
+        if (JSON_HEDLEY_UNLIKELY(this != first.m_object || this != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(203, "iterators do not fit current value", this));
+        }
+
+        IteratorType result = end();
+
+        switch (m_data.m_type)
+        {
+            case value_t::boolean:
+            case value_t::number_float:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::string:
+            case value_t::binary:
+            {
+                if (JSON_HEDLEY_LIKELY(!first.m_it.primitive_iterator.is_begin()
+                                       || !last.m_it.primitive_iterator.is_end()))
+                {
+                    JSON_THROW(invalid_iterator::create(204, "iterators out of range", this));
+                }
+
+                if (is_string())
+                {
+                    AllocatorType<string_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.string);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.string, 1);
+                    m_data.m_value.string = nullptr;
+                }
+                else if (is_binary())
+                {
+                    AllocatorType<binary_t> alloc;
+                    std::allocator_traits<decltype(alloc)>::destroy(alloc, m_data.m_value.binary);
+                    std::allocator_traits<decltype(alloc)>::deallocate(alloc, m_data.m_value.binary, 1);
+                    m_data.m_value.binary = nullptr;
+                }
+
+                m_data.m_type = value_t::null;
+                assert_invariant();
+                break;
+            }
+
+            case value_t::object:
+            {
+                result.m_it.object_iterator = m_data.m_value.object->erase(first.m_it.object_iterator,
+                                              last.m_it.object_iterator);
+                break;
+            }
+
+            case value_t::array:
+            {
+                result.m_it.array_iterator = m_data.m_value.array->erase(first.m_it.array_iterator,
+                                             last.m_it.array_iterator);
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        return result;
+    }
+
+  private:
+    template < typename KeyType, detail::enable_if_t <
+                   detail::has_erase_with_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    size_type erase_internal(KeyType && key)
+    {
+        // this erase only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        return m_data.m_value.object->erase(std::forward<KeyType>(key));
+    }
+
+    template < typename KeyType, detail::enable_if_t <
+                   !detail::has_erase_with_key_type<basic_json_t, KeyType>::value, int > = 0 >
+    size_type erase_internal(KeyType && key)
+    {
+        // this erase only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+
+        const auto it = m_data.m_value.object->find(std::forward<KeyType>(key));
+        if (it != m_data.m_value.object->end())
+        {
+            m_data.m_value.object->erase(it);
+            return 1;
+        }
+        return 0;
+    }
+
+  public:
+
+    /// @brief remove element from a JSON object given a key
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    size_type erase(const typename object_t::key_type& key)
+    {
+        // the indirection via erase_internal() is added to avoid making this
+        // function a template and thus de-rank it during overload resolution
+        return erase_internal(key);
+    }
+
+    /// @brief remove element from a JSON object given a key
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    size_type erase(KeyType && key)
+    {
+        return erase_internal(std::forward<KeyType>(key));
+    }
+
+    /// @brief remove element from a JSON array given an index
+    /// @sa https://json.nlohmann.me/api/basic_json/erase/
+    void erase(const size_type idx)
+    {
+        // this erase only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            if (JSON_HEDLEY_UNLIKELY(idx >= size()))
+            {
+                JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), this));
+            }
+
+            m_data.m_value.array->erase(m_data.m_value.array->begin() + static_cast<difference_type>(idx));
+        }
+        else
+        {
+            JSON_THROW(type_error::create(307, detail::concat("cannot use erase() with ", type_name()), this));
+        }
+    }
+
+    /// @}
+
+    ////////////
+    // lookup //
+    ////////////
+
+    /// @name lookup
+    /// @{
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    iterator find(const typename object_t::key_type& key)
+    {
+        auto result = end();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(key);
+        }
+
+        return result;
+    }
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    const_iterator find(const typename object_t::key_type& key) const
+    {
+        auto result = cend();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(key);
+        }
+
+        return result;
+    }
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    iterator find(KeyType && key)
+    {
+        auto result = end();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(std::forward<KeyType>(key));
+        }
+
+        return result;
+    }
+
+    /// @brief find an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/find/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    const_iterator find(KeyType && key) const
+    {
+        auto result = cend();
+
+        if (is_object())
+        {
+            result.m_it.object_iterator = m_data.m_value.object->find(std::forward<KeyType>(key));
+        }
+
+        return result;
+    }
+
+    /// @brief returns the number of occurrences of a key in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/count/
+    size_type count(const typename object_t::key_type& key) const
+    {
+        // return 0 for all nonobject types
+        return is_object() ? m_data.m_value.object->count(key) : 0;
+    }
+
+    /// @brief returns the number of occurrences of a key in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/count/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    size_type count(KeyType && key) const
+    {
+        // return 0 for all nonobject types
+        return is_object() ? m_data.m_value.object->count(std::forward<KeyType>(key)) : 0;
+    }
+
+    /// @brief check the existence of an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/contains/
+    bool contains(const typename object_t::key_type& key) const
+    {
+        return is_object() && m_data.m_value.object->find(key) != m_data.m_value.object->end();
+    }
+
+    /// @brief check the existence of an element in a JSON object
+    /// @sa https://json.nlohmann.me/api/basic_json/contains/
+    template<class KeyType, detail::enable_if_t<
+                 detail::is_usable_as_basic_json_key_type<basic_json_t, KeyType>::value, int> = 0>
+    bool contains(KeyType && key) const
+    {
+        return is_object() && m_data.m_value.object->find(std::forward<KeyType>(key)) != m_data.m_value.object->end();
+    }
+
+    /// @brief check the existence of an element in a JSON object given a JSON pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/contains/
+    bool contains(const json_pointer& ptr) const
+    {
+        return ptr.contains(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    bool contains(const typename ::nlohmann::json_pointer<BasicJsonType>& ptr) const
+    {
+        return ptr.contains(this);
+    }
+
+    /// @}
+
+    ///////////////
+    // iterators //
+    ///////////////
+
+    /// @name iterators
+    /// @{
+
+    /// @brief returns an iterator to the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/begin/
+    iterator begin() noexcept
+    {
+        iterator result(this);
+        result.set_begin();
+        return result;
+    }
+
+    /// @brief returns an iterator to the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/begin/
+    const_iterator begin() const noexcept
+    {
+        return cbegin();
+    }
+
+    /// @brief returns a const iterator to the first element
+    /// @sa https://json.nlohmann.me/api/basic_json/cbegin/
+    const_iterator cbegin() const noexcept
+    {
+        const_iterator result(this);
+        result.set_begin();
+        return result;
+    }
+
+    /// @brief returns an iterator to one past the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/end/
+    iterator end() noexcept
+    {
+        iterator result(this);
+        result.set_end();
+        return result;
+    }
+
+    /// @brief returns an iterator to one past the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/end/
+    const_iterator end() const noexcept
+    {
+        return cend();
+    }
+
+    /// @brief returns an iterator to one past the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/cend/
+    const_iterator cend() const noexcept
+    {
+        const_iterator result(this);
+        result.set_end();
+        return result;
+    }
+
+    /// @brief returns an iterator to the reverse-beginning
+    /// @sa https://json.nlohmann.me/api/basic_json/rbegin/
+    reverse_iterator rbegin() noexcept
+    {
+        return reverse_iterator(end());
+    }
+
+    /// @brief returns an iterator to the reverse-beginning
+    /// @sa https://json.nlohmann.me/api/basic_json/rbegin/
+    const_reverse_iterator rbegin() const noexcept
+    {
+        return crbegin();
+    }
+
+    /// @brief returns an iterator to the reverse-end
+    /// @sa https://json.nlohmann.me/api/basic_json/rend/
+    reverse_iterator rend() noexcept
+    {
+        return reverse_iterator(begin());
+    }
+
+    /// @brief returns an iterator to the reverse-end
+    /// @sa https://json.nlohmann.me/api/basic_json/rend/
+    const_reverse_iterator rend() const noexcept
+    {
+        return crend();
+    }
+
+    /// @brief returns a const reverse iterator to the last element
+    /// @sa https://json.nlohmann.me/api/basic_json/crbegin/
+    const_reverse_iterator crbegin() const noexcept
+    {
+        return const_reverse_iterator(cend());
+    }
+
+    /// @brief returns a const reverse iterator to one before the first
+    /// @sa https://json.nlohmann.me/api/basic_json/crend/
+    const_reverse_iterator crend() const noexcept
+    {
+        return const_reverse_iterator(cbegin());
+    }
+
+  public:
+    /// @brief wrapper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    /// @deprecated This function is deprecated since 3.1.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use @ref items() instead;
+    ///             that is, replace `json::iterator_wrapper(j)` with `j.items()`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.1.0, items())
+    static iteration_proxy<iterator> iterator_wrapper(reference ref) noexcept
+    {
+        return ref.items();
+    }
+
+    /// @brief wrapper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    /// @deprecated This function is deprecated since 3.1.0 and will be removed in
+    ///         version 4.0.0 of the library. Please use @ref items() instead;
+    ///         that is, replace `json::iterator_wrapper(j)` with `j.items()`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.1.0, items())
+    static iteration_proxy<const_iterator> iterator_wrapper(const_reference ref) noexcept
+    {
+        return ref.items();
+    }
+
+    /// @brief helper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    iteration_proxy<iterator> items() noexcept
+    {
+        return iteration_proxy<iterator>(*this);
+    }
+
+    /// @brief helper to access iterator member functions in range-based for
+    /// @sa https://json.nlohmann.me/api/basic_json/items/
+    iteration_proxy<const_iterator> items() const noexcept
+    {
+        return iteration_proxy<const_iterator>(*this);
+    }
+
+    /// @}
+
+    //////////////
+    // capacity //
+    //////////////
+
+    /// @name capacity
+    /// @{
+
+    /// @brief checks whether the container is empty.
+    /// @sa https://json.nlohmann.me/api/basic_json/empty/
+    bool empty() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::null:
+            {
+                // null values are empty
+                return true;
+            }
+
+            case value_t::array:
+            {
+                // delegate call to array_t::empty()
+                return m_data.m_value.array->empty();
+            }
+
+            case value_t::object:
+            {
+                // delegate call to object_t::empty()
+                return m_data.m_value.object->empty();
+            }
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // all other types are nonempty
+                return false;
+            }
+        }
+    }
+
+    /// @brief returns the number of elements
+    /// @sa https://json.nlohmann.me/api/basic_json/size/
+    size_type size() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::null:
+            {
+                // null values are empty
+                return 0;
+            }
+
+            case value_t::array:
+            {
+                // delegate call to array_t::size()
+                return m_data.m_value.array->size();
+            }
+
+            case value_t::object:
+            {
+                // delegate call to object_t::size()
+                return m_data.m_value.object->size();
+            }
+
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // all other types have size 1
+                return 1;
+            }
+        }
+    }
+
+    /// @brief returns the maximum possible number of elements
+    /// @sa https://json.nlohmann.me/api/basic_json/max_size/
+    size_type max_size() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::array:
+            {
+                // delegate call to array_t::max_size()
+                return m_data.m_value.array->max_size();
+            }
+
+            case value_t::object:
+            {
+                // delegate call to object_t::max_size()
+                return m_data.m_value.object->max_size();
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // all other types have max_size() == size()
+                return size();
+            }
+        }
+    }
+
+    /// @}
+
+    ///////////////
+    // modifiers //
+    ///////////////
+
+    /// @name modifiers
+    /// @{
+
+    /// @brief clears the contents
+    /// @sa https://json.nlohmann.me/api/basic_json/clear/
+    void clear() noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::number_integer:
+            {
+                m_data.m_value.number_integer = 0;
+                break;
+            }
+
+            case value_t::number_unsigned:
+            {
+                m_data.m_value.number_unsigned = 0;
+                break;
+            }
+
+            case value_t::number_float:
+            {
+                m_data.m_value.number_float = 0.0;
+                break;
+            }
+
+            case value_t::boolean:
+            {
+                m_data.m_value.boolean = false;
+                break;
+            }
+
+            case value_t::string:
+            {
+                m_data.m_value.string->clear();
+                break;
+            }
+
+            case value_t::binary:
+            {
+                m_data.m_value.binary->clear();
+                break;
+            }
+
+            case value_t::array:
+            {
+                m_data.m_value.array->clear();
+                break;
+            }
+
+            case value_t::object:
+            {
+                m_data.m_value.object->clear();
+                break;
+            }
+
+            case value_t::null:
+            case value_t::discarded:
+            default:
+                break;
+        }
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(basic_json&& val)
+    {
+        // push_back only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))
+        {
+            JSON_THROW(type_error::create(308, detail::concat("cannot use push_back() with ", type_name()), this));
+        }
+
+        // transform null object into an array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value = value_t::array;
+            assert_invariant();
+        }
+
+        // add element to array (move semantics)
+        const auto old_capacity = m_data.m_value.array->capacity();
+        m_data.m_value.array->push_back(std::move(val));
+        set_parent(m_data.m_value.array->back(), old_capacity);
+        // if val is moved from, basic_json move constructor marks it null, so we do not call the destructor
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(basic_json&& val)
+    {
+        push_back(std::move(val));
+        return *this;
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(const basic_json& val)
+    {
+        // push_back only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))
+        {
+            JSON_THROW(type_error::create(308, detail::concat("cannot use push_back() with ", type_name()), this));
+        }
+
+        // transform null object into an array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value = value_t::array;
+            assert_invariant();
+        }
+
+        // add element to array
+        const auto old_capacity = m_data.m_value.array->capacity();
+        m_data.m_value.array->push_back(val);
+        set_parent(m_data.m_value.array->back(), old_capacity);
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(const basic_json& val)
+    {
+        push_back(val);
+        return *this;
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(const typename object_t::value_type& val)
+    {
+        // push_back only works for null objects or objects
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_object())))
+        {
+            JSON_THROW(type_error::create(308, detail::concat("cannot use push_back() with ", type_name()), this));
+        }
+
+        // transform null object into an object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value = value_t::object;
+            assert_invariant();
+        }
+
+        // add element to object
+        auto res = m_data.m_value.object->insert(val);
+        set_parent(res.first->second);
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(const typename object_t::value_type& val)
+    {
+        push_back(val);
+        return *this;
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/push_back/
+    void push_back(initializer_list_t init)
+    {
+        if (is_object() && init.size() == 2 && (*init.begin())->is_string())
+        {
+            basic_json&& key = init.begin()->moved_or_copied();
+            push_back(typename object_t::value_type(
+                          std::move(key.get_ref<string_t&>()), (init.begin() + 1)->moved_or_copied()));
+        }
+        else
+        {
+            push_back(basic_json(init));
+        }
+    }
+
+    /// @brief add an object to an object
+    /// @sa https://json.nlohmann.me/api/basic_json/operator+=/
+    reference operator+=(initializer_list_t init)
+    {
+        push_back(init);
+        return *this;
+    }
+
+    /// @brief add an object to an array
+    /// @sa https://json.nlohmann.me/api/basic_json/emplace_back/
+    template<class... Args>
+    reference emplace_back(Args&& ... args)
+    {
+        // emplace_back only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_array())))
+        {
+            JSON_THROW(type_error::create(311, detail::concat("cannot use emplace_back() with ", type_name()), this));
+        }
+
+        // transform null object into an array
+        if (is_null())
+        {
+            m_data.m_type = value_t::array;
+            m_data.m_value = value_t::array;
+            assert_invariant();
+        }
+
+        // add element to array (perfect forwarding)
+        const auto old_capacity = m_data.m_value.array->capacity();
+        m_data.m_value.array->emplace_back(std::forward<Args>(args)...);
+        return set_parent(m_data.m_value.array->back(), old_capacity);
+    }
+
+    /// @brief add an object to an object if key does not exist
+    /// @sa https://json.nlohmann.me/api/basic_json/emplace/
+    template<class... Args>
+    std::pair<iterator, bool> emplace(Args&& ... args)
+    {
+        // emplace only works for null objects or arrays
+        if (JSON_HEDLEY_UNLIKELY(!(is_null() || is_object())))
+        {
+            JSON_THROW(type_error::create(311, detail::concat("cannot use emplace() with ", type_name()), this));
+        }
+
+        // transform null object into an object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value = value_t::object;
+            assert_invariant();
+        }
+
+        // add element to array (perfect forwarding)
+        auto res = m_data.m_value.object->emplace(std::forward<Args>(args)...);
+        set_parent(res.first->second);
+
+        // create result iterator and set iterator to the result of emplace
+        auto it = begin();
+        it.m_it.object_iterator = res.first;
+
+        // return pair of iterator and boolean
+        return {it, res.second};
+    }
+
+    /// Helper for insertion of an iterator
+    /// @note: This uses std::distance to support GCC 4.8,
+    ///        see https://github.com/nlohmann/json/pull/1257
+    template<typename... Args>
+    iterator insert_iterator(const_iterator pos, Args&& ... args) // NOLINT(performance-unnecessary-value-param)
+    {
+        iterator result(this);
+        JSON_ASSERT(m_data.m_value.array != nullptr);
+
+        auto insert_pos = std::distance(m_data.m_value.array->begin(), pos.m_it.array_iterator);
+        m_data.m_value.array->insert(pos.m_it.array_iterator, std::forward<Args>(args)...);
+        result.m_it.array_iterator = m_data.m_value.array->begin() + insert_pos;
+
+        // This could have been written as:
+        // result.m_it.array_iterator = m_data.m_value.array->insert(pos.m_it.array_iterator, cnt, val);
+        // but the return value of insert is missing in GCC 4.8, so it is written this way instead.
+
+        set_parents();
+        return result;
+    }
+
+    /// @brief inserts element into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, const basic_json& val) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            // check if iterator pos fits to this JSON value
+            if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+            {
+                JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+            }
+
+            // insert to array and return iterator
+            return insert_iterator(pos, val);
+        }
+
+        JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+    }
+
+    /// @brief inserts element into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, basic_json&& val) // NOLINT(performance-unnecessary-value-param)
+    {
+        return insert(pos, val);
+    }
+
+    /// @brief inserts copies of element into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, size_type cnt, const basic_json& val) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            // check if iterator pos fits to this JSON value
+            if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+            {
+                JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+            }
+
+            // insert to array and return iterator
+            return insert_iterator(pos, cnt, val);
+        }
+
+        JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+    }
+
+    /// @brief inserts range of elements into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, const_iterator first, const_iterator last) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_UNLIKELY(!is_array()))
+        {
+            JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+        }
+
+        // check if iterator pos fits to this JSON value
+        if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+        }
+
+        // check if range iterators belong to the same JSON object
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(210, "iterators do not fit", this));
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(first.m_object == this))
+        {
+            JSON_THROW(invalid_iterator::create(211, "passed iterators may not belong to container", this));
+        }
+
+        // insert to array and return iterator
+        return insert_iterator(pos, first.m_it.array_iterator, last.m_it.array_iterator);
+    }
+
+    /// @brief inserts elements from initializer list into array
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    iterator insert(const_iterator pos, initializer_list_t ilist) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for arrays
+        if (JSON_HEDLEY_UNLIKELY(!is_array()))
+        {
+            JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+        }
+
+        // check if iterator pos fits to this JSON value
+        if (JSON_HEDLEY_UNLIKELY(pos.m_object != this))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterator does not fit current value", this));
+        }
+
+        // insert to array and return iterator
+        return insert_iterator(pos, ilist.begin(), ilist.end());
+    }
+
+    /// @brief inserts range of elements into object
+    /// @sa https://json.nlohmann.me/api/basic_json/insert/
+    void insert(const_iterator first, const_iterator last) // NOLINT(performance-unnecessary-value-param)
+    {
+        // insert only works for objects
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(309, detail::concat("cannot use insert() with ", type_name()), this));
+        }
+
+        // check if range iterators belong to the same JSON object
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(210, "iterators do not fit", this));
+        }
+
+        // passed iterators must belong to objects
+        if (JSON_HEDLEY_UNLIKELY(!first.m_object->is_object()))
+        {
+            JSON_THROW(invalid_iterator::create(202, "iterators first and last must point to objects", this));
+        }
+
+        m_data.m_value.object->insert(first.m_it.object_iterator, last.m_it.object_iterator);
+        set_parents();
+    }
+
+    /// @brief updates a JSON object from another object, overwriting existing keys
+    /// @sa https://json.nlohmann.me/api/basic_json/update/
+    void update(const_reference j, bool merge_objects = false)
+    {
+        update(j.begin(), j.end(), merge_objects);
+    }
+
+    /// @brief updates a JSON object from another object, overwriting existing keys
+    /// @sa https://json.nlohmann.me/api/basic_json/update/
+    void update(const_iterator first, const_iterator last, bool merge_objects = false) // NOLINT(performance-unnecessary-value-param)
+    {
+        // implicitly convert null value to an empty object
+        if (is_null())
+        {
+            m_data.m_type = value_t::object;
+            m_data.m_value.object = create<object_t>();
+            assert_invariant();
+        }
+
+        if (JSON_HEDLEY_UNLIKELY(!is_object()))
+        {
+            JSON_THROW(type_error::create(312, detail::concat("cannot use update() with ", type_name()), this));
+        }
+
+        // check if range iterators belong to the same JSON object
+        if (JSON_HEDLEY_UNLIKELY(first.m_object != last.m_object))
+        {
+            JSON_THROW(invalid_iterator::create(210, "iterators do not fit", this));
+        }
+
+        // passed iterators must belong to objects
+        if (JSON_HEDLEY_UNLIKELY(!first.m_object->is_object()))
+        {
+            JSON_THROW(type_error::create(312, detail::concat("cannot use update() with ", first.m_object->type_name()), first.m_object));
+        }
+
+        for (auto it = first; it != last; ++it)
+        {
+            if (merge_objects && it.value().is_object())
+            {
+                auto it2 = m_data.m_value.object->find(it.key());
+                if (it2 != m_data.m_value.object->end())
+                {
+                    it2->second.update(it.value(), true);
+                    continue;
+                }
+            }
+            m_data.m_value.object->operator[](it.key()) = it.value();
+#if JSON_DIAGNOSTICS
+            m_data.m_value.object->operator[](it.key()).m_parent = this;
+#endif
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(reference other) noexcept (
+        std::is_nothrow_move_constructible<value_t>::value&&
+        std::is_nothrow_move_assignable<value_t>::value&&
+        std::is_nothrow_move_constructible<json_value>::value&& // NOLINT(cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+        std::is_nothrow_move_assignable<json_value>::value
+    )
+    {
+        std::swap(m_data.m_type, other.m_data.m_type);
+        std::swap(m_data.m_value, other.m_data.m_value);
+
+        set_parents();
+        other.set_parents();
+        assert_invariant();
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    friend void swap(reference left, reference right) noexcept (
+        std::is_nothrow_move_constructible<value_t>::value&&
+        std::is_nothrow_move_assignable<value_t>::value&&
+        std::is_nothrow_move_constructible<json_value>::value&& // NOLINT(cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+        std::is_nothrow_move_assignable<json_value>::value
+    )
+    {
+        left.swap(right);
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(array_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for arrays
+        if (JSON_HEDLEY_LIKELY(is_array()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.array), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(array_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(object_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for objects
+        if (JSON_HEDLEY_LIKELY(is_object()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.object), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(object_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(string_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for strings
+        if (JSON_HEDLEY_LIKELY(is_string()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.string), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(string_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(binary_t& other) // NOLINT(bugprone-exception-escape,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    {
+        // swap only works for strings
+        if (JSON_HEDLEY_LIKELY(is_binary()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.binary), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(binary_t&) with ", type_name()), this));
+        }
+    }
+
+    /// @brief exchanges the values
+    /// @sa https://json.nlohmann.me/api/basic_json/swap/
+    void swap(typename binary_t::container_type& other) // NOLINT(bugprone-exception-escape)
+    {
+        // swap only works for strings
+        if (JSON_HEDLEY_LIKELY(is_binary()))
+        {
+            using std::swap;
+            swap(*(m_data.m_value.binary), other);
+        }
+        else
+        {
+            JSON_THROW(type_error::create(310, detail::concat("cannot use swap(binary_t::container_type&) with ", type_name()), this));
+        }
+    }
+
+    /// @}
+
+    //////////////////////////////////////////
+    // lexicographical comparison operators //
+    //////////////////////////////////////////
+
+    /// @name lexicographical comparison operators
+    /// @{
+
+    // note parentheses around operands are necessary; see
+    // https://github.com/nlohmann/json/issues/1530
+#define JSON_IMPLEMENT_OPERATOR(op, null_result, unordered_result, default_result)                       \
+    const auto lhs_type = lhs.type();                                                                    \
+    const auto rhs_type = rhs.type();                                                                    \
+    \
+    if (lhs_type == rhs_type) /* NOLINT(readability/braces) */                                           \
+    {                                                                                                    \
+        switch (lhs_type)                                                                                \
+        {                                                                                                \
+            case value_t::array:                                                                         \
+                return (*lhs.m_data.m_value.array) op (*rhs.m_data.m_value.array);                                     \
+                \
+            case value_t::object:                                                                        \
+                return (*lhs.m_data.m_value.object) op (*rhs.m_data.m_value.object);                                   \
+                \
+            case value_t::null:                                                                          \
+                return (null_result);                                                                    \
+                \
+            case value_t::string:                                                                        \
+                return (*lhs.m_data.m_value.string) op (*rhs.m_data.m_value.string);                                   \
+                \
+            case value_t::boolean:                                                                       \
+                return (lhs.m_data.m_value.boolean) op (rhs.m_data.m_value.boolean);                                   \
+                \
+            case value_t::number_integer:                                                                \
+                return (lhs.m_data.m_value.number_integer) op (rhs.m_data.m_value.number_integer);                     \
+                \
+            case value_t::number_unsigned:                                                               \
+                return (lhs.m_data.m_value.number_unsigned) op (rhs.m_data.m_value.number_unsigned);                   \
+                \
+            case value_t::number_float:                                                                  \
+                return (lhs.m_data.m_value.number_float) op (rhs.m_data.m_value.number_float);                         \
+                \
+            case value_t::binary:                                                                        \
+                return (*lhs.m_data.m_value.binary) op (*rhs.m_data.m_value.binary);                                   \
+                \
+            case value_t::discarded:                                                                     \
+            default:                                                                                     \
+                return (unordered_result);                                                               \
+        }                                                                                                \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_integer && rhs_type == value_t::number_float)                   \
+    {                                                                                                    \
+        return static_cast<number_float_t>(lhs.m_data.m_value.number_integer) op rhs.m_data.m_value.number_float;      \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_float && rhs_type == value_t::number_integer)                   \
+    {                                                                                                    \
+        return lhs.m_data.m_value.number_float op static_cast<number_float_t>(rhs.m_data.m_value.number_integer);      \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_unsigned && rhs_type == value_t::number_float)                  \
+    {                                                                                                    \
+        return static_cast<number_float_t>(lhs.m_data.m_value.number_unsigned) op rhs.m_data.m_value.number_float;     \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_float && rhs_type == value_t::number_unsigned)                  \
+    {                                                                                                    \
+        return lhs.m_data.m_value.number_float op static_cast<number_float_t>(rhs.m_data.m_value.number_unsigned);     \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_unsigned && rhs_type == value_t::number_integer)                \
+    {                                                                                                    \
+        return static_cast<number_integer_t>(lhs.m_data.m_value.number_unsigned) op rhs.m_data.m_value.number_integer; \
+    }                                                                                                    \
+    else if (lhs_type == value_t::number_integer && rhs_type == value_t::number_unsigned)                \
+    {                                                                                                    \
+        return lhs.m_data.m_value.number_integer op static_cast<number_integer_t>(rhs.m_data.m_value.number_unsigned); \
+    }                                                                                                    \
+    else if(compares_unordered(lhs, rhs))\
+    {\
+        return (unordered_result);\
+    }\
+    \
+    return (default_result);
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    // returns true if:
+    // - any operand is NaN and the other operand is of number type
+    // - any operand is discarded
+    // in legacy mode, discarded values are considered ordered if
+    // an operation is computed as an odd number of inverses of others
+    static bool compares_unordered(const_reference lhs, const_reference rhs, bool inverse = false) noexcept
+    {
+        if ((lhs.is_number_float() && std::isnan(lhs.m_data.m_value.number_float) && rhs.is_number())
+                || (rhs.is_number_float() && std::isnan(rhs.m_data.m_value.number_float) && lhs.is_number()))
+        {
+            return true;
+        }
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+        return (lhs.is_discarded() || rhs.is_discarded()) && !inverse;
+#else
+        static_cast<void>(inverse);
+        return lhs.is_discarded() || rhs.is_discarded();
+#endif
+    }
+
+  private:
+    bool compares_unordered(const_reference rhs, bool inverse = false) const noexcept
+    {
+        return compares_unordered(*this, rhs, inverse);
+    }
+
+  public:
+#if JSON_HAS_THREE_WAY_COMPARISON
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    bool operator==(const_reference rhs) const noexcept
+    {
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+        const_reference lhs = *this;
+        JSON_IMPLEMENT_OPERATOR( ==, true, false, false)
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+    }
+
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    bool operator==(ScalarType rhs) const noexcept
+    {
+        return *this == basic_json(rhs);
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    bool operator!=(const_reference rhs) const noexcept
+    {
+        if (compares_unordered(rhs, true))
+        {
+            return false;
+        }
+        return !operator==(rhs);
+    }
+
+    /// @brief comparison: 3-way
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_spaceship/
+    std::partial_ordering operator<=>(const_reference rhs) const noexcept // *NOPAD*
+    {
+        const_reference lhs = *this;
+        // default_result is used if we cannot compare values. In that case,
+        // we compare types.
+        JSON_IMPLEMENT_OPERATOR(<=>, // *NOPAD*
+                                std::partial_ordering::equivalent,
+                                std::partial_ordering::unordered,
+                                lhs_type <=> rhs_type) // *NOPAD*
+    }
+
+    /// @brief comparison: 3-way
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_spaceship/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    std::partial_ordering operator<=>(ScalarType rhs) const noexcept // *NOPAD*
+    {
+        return *this <=> basic_json(rhs); // *NOPAD*
+    }
+
+#if JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+    // all operators that are computed as an odd number of inverses of others
+    // need to be overloaded to emulate the legacy comparison behavior
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON)
+    bool operator<=(const_reference rhs) const noexcept
+    {
+        if (compares_unordered(rhs, true))
+        {
+            return false;
+        }
+        return !(rhs < *this);
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    bool operator<=(ScalarType rhs) const noexcept
+    {
+        return *this <= basic_json(rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON)
+    bool operator>=(const_reference rhs) const noexcept
+    {
+        if (compares_unordered(rhs, true))
+        {
+            return false;
+        }
+        return !(*this < rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    template<typename ScalarType>
+    requires std::is_scalar_v<ScalarType>
+    bool operator>=(ScalarType rhs) const noexcept
+    {
+        return *this >= basic_json(rhs);
+    }
+#endif
+#else
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    friend bool operator==(const_reference lhs, const_reference rhs) noexcept
+    {
+#ifdef __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wfloat-equal"
+#endif
+        JSON_IMPLEMENT_OPERATOR( ==, true, false, false)
+#ifdef __GNUC__
+#pragma GCC diagnostic pop
+#endif
+    }
+
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator==(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs == basic_json(rhs);
+    }
+
+    /// @brief comparison: equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_eq/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator==(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) == rhs;
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    friend bool operator!=(const_reference lhs, const_reference rhs) noexcept
+    {
+        if (compares_unordered(lhs, rhs, true))
+        {
+            return false;
+        }
+        return !(lhs == rhs);
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator!=(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs != basic_json(rhs);
+    }
+
+    /// @brief comparison: not equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ne/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator!=(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) != rhs;
+    }
+
+    /// @brief comparison: less than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/
+    friend bool operator<(const_reference lhs, const_reference rhs) noexcept
+    {
+        // default_result is used if we cannot compare values. In that case,
+        // we compare types. Note we have to call the operator explicitly,
+        // because MSVC has problems otherwise.
+        JSON_IMPLEMENT_OPERATOR( <, false, false, operator<(lhs_type, rhs_type))
+    }
+
+    /// @brief comparison: less than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs < basic_json(rhs);
+    }
+
+    /// @brief comparison: less than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_lt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) < rhs;
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    friend bool operator<=(const_reference lhs, const_reference rhs) noexcept
+    {
+        if (compares_unordered(lhs, rhs, true))
+        {
+            return false;
+        }
+        return !(rhs < lhs);
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<=(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs <= basic_json(rhs);
+    }
+
+    /// @brief comparison: less than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_le/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator<=(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) <= rhs;
+    }
+
+    /// @brief comparison: greater than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/
+    friend bool operator>(const_reference lhs, const_reference rhs) noexcept
+    {
+        // double inverse
+        if (compares_unordered(lhs, rhs))
+        {
+            return false;
+        }
+        return !(lhs <= rhs);
+    }
+
+    /// @brief comparison: greater than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs > basic_json(rhs);
+    }
+
+    /// @brief comparison: greater than
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gt/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) > rhs;
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    friend bool operator>=(const_reference lhs, const_reference rhs) noexcept
+    {
+        if (compares_unordered(lhs, rhs, true))
+        {
+            return false;
+        }
+        return !(lhs < rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>=(const_reference lhs, ScalarType rhs) noexcept
+    {
+        return lhs >= basic_json(rhs);
+    }
+
+    /// @brief comparison: greater than or equal
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ge/
+    template<typename ScalarType, typename std::enable_if<
+                 std::is_scalar<ScalarType>::value, int>::type = 0>
+    friend bool operator>=(ScalarType lhs, const_reference rhs) noexcept
+    {
+        return basic_json(lhs) >= rhs;
+    }
+#endif
+
+#undef JSON_IMPLEMENT_OPERATOR
+
+    /// @}
+
+    ///////////////////
+    // serialization //
+    ///////////////////
+
+    /// @name serialization
+    /// @{
+#ifndef JSON_NO_IO
+    /// @brief serialize to stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/
+    friend std::ostream& operator<<(std::ostream& o, const basic_json& j)
+    {
+        // read width member and use it as indentation parameter if nonzero
+        const bool pretty_print = o.width() > 0;
+        const auto indentation = pretty_print ? o.width() : 0;
+
+        // reset width to 0 for subsequent calls to this stream
+        o.width(0);
+
+        // do the actual serialization
+        serializer s(detail::output_adapter<char>(o), o.fill());
+        s.dump(j, pretty_print, false, static_cast<unsigned int>(indentation));
+        return o;
+    }
+
+    /// @brief serialize to stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_ltlt/
+    /// @deprecated This function is deprecated since 3.0.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use
+    ///             operator<<(std::ostream&, const basic_json&) instead; that is,
+    ///             replace calls like `j >> o;` with `o << j;`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.0.0, operator<<(std::ostream&, const basic_json&))
+    friend std::ostream& operator>>(const basic_json& j, std::ostream& o)
+    {
+        return o << j;
+    }
+#endif  // JSON_NO_IO
+    /// @}
+
+    /////////////////////
+    // deserialization //
+    /////////////////////
+
+    /// @name deserialization
+    /// @{
+
+    /// @brief deserialize from a compatible input
+    /// @sa https://json.nlohmann.me/api/basic_json/parse/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json parse(InputType&& i,
+                            parser_callback_t cb = nullptr,
+                            const bool allow_exceptions = true,
+                            const bool ignore_comments = false)
+    {
+        basic_json result;
+        parser(detail::input_adapter(std::forward<InputType>(i)), std::move(cb), allow_exceptions, ignore_comments).parse(true, result); // cppcheck-suppress[accessMoved,accessForwarded]
+        return result;
+    }
+
+    /// @brief deserialize from a pair of character iterators
+    /// @sa https://json.nlohmann.me/api/basic_json/parse/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json parse(IteratorType first,
+                            IteratorType last,
+                            parser_callback_t cb = nullptr,
+                            const bool allow_exceptions = true,
+                            const bool ignore_comments = false)
+    {
+        basic_json result;
+        parser(detail::input_adapter(std::move(first), std::move(last)), std::move(cb), allow_exceptions, ignore_comments).parse(true, result); // cppcheck-suppress[accessMoved]
+        return result;
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, parse(ptr, ptr + len))
+    static basic_json parse(detail::span_input_adapter&& i,
+                            parser_callback_t cb = nullptr,
+                            const bool allow_exceptions = true,
+                            const bool ignore_comments = false)
+    {
+        basic_json result;
+        parser(i.get(), std::move(cb), allow_exceptions, ignore_comments).parse(true, result); // cppcheck-suppress[accessMoved]
+        return result;
+    }
+
+    /// @brief check if the input is valid JSON
+    /// @sa https://json.nlohmann.me/api/basic_json/accept/
+    template<typename InputType>
+    static bool accept(InputType&& i,
+                       const bool ignore_comments = false)
+    {
+        return parser(detail::input_adapter(std::forward<InputType>(i)), nullptr, false, ignore_comments).accept(true);
+    }
+
+    /// @brief check if the input is valid JSON
+    /// @sa https://json.nlohmann.me/api/basic_json/accept/
+    template<typename IteratorType>
+    static bool accept(IteratorType first, IteratorType last,
+                       const bool ignore_comments = false)
+    {
+        return parser(detail::input_adapter(std::move(first), std::move(last)), nullptr, false, ignore_comments).accept(true);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, accept(ptr, ptr + len))
+    static bool accept(detail::span_input_adapter&& i,
+                       const bool ignore_comments = false)
+    {
+        return parser(i.get(), nullptr, false, ignore_comments).accept(true);
+    }
+
+    /// @brief generate SAX events
+    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/
+    template <typename InputType, typename SAX>
+    JSON_HEDLEY_NON_NULL(2)
+    static bool sax_parse(InputType&& i, SAX* sax,
+                          input_format_t format = input_format_t::json,
+                          const bool strict = true,
+                          const bool ignore_comments = false)
+    {
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        return format == input_format_t::json
+               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)
+               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);
+    }
+
+    /// @brief generate SAX events
+    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/
+    template<class IteratorType, class SAX>
+    JSON_HEDLEY_NON_NULL(3)
+    static bool sax_parse(IteratorType first, IteratorType last, SAX* sax,
+                          input_format_t format = input_format_t::json,
+                          const bool strict = true,
+                          const bool ignore_comments = false)
+    {
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        return format == input_format_t::json
+               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)
+               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);
+    }
+
+    /// @brief generate SAX events
+    /// @sa https://json.nlohmann.me/api/basic_json/sax_parse/
+    /// @deprecated This function is deprecated since 3.8.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use
+    ///             sax_parse(ptr, ptr + len) instead.
+    template <typename SAX>
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, sax_parse(ptr, ptr + len, ...))
+    JSON_HEDLEY_NON_NULL(2)
+    static bool sax_parse(detail::span_input_adapter&& i, SAX* sax,
+                          input_format_t format = input_format_t::json,
+                          const bool strict = true,
+                          const bool ignore_comments = false)
+    {
+        auto ia = i.get();
+        return format == input_format_t::json
+               // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+               ? parser(std::move(ia), nullptr, true, ignore_comments).sax_parse(sax, strict)
+               // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+               : detail::binary_reader<basic_json, decltype(ia), SAX>(std::move(ia), format).sax_parse(format, sax, strict);
+    }
+#ifndef JSON_NO_IO
+    /// @brief deserialize from stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gtgt/
+    /// @deprecated This stream operator is deprecated since 3.0.0 and will be removed in
+    ///             version 4.0.0 of the library. Please use
+    ///             operator>>(std::istream&, basic_json&) instead; that is,
+    ///             replace calls like `j << i;` with `i >> j;`.
+    JSON_HEDLEY_DEPRECATED_FOR(3.0.0, operator>>(std::istream&, basic_json&))
+    friend std::istream& operator<<(basic_json& j, std::istream& i)
+    {
+        return operator>>(i, j);
+    }
+
+    /// @brief deserialize from stream
+    /// @sa https://json.nlohmann.me/api/basic_json/operator_gtgt/
+    friend std::istream& operator>>(std::istream& i, basic_json& j)
+    {
+        parser(detail::input_adapter(i)).parse(false, j);
+        return i;
+    }
+#endif  // JSON_NO_IO
+    /// @}
+
+    ///////////////////////////
+    // convenience functions //
+    ///////////////////////////
+
+    /// @brief return the type as string
+    /// @sa https://json.nlohmann.me/api/basic_json/type_name/
+    JSON_HEDLEY_RETURNS_NON_NULL
+    const char* type_name() const noexcept
+    {
+        switch (m_data.m_type)
+        {
+            case value_t::null:
+                return "null";
+            case value_t::object:
+                return "object";
+            case value_t::array:
+                return "array";
+            case value_t::string:
+                return "string";
+            case value_t::boolean:
+                return "boolean";
+            case value_t::binary:
+                return "binary";
+            case value_t::discarded:
+                return "discarded";
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            default:
+                return "number";
+        }
+    }
+
+  JSON_PRIVATE_UNLESS_TESTED:
+    //////////////////////
+    // member variables //
+    //////////////////////
+
+    struct data
+    {
+        /// the type of the current element
+        value_t m_type = value_t::null;
+
+        /// the value of the current element
+        json_value m_value = {};
+
+        data(const value_t v)
+            : m_type(v), m_value(v)
+        {
+        }
+
+        data(size_type cnt, const basic_json& val)
+            : m_type(value_t::array)
+        {
+            m_value.array = create<array_t>(cnt, val);
+        }
+
+        data() noexcept = default;
+        data(data&&) noexcept = default;
+        data(const data&) noexcept = delete;
+        data& operator=(data&&) noexcept = delete;
+        data& operator=(const data&) noexcept = delete;
+
+        ~data() noexcept
+        {
+            m_value.destroy(m_type);
+        }
+    };
+
+    data m_data = {};
+
+#if JSON_DIAGNOSTICS
+    /// a pointer to a parent value (for debugging purposes)
+    basic_json* m_parent = nullptr;
+#endif
+
+#if JSON_DIAGNOSTIC_POSITIONS
+    /// the start position of the value
+    std::size_t start_position = std::string::npos;
+    /// the end position of the value
+    std::size_t end_position = std::string::npos;
+  public:
+    constexpr std::size_t start_pos() const noexcept
+    {
+        return start_position;
+    }
+
+    constexpr std::size_t end_pos() const noexcept
+    {
+        return end_position;
+    }
+#endif
+
+    //////////////////////////////////////////
+    // binary serialization/deserialization //
+    //////////////////////////////////////////
+
+    /// @name binary serialization/deserialization support
+    /// @{
+
+  public:
+    /// @brief create a CBOR serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/
+    static std::vector<std::uint8_t> to_cbor(const basic_json& j)
+    {
+        std::vector<std::uint8_t> result;
+        to_cbor(j, result);
+        return result;
+    }
+
+    /// @brief create a CBOR serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/
+    static void to_cbor(const basic_json& j, detail::output_adapter<std::uint8_t> o)
+    {
+        binary_writer<std::uint8_t>(o).write_cbor(j);
+    }
+
+    /// @brief create a CBOR serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_cbor/
+    static void to_cbor(const basic_json& j, detail::output_adapter<char> o)
+    {
+        binary_writer<char>(o).write_cbor(j);
+    }
+
+    /// @brief create a MessagePack serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/
+    static std::vector<std::uint8_t> to_msgpack(const basic_json& j)
+    {
+        std::vector<std::uint8_t> result;
+        to_msgpack(j, result);
+        return result;
+    }
+
+    /// @brief create a MessagePack serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/
+    static void to_msgpack(const basic_json& j, detail::output_adapter<std::uint8_t> o)
+    {
+        binary_writer<std::uint8_t>(o).write_msgpack(j);
+    }
+
+    /// @brief create a MessagePack serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_msgpack/
+    static void to_msgpack(const basic_json& j, detail::output_adapter<char> o)
+    {
+        binary_writer<char>(o).write_msgpack(j);
+    }
+
+    /// @brief create a UBJSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/
+    static std::vector<std::uint8_t> to_ubjson(const basic_json& j,
+            const bool use_size = false,
+            const bool use_type = false)
+    {
+        std::vector<std::uint8_t> result;
+        to_ubjson(j, result, use_size, use_type);
+        return result;
+    }
+
+    /// @brief create a UBJSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/
+    static void to_ubjson(const basic_json& j, detail::output_adapter<std::uint8_t> o,
+                          const bool use_size = false, const bool use_type = false)
+    {
+        binary_writer<std::uint8_t>(o).write_ubjson(j, use_size, use_type);
+    }
+
+    /// @brief create a UBJSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_ubjson/
+    static void to_ubjson(const basic_json& j, detail::output_adapter<char> o,
+                          const bool use_size = false, const bool use_type = false)
+    {
+        binary_writer<char>(o).write_ubjson(j, use_size, use_type);
+    }
+
+    /// @brief create a BJData serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/
+    static std::vector<std::uint8_t> to_bjdata(const basic_json& j,
+            const bool use_size = false,
+            const bool use_type = false,
+            const bjdata_version_t version = bjdata_version_t::draft2)
+    {
+        std::vector<std::uint8_t> result;
+        to_bjdata(j, result, use_size, use_type, version);
+        return result;
+    }
+
+    /// @brief create a BJData serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/
+    static void to_bjdata(const basic_json& j, detail::output_adapter<std::uint8_t> o,
+                          const bool use_size = false, const bool use_type = false,
+                          const bjdata_version_t version = bjdata_version_t::draft2)
+    {
+        binary_writer<std::uint8_t>(o).write_ubjson(j, use_size, use_type, true, true, version);
+    }
+
+    /// @brief create a BJData serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bjdata/
+    static void to_bjdata(const basic_json& j, detail::output_adapter<char> o,
+                          const bool use_size = false, const bool use_type = false,
+                          const bjdata_version_t version = bjdata_version_t::draft2)
+    {
+        binary_writer<char>(o).write_ubjson(j, use_size, use_type, true, true, version);
+    }
+
+    /// @brief create a BSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/
+    static std::vector<std::uint8_t> to_bson(const basic_json& j)
+    {
+        std::vector<std::uint8_t> result;
+        to_bson(j, result);
+        return result;
+    }
+
+    /// @brief create a BSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/
+    static void to_bson(const basic_json& j, detail::output_adapter<std::uint8_t> o)
+    {
+        binary_writer<std::uint8_t>(o).write_bson(j);
+    }
+
+    /// @brief create a BSON serialization of a given JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/to_bson/
+    static void to_bson(const basic_json& j, detail::output_adapter<char> o)
+    {
+        binary_writer<char>(o).write_bson(j);
+    }
+
+    /// @brief create a JSON value from an input in CBOR format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_cbor/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_cbor(InputType&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in CBOR format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_cbor/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_cbor(IteratorType first, IteratorType last,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_cbor(ptr, ptr + len))
+    static basic_json from_cbor(const T* ptr, std::size_t len,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        return from_cbor(ptr, ptr + len, strict, allow_exceptions, tag_handler);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_cbor(ptr, ptr + len))
+    static basic_json from_cbor(detail::span_input_adapter&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true,
+                                const cbor_tag_handler_t tag_handler = cbor_tag_handler_t::error)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::cbor).sax_parse(input_format_t::cbor, &sdp, strict, tag_handler); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in MessagePack format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_msgpack/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_msgpack(InputType&& i,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in MessagePack format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_msgpack/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_msgpack(IteratorType first, IteratorType last,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_msgpack(ptr, ptr + len))
+    static basic_json from_msgpack(const T* ptr, std::size_t len,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        return from_msgpack(ptr, ptr + len, strict, allow_exceptions);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_msgpack(ptr, ptr + len))
+    static basic_json from_msgpack(detail::span_input_adapter&& i,
+                                   const bool strict = true,
+                                   const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::msgpack).sax_parse(input_format_t::msgpack, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in UBJSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_ubjson/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_ubjson(InputType&& i,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in UBJSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_ubjson/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_ubjson(IteratorType first, IteratorType last,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_ubjson(ptr, ptr + len))
+    static basic_json from_ubjson(const T* ptr, std::size_t len,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        return from_ubjson(ptr, ptr + len, strict, allow_exceptions);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_ubjson(ptr, ptr + len))
+    static basic_json from_ubjson(detail::span_input_adapter&& i,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::ubjson).sax_parse(input_format_t::ubjson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BJData format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bjdata/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bjdata(InputType&& i,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bjdata).sax_parse(input_format_t::bjdata, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BJData format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bjdata/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bjdata(IteratorType first, IteratorType last,
+                                  const bool strict = true,
+                                  const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bjdata).sax_parse(input_format_t::bjdata, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bson/
+    template<typename InputType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bson(InputType&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::forward<InputType>(i));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    /// @brief create a JSON value from an input in BSON format
+    /// @sa https://json.nlohmann.me/api/basic_json/from_bson/
+    template<typename IteratorType>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json from_bson(IteratorType first, IteratorType last,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = detail::input_adapter(std::move(first), std::move(last));
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+
+    template<typename T>
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_bson(ptr, ptr + len))
+    static basic_json from_bson(const T* ptr, std::size_t len,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        return from_bson(ptr, ptr + len, strict, allow_exceptions);
+    }
+
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    JSON_HEDLEY_DEPRECATED_FOR(3.8.0, from_bson(ptr, ptr + len))
+    static basic_json from_bson(detail::span_input_adapter&& i,
+                                const bool strict = true,
+                                const bool allow_exceptions = true)
+    {
+        basic_json result;
+        auto ia = i.get();
+        detail::json_sax_dom_parser<basic_json, decltype(ia)> sdp(result, allow_exceptions);
+        // NOLINTNEXTLINE(hicpp-move-const-arg,performance-move-const-arg)
+        const bool res = binary_reader<decltype(ia)>(std::move(ia), input_format_t::bson).sax_parse(input_format_t::bson, &sdp, strict); // cppcheck-suppress[accessMoved]
+        return res ? result : basic_json(value_t::discarded);
+    }
+    /// @}
+
+    //////////////////////////
+    // JSON Pointer support //
+    //////////////////////////
+
+    /// @name JSON Pointer functions
+    /// @{
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    reference operator[](const json_pointer& ptr)
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    reference operator[](const ::nlohmann::json_pointer<BasicJsonType>& ptr)
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/operator%5B%5D/
+    const_reference operator[](const json_pointer& ptr) const
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    const_reference operator[](const ::nlohmann::json_pointer<BasicJsonType>& ptr) const
+    {
+        return ptr.get_unchecked(this);
+    }
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    reference at(const json_pointer& ptr)
+    {
+        return ptr.get_checked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    reference at(const ::nlohmann::json_pointer<BasicJsonType>& ptr)
+    {
+        return ptr.get_checked(this);
+    }
+
+    /// @brief access specified element via JSON Pointer
+    /// @sa https://json.nlohmann.me/api/basic_json/at/
+    const_reference at(const json_pointer& ptr) const
+    {
+        return ptr.get_checked(this);
+    }
+
+    template<typename BasicJsonType, detail::enable_if_t<detail::is_basic_json<BasicJsonType>::value, int> = 0>
+    JSON_HEDLEY_DEPRECATED_FOR(3.11.0, basic_json::json_pointer or nlohmann::json_pointer<basic_json::string_t>) // NOLINT(readability/alt_tokens)
+    const_reference at(const ::nlohmann::json_pointer<BasicJsonType>& ptr) const
+    {
+        return ptr.get_checked(this);
+    }
+
+    /// @brief return flattened JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/flatten/
+    basic_json flatten() const
+    {
+        basic_json result(value_t::object);
+        json_pointer::flatten("", *this, result);
+        return result;
+    }
+
+    /// @brief unflatten a previously flattened JSON value
+    /// @sa https://json.nlohmann.me/api/basic_json/unflatten/
+    basic_json unflatten() const
+    {
+        return json_pointer::unflatten(*this);
+    }
+
+    /// @}
+
+    //////////////////////////
+    // JSON Patch functions //
+    //////////////////////////
+
+    /// @name JSON Patch functions
+    /// @{
+
+    /// @brief applies a JSON patch in-place without copying the object
+    /// @sa https://json.nlohmann.me/api/basic_json/patch/
+    void patch_inplace(const basic_json& json_patch)
+    {
+        basic_json& result = *this;
+        // the valid JSON Patch operations
+        enum class patch_operations {add, remove, replace, move, copy, test, invalid};
+
+        const auto get_op = [](const string_t& op)
+        {
+            if (op == "add")
+            {
+                return patch_operations::add;
+            }
+            if (op == "remove")
+            {
+                return patch_operations::remove;
+            }
+            if (op == "replace")
+            {
+                return patch_operations::replace;
+            }
+            if (op == "move")
+            {
+                return patch_operations::move;
+            }
+            if (op == "copy")
+            {
+                return patch_operations::copy;
+            }
+            if (op == "test")
+            {
+                return patch_operations::test;
+            }
+
+            return patch_operations::invalid;
+        };
+
+        // wrapper for "add" operation; add value at ptr
+        const auto operation_add = [&result](json_pointer & ptr, const basic_json & val)
+        {
+            // adding to the root of the target document means replacing it
+            if (ptr.empty())
+            {
+                result = val;
+                return;
+            }
+
+            // make sure the top element of the pointer exists
+            json_pointer const top_pointer = ptr.top();
+            if (top_pointer != ptr)
+            {
+                result.at(top_pointer);
+            }
+
+            // get reference to parent of JSON pointer ptr
+            const auto last_path = ptr.back();
+            ptr.pop_back();
+            // parent must exist when performing patch add per RFC6902 specs
+            basic_json& parent = result.at(ptr);
+
+            switch (parent.m_data.m_type)
+            {
+                case value_t::null:
+                case value_t::object:
+                {
+                    // use operator[] to add value
+                    parent[last_path] = val;
+                    break;
+                }
+
+                case value_t::array:
+                {
+                    if (last_path == "-")
+                    {
+                        // special case: append to back
+                        parent.push_back(val);
+                    }
+                    else
+                    {
+                        const auto idx = json_pointer::template array_index<basic_json_t>(last_path);
+                        if (JSON_HEDLEY_UNLIKELY(idx > parent.size()))
+                        {
+                            // avoid undefined behavior
+                            JSON_THROW(out_of_range::create(401, detail::concat("array index ", std::to_string(idx), " is out of range"), &parent));
+                        }
+
+                        // default case: insert add offset
+                        parent.insert(parent.begin() + static_cast<difference_type>(idx), val);
+                    }
+                    break;
+                }
+
+                // if there exists a parent it cannot be primitive
+                case value_t::string: // LCOV_EXCL_LINE
+                case value_t::boolean: // LCOV_EXCL_LINE
+                case value_t::number_integer: // LCOV_EXCL_LINE
+                case value_t::number_unsigned: // LCOV_EXCL_LINE
+                case value_t::number_float: // LCOV_EXCL_LINE
+                case value_t::binary: // LCOV_EXCL_LINE
+                case value_t::discarded: // LCOV_EXCL_LINE
+                default:            // LCOV_EXCL_LINE
+                    JSON_ASSERT(false); // NOLINT(cert-dcl03-c,hicpp-static-assert,misc-static-assert) LCOV_EXCL_LINE
+            }
+        };
+
+        // wrapper for "remove" operation; remove value at ptr
+        const auto operation_remove = [this, & result](json_pointer & ptr)
+        {
+            // get reference to parent of JSON pointer ptr
+            const auto last_path = ptr.back();
+            ptr.pop_back();
+            basic_json& parent = result.at(ptr);
+
+            // remove child
+            if (parent.is_object())
+            {
+                // perform range check
+                auto it = parent.find(last_path);
+                if (JSON_HEDLEY_LIKELY(it != parent.end()))
+                {
+                    parent.erase(it);
+                }
+                else
+                {
+                    JSON_THROW(out_of_range::create(403, detail::concat("key '", last_path, "' not found"), this));
+                }
+            }
+            else if (parent.is_array())
+            {
+                // note erase performs range check
+                parent.erase(json_pointer::template array_index<basic_json_t>(last_path));
+            }
+        };
+
+        // type check: top level value must be an array
+        if (JSON_HEDLEY_UNLIKELY(!json_patch.is_array()))
+        {
+            JSON_THROW(parse_error::create(104, 0, "JSON patch must be an array of objects", &json_patch));
+        }
+
+        // iterate and apply the operations
+        for (const auto& val : json_patch)
+        {
+            // wrapper to get a value for an operation
+            const auto get_value = [&val](const string_t& op,
+                                          const string_t& member,
+                                          bool string_type) -> basic_json &
+            {
+                // find value
+                auto it = val.m_data.m_value.object->find(member);
+
+                // context-sensitive error message
+                const auto error_msg = (op == "op") ? "operation" : detail::concat("operation '", op, '\''); // NOLINT(bugprone-unused-local-non-trivial-variable)
+
+                // check if desired value is present
+                if (JSON_HEDLEY_UNLIKELY(it == val.m_data.m_value.object->end()))
+                {
+                    // NOLINTNEXTLINE(performance-inefficient-string-concatenation)
+                    JSON_THROW(parse_error::create(105, 0, detail::concat(error_msg, " must have member '", member, "'"), &val));
+                }
+
+                // check if result is of type string
+                if (JSON_HEDLEY_UNLIKELY(string_type && !it->second.is_string()))
+                {
+                    // NOLINTNEXTLINE(performance-inefficient-string-concatenation)
+                    JSON_THROW(parse_error::create(105, 0, detail::concat(error_msg, " must have string member '", member, "'"), &val));
+                }
+
+                // no error: return value
+                return it->second;
+            };
+
+            // type check: every element of the array must be an object
+            if (JSON_HEDLEY_UNLIKELY(!val.is_object()))
+            {
+                JSON_THROW(parse_error::create(104, 0, "JSON patch must be an array of objects", &val));
+            }
+
+            // collect mandatory members
+            const auto op = get_value("op", "op", true).template get<string_t>();
+            const auto path = get_value(op, "path", true).template get<string_t>();
+            json_pointer ptr(path);
+
+            switch (get_op(op))
+            {
+                case patch_operations::add:
+                {
+                    operation_add(ptr, get_value("add", "value", false));
+                    break;
+                }
+
+                case patch_operations::remove:
+                {
+                    operation_remove(ptr);
+                    break;
+                }
+
+                case patch_operations::replace:
+                {
+                    // the "path" location must exist - use at()
+                    result.at(ptr) = get_value("replace", "value", false);
+                    break;
+                }
+
+                case patch_operations::move:
+                {
+                    const auto from_path = get_value("move", "from", true).template get<string_t>();
+                    json_pointer from_ptr(from_path);
+
+                    // the "from" location must exist - use at()
+                    basic_json const v = result.at(from_ptr);
+
+                    // The move operation is functionally identical to a
+                    // "remove" operation on the "from" location, followed
+                    // immediately by an "add" operation at the target
+                    // location with the value that was just removed.
+                    operation_remove(from_ptr);
+                    operation_add(ptr, v);
+                    break;
+                }
+
+                case patch_operations::copy:
+                {
+                    const auto from_path = get_value("copy", "from", true).template get<string_t>();
+                    const json_pointer from_ptr(from_path);
+
+                    // the "from" location must exist - use at()
+                    basic_json const v = result.at(from_ptr);
+
+                    // The copy is functionally identical to an "add"
+                    // operation at the target location using the value
+                    // specified in the "from" member.
+                    operation_add(ptr, v);
+                    break;
+                }
+
+                case patch_operations::test:
+                {
+                    bool success = false;
+                    JSON_TRY
+                    {
+                        // check if "value" matches the one at "path"
+                        // the "path" location must exist - use at()
+                        success = (result.at(ptr) == get_value("test", "value", false));
+                    }
+                    JSON_INTERNAL_CATCH (out_of_range&)
+                    {
+                        // ignore out of range errors: success remains false
+                    }
+
+                    // throw an exception if test fails
+                    if (JSON_HEDLEY_UNLIKELY(!success))
+                    {
+                        JSON_THROW(other_error::create(501, detail::concat("unsuccessful: ", val.dump()), &val));
+                    }
+
+                    break;
+                }
+
+                case patch_operations::invalid:
+                default:
+                {
+                    // op must be "add", "remove", "replace", "move", "copy", or
+                    // "test"
+                    JSON_THROW(parse_error::create(105, 0, detail::concat("operation value '", op, "' is invalid"), &val));
+                }
+            }
+        }
+    }
+
+    /// @brief applies a JSON patch to a copy of the current object
+    /// @sa https://json.nlohmann.me/api/basic_json/patch/
+    basic_json patch(const basic_json& json_patch) const
+    {
+        basic_json result = *this;
+        result.patch_inplace(json_patch);
+        return result;
+    }
+
+    /// @brief creates a diff as a JSON patch
+    /// @sa https://json.nlohmann.me/api/basic_json/diff/
+    JSON_HEDLEY_WARN_UNUSED_RESULT
+    static basic_json diff(const basic_json& source, const basic_json& target,
+                           const string_t& path = "")
+    {
+        // the patch
+        basic_json result(value_t::array);
+
+        // if the values are the same, return empty patch
+        if (source == target)
+        {
+            return result;
+        }
+
+        if (source.type() != target.type())
+        {
+            // different types: replace value
+            result.push_back(
+            {
+                {"op", "replace"}, {"path", path}, {"value", target}
+            });
+            return result;
+        }
+
+        switch (source.type())
+        {
+            case value_t::array:
+            {
+                // first pass: traverse common elements
+                std::size_t i = 0;
+                while (i < source.size() && i < target.size())
+                {
+                    // recursive call to compare array values at index i
+                    auto temp_diff = diff(source[i], target[i], detail::concat<string_t>(path, '/', detail::to_string<string_t>(i)));
+                    result.insert(result.end(), temp_diff.begin(), temp_diff.end());
+                    ++i;
+                }
+
+                // We now reached the end of at least one array
+                // in a second pass, traverse the remaining elements
+
+                // remove my remaining elements
+                const auto end_index = static_cast<difference_type>(result.size());
+                while (i < source.size())
+                {
+                    // add operations in reverse order to avoid invalid
+                    // indices
+                    result.insert(result.begin() + end_index, object(
+                    {
+                        {"op", "remove"},
+                        {"path", detail::concat<string_t>(path, '/', detail::to_string<string_t>(i))}
+                    }));
+                    ++i;
+                }
+
+                // add other remaining elements
+                while (i < target.size())
+                {
+                    result.push_back(
+                    {
+                        {"op", "add"},
+                        {"path", detail::concat<string_t>(path, "/-")},
+                        {"value", target[i]}
+                    });
+                    ++i;
+                }
+
+                break;
+            }
+
+            case value_t::object:
+            {
+                // first pass: traverse this object's elements
+                for (auto it = source.cbegin(); it != source.cend(); ++it)
+                {
+                    // escape the key name to be used in a JSON patch
+                    const auto path_key = detail::concat<string_t>(path, '/', detail::escape(it.key()));
+
+                    if (target.find(it.key()) != target.end())
+                    {
+                        // recursive call to compare object values at key it
+                        auto temp_diff = diff(it.value(), target[it.key()], path_key);
+                        result.insert(result.end(), temp_diff.begin(), temp_diff.end());
+                    }
+                    else
+                    {
+                        // found a key that is not in o -> remove it
+                        result.push_back(object(
+                        {
+                            {"op", "remove"}, {"path", path_key}
+                        }));
+                    }
+                }
+
+                // second pass: traverse other object's elements
+                for (auto it = target.cbegin(); it != target.cend(); ++it)
+                {
+                    if (source.find(it.key()) == source.end())
+                    {
+                        // found a key that is not in this -> add it
+                        const auto path_key = detail::concat<string_t>(path, '/', detail::escape(it.key()));
+                        result.push_back(
+                        {
+                            {"op", "add"}, {"path", path_key},
+                            {"value", it.value()}
+                        });
+                    }
+                }
+
+                break;
+            }
+
+            case value_t::null:
+            case value_t::string:
+            case value_t::boolean:
+            case value_t::number_integer:
+            case value_t::number_unsigned:
+            case value_t::number_float:
+            case value_t::binary:
+            case value_t::discarded:
+            default:
+            {
+                // both primitive type: replace value
+                result.push_back(
+                {
+                    {"op", "replace"}, {"path", path}, {"value", target}
+                });
+                break;
+            }
+        }
+
+        return result;
+    }
+    /// @}
+
+    ////////////////////////////////
+    // JSON Merge Patch functions //
+    ////////////////////////////////
+
+    /// @name JSON Merge Patch functions
+    /// @{
+
+    /// @brief applies a JSON Merge Patch
+    /// @sa https://json.nlohmann.me/api/basic_json/merge_patch/
+    void merge_patch(const basic_json& apply_patch)
+    {
+        if (apply_patch.is_object())
+        {
+            if (!is_object())
+            {
+                *this = object();
+            }
+            for (auto it = apply_patch.begin(); it != apply_patch.end(); ++it)
+            {
+                if (it.value().is_null())
+                {
+                    erase(it.key());
+                }
+                else
+                {
+                    operator[](it.key()).merge_patch(it.value());
+                }
+            }
+        }
+        else
+        {
+            *this = apply_patch;
+        }
+    }
+
+    /// @}
+};
+
+/// @brief user-defined to_string function for JSON values
+/// @sa https://json.nlohmann.me/api/basic_json/to_string/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+std::string to_string(const NLOHMANN_BASIC_JSON_TPL& j)
+{
+    return j.dump();
+}
+
+inline namespace literals
+{
+inline namespace json_literals
+{
+
+/// @brief user-defined string literal for JSON values
+/// @sa https://json.nlohmann.me/api/basic_json/operator_literal_json/
+JSON_HEDLEY_NON_NULL(1)
+#if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)
+    inline nlohmann::json operator ""_json(const char* s, std::size_t n)
+#else
+    inline nlohmann::json operator "" _json(const char* s, std::size_t n)
+#endif
+{
+    return nlohmann::json::parse(s, s + n);
+}
+
+/// @brief user-defined string literal for JSON pointer
+/// @sa https://json.nlohmann.me/api/basic_json/operator_literal_json_pointer/
+JSON_HEDLEY_NON_NULL(1)
+#if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)
+    inline nlohmann::json::json_pointer operator ""_json_pointer(const char* s, std::size_t n)
+#else
+    inline nlohmann::json::json_pointer operator "" _json_pointer(const char* s, std::size_t n)
+#endif
+{
+    return nlohmann::json::json_pointer(std::string(s, n));
+}
+
+}  // namespace json_literals
+}  // namespace literals
+NLOHMANN_JSON_NAMESPACE_END
+
+///////////////////////
+// nonmember support //
+///////////////////////
+
+namespace std // NOLINT(cert-dcl58-cpp)
+{
+
+/// @brief hash value for JSON objects
+/// @sa https://json.nlohmann.me/api/basic_json/std_hash/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+struct hash<nlohmann::NLOHMANN_BASIC_JSON_TPL> // NOLINT(cert-dcl58-cpp)
+{
+    std::size_t operator()(const nlohmann::NLOHMANN_BASIC_JSON_TPL& j) const
+    {
+        return nlohmann::detail::hash(j);
+    }
+};
+
+// specialization for std::less<value_t>
+template<>
+struct less< ::nlohmann::detail::value_t> // do not remove the space after '<', see https://github.com/nlohmann/json/pull/679
+{
+    /*!
+    @brief compare two value_t enum values
+    @since version 3.0.0
+    */
+    bool operator()(::nlohmann::detail::value_t lhs,
+                    ::nlohmann::detail::value_t rhs) const noexcept
+    {
+#if JSON_HAS_THREE_WAY_COMPARISON
+        return std::is_lt(lhs <=> rhs); // *NOPAD*
+#else
+        return ::nlohmann::detail::operator<(lhs, rhs);
+#endif
+    }
+};
+
+// C++20 prohibit function specialization in the std namespace.
+#ifndef JSON_HAS_CPP_20
+
+/// @brief exchanges the values of two JSON objects
+/// @sa https://json.nlohmann.me/api/basic_json/std_swap/
+NLOHMANN_BASIC_JSON_TPL_DECLARATION
+inline void swap(nlohmann::NLOHMANN_BASIC_JSON_TPL& j1, nlohmann::NLOHMANN_BASIC_JSON_TPL& j2) noexcept(  // NOLINT(readability-inconsistent-declaration-parameter-name, cert-dcl58-cpp)
+    is_nothrow_move_constructible<nlohmann::NLOHMANN_BASIC_JSON_TPL>::value&&                          // NOLINT(misc-redundant-expression,cppcoreguidelines-noexcept-swap,performance-noexcept-swap)
+    is_nothrow_move_assignable<nlohmann::NLOHMANN_BASIC_JSON_TPL>::value)
+{
+    j1.swap(j2);
+}
+
+#endif
+
+}  // namespace std
+
+#if JSON_USE_GLOBAL_UDLS
+    #if !defined(JSON_HEDLEY_GCC_VERSION) || JSON_HEDLEY_GCC_VERSION_CHECK(4,9,0)
+        using nlohmann::literals::json_literals::operator ""_json; // NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+        using nlohmann::literals::json_literals::operator ""_json_pointer; //NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+    #else
+        using nlohmann::literals::json_literals::operator "" _json; // NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+        using nlohmann::literals::json_literals::operator "" _json_pointer; //NOLINT(misc-unused-using-decls,google-global-names-in-headers)
+    #endif
+#endif
+
+// #include <nlohmann/detail/macro_unscope.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+// restore clang diagnostic settings
+#if defined(__clang__)
+    #pragma clang diagnostic pop
+#endif
+
+// clean up
+#undef JSON_ASSERT
+#undef JSON_INTERNAL_CATCH
+#undef JSON_THROW
+#undef JSON_PRIVATE_UNLESS_TESTED
+#undef NLOHMANN_BASIC_JSON_TPL_DECLARATION
+#undef NLOHMANN_BASIC_JSON_TPL
+#undef JSON_EXPLICIT
+#undef NLOHMANN_CAN_CALL_STD_FUNC_IMPL
+#undef JSON_INLINE_VARIABLE
+#undef JSON_NO_UNIQUE_ADDRESS
+#undef JSON_DISABLE_ENUM_SERIALIZATION
+#undef JSON_USE_GLOBAL_UDLS
+
+#ifndef JSON_TEST_KEEP_MACROS
+    #undef JSON_CATCH
+    #undef JSON_TRY
+    #undef JSON_HAS_CPP_11
+    #undef JSON_HAS_CPP_14
+    #undef JSON_HAS_CPP_17
+    #undef JSON_HAS_CPP_20
+    #undef JSON_HAS_CPP_23
+    #undef JSON_HAS_FILESYSTEM
+    #undef JSON_HAS_EXPERIMENTAL_FILESYSTEM
+    #undef JSON_HAS_THREE_WAY_COMPARISON
+    #undef JSON_HAS_RANGES
+    #undef JSON_HAS_STATIC_RTTI
+    #undef JSON_USE_LEGACY_DISCARDED_VALUE_COMPARISON
+#endif
+
+// #include <nlohmann/thirdparty/hedley/hedley_undef.hpp>
+//     __ _____ _____ _____
+//  __|  |   __|     |   | |  JSON for Modern C++
+// |  |  |__   |  |  | | | |  version 3.12.0
+// |_____|_____|_____|_|___|  https://github.com/nlohmann/json
+//
+// SPDX-FileCopyrightText: 2013 - 2025 Niels Lohmann <https://nlohmann.me>
+// SPDX-License-Identifier: MIT
+
+
+
+#undef JSON_HEDLEY_ALWAYS_INLINE
+#undef JSON_HEDLEY_ARM_VERSION
+#undef JSON_HEDLEY_ARM_VERSION_CHECK
+#undef JSON_HEDLEY_ARRAY_PARAM
+#undef JSON_HEDLEY_ASSUME
+#undef JSON_HEDLEY_BEGIN_C_DECLS
+#undef JSON_HEDLEY_CLANG_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_CLANG_HAS_BUILTIN
+#undef JSON_HEDLEY_CLANG_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_CLANG_HAS_DECLSPEC_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_CLANG_HAS_EXTENSION
+#undef JSON_HEDLEY_CLANG_HAS_FEATURE
+#undef JSON_HEDLEY_CLANG_HAS_WARNING
+#undef JSON_HEDLEY_COMPCERT_VERSION
+#undef JSON_HEDLEY_COMPCERT_VERSION_CHECK
+#undef JSON_HEDLEY_CONCAT
+#undef JSON_HEDLEY_CONCAT3
+#undef JSON_HEDLEY_CONCAT3_EX
+#undef JSON_HEDLEY_CONCAT_EX
+#undef JSON_HEDLEY_CONST
+#undef JSON_HEDLEY_CONSTEXPR
+#undef JSON_HEDLEY_CONST_CAST
+#undef JSON_HEDLEY_CPP_CAST
+#undef JSON_HEDLEY_CRAY_VERSION
+#undef JSON_HEDLEY_CRAY_VERSION_CHECK
+#undef JSON_HEDLEY_C_DECL
+#undef JSON_HEDLEY_DEPRECATED
+#undef JSON_HEDLEY_DEPRECATED_FOR
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CAST_QUAL
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_CPP98_COMPAT_WRAP_
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_DEPRECATED
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_CPP_ATTRIBUTES
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNKNOWN_PRAGMAS
+#undef JSON_HEDLEY_DIAGNOSTIC_DISABLE_UNUSED_FUNCTION
+#undef JSON_HEDLEY_DIAGNOSTIC_POP
+#undef JSON_HEDLEY_DIAGNOSTIC_PUSH
+#undef JSON_HEDLEY_DMC_VERSION
+#undef JSON_HEDLEY_DMC_VERSION_CHECK
+#undef JSON_HEDLEY_EMPTY_BASES
+#undef JSON_HEDLEY_EMSCRIPTEN_VERSION
+#undef JSON_HEDLEY_EMSCRIPTEN_VERSION_CHECK
+#undef JSON_HEDLEY_END_C_DECLS
+#undef JSON_HEDLEY_FLAGS
+#undef JSON_HEDLEY_FLAGS_CAST
+#undef JSON_HEDLEY_GCC_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_GCC_HAS_BUILTIN
+#undef JSON_HEDLEY_GCC_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_GCC_HAS_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_GCC_HAS_EXTENSION
+#undef JSON_HEDLEY_GCC_HAS_FEATURE
+#undef JSON_HEDLEY_GCC_HAS_WARNING
+#undef JSON_HEDLEY_GCC_NOT_CLANG_VERSION_CHECK
+#undef JSON_HEDLEY_GCC_VERSION
+#undef JSON_HEDLEY_GCC_VERSION_CHECK
+#undef JSON_HEDLEY_GNUC_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_GNUC_HAS_BUILTIN
+#undef JSON_HEDLEY_GNUC_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_GNUC_HAS_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_GNUC_HAS_EXTENSION
+#undef JSON_HEDLEY_GNUC_HAS_FEATURE
+#undef JSON_HEDLEY_GNUC_HAS_WARNING
+#undef JSON_HEDLEY_GNUC_VERSION
+#undef JSON_HEDLEY_GNUC_VERSION_CHECK
+#undef JSON_HEDLEY_HAS_ATTRIBUTE
+#undef JSON_HEDLEY_HAS_BUILTIN
+#undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE
+#undef JSON_HEDLEY_HAS_CPP_ATTRIBUTE_NS
+#undef JSON_HEDLEY_HAS_DECLSPEC_ATTRIBUTE
+#undef JSON_HEDLEY_HAS_EXTENSION
+#undef JSON_HEDLEY_HAS_FEATURE
+#undef JSON_HEDLEY_HAS_WARNING
+#undef JSON_HEDLEY_IAR_VERSION
+#undef JSON_HEDLEY_IAR_VERSION_CHECK
+#undef JSON_HEDLEY_IBM_VERSION
+#undef JSON_HEDLEY_IBM_VERSION_CHECK
+#undef JSON_HEDLEY_IMPORT
+#undef JSON_HEDLEY_INLINE
+#undef JSON_HEDLEY_INTEL_CL_VERSION
+#undef JSON_HEDLEY_INTEL_CL_VERSION_CHECK
+#undef JSON_HEDLEY_INTEL_VERSION
+#undef JSON_HEDLEY_INTEL_VERSION_CHECK
+#undef JSON_HEDLEY_IS_CONSTANT
+#undef JSON_HEDLEY_IS_CONSTEXPR_
+#undef JSON_HEDLEY_LIKELY
+#undef JSON_HEDLEY_MALLOC
+#undef JSON_HEDLEY_MCST_LCC_VERSION
+#undef JSON_HEDLEY_MCST_LCC_VERSION_CHECK
+#undef JSON_HEDLEY_MESSAGE
+#undef JSON_HEDLEY_MSVC_VERSION
+#undef JSON_HEDLEY_MSVC_VERSION_CHECK
+#undef JSON_HEDLEY_NEVER_INLINE
+#undef JSON_HEDLEY_NON_NULL
+#undef JSON_HEDLEY_NO_ESCAPE
+#undef JSON_HEDLEY_NO_RETURN
+#undef JSON_HEDLEY_NO_THROW
+#undef JSON_HEDLEY_NULL
+#undef JSON_HEDLEY_PELLES_VERSION
+#undef JSON_HEDLEY_PELLES_VERSION_CHECK
+#undef JSON_HEDLEY_PGI_VERSION
+#undef JSON_HEDLEY_PGI_VERSION_CHECK
+#undef JSON_HEDLEY_PREDICT
+#undef JSON_HEDLEY_PRINTF_FORMAT
+#undef JSON_HEDLEY_PRIVATE
+#undef JSON_HEDLEY_PUBLIC
+#undef JSON_HEDLEY_PURE
+#undef JSON_HEDLEY_REINTERPRET_CAST
+#undef JSON_HEDLEY_REQUIRE
+#undef JSON_HEDLEY_REQUIRE_CONSTEXPR
+#undef JSON_HEDLEY_REQUIRE_MSG
+#undef JSON_HEDLEY_RESTRICT
+#undef JSON_HEDLEY_RETURNS_NON_NULL
+#undef JSON_HEDLEY_SENTINEL
+#undef JSON_HEDLEY_STATIC_ASSERT
+#undef JSON_HEDLEY_STATIC_CAST
+#undef JSON_HEDLEY_STRINGIFY
+#undef JSON_HEDLEY_STRINGIFY_EX
+#undef JSON_HEDLEY_SUNPRO_VERSION
+#undef JSON_HEDLEY_SUNPRO_VERSION_CHECK
+#undef JSON_HEDLEY_TINYC_VERSION
+#undef JSON_HEDLEY_TINYC_VERSION_CHECK
+#undef JSON_HEDLEY_TI_ARMCL_VERSION
+#undef JSON_HEDLEY_TI_ARMCL_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL2000_VERSION
+#undef JSON_HEDLEY_TI_CL2000_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL430_VERSION
+#undef JSON_HEDLEY_TI_CL430_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL6X_VERSION
+#undef JSON_HEDLEY_TI_CL6X_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CL7X_VERSION
+#undef JSON_HEDLEY_TI_CL7X_VERSION_CHECK
+#undef JSON_HEDLEY_TI_CLPRU_VERSION
+#undef JSON_HEDLEY_TI_CLPRU_VERSION_CHECK
+#undef JSON_HEDLEY_TI_VERSION
+#undef JSON_HEDLEY_TI_VERSION_CHECK
+#undef JSON_HEDLEY_UNAVAILABLE
+#undef JSON_HEDLEY_UNLIKELY
+#undef JSON_HEDLEY_UNPREDICTABLE
+#undef JSON_HEDLEY_UNREACHABLE
+#undef JSON_HEDLEY_UNREACHABLE_RETURN
+#undef JSON_HEDLEY_VERSION
+#undef JSON_HEDLEY_VERSION_DECODE_MAJOR
+#undef JSON_HEDLEY_VERSION_DECODE_MINOR
+#undef JSON_HEDLEY_VERSION_DECODE_REVISION
+#undef JSON_HEDLEY_VERSION_ENCODE
+#undef JSON_HEDLEY_WARNING
+#undef JSON_HEDLEY_WARN_UNUSED_RESULT
+#undef JSON_HEDLEY_WARN_UNUSED_RESULT_MSG
+#undef JSON_HEDLEY_FALL_THROUGH
+
+
+
+#endif  // INCLUDE_NLOHMANN_JSON_HPP_
diff --git a/research/gen4-retiming-entrances/vendor/pr276/BANK-PROOF.md b/research/gen4-retiming-entrances/vendor/pr276/BANK-PROOF.md
new file mode 100644
index 0000000000..62560a4fb9
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/BANK-PROOF.md
@@ -0,0 +1,37 @@
+# Five-stage stage-private completed banks
+
+This is a finite bank-allocation extension of the PR197/PR200 completed-bank construction to PR234's five-stage bit geometry, retained from eumemic's source527 package and applied here to the gen4 independent helper census. It does not claim a new all-size compiler theorem or replace the scalar admission.
+
+For one complete local invocation, the source-bound physical telescope has no data/helper cross blocks. On an independent helper with genuine entrance projector sigma its endpoint is the exact partial swap D_(I24-sigma), supported in the active local window. This holds on arbitrary correlated dirty contents. The complemented inverse invocation has the same residual: its reversed endpoints are 0 and I24-sigma. Source-owned gauges are visible-data paths and are excluded from the independent helper census.
+
+In stage i, PR234 routes the helper at local class d to physical class g=d*tau_i. Relative to g, the residual is P_i=tau_i*diag(I24-sigma,0,...,0)*tau_i, supported only in H_i. We give each stage a disjoint collection of banks. Every bank is filled by disjoint coordinate blocks of total dimension120. For the actual gauge chart B whose columns are residual columns followed by gauge columns, set
+
+    N_b=(b+1)*Pi_b*embed_i(B^-1).
+
+For an ungauged role B=I24. Pi_b is the explicit coordinate permutation sending the first residual coordinates in H_i to the assigned bank interval. Thus N_b*P_i*N_b^-1 is exactly that coordinate projector. The scalar leaves conjugation unchanged. The checker reconstructs every actual chart, checks both inverse identities, the G-orthogonality of its two summands, its residual action and its elementary factorization. Therefore this is a projector identity for the actual bases, not a rank substitution.
+
+The bank route is g -> g*N_b^-1, hence d*tau_i*N_b^-1 in the original local invocation. If the bank class is h, its residual is h*N_b*P_i*N_b^-1*h^-1. Every occurrence visits every bank class once because right multiplication is a bijection on the complete GL cover. If two roles in one local invocation are assigned the same bank family, their distinct N_b give distinct bank classes. Distinctness is literal: choose a coordinate j outside H_i. The embedded inverse fixes e_j; N_b*e_j=(b+1)e_(Pi_b(j)). The resulting columns differ for all b, at every eligible prime q>2^80 and every local ring Z/q^w. All scalars are between 1 and 40 and remain distinct units. The proof uses the full GL cover, not a projective quotient.
+
+Complete the entire cover sweep for each stage and replica in fixed order before its boundary phase. The complete local source endpoint separates every bank from the data and other banks, so each subsequent invocation may receive arbitrary dirty bank contents. For each bank, its block projectors are disjoint and sum to I120. The literal partial swaps therefore compose to D_I120 on every address column. The common inherited ancestor chart is the same for each block and cancels between blocks. The checker verifies all240 address columns, the reverse schedule, and failures from omitting or repeating a block. No new independence assumption on dirt is used.
+
+The five bank collections remain separate, and each is touched only in its own stage. This gives every physical bank its full required endpoint once. The data stage routes, bridge maps, idle children and final exchanges remain PR234's. Consequently there are no independent exterior rank5a children. Their removal follows from the completed bank endpoint; no internal, data, compensation or copied-center child is removed.
+
+For gen4 the actual residual families are 3:266 (rank-21 entrances), 4:2200 (rank-20 entrances) and 24:13944 (ungauged roles). Sixty physical replicas fill each stage with these exact 120-dimensional patterns:
+
+| Blocks | Banks per stage |
+| --- | ---: |
+| 40 of dimension 3 | 399 |
+| 30 of dimension 4 | 4400 |
+| 5 of dimension 24 | 167328 |
+
+There are 172127 banks per stage, 860635 total banks and 422400 data families. Literal stock is 1283035. Its per-replica normalized value is 256607/12. The checker enumerates each of 4923000 actual role/replica/stage assignments exactly once, verifies the actual role's chart rank, and hashes the complete allocation.
+
+Every actual chart (370 distinct entrance bases) uses at most 186 factors. At most 119 coordinate transpositions and 120 scalar-coordinate factors give 425 normalizer factors. A conservative added out-and-back selector bill, in addition to all retained PR234 route and scalar bills, is
+
+    2*5*60*((1283035-1)+16410*120*425)=502915820400 < 2^40.
+
+The literal stock, not the rational per-replica stock, must be used for physical role routing and finite storage. All60 scalar replicas execute, and all recursive child counts are multiplied by60 in a literal realization. Any smaller integer normalization used only in the moment arithmetic must be distinguished from the literal replica count. Serial execution may share an external copied-center work stream only after erasure. The fixed bank selector bill is explicitly charged before the inherited positive ordinary-leaf gap absorbs it. After completion removal the maximum child is50 of120, so a single level halves; the histogram remains a one-level profile.
+
+This witness leaves the full scalar/integer/sign audits, frame ledgers, exact global lowering, prime guard, complete fallback profile and 47 outer inequalities to the integrator (verify.py). Its input charts/census are the independently admitted gen4 helper. Existing compiler, common weighted chart, restored selectors, complete-stream routing and all-size analytic hypotheses remain conditional as in the cited sources.
+
+Prepared with OpenAI Codex assistance (source527 package, eumemic); gen4 numbers rebound with Claude assistance. Apache-2.0; inherited source attribution remains unchanged.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/LICENSE b/research/gen4-retiming-entrances/vendor/pr276/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gen4-retiming-entrances/vendor/pr276/MANIFEST.json b/research/gen4-retiming-entrances/vendor/pr276/MANIFEST.json
new file mode 100644
index 0000000000..f248218f71
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/MANIFEST.json
@@ -0,0 +1,115 @@
+{
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+    "inputs/complex/sources/Work__GCert__Data__P193Price.lean": "0299bcd0fe255960eec682eef0f045f7e5cb1e4711af2aab4393526eae2caea3",
+    "inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean": "479434815822e98f015e335361089c3788d00dc3dd39c2944f75410aa0c158fe",
+    "inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean": "6b40cac1481c931d47b1a092e382d04716ede0e785c492a2f2983e886a257c3f",
+    "inputs/complex/sources/Work__GCert__Data__Raw.lean": "aba94a004c94dcae7cf3047c88a6da9561555f4ebe8ab92e299e6ce09ee7aa66",
+    "inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean": "45c768c9d71a7cc18bd6db74cb036db880d89580ca60557bb4a492280296b169",
+    "inputs/complex/sources/Work__GFrame__Engine__Adapt.lean": "feec0a3828867968a5c7c2c30b86ed70449abc3c660a60ada67203a75bae2ef7",
+    "inputs/complex/sources/Work__GFrame__Engine__Letters.lean": "34906dbf5ae16b5174db00b4881a5cc1d2e583b8c8806db6523a5e2f86565f09",
+    "inputs/complex/sources/Work__GFrame__Engine__Level.lean": "80fb3daa9a45de0ed6da570eb4476b9104734be65d0116f58bcfcbcd67f771d0",
+    "inputs/complex/sources/tools__gx__ORIGIN.md": "6ba897a9495ddadcf8558b93133fdfaf66fc35ce7fa2c53e2d5667335c315e0b",
+    "inputs/complex/sources/tools__gx__gxbind.py": "9c9dcfac47f0535bf3aa8ebf7c662cdef0ebda50a9f0a9282b8f3cf34809f835",
+    "inputs/complex/sources/tools__gx__gxconv.py": "dab7fec9f44c2d368ed334055d7126e202017feb46e41a8d86e2d998720f67c2",
+    "inputs/complex/sources/tools__gx__gxcore.py": "eb972c06fe8c322db2d9a8d9a7d05596e8f40c4ca8e5f42eb6df3c7361b5d517",
+    "math_check.py": "706d9e0a2e2092393914809109be39012c0182edf4eb1bb76bf05f9e51fde713",
+    "moment.py": "9d465c716c6b910ff66e1453e3bf0057608a787b5f5361be93781f42cb3370f7",
+    "notices/PR210-coordinated-crossover-NOTICE": "9fc5561c0995892dbdde777c713899486920c32d3562392f5f72377a4953bf98",
+    "notices/PR230-NOTICE": "7dfbad087ee49b74fd5075d517eaa263c5dd3d4fbd4c69bfba34ee1cb55e837f",
+    "notices/PR230-PROVENANCE.json": "19957e28a8ad26281bfe8bfaf8ae16191be53e729a8870a6154671b3384959d4",
+    "notices/README.md": "a4c288228cf8360d8d04c62b0f51177de5682d1f5d3bae341e6b850af766c26e",
+    "notices/base-bit-PR200-PR202-NOTICE": "c9850418622aea8d1382a230306c940947b5da818f4854b4b272ed60cf239f6c",
+    "notices/source527-loader-NOTICE.md": "ee632728cc4d89565292d288f8289f483ac794b5d02cc6e42c2b2c43c43ff1d8",
+    "outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+    "parity_transform.py": "9ed3ff2767c046d11aa1be248eaba93755740131745f673ad9d26a3e77e7b02a",
+    "portable_bit.py": "c8d18bdc5a123f14be330e94d96509be8b5eec71ccc68e0fabc649ac1ee6f218",
+    "portable_complex.py": "797e144c0040d78a4731a6eaa61c0edb9803a08462f885ed014cbca9d9991d82",
+    "prepare.py": "00b13cb18e2d1dd26f207a20a7183b9e357a92a9b2906371e6fae9cb8cc197b3",
+    "prime_check.py": "d1682e044773ca8e8b131b82e58186c8d97e597f0d8a7d74aaeee06cf5204973",
+    "prime_witnesses.py": "98cd03bc9582e7bd0ab194c191ea8eea940539e510051443ab9fd3e572a364ab",
+    "proof/FINITE_BIT_ACCOUNTING.md": "602923520af184670170bf159fde7b4c72e79a72570eddd7746b7c97bc51fc5b",
+    "proof/INTEGRATED_PROOF.md": "cff22391e71a50bad27a1e832d5c0a2c8b2446df55adb1297c8b1485b3761257",
+    "proof/PARITY-CONTRACT.md": "a9246be656e31f1a21d5ec714e002f51be0aa07c36e1528066a25b2c7a02db91",
+    "proof/README.md": "5f40cb6dda3992f98ffc43159af1be080bd6c18411bc7d02464f230993f3074f",
+    "proof/copied-centers-lemma.tex": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe",
+    "proof/primary/03-motifs.tex": "ed76761194988a01af77ead0ea6469cb5dcd29690ab985a0b5a4006b0f2b69bb",
+    "proof/primary/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "proof/primary/PROVENANCE.md": "dd9054c58aa92c44b0ef5f691ad4dc52b8ead2f20a9843d4399d6c300d616023",
+    "proof/primary/UPSTREAM-README.md": "8d1ceff898a4e0e681679f91c4def485820be9e99f04e4861f2ce601a364723e",
+    "proof/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "proof/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "raw_ledger.py": "e9701ab9d4f30c6bac6fa69853a2069624ad237666b85cfe6d31a8a7c806e28b",
+    "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
+    "scalar/word.py": "e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42",
+    "scalar_check.py": "bbc25d3df09bf0ce2cb92f623f46579b504b37a9447a144a6cd1cb8e63701b7f",
+    "verify.py": "996789f2c0e1ee17ccd6b9e634ce67384578595846cd5bac7f2c3901df2da307",
+    "virtual_check.py": "155144478a5c45d630c1b0d43cadbeb53b96306270fa4e0ad8c4d403d9045971"
+  },
+  "schema": "gen4-parity-fused-five-stage-banks-inputs/1"
+}
diff --git a/research/gen4-retiming-entrances/vendor/pr276/NOTICE.md b/research/gen4-retiming-entrances/vendor/pr276/NOTICE.md
new file mode 100644
index 0000000000..37e2779a2e
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/NOTICE.md
@@ -0,0 +1,52 @@
+# Attribution and licence
+
+Apache-2.0 applies. Original headers, licences, notices and AI-assistance disclosures are preserved. The
+credits below do not imply review or endorsement.
+
+## Inherited, unchanged or with rebound constants
+
+- **Five-stage architecture and finite interface package:** Henry Grant (hcg890), PR234, and Jacob
+  Sussman's five-stage construction and gcert/1 export. The complete inherited five-stage credits are in
+  `UPSTREAM-PR234-NOTICE.md`.
+- **Package machinery:** eumemic's source527 package, prepared with substantial OpenAI Codex assistance,
+  with its lineage: Dugongue's PR207/PR216 finite and bank admissions, Rohan Arun's PR211 and sennemmi's
+  PR230 frame work, and eumemic's PR210. Their notices are retained verbatim in `notices/`.
+  This covers the scalar program `scalar/word.py` (byte-identical), the physical event emitter, the parity
+  fusion, the raw-ledger census, the stage-private bank template and checker, the moment, prime and
+  finite-bill checks, and `verify.py`. In this package they are rebound to the gen4 helper's constants;
+  the logic is unchanged.
+- **Banks:** Evan McKinney's PR197 completed-bank method. Rohan Arun's PR237 published the width-120
+  application first.
+- **Complex supplier:** Avi Eisenberg (ikeboy)'s PR193 helper, inside Sussman's five-stage certificate.
+  The original disclosures are in `inputs/complex`.
+- **Physical-word classes:** Chafik Boukhalfa (chafreaky)'s PR200 `bit/word.py` and `bit/base_word.py`,
+  vendored unchanged in `gen4bit/bit`. `gen4bit/NOTICE-PR200` is PR200's own notice.
+- **Checker:** eumemic's PR168-v4 `check_paired_cube_bit.py`, vendored unchanged.
+- **Paired-cube framework and its developments:**
+  - icekylinx's PR144: paired-coordinate/shared-core framework and configurable local channels.
+  - PR161/PR168 (eumemic): annealed modules, nested schedules and the generator.
+  - James Chang's PR166 and PR162's carrier rule.
+
+## New in this package
+
+**The gen4 bit word.** This covers:
+
+- the arc-aware per-cube local design (`local_design()` recipe trees and `data/local_design_p12.json`);
+- the re-annealed all-but-one module (`data/qmod_p12.json`);
+- the centre-sharing pair module (`data/pair_module_p12.json` and the patch in `finish()`);
+- the frozen arcs (`data/arcs_p12.json`).
+
+**Its physical-layer producers.** `gen4bit/producer/make_physical.py` and `descent.py` are new
+implementations of PR200's stated rules.
+
+**Package integration.** This covers:
+
+- `prepare.py` and `virtual_check.py`;
+- the rewritten `scalar_check.py` controls;
+- the rank-21 geometry check;
+- the gen4 bank patterns and documentation.
+
+All of this was prepared by DreamingOfClouds with Anthropic Claude assistance. The circuit and module
+search was run by Claude agents (simulated annealing, CP-SAT and exact one-instance compiles), and every
+reported number was re-run with the exact generator. No exclusive priority is claimed for any inherited
+design or theorem interface.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/PR-STATEMENT.md b/research/gen4-retiming-entrances/vendor/pr276/PR-STATEMENT.md
new file mode 100644
index 0000000000..645ae4de4f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/PR-STATEMENT.md
@@ -0,0 +1,57 @@
+κ = 7.22869827347495e-4
+
+# gen4 bit word in the five-stage completed banks
+
+A conditional finite construction with **κ = 144573965469499/(2·10¹⁷) ≈ 7.22869827347495 × 10⁻⁴**.
+
+The package keeps PR234's five-stage layout, the completed width-120 entrance banks and the whole
+verification chain of eumemic's source527 package. Only the bit helper changes. It is a new paired-cube
+bit word, **gen4**, with three changes to PR168's generator:
+
+- a different per-cube local circuit;
+- a pair module whose extra root is the copied centre;
+- a re-annealed all-but-one module.
+
+Its virtual word needs 17,904 auxiliary roles, against 18,908 for PR200's word. After 1,494
+compensated reuse pairs and descended operation frames, the physical helper has **16,410** independent
+dirty registers, against source527's 16,587, which needed 527 source loans and 34 terminal sinks. The bit
+supplier still binds.
+
+| one invocation, m = 120 | source527 (current package) | gen4 (this package) |
+| --- | ---: | ---: |
+| virtual auxiliary roles | 18,908 (PR200 word) | 17,904 |
+| compensated reuse pairs | 1,760 | 1,494 |
+| source loans / terminal sinks | 527 / 34 | 0 / 0 |
+| independent dirty registers R | 16,587 | 16,410 |
+| independent entrances (ranks) | 2,279 (12, 13, 18, 20) | 2,466 (20, 21) |
+| literal stock, 60 replicas | 1,304,935 | 1,283,035 |
+| normalized stock / deficit | 260,987 / 52,800 | 256,607 / 52,800 |
+| bit coarse saving | 7.10573897320284e-4 | 7.23392746398452e-4 |
+| κ | 7.10069340338651e-4 | **7.22869827347495e-4** |
+
+Run with Python 3.11+ and assertions enabled:
+
+```sh
+python3 -m pip install -r requirements.txt
+python3 -B verify.py --output /tmp/gen4-five-stage-verification
+```
+
+The output directory must be new and outside this immutable package. Verification takes about five
+minutes, uses no network and runs no producer. It performs these checks:
+
+- the PR168-v4 checker on the virtual word, with its five mutation controls;
+- PR200's physical-word proof, exactly as PR200 ran it: frames, handoffs, the physical row and all-column replays, with 4 adverse controls;
+- the retained source527 scalar program on all 19,930 formal F₂ columns, both integer decoder signs and 11 corruptions;
+- the physical event emitter, parity fusion and five-stage global lowering, with exact h=24/m=120 geometry;
+- exact determinants for 26,249 bases;
+- 370 bank charts and all 4,923,000 bank assignments;
+- the retained complex supplier, both rational moment engines, the 47 outer inequalities and the finite bill.
+
+`gen4bit/producer/regenerate.py` rebuilds the five pinned bit-word files from the generator and the two
+physical-layer producers, and checks them byte for byte. This is provenance only, not part of the proof.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows,
+selectors, tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic
+reduction. The included finite checks do not replace those hypotheses. See `PROOF.md` for the
+verification chain, `BANK-PROOF.md` for the banks, `gen4bit/README.md` for the bit word and `NOTICE.md`
+for attribution.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/PROOF.md b/research/gen4-retiming-entrances/vendor/pr276/PROOF.md
new file mode 100644
index 0000000000..6145c8e686
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/PROOF.md
@@ -0,0 +1,150 @@
+κ = 7.22869827347495e-4
+
+# Source-bound finite verification
+
+The bit helper is the gen4 paired-cube bit word, a reversible local word in which all inputs and dirty
+registers are formal variables. Every later stage is the source527 package's (eumemic). This file states
+what each stage checks for gen4 and what changed relative to source527.
+
+## The bit word
+
+`gen4bit/selected/bit` pins five files: the signed graph, the virtual profile, the physical word, the exact
+frames and the partner-pair chronology.
+
+**Virtual word.** `virtual_check.py` runs eumemic's PR168-v4 package checker, unmodified and vendored in
+`gen4bit/references/pr168-v4`. It checks:
+
+- exact frames (A·Bᵀ = 0, complementary ranks) and the mod-2 decoder with stars and side parts;
+- geometry: source lines, side-root common caps, operand nesting and centre star spans;
+- role and target chains on node frames, and the partner chronology;
+- G-nondegeneracy of every used frame;
+- a literal F₂ dirty-scratch replay and the independent ledger recount.
+
+All five mutation controls are rejected. The profile is R = 17,904, W = 21,424, m = 72, deficit 1,936,
+the same deficit as every PR168-derived word.
+
+**Physical layer.** The same `virtual` stage then runs Chafik Boukhalfa's PR200 classes
+(`gen4bit/bit/word.py` and `base_word.py`), also unmodified, exactly as PR200's `bit/prove.py` runs them on
+its own word. `prepare.py` builds the verifier context from the same classes. They check:
+
+- every changed operation frame (1,802) is nondegenerate and contains its node's value span;
+- the execution order preserves each role chronology;
+- gauges are untouched in phase one, every gauge read precedes its role's first use, and gauge targets equal response supports;
+- the 1,494 handoffs are one-to-one between ungauged non-root donors and gauged recipients;
+- each donor is dead before its recipient's read, and its last frame lies in the recipient's gauge frame;
+- all gate ports are distinct.
+
+The stage also recomputes the physical row:
+
+- phase one is exactly the centre closure;
+- every addition's actual operands are checked;
+- every physical role chain and the actual target chronology are nested;
+- the deficit telescopes, at 1,936.
+
+It executes the physical word on all 19,930 formal columns over F₂ and on the defining integer decoder.
+Four adverse controls are rejected: an omitted compensation, a missing partner delivery, a stale recipient
+read, and a zero operation frame. `prepare.py` also recomputes the literal adjoint and asserts it equals
+PR200's.
+
+The handoffs follow PR200's rule. A recipient is read immediately before its first operation. The only
+recipients used are rank-21 gauges with no strictly larger gauge later on any of their targets, so every
+target chain stays nested. The actual chronology is rechecked by the scalar program.
+
+## Unchanged scalar program and empty selections
+
+`scalar/word.py` is the source527 scalar program, byte-identical (sha256 e675d4eb…). Its source527
+selections are all empty for gen4:
+
+- source loans, early and gauge mixes, retimed prefixes;
+- aggregation, rank and echelon groups;
+- fresh and paired source reads, terminal sinks.
+
+The program then executes exactly the PR200 physical word:
+
+1. dirty compensation at D0;
+2. V injection and the phase-one gates;
+3. the 24 copied-centre scatters;
+4. gauge reads at their read times, interleaved with the remaining gates;
+5. side roots, then partner mixes and deliveries;
+6. cleanup, the inverse gates, and V removal.
+
+`scalar_check.py` runs it on all 19,930 formal F₂ columns (1,760 sources, 1,760 targets and 16,410 dirty
+registers) and in both defining-integer directions with 24-bit packing.
+
+The 25 source527 mutations exercise selections that gen4 does not have. They are replaced by 11
+corruptions of the actual gen4 context, each of which must make the unchanged program fail:
+
+- a dropped gauge, dirty or recipient compensation;
+- a misrouted gauge response;
+- a flipped compensation sign, checked over Z;
+- a recipient read before its donor's last write;
+- a gauge read after its first use;
+- an omitted gate, centre scatter, partner delivery or source injection.
+
+## Physical events, parity fusion and global lowering
+
+`code/physical527.py` observes the scalar program and emits the physical frame tags. The emitter is
+source527's, unchanged except the register count. The local scalar projection must equal the independent
+observer, and every MOVE is checked as an exact frame inclusion.
+
+`parity_transform.py` deletes the 1,510,656 even-coefficient payload ADDs, which are identities over F₂.
+It merges no MOVE chains for gen4, so the paid local histogram is unchanged. The independent
+required-use census rebuilds every path from the surviving operations and mathematical endpoints, checks
+both reflected inclusions, and matches the instruction histogram. The 626,360 surviving payload additions
+and their literal inverse are replayed on every F₂ column, with cancellation-free signed prefix bounds
+21,725 (forward) and 1,850,360 (inverse). The proof/PARITY-CONTRACT.md argument applies unchanged.
+
+`code/global_lowering.py` is PR234's lowering with the register count and the entrance census rebound. It
+expands all five stages, the idle and bridge phases, the 2,466 completions and the terminal exchange. It
+checks every operand namespace and the paid five-stage histogram:
+
+- 487,546 calls;
+- rank mass 2,809,600;
+- deficit 4,400 = 4v − 5ℓ.
+
+`code/geometry527.py` checks the exact rational h=24/m=120 routes, the eight idle boundary pairs for two
+actual ports, and the completion projectors and five disjoint windows. It does so for two actual rank-20
+entrance bases and, newly, one actual rank-21 basis.
+
+## Primes, banks, moments and finite bill
+
+**Primes.** `prime_check.py` recomputes the cleared-Gram determinant of every consumed basis: 26,249
+distinct bases, at most 118 bits. Only 2, 3 and 5 are stripped, every residual is below 2⁸⁰, and the
+retained prime range q > 2⁸⁰ is unchanged.
+
+**Banks.** The independent entrances are 2,200 of rank 20 and 266 of rank 21, with 370 distinct bases.
+Their residual families have widths 4 and 3. `BANK-PROOF.md` gives the stage-private banks:
+
+- (3⁴⁰) × 399 banks;
+- (4³⁰) × 4,400 banks;
+- (24⁵) × 167,328 banks.
+
+`bank_check.py` rebuilds the 370 charts (at most 186 factors) and enumerates all 4,923,000
+role/replica/stage assignments, checking the callable route map and both endpoint directions. It removes
+exactly the 2,466 rank-5a exterior completions.
+
+**Moments.** Literal stock is 1,283,035. The normalized profile has m = 120, W = 256,607, rank mass
+30,740,040, deficit 52,800 and largest child 50. Two independent rational moment engines, including the
+complete 10⁻¹⁶ bad-class fallback, give the bit coarse saving 180848186599613/(2.5·10¹⁷). The adjacent
+10⁻¹⁸ grid point is rejected.
+
+**Assembly.** The retained complex supplier (PR234/PR193 at m = 110, coarse 747454944651775/10¹⁸) is
+rerun. The bit supplier binds. Three completed ordinary-leaf levels feed the unchanged balanced outer
+assembly: all 47 strict inequalities and seven margins are positive, and the adjacent final grid point
+fails.
+
+**Finite bill.** `finite_check.py` pays every PR234 primitive and router allowance on the literal 60
+replicas and stock, and adds all 502,915,820,400 bank selector calls.
+
+## Scope
+
+The proof boundary is unchanged and conditional. The following are inherited interfaces:
+
+- the all-size weighted compiler and common ancestor charts;
+- restored rows and completed ordinary leaves;
+- selectors, exact-tape routing and prime supply;
+- precision/recovery and retained complex symbolic correctness;
+- analytic transfer.
+
+These checks establish the stated finite construction under those interfaces. They do not rebuild Lean or
+execute a multiplier at all input sizes.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/README.md b/research/gen4-retiming-entrances/vendor/pr276/README.md
new file mode 100644
index 0000000000..645ae4de4f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/README.md
@@ -0,0 +1,57 @@
+κ = 7.22869827347495e-4
+
+# gen4 bit word in the five-stage completed banks
+
+A conditional finite construction with **κ = 144573965469499/(2·10¹⁷) ≈ 7.22869827347495 × 10⁻⁴**.
+
+The package keeps PR234's five-stage layout, the completed width-120 entrance banks and the whole
+verification chain of eumemic's source527 package. Only the bit helper changes. It is a new paired-cube
+bit word, **gen4**, with three changes to PR168's generator:
+
+- a different per-cube local circuit;
+- a pair module whose extra root is the copied centre;
+- a re-annealed all-but-one module.
+
+Its virtual word needs 17,904 auxiliary roles, against 18,908 for PR200's word. After 1,494
+compensated reuse pairs and descended operation frames, the physical helper has **16,410** independent
+dirty registers, against source527's 16,587, which needed 527 source loans and 34 terminal sinks. The bit
+supplier still binds.
+
+| one invocation, m = 120 | source527 (current package) | gen4 (this package) |
+| --- | ---: | ---: |
+| virtual auxiliary roles | 18,908 (PR200 word) | 17,904 |
+| compensated reuse pairs | 1,760 | 1,494 |
+| source loans / terminal sinks | 527 / 34 | 0 / 0 |
+| independent dirty registers R | 16,587 | 16,410 |
+| independent entrances (ranks) | 2,279 (12, 13, 18, 20) | 2,466 (20, 21) |
+| literal stock, 60 replicas | 1,304,935 | 1,283,035 |
+| normalized stock / deficit | 260,987 / 52,800 | 256,607 / 52,800 |
+| bit coarse saving | 7.10573897320284e-4 | 7.23392746398452e-4 |
+| κ | 7.10069340338651e-4 | **7.22869827347495e-4** |
+
+Run with Python 3.11+ and assertions enabled:
+
+```sh
+python3 -m pip install -r requirements.txt
+python3 -B verify.py --output /tmp/gen4-five-stage-verification
+```
+
+The output directory must be new and outside this immutable package. Verification takes about five
+minutes, uses no network and runs no producer. It performs these checks:
+
+- the PR168-v4 checker on the virtual word, with its five mutation controls;
+- PR200's physical-word proof, exactly as PR200 ran it: frames, handoffs, the physical row and all-column replays, with 4 adverse controls;
+- the retained source527 scalar program on all 19,930 formal F₂ columns, both integer decoder signs and 11 corruptions;
+- the physical event emitter, parity fusion and five-stage global lowering, with exact h=24/m=120 geometry;
+- exact determinants for 26,249 bases;
+- 370 bank charts and all 4,923,000 bank assignments;
+- the retained complex supplier, both rational moment engines, the 47 outer inequalities and the finite bill.
+
+`gen4bit/producer/regenerate.py` rebuilds the five pinned bit-word files from the generator and the two
+physical-layer producers, and checks them byte for byte. This is provenance only, not part of the proof.
+
+The result is conditional on the retained all-size compiler, common weighted chart, restored rows,
+selectors, tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic
+reduction. The included finite checks do not replace those hypotheses. See `PROOF.md` for the
+verification chain, `BANK-PROOF.md` for the banks, `gen4bit/README.md` for the bit word and `NOTICE.md`
+for attribution.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/UPSTREAM-PR234-NOTICE.md b/research/gen4-retiming-entrances/vendor/pr276/UPSTREAM-PR234-NOTICE.md
new file mode 100644
index 0000000000..5f8fbb25c1
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/UPSTREAM-PR234-NOTICE.md
@@ -0,0 +1,13 @@
+# Attribution and licence
+
+This contribution uses Apache-2.0. Original source headers, licences and notices are preserved. These credits do not imply review or endorsement by the named contributors or OpenAI.
+
+- Jacob Sussman: five-stage complex geometry and published gcert/1 export in wht-power-saving-lean at f010392c923279e3dd59ef3aa5fedad23affc5fd. Original Claude assistance disclosure retained in inputs/complex/NOTICE.
+- Avi Eisenberg / ikeboy: retained PR193 source-assisted complex helper and donor selection at 187e1010ac8b259af8e9b5166f68b64bc27b4b47.
+- eumemic: current PR210 frames, gauges, source borrowing and retimed bit helper at df95878d11190518e45ef9717c9ee05011f88ace.
+- Chafik Boukhalfa / chafreaky: PR200 physical bit construction carried by PR202 at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, Douglas Colkitt, OpenAI and earlier contributors retain the attribution and original assistance disclosures in the supplied source notices. The exact outer assembly also credits Zhihao Chen and the RaD / hipotures balanced reduction in its original header.
+
+The paired-cube helper design predates Sussman’s certificate export. The new contribution here is the explicit source-bound five-stage composition, adapters, paid accounting and reproducible finite verification. No exclusive priority is claimed for the inherited designs or theorem interfaces.
+
+Assisted with ChatGPT.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/UPSTREAM-PR234-PROOF.md b/research/gen4-retiming-entrances/vendor/pr276/UPSTREAM-PR234-PROOF.md
new file mode 100644
index 0000000000..dbd8806967
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/UPSTREAM-PR234-PROOF.md
@@ -0,0 +1,29 @@
+# Five-stage finite composition and retained hypotheses
+
+The expected conditional saving is κ = 703701743496697 / 10^18. The fresh verifier establishes the finite construction and exact arithmetic under the inherited source and all-size interfaces below.
+
+## Bit construction
+
+The pinned source471 helper is checked on all 20,163 independent F2 source, target and dirty columns. Its physical realization is the exact input/output frame telescope, with all source loans, donor/recipient identifications, compensated reads, terminal substitutions and cleanup retained. Copied centers are complete temporary streams; their reverse implementation copies the original anew, transforms and scatters that copy, then erases it. It does not reverse an erasure.
+
+The five phase-major invocations use the explicitly routed source owners X1, Y1, X1, Y2 and X2. Each helper's five separated residuals occupy disjoint windows. One split rank-5a exterior correction completes each genuine independent entrance of rank a. All 2,279 corrections remain paid, and source-owned gauges stay within the visible-data paths. Actual rational matrix checks establish bridge equality, nested idle changes and terminal exchanges. Cover expansion has a barrier after each phase, across every class.
+
+The fresh program has m=120, W=23,683, 495,304 children, rank mass 2,837,560 and deficit 4,400. All 120 rank-22 copied-center calls are included. Exact cleared-Gram determinants and factor witnesses are recomputed for every consumed basis. Fivefold direct sums introduce no new excluded primes. The retained weighted q-local compiler, unit-pivot fallback, prime-supply and complete-stream tape proofs remain hypotheses.
+
+The proper child ratio 5/6 requires halving degree four. The one-level weighted recurrence is retained; its histogram is not multiplied by four. The finite accounting rederives route factors, scalar work, internal row stock, strict moment/linear gaps and explicit finite cutoff expressions. Unknown constants of inherited primitive implementations remain quantified constants, not invented measured costs. See proof/FINITE_BIT_ACCOUNTING.md and the included original bit/row/copied-center source texts.
+
+## Complex construction
+
+The published gcert/1 baseline is pinned to Sussman's f010392 revision and the PR193 paired-cube helper. Its live-label walk, scalar programs, copied-center lifetimes, final climbs before cleanup, exact symbolic splice and finite guard are regenerated. Exact complex frame identities retain their phase representatives. Physical work stock 24,127 is separately charged; the live recursion denominator remains 14,692.
+
+The pinned scalar identities hAi, hBi, hx, hy and hid, the Lab.inv dirty-lifting theorem and five-window geometry/NetCert theorems are inherited source proofs. The command does not rebuild their Lean proof chain or claim a fresh all-column complex scalar proof. General Clifford synthesis, charged complete-stream movement, common-grid precision and restored-row proofs remain stated analytic dependencies. Their consumed declarations and sources are hash-pinned under inputs/complex/.
+
+## Arithmetic and outer reduction
+
+Both rational moments are freshly enclosed. Three finite ordinary-leaf levels start from the retained completed ordinary saving 384599/10^10; the unattained coarse limiting saving is not used as an ordinary leaf. Exact outer assembly checks all 47 strict inequalities and seven margins and rejects the next 10^-18 κ grid point. Precision/recovery, prime supply, completed ordinary leaves and the fixed-tape all-size reduction remain hypotheses.
+
+proof/INTEGRATED_PROOF.md preserves the detailed original composition argument. Its development filenames identify the original evidence; V8's executable dependency closure is exclusively MANIFEST.json and the fresh calls in verify.py. Development receipts and their historical source trees are not runtime inputs.
+
+No claim is made of unconditional all-size formalization, global optimality or measured multiplier performance. Original lineage and assistance disclosures are preserved in NOTICE.md and the supplied source notices.
+
+Assisted with ChatGPT.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/bank_check.py b/research/gen4-retiming-entrances/vendor/pr276/bank_check.py
new file mode 100644
index 0000000000..ad7bed1610
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/bank_check.py
@@ -0,0 +1,254 @@
+"""Fresh context-bound stage-private120-coordinate completed bank admission.
+
+No saved chart, receipt, physical census or old source tree is consumed.
+The fraction-free inverse routine derives from the retained PR197/PR200 bank
+checker. Inherited attribution/notices apply. Apache-2.0.
+Prepared with substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from math import gcd
+from pathlib import Path
+import hashlib,json,struct,time
+from bank_template import BankPlan
+
+assert __debug__, 'Do not run bank admission under -O.'
+HERE=Path(__file__).resolve().parent
+
+def inverse_integer(a):
+    """Fraction-free Gauss-Jordan, returning C,d with aC=Ca=dI."""
+    n=len(a);m=[list(row)+[int(i==j)for j in range(n)]for i,row in enumerate(a)]
+    previous=1;factors=[]
+    for k in range(n):
+        pivot=next((i for i in range(k,n)if m[i][k]),None)
+        assert pivot is not None,'singular actual bank chart'
+        m[k],m[pivot]=m[pivot],m[k]
+        if pivot!=k:factors.append(('swap',k,pivot,1,1))
+        p=m[k][k]
+        if p!=previous:
+            ratio=Q(previous,p);factors.append(('scale',k,k,ratio.numerator,ratio.denominator))
+        for i in range(n):
+            if i==k:continue
+            u=m[i][k]
+            if u:
+                ratio=Q(-u,previous);factors.append(('add',i,k,ratio.numerator,ratio.denominator))
+            for j in range(2*n):
+                if j==k:continue
+                value=p*m[i][j]-u*m[k][j];assert value%previous==0;m[i][j]=value//previous
+            m[i][k]=0
+        previous=p
+    d=m[0][0];assert d and all(m[i][j]==d*int(i==j)for i in range(n)for j in range(n))
+    c=[row[n:]for row in m];common=abs(d)
+    for row in c:
+        for x in row:common=gcd(common,x)
+    d//=common;c=[[x//common for x in row]for row in c]
+    if d<0:d=-d;c=[[-x for x in row]for row in c]
+    return c,d,factors
+
+def census(context):
+    W,C,roles=context['W'],context['C'],context['regs']
+    assert len(roles)==len(set(roles))==16410 and roles==sorted(roles)
+    assert set(roles)==set(W.phys.values())-set(context['borrow'])-context['removed']
+    assert not(set(roles)&set(context['borrow']))
+    gauge_frames={role:W.gauge[role]['frame']for role in roles if role in W.gauge}
+    assert Counter(C.dimf[f]for f in gauge_frames.values())=={20:2200,21:266}
+    families={}
+    for role in roles:
+        rank=24-C.dimf[gauge_frames[role]]if role in gauge_frames else 24
+        families.setdefault(rank,[]).append(role)
+    assert {r:len(xs)for r,xs in families.items()}=={3:266,4:2200,24:13944}
+    return families,gauge_frames
+
+class BankLowerer:
+    """Final full-address lowering of the already checked logical IR.
+
+    Scalar/projection/geometry fields are retained byte-for-byte; only stream
+    operands change to the proven bank namespaces. Completion discharge is
+    checked separately by run(), and no completion opcode is emitted.
+    """
+    def __init__(self,context,lower):
+        families,gauges=census(context)
+        self.plan=BankPlan(families,gauges,context['regs']);self.lower=lower
+    def iter_stage(self,stage,replica):
+        for row in self.lower.iter_stage(stage):yield self.plan.map_stage_row(stage,replica,row)
+    def iter_idle(self,which,replica):
+        for row in self.lower.iter_idle(which):yield self.plan.map_boundary_row(replica,row)
+    def iter_bridges(self,which,replica):
+        for row in self.lower.iter_bridges(which):yield self.plan.map_boundary_row(replica,row)
+    def iter_exchanges(self,replica):
+        for row in self.lower.iter_exchanges():yield self.plan.map_boundary_row(replica,row)
+    def phases(self):
+        """Each iterator is expanded over all cover classes before next phase."""
+        for stage in range(5):
+            for replica in range(60):
+                yield('helper',stage,replica,lambda s=stage,r=replica:self.iter_stage(s,r))
+            if stage in(1,2,4):
+                which={1:0,2:1,4:2}[stage]
+                for replica in range(60):
+                    yield('idle',which,replica,lambda i=which,r=replica:self.iter_idle(i,r))
+                    yield('bridge',which,replica,lambda i=which,r=replica:self.iter_bridges(i,r))
+        for replica in range(60):yield('terminal_exchange',0,replica,lambda r=replica:self.iter_exchanges(r))
+
+def bind(context,lower):return BankLowerer(context,lower)
+
+def run(context,global_result,lower,progress=lambda text:None):
+    begun=time.monotonic();W,C=context['W'],context['C']
+    api_pin=hashlib.sha256((HERE/'bank_template.py').read_bytes()).hexdigest()
+    families,gauge_frames=census(context);bound=bind(context,lower);plan=bound.plan
+    assert lower.W is W and lower.C is C
+    # Derive all actual chart bases and exact inverse/factor programs afresh.
+    charts=[];maxops=maxnum=maxden=0
+    for frame,count in sorted(Counter(gauge_frames.values()).items()):
+        residual=[]
+        for a in C.A[frame]:
+            row=[15*x-sum(a)for x in a];d=gcd(*row);assert d;residual.append([x//d for x in row])
+        source=C.B[frame];rank=len(residual)
+        assert rank+len(source)==24 and len(source)==C.dimf[frame]
+        assert all(9*sum(x*y for x,y in zip(a,b))-sum(a)*sum(b)==0 for a in residual for b in source)
+        B=list(map(list,zip(*(residual+list(source)))));A,d,ops=inverse_integer(B)
+        for L,R in((A,B),(B,A)):
+            assert all(sum(x*y for x,y in zip(row,col))==d*int(i==j)for i,row in enumerate(L)for j,col in enumerate(zip(*R)))
+        P=[[sum(B[i][k]*A[k][j]for k in range(rank))for j in range(24)]for i in range(24)]
+        assert sum(P[i][i]for i in range(24))==d*rank
+        assert all(sum(P[i][k]*B[k][j]for k in range(24))==(d*B[i][j]if j<rank else 0)for i in range(24)for j in range(24))
+        replay=[list(map(Q,row))for row in B]
+        for op,i,j,a,b in ops:
+            if op=='swap':replay[i],replay[j]=replay[j],replay[i]
+            elif op=='scale':replay[i]=[Q(a,b)*x for x in replay[i]]
+            else:
+                assert op=='add';replay[i]=[x+Q(a,b)*y for x,y in zip(replay[i],replay[j])]
+        assert all(x==int(i==j)for i,row in enumerate(replay)for j,x in enumerate(row))
+        maxops=max(maxops,len(ops));maxnum=max(maxnum,max(abs(op[3])for op in ops));maxden=max(maxden,d,max(op[4]for op in ops))
+        charts.append(dict(frame=frame,count=count,residual_rank=rank,basis=B,inverse_numerator=A,inverse_denominator=d,factors=ops))
+    assert len(charts)==370 and max(maxnum,maxden)<2**80 and maxops==186
+    progress('Rebuilt370 exact actual gauge charts')
+    # Match each consumed completion to one actual independent entrance.
+    expected=[]
+    for j,role in enumerate(context['regs']):
+        f=gauge_frames.get(role,lower.ZERO)
+        assert lower.initial[2*W.v+j]==f
+        if role in gauge_frames:expected.append((4*W.v+j,f,C.dimf[f]))
+    assert list(lower.entrances)==expected and len(expected)==2466
+    completions=list(lower.iter_completions())
+    assert completions==[(6,family,-1,0,5*a,f,-1,0)for family,f,a in expected]
+    removed=Counter(row[4]for row in completions)
+    assert removed=={100:2200,105:266}
+    H=Counter({int(r):n for r,n in global_result['paid_histogram'].items()})
+    assert sum(H.values())==global_result['paid_calls']
+    for r,n in removed.items():assert H[r]==n;del H[r]
+    assert max(H)==50 and sum(H.values())==485080 and sum(r*n for r,n in H.items())==2561670
+    literal=Counter({r:60*n for r,n in H.items()})
+    assert 120*plan.live_families-sum(r*n for r,n in literal.items())==60*4400
+    # Independently enumerate each physical role/replica/stage slot.
+    incidence=hashlib.sha256();assignments=0;normalizers_checked=set();endpoint_controls=[]
+    for stage in range(5):
+        used=Counter();bank=0;assigned=set()
+        outside=next(j for j in range(120)if not 24*stage<=j<24*(stage+1))
+        for pattern,(widths,count)in enumerate(plan.patterns):
+            offset=0;witnesses=[]
+            for block,rank in enumerate(widths):
+                original=list(range(24*stage,24*stage+rank));target=list(range(offset,offset+rank))
+                src=original+[j for j in range(120)if j not in original];dst=target+[j for j in range(120)if j not in target];pi=dict(zip(src,dst))
+                witnesses.append((pi[outside],block+1));offset+=rank
+            assert len(set(witnesses))==len(widths)
+            if stage==0:
+                offsets=[sum(widths[:b])for b in range(len(widths))]
+                def endpoint(blocks):
+                    state=list(range(240))
+                    for b in blocks:
+                        for j in range(offsets[b],offsets[b]+widths[b]):state[j],state[120+j]=state[120+j],state[j]
+                    return state
+                blocks=list(range(len(widths)));full=list(range(120,240))+list(range(120))
+                assert endpoint(blocks)==full and endpoint(blocks+blocks[::-1])==list(range(240))
+                assert endpoint(blocks[:-1])!=full and endpoint(blocks+[0])!=full
+                endpoint_controls.append(dict(pattern=pattern,forward_columns=240,inverse_columns=240,omitted_rejected=True,repeated_rejected=True))
+            for b in range(bank,bank+count):
+                offset=0
+                for block,rank in enumerate(widths):
+                    q=used[rank];role=families[rank][q//60];replica=q%60;used[rank]+=1
+                    assert(role,replica)not in assigned;assigned.add((role,replica))
+                    a=plan.assignment(stage,replica,role);frame=gauge_frames.get(role)
+                    assert a==dict(family=plan.data_families+stage*plan.banks_per_stage+b,stage_bank=b,pattern=pattern,block=block,offset=offset,rank=rank,frame=frame,scalar=block+1)
+                    key=stage,pattern,block,frame
+                    if key not in normalizers_checked:
+                        N=plan.normalizer(stage,replica,role)
+                        assert N['unit_column_witness']==witnesses[block]and N['inverse_chart_frame']==frame and N['chart_window']==stage
+                        assert N['permutation'][24*stage:24*stage+rank]==tuple(range(offset,offset+rank))
+                        normalizers_checked.add(key)
+                    incidence.update(f'{stage},{pattern},{role},{replica},{b},{block},{offset},{rank}\n'.encode())
+                    assignments+=1;offset+=rank
+                assert offset==120
+            bank+=count
+        assert bank==plan.banks_per_stage and len(assigned)==60*len(context['regs'])and used=={r:60*len(xs)for r,xs in families.items()}
+    assert assignments==4923000
+    progress('Matched all4923000 literal bank assignments')
+    namespace=hashlib.sha256();collisions=0
+    for stage in range(5):
+        for replica in range(60):
+            addresses=[plan.local_address(stage,replica,i)for i in range(plan.local_work+1)]
+            assert len(set(addresses))==len(addresses)and addresses[-1]==(plan.work_family,('external_work',0))
+            assert all(f<plan.live_families for f,route in addresses[:-1])
+            collisions+=len(addresses)-len({f for f,route in addresses})
+            for f,route in addresses:namespace.update(f'{stage},{replica},{f},{route}\n'.encode())
+    assert collisions==0
+    # Bind every actual logical operand and mathematical field to the callable
+    # address substitution once per stage. The300 injective namespace maps
+    # above then instantiate all sixty replicas without replaying scalar algebra.
+    stream=struct.Struct('<8i');stage_checks=[];actual_helper_uses=set();paid=Counter()
+    for stage in range(5):
+        digest=hashlib.sha256();rows=0;stage_paid=Counter();kinds=Counter()
+        # Full addresses indexed by the original logical family; wrappers use
+        # exactly this tested local inverse and namespace construction.
+        addresses={}
+        for local in range(plan.local_work+1):
+            family=4*W.v+len(context['regs'])if local==plan.local_work else plan.active[stage][0]*W.v+local if local<W.v else plan.active[stage][1]*W.v+local-W.v if local<2*W.v else 4*W.v+local-2*W.v
+            assert plan.local_from_logical_family(stage,family)==local
+            addresses[family]=plan.local_address(stage,0,local)
+        for row in lower.iter_stage(stage):
+            op,a,b,c,f,z,s,rev=row;assert s==stage and rev==int(stage in(1,3))
+            mapped=plan.map_stage_row(stage,0,row)
+            assert mapped==(op,addresses[a],addresses[b]if op in(1,2)else b,c,f,z,s,rev)
+            for family in([a,b]if op in(1,2)else[a]):
+                if 4*W.v<=family<4*W.v+len(context['regs']):actual_helper_uses.add(family-4*W.v)
+            if op==0 and f:stage_paid[f]+=1
+            digest.update(stream.pack(*row));rows+=1;kinds[op]+=1
+        assert stage_paid==Counter({int(r):n for r,n in lower.ns['result']['paid_histogram'].items()})
+        paid.update(stage_paid)
+        stage_checks.append(dict(stage=stage,records=rows,logical_operand_binding_sha256=digest.hexdigest(),opcode_counts=dict(kinds),all_actual_operands_mapped=True))
+    assert actual_helper_uses==set(range(len(context['regs'])))
+    for which in range(3):
+        for row in lower.iter_idle(which):
+            mapped=plan.map_boundary_row(0,row);assert mapped[0]==4;paid[row[4]]+=1
+        for row in lower.iter_bridges(which):assert plan.map_boundary_row(0,row)[0]==5
+    exchanges=sum(1 for row in lower.iter_exchanges()if plan.map_boundary_row(0,row)[0]==7)
+    assert exchanges==2*W.v and paid==H
+    phases=[(kind,stage,replica)for kind,stage,replica,fn in bound.phases()]
+    assert len(phases)==720 and sum(kind=='helper'for kind,s,r in phases)==300
+    assert all(phases.index(('idle',which,r))<phases.index(('bridge',which,r))for which in range(3)for r in range(60))
+    controls=[]
+    try:plan.map_boundary_row(0,completions[0])
+    except AssertionError:controls.append('silent completion discharge')
+    else:raise AssertionError('completion passed address mapper')
+    assert hashlib.sha256((HERE/'bank_template.py').read_bytes()).hexdigest()==api_pin
+    factors=maxops+119+120;K=2*5*60*((plan.live_families-1)+len(context['regs'])*120*factors)
+    assert factors==425 and K==502915820400<2**40
+    result=dict(status='PASS_FRESH_CONTEXT_BOUND_COMPLETE_BANKS_AND_CALLABLE_LOWERING',
+        all_assignments_match=True,all_logical_helpers_bound=True,independent_completions_removed=len(completions),
+        removed_completion_histogram=dict(removed),literal_paid_histogram=dict(sorted(literal.items())),literal_stock=plan.live_families,
+        normalized_stock=str(Q(plan.live_families,60)),physical_replicas=60,bank_families=5*plan.banks_per_stage,data_families=plan.data_families,
+        assignments=assignments,incidence_sha256=incidence.hexdigest(),charts=len(charts),
+        chart_sha256=hashlib.sha256(json.dumps(charts,sort_keys=True,separators=(',',':')).encode()).hexdigest(),
+        max_chart_factors=maxops,max_factor_numerator=maxnum,max_denominator=maxden,normalizer_factor_bound=factors,
+        conservative_extra_selector_calls=K,distinct_actual_normalizers=len(normalizers_checked),
+        full_namespaces_checked=300,namespace_sha256=namespace.hexdigest(),intentional_family_collisions=collisions,
+        local_instruction_bindings=stage_checks,endpoint_checks=endpoint_controls,phase_schedule=phases,
+        completions_discharged_by='Each stage-private bank partitions all120 coordinates; all240 arbitrary-dirty address columns and inverse checked.',
+        inherited_geometry='Helper originalclass d*tau_i maps to bank d*tau_i*N^-1. N conjugates its actual residual in H_i into the assigned coordinate block. Data routes and boundary projectors remain PR234s.',
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),api_sha256=api_pin,
+        rejected_controls=controls,seconds=time.monotonic()-begun)
+    bank_keys=('literal_stock','normalized_stock','physical_replicas','bank_families','data_families','assignments',
+        'incidence_sha256','charts','chart_sha256','max_chart_factors','max_factor_numerator','max_denominator',
+        'normalizer_factor_bound','conservative_extra_selector_calls','distinct_actual_normalizers','endpoint_checks')
+    banks={k:result[k]for k in bank_keys};banks['status']='PASS_FRESH_ACTUAL_CHARTS_AND_COMPLETE_BANKS'
+    banks.update(gen4_roles=len(context['regs']),banks_total=5*plan.banks_per_stage)
+    return dict(banks=banks,banked_result=result)
diff --git a/research/gen4-retiming-entrances/vendor/pr276/bank_template.py b/research/gen4-retiming-entrances/vendor/pr276/bank_template.py
new file mode 100644
index 0000000000..d2bd3c0165
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/bank_template.py
@@ -0,0 +1,181 @@
+"""Callable stage-private120-coordinate bank address template.
+
+The caller supplies the freshly admitted actual helper role families and gauge
+chart IDs. This module owns no paths, global frame registry or source loading.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from collections import Counter
+
+
+class BankPlan:
+    m, h, stages, replicas, v = 120, 24, 5, 60, 1760
+    patterns = ((tuple([3]*40),399),
+                (tuple([4]*30),4400),
+                (tuple([24]*5),167328))
+
+    active = ((0,1),(1,0),(0,1),(3,2),(2,3))
+
+    def __init__(self, families, gauge_frames, helper_roles=None):
+        self.families = {r:tuple(rows) for r,rows in families.items() if rows}
+        assert {r:len(rows) for r,rows in self.families.items()} == {3:266,4:2200,24:13944}
+        self.role_index = {}
+        for rank,rows in self.families.items():
+            assert tuple(sorted(rows)) == rows and len(set(rows)) == len(rows)
+            for i,role in enumerate(rows):
+                assert role not in self.role_index
+                self.role_index[role]=(rank,i)
+        self.gauge_frames = dict(gauge_frames)
+        assert set(self.gauge_frames) == {role for r,rows in self.families.items() if r<self.h for role in rows}
+        self.helper_roles=tuple(sorted(self.role_index) if helper_roles is None else helper_roles)
+        assert len(self.helper_roles)==len(self.role_index) and set(self.helper_roles)==set(self.role_index)
+        self.local_work=2*self.v+len(self.helper_roles)
+        self.banks_per_stage=sum(count for widths,count in self.patterns)
+        self.data_families=self.replicas*4*self.v
+        self.live_families=self.data_families+self.stages*self.banks_per_stage
+        self.work_family=self.live_families
+        assert (self.banks_per_stage,self.data_families,self.live_families)==(172127,422400,1283035)
+        self.segments={}
+        used=Counter();bank_start=0
+        for pattern,(widths,count) in enumerate(self.patterns):
+            assert sum(widths)==self.m
+            for rank in set(widths):
+                blocks=tuple(b for b,r in enumerate(widths) if r==rank)
+                n=len(blocks)*count
+                self.segments.setdefault(rank,[]).append((used[rank],used[rank]+n,pattern,bank_start,blocks))
+                used[rank]+=n
+            bank_start+=count
+        assert used=={r:self.replicas*len(rows) for r,rows in self.families.items()}
+
+    def assignment(self, stage, replica, role):
+        """Exact bank family/block for one actual independent helper occurrence."""
+        assert 0<=stage<self.stages and 0<=replica<self.replicas
+        rank,role_index=self.role_index[role]
+        q=role_index*self.replicas+replica
+        for lo,hi,pattern,bank_start,blocks in self.segments[rank]:
+            if lo<=q<hi:
+                bank_offset,within=divmod(q-lo,len(blocks))
+                bank=bank_start+bank_offset;block=blocks[within]
+                widths=self.patterns[pattern][0]
+                return dict(family=self.data_families+stage*self.banks_per_stage+bank,
+                            stage_bank=bank,pattern=pattern,block=block,
+                            offset=sum(widths[:block]),rank=rank,
+                            frame=self.gauge_frames.get(role),scalar=block+1)
+        raise AssertionError('unallocated actual helper occurrence')
+
+    def data_family(self, replica, bank, port):
+        assert 0<=replica<self.replicas and 0<=bank<4 and 0<=port<self.v
+        return (4*replica+bank)*self.v+port
+
+    def normalizer(self, stage, replica, role):
+        """Finite exact data for N=scalar Pi embed_stage(B^-1).
+
+        frame=None denotes identity B=I24. The caller resolves other IDs in
+        its freshly admitted frame registry/charts. inverse_chart remains an
+        exact rational factor program; no floating matrix is consumed.
+        """
+        a=self.assignment(stage,replica,role)
+        original=tuple(range(self.h*stage,self.h*stage+a['rank']))
+        target=tuple(range(a['offset'],a['offset']+a['rank']))
+        src=original+tuple(j for j in range(self.m) if j not in original)
+        dst=target+tuple(j for j in range(self.m) if j not in target)
+        pi=dict(zip(src,dst))
+        assert set(pi)==set(pi.values())==set(range(self.m))
+        permutation=tuple(pi[j] for j in range(self.m))
+        outside=next(j for j in range(self.m) if not self.h*stage<=j<self.h*(stage+1))
+        return dict(scalar=a['scalar'],permutation=permutation,
+                    inverse_chart_frame=a['frame'],chart_window=stage,
+                    outside_column=outside,unit_column_witness=(pi[outside],a['scalar']))
+
+    def address(self, stage, replica, role, cover='d'):
+        """Original class d*tau_i routed to the actual bank by N^-1.
+
+        Multiplication order is literal. A consumer must lower the factor
+        list right-to-left for inverse N, keeping chart/scalar denominators.
+        """
+        a=self.assignment(stage,replica,role)
+        N=('normalizer',stage,a['pattern'],a['block'],a['frame'])
+        return a['family'],('right',cover,('tau',stage),('inverse',N))
+
+    def local_family(self, stage, replica, local):
+        """Live family for the admitted local physical register index.
+
+        Family equality does not imply address equality for banked helpers.
+        Consumers must use local_address for ADD nonalias/namespace checks.
+        """
+        assert 0<=stage<self.stages and 0<=replica<self.replicas
+        assert 0<=local<=self.local_work
+        if local==self.local_work:return self.work_family
+        if local<self.v:return self.data_family(replica,self.active[stage][0],local)
+        if local<2*self.v:return self.data_family(replica,self.active[stage][1],local-self.v)
+        return self.assignment(stage,replica,self.helper_roles[local-2*self.v])['family']
+
+    def local_address(self, stage, replica, local, cover='d'):
+        family=self.local_family(stage,replica,local)
+        if local==self.local_work:return family,('external_work',0)
+        if local<2*self.v:
+            route=('class',cover) if stage==0 else ('right',cover,('rho',stage,local%self.v))
+            return family,route
+        return self.address(stage,replica,self.helper_roles[local-2*self.v],cover)
+
+    def local_from_logical_family(self, stage, family):
+        """Invert PR234's logical five-stage family map for one active stage."""
+        logical_work=4*self.v+len(self.helper_roles)
+        assert 0<=family<=logical_work
+        if family==logical_work:return self.local_work
+        if family>=4*self.v:return 2*self.v+family-4*self.v
+        bank,port=divmod(family,self.v)
+        if bank==self.active[stage][0]:return port
+        assert bank==self.active[stage][1], 'stage references an inactive data bank'
+        return self.v+port
+
+    def map_stage_row(self, stage, replica, row, cover='d'):
+        """Lower an unchanged logical8-field MOVE/ADD/COPY/ERASE record.
+
+        All mathematical fields remain unchanged. The two operand slots now
+        contain exact (family,route) keys when they denote streams; frame IDs
+        in MOVE's old/new slots are not mistaken for stream operands.
+        """
+        op,a,b,c,f,z,s,rev=row
+        assert op in(0,1,2,3) and s==stage and rev==int(stage in(1,3))
+        def address(family):
+            return self.local_address(stage,replica,self.local_from_logical_family(stage,family),cover)
+        physical_a=address(a)
+        physical_b=address(b) if op in(1,2) else b
+        if op in(1,2):assert physical_a!=physical_b
+        return (op,physical_a,physical_b,c,f,z,s,rev)
+
+    def map_boundary_row(self, replica, row, cover='d'):
+        """Lower an IDLE/BRIDGE/EXCHANGE with its existing exact projector.
+
+        Boundary projectors already include the checked data-route conjugacy;
+        their physical class is d. Independent completion rows must be
+        discharged explicitly by the bank endpoint verifier, never skipped
+        implicitly by this address mapper.
+        """
+        op,a,b,c,f,z,s,rev=row
+        assert op in(4,5,7), 'only proved bank completion may discharge opcode6'
+        def address(family):
+            assert 0<=family<4*self.v
+            bank,port=divmod(family,self.v)
+            return self.data_family(replica,bank,port),('class',cover)
+        physical_a=address(a)
+        physical_b=address(b) if op in(5,7) else b
+        if op in(5,7):assert physical_a!=physical_b
+        return (op,physical_a,physical_b,c,f,z,s,rev)
+
+    def phase_schedule(self):
+        """Phase-major schedule; every cover class is completed per replica.
+
+        Each emitted stage phase means: for the indicated replica, iterate
+        every cover class and execute the entire local scalar telescope.
+        Boundary phases occur after all60 replicas of that stage finish.
+        """
+        for stage in range(self.stages):
+            for replica in range(self.replicas):
+                yield ('stage',stage,replica,'all_cover_classes')
+            if stage in (1,2,4):
+                for replica in range(self.replicas):
+                    yield ('idle',stage,replica,'all_cover_classes')
+                    yield ('bridge',stage,replica,'all_cover_classes')
+        for replica in range(self.replicas):
+            yield ('terminal_exchange',replica,'all_cover_classes')
diff --git a/research/gen4-retiming-entrances/vendor/pr276/base_two_moment.py b/research/gen4-retiming-entrances/vendor/pr276/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/complex_basis.py b/research/gen4-retiming-entrances/vendor/pr276/code/complex_basis.py
new file mode 100644
index 0000000000..8c400798a5
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/complex_basis.py
@@ -0,0 +1,35 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+def need(b, why):
+    if not b: raise ValueError(why)
+
+def gl_count_test():
+    # Exhaustively test a literal binary Gaussian-elimination implementation
+    # through m=4. Row swaps cost three selected-bit additions.
+    out=[]
+    for m in range(1,5):
+        good=mx=0
+        for word in range(1<<(m*m)):
+            rows=[(word>>(m*i))&((1<<m)-1) for i in range(m)]
+            ops=0
+            for k in range(m):
+                p=next((i for i in range(k,m) if rows[i]>>k&1),None)
+                if p is None: break
+                if p!=k: rows[p],rows[k]=rows[k],rows[p];ops+=3
+                for i in range(m):
+                    if i!=k and rows[i]>>k&1: rows[i]^=rows[k];ops+=1
+            else:
+                need(rows==[1<<i for i in range(m)],'basis reduction endpoint')
+                need(ops<=m*(m-1)+3*m,'row-addition count')
+                good+=1;mx=max(mx,ops)
+        need(good==prod((1<<m)-(1<<i) for i in range(m)),'GL coverage')
+        out.append(dict(m=m,invertible_matrices=good,maximum_selected_bit_additions=mx))
+    return out
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/complex_labels.py b/research/gen4-retiming-entrances/vendor/pr276/code/complex_labels.py
new file mode 100644
index 0000000000..1f27d6de34
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/complex_labels.py
@@ -0,0 +1,176 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+BASE = dict(h=22, v=1320, R=9412, cst=440, N=262944)
+EXPECTED_H = {1:29178,2:12398,3:9923,4:4209,5:1950,6:1605,7:706,8:1531,
+              9:429,10:930,11:354,12:1197,13:127,14:742,15:1879,16:88,
+              17:81,18:2653,19:167,20:22}
+class Reject(ValueError):
+    pass
+
+def need(ok, msg):
+    if not ok:
+        raise Reject(msg)
+
+def digest(obj):
+    return sha256(json.dumps(obj, separators=(",",":"), sort_keys=True).encode()).hexdigest()
+
+def hist(counter):
+    return {str(k):v for k,v in sorted(counter.items()) if v}
+
+def role(r,v):
+    return "x" if r < v else "y" if r < 2*v else "s"
+
+def reduce_binary(x, frame):
+    for b in frame:
+        if x & (1 << (b.bit_length()-1)):
+            x ^= b
+    return x
+
+def coeff(a,b, where):
+    need(type(a) is int and type(b) is int and b>0, f"{where}: coefficient shape")
+    q=Fraction(a,b)
+    odd=q.denominator
+    while odd%2==0:
+        odd//=2
+    need(odd in (1,3), f"{where}: literal coefficient outside dyadic/divisor-three grid")
+    return q
+
+def replay_label_counts(c):
+    """Full finite LABEL walk only. Never multiplies the 12,052-square scalar map."""
+    need(c.get("format")=="gcert/1", "format")
+    need(all(c.get(k)==v for k,v in BASE.items()), "baseline parameter/count mismatch")
+    h,v,R=c["h"],c["v"],c["R"]; n=2*v+R
+    need(c.get("ext")==[], "baseline has no exterior-gauged helper inputs")
+    frames=c["frames"]; dim=list(map(len,frames))
+    need(len(frames)==18248, "baseline frame-table count")
+    need(frames[0]==[] and frames[1]==[1<<i for i in range(h-1,-1,-1)], "zero/full frames")
+    need(len({tuple(f) for f in frames})==len(frames), "duplicate frames")
+    for f in frames:
+        need(all(type(b) is int and 0<b<1<<h for b in f), "frame bit range")
+        piv=[b.bit_length()-1 for b in f]
+        need(all(piv[i]>piv[i+1] for i in range(len(piv)-1)), "frame pivot order")
+        need(all(not(b>>p&1) for i,b in enumerate(f) for j,p in enumerate(piv) if i!=j),
+             "frame is not reduced echelon")
+    ports=c["ports"]
+    need(len(ports)==v==len(set(ports)), "port count/uniqueness")
+    need(all(type(p) is int and 0<p<(1<<h)-1 and p.bit_count()%2 for p in ports), "unit port/gap")
+    start=c["start"]; final=c["final"]
+    need(len(start)==len(final)==n, "live invocation role count")
+    need(all(type(f) is int and 0<=f<len(frames) for f in start+final), "endpoint frame ID")
+    for t,p in enumerate(ports):
+        need(frames[start[t]]==[p] and final[t]==1, "X endpoint")
+        need(start[v+t]==0 and dim[final[v+t]]==h-1 and
+             all((p&u).bit_count()%2==0 for u in frames[final[v+t]]), "Y endpoint")
+    need(all(f==0 for f in start[2*v:]) and all(f==1 for f in final[2*v:]), "helper endpoints")
+    need(c["ret"] and len(c["ret"])==22, "temporary-center count")
+    need([x[0] for x in c["ret"]]==list(range(22)), "center numbering")
+    need(len({x[1] for x in c["ret"]})==22, "center retained slots repeat")
+    need(c["scat"]=={"inside":[1,3],"outside":[-1,6]}, "baseline scatter rule")
+    need(len(c["A"])==12158 and len(c["B"])==30878, "phase gate count")
+    cur=start.copy(); pairs=set()
+    by_role={r:Counter() for r in "xysc"}
+    by_phase={p:Counter() for p in ("A","copy","B","final")}
+    literal=Counter(); kind=Counter(); ybracket=Counter(); ypiv=set(); ytarget=set()
+    totals={p:dict(gates=0,scalar_additions=0,register_visits=0,spectator_visits=0)
+            for p in ("A","B")}
+    transitions=0
+    def climb(reg,new,phase):
+        nonlocal transitions
+        old=cur[reg]
+        if old==new:
+            return
+        need(dim[old]<dim[new], f"{phase}: frame does not strictly climb")
+        pair=(old,new)
+        if pair not in pairs:
+            need(all(reduce_binary(b,frames[new])==0 for b in frames[old]), f"{phase}: nonnested frames")
+            pairs.add(pair)
+        rank=dim[new]-dim[old]
+        by_role[role(reg,v)][rank]+=1; by_phase[phase][rank]+=1
+        cur[reg]=new;transitions+=1
+    for phase in ("A","B"):
+        for i,g in enumerate(c[phase]):
+            where=f"{phase}[{i}]"
+            need(isinstance(g,list) and len(g)>=4 and g[0] in ("out","in"), where+": gate shape")
+            tag,f,pivot,terms=g[:4]
+            need(len(g)==(5 if tag=="out" else 4), where+": gate arity")
+            need(type(f) is int and 0<=f<len(frames), where+": frame ID")
+            need(all(isinstance(x,list) and len(x)==3 for x in terms), where+": terms")
+            spectators=g[4] if tag=="out" else []
+            regs=[pivot]+[x[0] for x in terms]+spectators
+            need(all(type(r) is int and 0<=r<n for r in regs) and len(set(regs))==len(regs),
+                 where+": duplicate/out-of-range register")
+            need(phase!="A" or all(not(v<=r<2*v) for r in regs), where+": Y role before scatter")
+            totals[phase]["gates"]+=1
+            totals[phase]["register_visits"]+=len(regs)
+            totals[phase]["spectator_visits"]+=len(spectators)
+            for reg,a,b in terms:
+                target,source=(reg,pivot) if tag=="out" else (pivot,reg)
+                sr,tr=role(source,v),role(target,v)
+                need((sr,tr) in {("x","s"),("s","s"),("s","y"),("x","y"),("x","x"),("y","y")},
+                     where+": forbidden role direction")
+                need(phase!="A" or (sr,tr) in {("x","s"),("s","s")}, where+": phase A role direction")
+                q=coeff(a,b,where)
+                need(q!=0,where+": zero scalar addition")
+                literal[str(q)]+=1;kind[f"{phase}:{sr}->{tr}"]+=1
+                totals[phase]["scalar_additions"]+=1
+                if sr==tr=="y":
+                    ybracket[(source,target)]+=q;ypiv.add(source);ytarget.add(target)
+            for r in regs:
+                climb(r,f,phase)
+        if phase=="A":
+            cut=cur.copy()
+            need(all(cur[v+t]==0 for t in range(v)), "scatter: Y role moved too early")
+            for k,r,f in c["ret"]:
+                need(type(r) is int and 2*v<=r<n, "scatter: center source is not a helper role")
+                need(type(f) is int and 0<=f<len(frames) and cur[r]==f and dim[f]==20,
+                     "scatter: center label/rank mismatch")
+                by_role["c"][20]+=1;by_phase["copy"][20]+=1
+    need(not ypiv.intersection(ytarget) and all(q==0 for q in ybracket.values()), "Y bracket cancellation")
+    before_final=cur.copy()
+    for r,f in enumerate(final):
+        climb(r,f,"final")
+    need(cur==final,"final label state")
+    measured={r:hist(cn) for r,cn in by_role.items()}
+    need(measured==c["blocks"], "role histogram/count mismatch")
+    combined=sum(by_role.values(),Counter())
+    need(dict(combined)==EXPECTED_H, "baseline invocation histogram mismatch")
+    mass=sum(r*k for r,k in combined.items())
+    need(mass==c["N"]==R*h+2*v*(h-1)+c["cst"], "rank mass")
+    need(sum(r*k for r,k in by_role["c"].items())==c["cst"],"temporary-center rank mass")
+    scatter=Counter(str(coeff(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]),"scatter"))
+                    for p in ports for k in range(22))
+    return {
+        "frame_count":len(frames),"tested_distinct_nested_pairs":len(pairs),
+        "live_registers_per_invocation":n,"temporary_centers":22,
+        "ranked_live_transitions":transitions,
+        "phase_stats":totals,"role_histograms":measured,
+        "phase_histograms":{p:hist(x) for p,x in by_phase.items()},
+        "invocation_histogram":hist(combined),"invocation_calls":sum(combined.values()),
+        "invocation_rank_mass":mass,"retained_centers":c["ret"],
+        "phase_state_sha256":{"start":digest(start),"after_A":digest(cut),
+                              "after_B":digest(before_final),"final":digest(final)},
+        "literal_gate_coefficients":dict(sorted(literal.items())),
+        "scalar_role_directions":dict(sorted(kind.items())),
+        "scatter_coefficients":dict(sorted(scatter.items())),
+        "scatter_additions":sum(scatter.values()),"Cc_copy_additions":22,
+        "two_hosts_metadata_count":len(c["two_hosts"]),
+        "two_hosts_note":"Metadata only; not an independent allocator or host-use proof.",
+        "Y_bracket_pairs":len(ybracket),
+        "literal_inverse":"Each nonself additive shear inverts by negating its coefficient; inverse phase reverses order; inverse transpose keeps chronological order and swaps source/target with negation.",
+        "limits":["No scalar all-column replay","No old-response or cleanup matrix formed",
+                  "No generated Lean data comparison or kernel build","No physical stream compiler"]
+    }
+
+def scalar_word(ops):
+    matrix=[[int(i==j) for j in range(4)] for i in range(4)]
+    for target,source,q in ops:
+        matrix[target]=[a+q*b for a,b in zip(matrix[target],matrix[source])]
+    return matrix
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/complex_scalars.py b/research/gen4-retiming-entrances/vendor/pr276/code/complex_scalars.py
new file mode 100644
index 0000000000..771057b567
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/complex_scalars.py
@@ -0,0 +1,216 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+V,R,H=1320,9412,22
+def need(x,msg):
+    if not x:raise ValueError(msg)
+
+def kind(r):return "X" if r<V else "Y" if r<2*V else "S"
+
+def live(r):return ("L",r)
+
+def tmp(r):return ("T",r-2*V)
+
+def center(k):return ("C",k)
+
+def add(t,s,q):return ("add",t,s,q.numerator,q.denominator)
+
+def clear(t):return ("clear",t)
+
+def copy(t,s):return ("copy",t,s)
+
+def flat(gs):
+    out=[]
+    for g in gs:
+        need(g[0] in ["in","out"],"literal additive gate")
+        for r,a,b in g[3]:
+            t,s=(r,g[2]) if g[0]=="out" else (g[2],r)
+            need(t!=s and kind(s)!="Y" and not(kind(s)=="S" and kind(t)=="X"),
+                 "projection requires Y never read and no helper-to-X gate")
+            out.append((t,s,Q(a,b)))
+    return out
+
+def old_positive(A,B,c):
+    """Circuit with inputs temp S and live Y; X fixed at zero.
+    tempS output is irrelevant. Y output is Y_in + K tempS_in."""
+    def part(gs):
+        for t,s,q in gs:
+            if kind(s)=="X":continue
+            need(kind(s)=="S" and kind(t) in ["S","Y"],"old-response shape")
+            yield add(tmp(t) if kind(t)=="S" else live(t),tmp(s),q)
+    yield from part(A)
+    for t,p in enumerate(c["ports"]):
+        for k,r,_ in c["ret"]:
+            q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+            yield add(live(V+t),tmp(r),q)
+    yield from part(B)
+
+def old_word(orientation,K):
+    if orientation=="forward":
+        yield from (copy(("T",q),live(2*V+q)) for q in range(R))
+        for e in K:
+            op,t,s,a,b=e
+            yield add(t,s,Q(-a if t[0]=="L" else a,b))
+    else:
+        yield from (clear(("T",q)) for q in range(R))
+        for op,t,s,a,b in reversed(K):
+            yield add(s,t,Q(a,b))
+        yield from (add(live(2*V+q),("T",q),Q(1)) for q in range(R))
+    yield from (clear(("T",q)) for q in range(R))
+
+def cleanup(orientation,AB):
+    for t,s,q in reversed(AB):
+        if kind(t)=="Y":continue
+        if orientation=="forward":yield add(live(t),live(s),-q)
+        else:yield add(live(s),live(t),q)
+
+def main_scalar(orientation,A,B,c):
+    def phase(gs):
+        for t,s,q in gs:
+            if orientation=="forward":yield add(live(t),live(s),q)
+            else:yield add(live(s),live(t),-q)
+    yield from phase(A)
+    # Every center is a complete temporary stream and one rank20 child,
+    # initialized/read/discarded before the next center uses the work stock.
+    for k,r,_ in c["ret"]:
+        yield clear(center(k))
+        if orientation=="forward":yield add(center(k),live(r),Q(1))
+        for t,p in enumerate(c["ports"]):
+            q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+            if orientation=="backward":yield add(center(k),live(V+t),q)
+        yield ("recursive_center",k,20)
+        if orientation=="forward":
+            for t,p in enumerate(c["ports"]):
+                q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"]))
+                yield add(live(V+t),center(k),q)
+        else:yield add(live(r),center(k),Q(-1))
+        yield clear(center(k))
+    yield from phase(B)
+
+def inv_schedule(orientation,A,B,c):
+    K=list(old_positive(A,B,c))
+    yield from ((p,e) for p,es in [
+       ("old_response",old_word(orientation,K)),
+       ("main",main_scalar(orientation,A,B,c)),
+       ("cleanup",cleanup(orientation,A+B))] for e in es)
+
+def coeff_steps(q):
+    """Non-destructive coefficient expansion using one complete work stream.
+    Copy source, double/halve/divide by3 as needed, add/subtract, clear.
+    Counts Gaussian operations; multiply by2 for real/imag component primitives."""
+    a,b=abs(q.numerator),q.denominator
+    need(a in (1,2) and b in (1,2,3,6),"unsupported new coefficient")
+    return 3+int(a==2)+int(b%2==0)+int(b%3==0)
+
+def bill(schedule):
+    phases={p:Counter() for p in ("old_response","main","cleanup")}
+    coeffs={p:Counter() for p in phases}
+    tape=sha256()
+    for p,e in schedule:
+        tape.update((json.dumps((p,e),separators=(",",":"))+"\n").encode())
+        phases[p]["all_macros"]+=1
+        if e[0]=="recursive_center":
+            phases[p]["recursive_centers"]+=1
+            phases[p]["recursive_rank_mass"]+=e[2]
+            continue
+        phases[p]["scalar_macros"]+=1
+        phases[p][e[0]]+=1
+        if e[0]=="add":
+            q=Q(e[3],e[4]);coeffs[p][str(q)]+=1
+            phases[p]["Gaussian_primitive_steps"]+=coeff_steps(q)
+            phases[p]["scalar_log2_magnitude_charge"]+=1+int(abs(q)==2)
+            phases[p]["halving_exposure"]+=int(q.denominator%2==0)
+            phases[p]["divisor3_exposure"]+=int(q.denominator%3==0)
+        else:phases[p]["Gaussian_primitive_steps"]+=1
+    for p in phases:phases[p]["real_component_primitive_steps"]=2*phases[p]["Gaussian_primitive_steps"]
+    total=sum((Counter({k:v for k,v in x.items() if k not in ["recursive_rank_mass"]}) for x in phases.values()),Counter())
+    return {"phases":{p:dict(x) for p,x in phases.items()},"coefficient_histograms":{p:dict(x) for p,x in coeffs.items()},
+            "totals":dict(total),"schedule_sha256":tape.hexdigest(),
+            "other_main_recursive_calls":"70147 existing live-label transitions, unchanged; not scalar macros"}
+
+def mm(A,B):return [[sum((x*y for x,y in zip(row,col)),Q(0)) for col in zip(*B)] for row in A]
+
+def lifecycle(schedule):
+    """Verify that new scalar-only work stock never survives into a child."""
+    initialized=set();dirty=set();active_centers=set();seen_main=False;children=0
+    for phase,e in schedule:
+        if phase=="main" and not seen_main:
+            need(not dirty,"old-response tableau survives into recursive main phase")
+            seen_main=True
+        need(e[0] in ("add","copy","clear","recursive_center"),"unknown or unpaid recursive operation")
+        if e[0]=="recursive_center":
+            k=e[1]
+            need(type(k) is int and 0<=k<22 and e[2]==20,"new temporary entered uncharged child")
+            need(phase=="main" and not dirty,"old-response temporary used during child")
+            need(active_centers<=set([k]),"other center was not discarded before next child")
+            children+=1
+            continue
+        target=e[1]
+        source=e[2] if e[0] in ("add","copy") else None
+        if source and source[0]=="T":need(source[1] in initialized,"uninitialized temporary read")
+        if target[0]=="T":
+            need(phase=="old_response","scalar-only tableau touched after recursive phase begins")
+            initialized.add(target[1])
+            if e[0]=="clear":dirty.discard(target[1])
+            else:dirty.add(target[1])
+        if target[0]=="C":
+            if e[0]=="clear":active_centers.discard(target[1])
+            else:active_centers.add(target[1])
+        if e[0]=="add":
+            # Coefficient expansion is deliberately local: copy into W,
+            # optionally double/halve/divide3, accumulate, and clear W.
+            expanded=["copy_work"]+["scale"]*(coeff_steps(Q(e[3],e[4]))-3)+["accumulate","clear_work"]
+            need(expanded[-1]=="clear_work","coefficient work survived scalar macro")
+    need(not dirty and not active_centers,"temporary stock not erased at invocation end")
+    need(children==22,"center child count changed")
+    return {"tableau_cleared_before_entire_main_phase":True,"tableau_absent_from_all_children":True,
+            "coefficient_work_cleared_per_add":True,"center_children":children,
+            "new_recursive_children":0,"moment_live_width":14692,
+            "new_work_stock_only":9413,"complete_stream_fraction":"1/(14692*|Orth(110,2)|)"}
+
+def ident(n):return [[Q(int(i==j)) for j in range(n)] for i in range(n)]
+
+def matrix(n,gs):
+    a=ident(n)
+    for t,s,q in gs:a[t]=[x+q*y for x,y in zip(a[t],a[s])]
+    return a
+
+def toy_checks():
+    # 2 X, 3 S, 2 Y. Explicit nontrivial X mixing is undone; helper map
+    # and K are otherwise arbitrary. Exact Fraction checks cover every column
+    # of THIS TINY TEMPLATE, not of the published 12052-register source.
+    n=7;X={0,1};S={2,3,4};Y={5,6}
+    gs=[(2,0,Q(1)),(3,2,Q(2)),(5,3,Q(-1,6)),(0,1,Q(1,2)),
+        (4,0,Q(2)),(2,4,Q(1,2)),(6,2,Q(1,3)),(0,1,Q(-1,2)),
+        (3,1,Q(-1)),(5,4,Q(1)),(6,0,Q(1))]
+    M=matrix(n,gs)
+    need(all(M[i]==ident(n)[i] for i in X),"toy source rows not restored")
+    Ugs=[e for e in gs if e[0] not in Y]
+    U=matrix(n,Ugs)
+    Uinv=matrix(n,[(t,s,-q) for t,s,q in reversed(Ugs)])
+    need(mm(Uinv,U)==ident(n),"restricted inverse identity")
+    Mi=matrix(n,[(t,s,-q) for t,s,q in reversed(gs)])
+    g8=[Mi[i] if i in S else ident(n)[i] for i in range(n)]
+    h8=[M[i] if i in S else ident(n)[i] for i in range(n)]
+    need(g8==Uinv and h8==U,"cleanup projection identities")
+    Ut=matrix(n,[(s,t,q) for t,s,q in reversed(Ugs)])
+    need(Ut==[list(x) for x in zip(*U)],"backward cleanup transpose")
+    Kgs=[e for e in gs if e[1] not in X]
+    Kmat=matrix(n,Kgs)
+    need(all(Kmat[i][j]==M[i][j] for i in Y for j in S),"zero-source old response")
+    Kt=matrix(n,[(s,t,q) for t,s,q in reversed(Kgs)])
+    need(all(Kt[i][j]==M[j][i] for i in S for j in Y),"old response adjoint")
+    bad=matrix(n,[(t,s,q) for t,s,q in reversed(Ugs)])
+    need(bad!=g8,"wrong inverse sign must fail")
+    bad_order=matrix(n,[(s,t,q) for t,s,q in Ugs])
+    need(bad_order!=Ut,"unreversed transpose must fail")
+    return {"tiny_exact_template_columns_checked":7,"checks_passed":7,
+            "wrong_inverse_sign_rejected":True,"unreversed_transpose_rejected":True,
+            "published_full_scalar_replay":False}
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/complex_splice.py b/research/gen4-retiming-entrances/vendor/pr276/code/complex_splice.py
new file mode 100644
index 0000000000..11373d1d57
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/complex_splice.py
@@ -0,0 +1,277 @@
+"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+Q=Fraction
+from hashlib import sha256
+from pathlib import Path
+from math import prod
+import gzip,json,sys
+
+V,R,H,N,W=1320,9412,22,12052,14692
+PHASES=["old_response","ad0","A","centers","B","final","adF","cleanup","done"]
+def need(x,s):
+    if not x:raise ValueError(s)
+
+def blobhash(p):return sha256(p.read_bytes()).hexdigest()
+
+def digest(x):return sha256(json.dumps(x,separators=(',',':'),sort_keys=True).encode()).hexdigest()
+
+def role(r):return 'X' if r<V else 'Y' if r<2*V else 'S'
+
+def add(t,s,q):return ('add',t,s,q.numerator,q.denominator)
+
+def L(r):return ('L',r)
+
+def T(r):return ('T',r-2*V)
+
+def C(k):return ('C',k)
+
+def clear(t):return ('clear',t)
+
+def copy(t,s):return ('copy',t,s)
+
+def flat(gs):
+    for g in gs:
+        for r,a,b in g[3]:
+            t,s=(r,g[2]) if g[0]=='out' else (g[2],r)
+            need(t!=s and role(s)!='Y' and (role(s),role(t))!=('S','X'),'scalar projection shape')
+            yield t,s,Q(a,b)
+
+def scal(phase,e,frame):return ('scalar',phase,e,frame)
+
+def lower_scalar(e):
+    # The coefficient work stream is disjoint from every live and center role.
+    if e[0] in ['copy','clear']:return [e]
+    _,t,s,a,b=e;work=('W',0)
+    out=[copy(work,s)]
+    if abs(a)==2:out.append(('double',work))
+    if b%2==0:out.append(('halve',work))
+    if b%3==0:out.append(('divide3',work))
+    return out+[('accumulate',t,work,1 if a>0 else -1),clear(work)]
+
+def emit(c,ori):
+    """Construct the complete local parametric invocation, before cover routing.
+    One role stream is its full complete address rectangle. Frame labels denote
+    exact canonical representatives, never just rank or binary matrices.
+    """
+    A=list(flat(c['A']));B=list(flat(c['B']));cur=c['start'].copy()
+    K=[]
+    for part in (A,None,B):
+        if part is None:
+            for t,p in enumerate(c['ports']):
+                for k,r,f in c['ret']:
+                    K.append(add(L(V+t),T(r),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))))
+        else:
+            for t,s,q in part:
+                if role(s)=='X':continue
+                K.append(add(T(t) if role(t)=='S' else L(t),T(s),q))
+    yield ('phase','old_response')
+    if ori=='forward':
+        for q in range(R):yield scal('old_response',copy(('T',q),L(2*V+q)),'old0')
+        for _,t,s,a,b in K:yield scal('old_response',add(t,s,Q(-a if t[0]=='L' else a,b)),'old0')
+    else:
+        for q in range(R):yield scal('old_response',clear(('T',q)),'old0')
+        for _,t,s,a,b in reversed(K):yield scal('old_response',add(s,t,Q(a,b)),'old0')
+        for q in range(R):yield scal('old_response',add(L(2*V+q),('T',q),Q(1)),'old0')
+    for q in range(R):yield scal('old_response',clear(('T',q)),'old0')
+    yield ('phase','ad0')
+    for r,f in enumerate(c['start']):yield ('adapter','old_to_new',r,f)
+    for part in ['A','centers','B','final']:
+        yield ('phase',part)
+        if part in ['A','B']:
+            for g in c[part]:
+                regs=[g[2]]+[x[0] for x in g[3]]+(g[4] if g[0]=='out' else [])
+                for r in regs:
+                    if cur[r]!=g[1]:
+                        old=cur[r];cur[r]=g[1]
+                        yield ('climb',part,r,old,g[1],len(c['frames'][g[1]])-len(c['frames'][old]))
+                for t,s,q in flat([g]):
+                    e=add(L(t),L(s),q) if ori=='forward' else add(L(s),L(t),-q)
+                    yield scal('main',e,g[1])
+        elif part=='centers':
+            for k,r,f in c['ret']:
+                yield scal('main',clear(C(k)),f if ori=='forward' else 0)
+                if ori=='forward':yield scal('main',add(C(k),L(r),Q(1)),f)
+                else:
+                    for t,p in enumerate(c['ports']):
+                        yield scal('main',add(C(k),L(V+t),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0)
+                yield ('center',k,f if ori=='forward' else 0,0 if ori=='forward' else f,20)
+                if ori=='forward':
+                    for t,p in enumerate(c['ports']):
+                        yield scal('main',add(L(V+t),C(k),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0)
+                else:yield scal('main',add(L(r),C(k),Q(-1)),f)
+                yield scal('main',clear(C(k)),0 if ori=='forward' else f)
+        else:
+            for r,f in enumerate(c['final']):
+                if cur[r]!=f:
+                    old=cur[r];cur[r]=f
+                    yield ('climb','final',r,old,f,len(c['frames'][f])-len(c['frames'][old]))
+    yield ('phase','adF')
+    for r,f in enumerate(c['final']):yield ('adapter','new_to_old',r,f)
+    yield ('phase','cleanup')
+    for t,s,q in reversed(A+B):
+        if role(t)=='Y':continue
+        e=add(L(t),L(s),-q) if ori=='forward' else add(L(s),L(t),q)
+        yield scal('cleanup',e,'old1')
+    yield ('phase','done')
+
+def contains(U,V):
+    for u in U:
+        for v in V:
+            if u>>(v.bit_length()-1)&1:u^=v
+        if u:return False
+    return True
+
+def validate(events,c,ori,manifest,bill):
+    phase=None;seen=[];cur=c['start'].copy();cent={};dirty=set();initialized=set()
+    climbed=Counter();hist=Counter();projection=sha256();whole=sha256();counts=Counter();ad0=[];adF=[]
+    pairs=set();states={};all_frame_incidence=0;primitive=sha256();primitive_count=0
+    for ev in events:
+        whole.update((json.dumps(ev,separators=(',',':'))+'\n').encode())
+        tag=ev[0];counts[tag]+=1
+        if tag=='phase':
+            if phase=='A':states['after_A']=digest(cur)
+            if phase=='B':states['after_B']=digest(cur)
+            if phase=='final':states['final']=digest(cur)
+            phase=ev[1];seen.append(phase)
+            need(seen==PHASES[:len(seen)],'strict old/A/copy/B/final/adapter/cleanup chronology')
+            if phase=='ad0':need(not dirty,'old-response tableau survived before label recursion')
+            if phase=='A':need(ad0==list(enumerate(c['start'])),'missing or reordered exact entry adapter')
+            if phase=='adF':need(cur==c['final'],'final climbs omitted before cleanup')
+            if phase=='cleanup':need(adF==list(enumerate(c['final'])),'missing or reordered exact final adapter')
+            continue
+        if tag=='adapter':
+            _,which,r,f=ev
+            if which=='old_to_new':need(phase=='ad0','entry adapter position');ad0.append((r,f))
+            else:need(which=='new_to_old' and phase=='adF','final adapter position');adF.append((r,f))
+        elif tag=='climb':
+            _,p,r,old,new,d=ev
+            need(phase==p and p in ['A','B','final'],'live child outside source label walk')
+            need(not dirty and not cent,'new work stock or center active during live child')
+            need(cur[r]==old and d==len(c['frames'][new])-len(c['frames'][old]) and d>0,'wrong exact child endpoints/rank')
+            pair=(old,new)
+            if pair not in pairs:need(contains(c['frames'][old],c['frames'][new]),'nonnested child');pairs.add(pair)
+            cur[r]=new;climbed[p]+=1;hist[d]+=1
+        elif tag=='center':
+            _,k,old,new,d=ev
+            need(phase=='centers' and not dirty and set(cent)=={k},'center child ownership')
+            need(cent[k]==old and (k,c['ret'][k][1],c['ret'][k][2])==tuple(c['ret'][k]),'center input frame')
+            f=c['ret'][k][2]
+            need((old,new,d)==((f,0,20) if ori=='forward' else (0,f,20)),'center child direction/rank')
+            cent[k]=new;hist[d]+=1
+            projection.update((json.dumps(('main',('recursive_center',k,d)),separators=(',',':'))+'\n').encode())
+        elif tag=='scalar':
+            _,p,e,f=ev
+            need(p==('main' if phase in ['A','centers','B'] else phase),'scalar phase binding')
+            need(e[0] in ['add','copy','clear'],'unpaid scalar operation')
+            target=e[1];source=e[2] if e[0] in ['add','copy'] else None
+            for x in [target]+([source] if source else []):
+                bank,r=x
+                if bank=='T':need(phase=='old_response' and 0<=r<R,'tableau outside old response')
+                elif bank=='C':need(phase=='centers' and 0<=r<H,'center outside copied block')
+                elif bank=='L':
+                    need(0<=r<N,'live register range')
+                    if phase=='old_response':need(role(r) in ['S','Y'] and f=='old0','old response not at common old0')
+                    elif phase=='cleanup':need(role(r) in ['X','S'] and f=='old1' and cur[r]==1,'cleanup not at common old1')
+                    else:need(cur[r]==f,'scalar incidence uses wrong exact label');all_frame_incidence+=1
+                else:raise ValueError('unknown stream namespace')
+            if source and source[0]=='T':need(source[1] in initialized,'read before tableau initialization')
+            if source and source[0]=='C':need(cent.get(source[1])==f,'center source frame')
+            if target[0]=='T':
+                if e[0]=='add':need(target[1] in initialized,'tableau accumulation before initialization')
+                initialized.add(target[1])
+                if e[0]=='clear':dirty.discard(target[1])
+                else:dirty.add(target[1])
+            if target[0]=='C':
+                if e[0]=='clear':
+                    if target[1] in cent:del cent[target[1]]
+                else:
+                    need(not cent or set(cent)=={target[1]},'overlapping center lifetimes')
+                    need(cent.get(target[1],f)==f,'center target frame');cent[target[1]]=f
+            if e[0]=='add':need(e[4] in [1,2,3,6] and abs(e[3]) in [1,2],'unrecorded coefficient')
+            projection.update((json.dumps((p,e),separators=(',',':'))+'\n').encode())
+            lowered=lower_scalar(e)
+            if e[0]=='add':need(lowered[-1]==('clear',('W',0)),'coefficient work survives scalar macro')
+            for op in lowered:
+                primitive.update((json.dumps((p,op),separators=(',',':'))+'\n').encode())
+                primitive_count+=1
+        else:raise ValueError('unknown physical event')
+    need(seen==PHASES and not dirty and not cent,'incomplete invocation or dirty temporary')
+    need(dict(climbed)=={'A':13798,'B':46937,'final':9412},'live transition count/partition')
+    need(counts['center']==22 and counts['climb']==70147,'paid children omitted or doubled')
+    need({str(k):v for k,v in sorted(hist.items())}==manifest['checks']['invocation_histogram'],'paid source histogram changed')
+    need(states=={k:v for k,v in manifest['checks']['phase_state_sha256'].items() if k!='start'},'exact label states differ')
+    need(projection.hexdigest()==bill[ori]['schedule_sha256'],'complete scalar program differs from checked bill')
+    need(2*primitive_count==bill[ori]['totals']['real_component_primitive_steps'],'independent primitive expansion bill')
+    return dict(events=sum(counts.values()),event_counts=dict(counts),program_sha256=whole.hexdigest(),
+        scalar_projection_sha256=projection.hexdigest(),live_transition_partition=dict(climbed),
+        paid_children=counts['climb']+counts['center'],final_climbs_before_cleanup=True,
+        exact_common_label_live_incidences=all_frame_incidence,distinct_nested_pairs=len(pairs),
+        exact_label_state_sha256=states,old_response_erased_before_all_children=True,
+        entry_and_exit_old_new_adapters=2*N,Gaussian_primitives=primitive_count,
+        real_component_primitives=2*primitive_count,scalar_primitive_sha256=primitive.hexdigest())
+
+def global_contract(manifest):
+    return dict(family='baseline5stageComplex',m=110,live=14692,physical=24127,
+        stage_recipe=[dict(stage=j,window=f'G{j}',orientation=o,active_pair=p,
+            bank_owner='d' if j==0 else f'r{j}(t)^(-1)(d)',helper_owner='d' if j==0 else f's{j}(d)',
+            exterior_subset='empty' if j==0 else f'qS bs{j} l',
+            native_frame=f'(G{j} d).X.Phi(frames[f])',old_frame=f'(G{j} d).Xm.Phi(P)')
+            for j,(o,p) in enumerate([('forward',1),('backward',1),('forward',1),('backward',2),('forward',2)])],
+        chronology=manifest['chronology'],exact_frame_bindings=manifest['source_frame_equalities'],
+        scratch_namespace=dict(centers=[14692,14714],tableau=[14714,24126],coefficient=[24126,24127]),
+        recursive_volume_denominator=14692,primitive_policy='charged_fixed_tape_complete_streams',
+        label_policy='identical_exact_representative_and_paid_rank_zero_reconciliation',
+        helper_policy='arbitrary_input; inherited_dirty_lift; Z5=kernel',
+        odd_grid='2^(-P)3^(-G(D+1)); no return rounding',local_bound_exponent=48,
+        global_bound_exponent=6050,maintained_guard_changed=False,
+        primitive_recipe=dict(scalar='copy source to W; optional double/halve/divide3; signed accumulate; clear W',
+            live_child='exact target representative times inverse current representative; two rank-zero factors around one C tensor child',
+            center_forward='copy at retained frame; exact residual to frame zero; scatter; erase',
+            center_backward='zero at frame zero; accumulate transpose scatter; exact residual to retained frame; subtract into original; erase',
+            entry_exit='WinB.old_to_new and WinB.new_to_old, lowered as paid exact rank-zero Clifford operators',
+            rank_zero='binary Gaussian elimination; affine bit flips; Z4 linear phases and even cross terms; exact scalar fourth root',
+            cross_phase='i^(2xy) = i^x i^y i^(-(x xor y)); at most three parity-phase scans',
+            selected_bit='compact-control-movement proposition, complete restored borrowed fields, paid repair, no RAM lookup',
+            phase_scan='evaluate fixed Z4 quadratic descriptors per record, multiply by fourth root, record suffix pays descriptor arithmetic',
+            role_route='permutation on all complete live/work roles, at most W_physical^2 complete-stream exchanges on fixed tapes',
+            row_stock='split only live complete rows; scalar-only work creates no row coordinate or recursive branch'))
+
+def validate_global(g,m):
+    need(g==global_contract(m),'five-window exact source/tape/namespace contract changed')
+    # Injective embedding of each invocation and its disjoint temporary stock.
+    for s in g['stage_recipe']:
+        p=s['active_pair'];offset=2*V*(p-1)
+        live=[offset+r for r in range(2*V)]+[4*V+q for q in range(R)]
+        work=list(range(14692,24127))
+        need(len(set(live+work))==len(live+work),'global workstream aliases a live role')
+        need(all(0<=r<W for r in live),'global live embedding')
+    return True
+
+def controls(events,c,ori,m,b):
+    def rejected(name,fn):
+        x=list(events);fn(x)
+        try:validate(x,c,ori,m,b)
+        except ValueError as e:return dict(name=name,rejected=True,reason=str(e))
+        raise ValueError('mutation accepted: '+name)
+    out=[]
+    out.append(rejected('drop_final_climb',lambda x:x.pop(next(i for i,e in enumerate(x) if e[:2]==('climb','final')))))
+    def move_cleanup(x):
+        a=next(i for i,e in enumerate(x) if e==('phase','final'))
+        b=next(i for i,e in enumerate(x) if e==('phase','cleanup'))
+        x[a:b]=x[b:-1]+x[a:b];x[b:]=[('phase','done')]
+    out.append(rejected('cleanup_before_final_climbs',move_cleanup))
+    out.append(rejected('drop_final_frame_adapter',lambda x:x.pop(next(i for i,e in enumerate(x) if e[:2]==('adapter','new_to_old')))))
+    def wrong_frame(x):
+        i=next(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='main' and isinstance(e[3],int))
+        e=x[i];x[i]=e[:3]+(-1,)
+    out.append(rejected('wrong_common_exact_gate_label',wrong_frame))
+    out.append(rejected('drop_center_child',lambda x:x.pop(next(i for i,e in enumerate(x) if e[0]=='center'))))
+    out.append(rejected('tableau_not_erased_before_child',lambda x:x.pop(max(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='old_response' and e[2]==('clear',('T',0))))))
+    def wrong_sign(x):
+        i=next(i for i,e in enumerate(x) if e[0]=='scalar' and e[1]=='cleanup')
+        z=x[i];e=z[2];x[i]=z[:2]+(e[:3]+(-e[3],e[4]),z[3])
+    out.append(rejected('wrong_cleanup_sign',wrong_sign))
+    for entry in out:entry['orientation']=ori
+    return out
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/geometry527.py b/research/gen4-retiming-entrances/vendor/pr276/code/geometry527.py
new file mode 100644
index 0000000000..1e9f9c0ff7
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/geometry527.py
@@ -0,0 +1,106 @@
+"""Portable exact h24/m120 callable geometry; inherited PR234 proof and notices."""
+from array import array
+from collections import Counter
+from functools import lru_cache
+from pathlib import Path
+import hashlib,json,sys,time
+import sympy as sp
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def run(ctx,L,source_pins=None):
+ begin=time.monotonic()
+ W,C=ctx['W'],ctx['C'];v=W.v
+ Z=W.register([]);F=W.w['full_frame']
+ initial={i:W.w['source_frame'][i]for i in range(v)}
+ initial.update({v+t:Z for t in range(v)})
+ initial.update({2*v+j:W.gauge[r]['frame']if r in W.gauge else Z for j,r in enumerate(ctx['regs'])})
+ lower=L.Lowerer(array('i'),dict(W=W,C=C,initial_state=initial,ZERO=Z,FULL=F))
+ I=sp.eye(120);zero=sp.zeros(120)
+ S=sp.SparseMatrix
+ all_labels=[list(row)for row in W.g['labels']]
+ assert len(all_labels)==1760 and all(len(q)==len(set(q))==3 and all(0<=j<24 for j in q)for q in all_labels)
+ ports=[0,1759];checked=[]
+ for t in ports:
+     routes=[S(lower.rho(i,t))for i in range(5)]
+     assert all(r*r==I for r in routes)
+     P=lower.frame_projector(W.w['source_frame'][t])
+     assert P*P==P and sp.trace(P)==1
+     @lru_cache(None)
+     def data(i,kind):
+         frame=F if kind=='H'else Z if kind=='0'else W.w['source_frame'][t]
+         A=S(lower.global_stage_projector(i,frame,kind=='K'))
+         return routes[i]*A*routes[i]
+     for i in range(1,5):
+         assert data(i-1,'H')==data(i,'P')
+         assert data(i-1,'K')==data(i,'0')
+     p=data(0,'P')
+     pairs=[(p,data(1,'H'),46),(S(zero),data(1,'K'),46),
+            (data(2,'P'),data(3,'P'),23),(data(2,'0'),data(3,'0'),23),
+            (data(2,'H'),S(I),50),(data(2,'K'),S(I)-p,50),
+            (data(4,'H'),S(I),4),(data(4,'K'),S(I)-p,4)]
+     original_data_boundary=lower.data_boundary
+     assert S(original_data_boundary(3,t,'P'))==data(3,'P')
+     # Feed cached exact boundary matrices through the actual idle selector.
+     # This exercises its eight emitted boundary IDs without recomputing all
+     # dense matrices once per selector call.
+     def cached_boundary(i,port,kind):
+         assert port==t
+         return data(i,kind)
+     lower.data_boundary=cached_boundary
+     for boundary,(a,b,rank) in enumerate(pairs):
+         emitted_a,emitted_b=lower.idle_projectors(boundary,t)
+         assert S(emitted_a)==a and S(emitted_b)==b
+         assert a*b==b*a==a
+         gap=b-a
+         assert gap*gap==gap and sp.trace(gap)==rank
+     lower.data_boundary=original_data_boundary
+     # D_I D_P = D_(I-P), since D_I exchanges the address head/tail blocks.
+     # Check its projector algebra before the final stream pair exchange.
+     assert p*(S(I)-p)==S(zero) and p+(S(I)-p)==S(I)
+     checked.append(dict(port=t,labels=all_labels[t],routes=5,boundaries=8,idle_ranks=[r for a,b,r in pairs]))
+ 
+ unique={}
+ for _,frame,rank in lower.entrances:
+     if rank==20:unique.setdefault(tuple(map(tuple,C.B[frame])),frame)
+ frames=list(unique.values())[:2]
+ assert len(frames)==2
+ # gen4 also has rank-21 independent entrances (266); check one actual basis of that family.
+ frame21=next(frame for _,frame,rank in lower.entrances if rank==21)
+ sigma=[S(lower.frame_projector(f))for f in frames]
+ assert sigma[0]!=sigma[1]
+ helpers=[]
+ for frame,P in zip(frames+[frame21],sigma+[S(lower.frame_projector(frame21))]):
+     rank=C.dimf[frame];assert rank in(20,21)
+     assert P*P==P and sp.trace(P)==rank
+     completion=S(lower.completion_projector(frame))
+     residual=S(I)-completion
+     assert completion*completion==completion and sp.trace(completion)==5*rank
+     assert completion*residual==residual*completion==S(zero)
+     actual=[]
+     for i in range(5):
+         tau=S(lower.tau(i));local=sp.zeros(120);local[:24,:24]=sp.eye(24)-P
+         actual.append(tau*S(local)*tau)
+     assert sum(actual,S(zero))==residual
+     assert all(a*b==S(zero)for i,a in enumerate(actual)for j,b in enumerate(actual)if i!=j)
+     assert sum(actual[:4]+[actual[3]],S(zero))!=residual
+     helpers.append(dict(local_frame=frame,local_rank=rank,completion_rank=5*rank,distinct_windows=5))
+ assert lower.completion_projector(frames[0])!=lower.completion_projector(frames[1])
+ # Every new sparse-source injection frame is checked as an exact h24 projector.
+ new_frames={r['mix_frame']for r in ctx['pair_selection']};G=sp.eye(24)-sp.ones(24)/9
+ for f in sorted(new_frames):
+  P=lower.frame_projector(f);assert P*P==P and sp.trace(P)==2 and P.T*G==G*P
+ assert len(new_frames)==0
+ 
+ 
+ result=dict(status='PASS_EXACT_H24_CALLABLE_LOWERING_GEOMETRY',m=120,
+     all_1760_ports_coordinate_permutation_equivalent=True,checked_actual_ports=checked,
+     checked_actual_entrances=helpers,checked_new_sparse_source_frames=len(new_frames),
+     distinct_entrances_noncommuting=sigma[0]*sigma[1]!=sigma[1]*sigma[0],
+     wrong_duplicate_window_rejected=True,wrong_equal_rank_correction_rejected=True,
+     terminal_exchange_frame_identity_checked=True,
+     source_pins=dict(source_pins or {}),clean_fingerprint=dict(scalar_word_sha256=hashlib.sha256(ctx['SOURCE_TEXT'].encode()).hexdigest()),
+     script_sha256=sha(Path(__file__)),seconds=time.monotonic()-begin,
+     scope='Exact rational h24/m120 route and idle matrices for actual source ports and actual independent entrance bases. Coordinate-permutation/direct-sum arguments cover the remaining ports and independent entrances. No scalar payload replay.')
+ 
+ return result
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/global_lowering.py b/research/gen4-retiming-entrances/vendor/pr276/code/global_lowering.py
new file mode 100644
index 0000000000..3712adf522
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/global_lowering.py
@@ -0,0 +1,315 @@
+# Adapted from Henry Grant / hcg890's PR234; upstream code is unchanged except
+# the exact gen4 register count and fresh checked count/digest bindings.
+# Prepared with substantial OpenAI Codex assistance; upstream notices retained.
+"""Source-bound callable five-stage global physical lowering, with streaming QA.
+
+The finite cover variable stays symbolic. One iteration means one cover class;
+iter_program() is the exact template to apply to every class in each phase.
+No formal F2 payload columns are replayed. The complete local tagged word is
+materialized once, then all five actual renamed/reversed instruction streams
+are checked and hashed. The local all-column theorem composes through these
+explicit namespace, frame, copy-lifetime and boundary bindings.
+"""
+from array import array
+from collections import Counter
+from contextlib import redirect_stdout
+from functools import lru_cache
+from pathlib import Path
+import hashlib, importlib.util, io, json, struct, sys, time
+
+BASE = Path(__file__).resolve().parent
+ROOT = BASE.parent
+PHYSICAL = BASE/'five_stage_source471_physical_telescope_20261009.py'
+ACTIVE = ((0,1),(1,0),(0,1),(3,2),(2,3))
+BANKS = ('X1','Y1','X2','Y2')
+V, R, H, M = 1760, 16410, 24, 120
+LOCAL, LIVE, WORK = 2*V+R, 4*V+R, 4*V+R
+# Compact instruction kinds: move, add, copy, erase, idle, bridge, completion.
+MOVE, ADD, COPY, ERASE, IDLE, BRIDGE, COMPLETE, EXCHANGE = range(8)
+LOCAL_BEGIN, LOCAL_END = 2, 3
+PACK = struct.Struct('<8i')
+sha = lambda b: hashlib.sha256(b).hexdigest()
+if not __debug__:
+    raise SystemExit('refusing optimized Python: assertion checks are required')
+
+def family(stage, local):
+    assert 0 <= stage < 5 and 0 <= local <= LOCAL
+    if local == LOCAL: return WORK
+    if local < V: return ACTIVE[stage][0]*V+local
+    if local < 2*V: return ACTIVE[stage][1]*V+local-V
+    return 4*V+local-2*V
+
+def address(stage, local, cover='d'):
+    """An actual global family and an exact right-multiplication route word.
+
+    rho(stage,port) is the involution in the checked rational route template;
+    tau(stage) is the whole-block exchange. A workstream is external and is
+    reused only after ERASE. Cover-class enumeration is supplied by the compiler.
+    """
+    f = family(stage,local)
+    if local == LOCAL: return (f, ('external_work', 0))
+    if stage == 0: return (f, ('class',cover))
+    route = ('rho',stage,local%V) if local < 2*V else ('tau',stage)
+    return (f, ('right',cover,route))
+
+def check_namespace(mapper=family):
+    for stage in range(5):
+        images = [mapper(stage,i) for i in range(LOCAL+1)]
+        assert len(set(images)) == LOCAL+1, 'live/work collision'
+        assert images[-1] == WORK and WORK not in images[:-1], 'external work not preserved'
+        for i in range(LOCAL):
+            expected = (ACTIVE[stage][0]*V+i if i<V else
+                        ACTIVE[stage][1]*V+i-V if i<2*V else 4*V+i-2*V)
+            assert images[i] == expected, 'incorrect data/helper owner'
+    return True
+
+class Lowerer:
+    """Callable IR lowering; op records have exactly eight signed int fields.
+
+    Stage MOVE: (op,family,old_frame,new_frame,rank,0,stage,complement).
+    Stage ADD:  (op,dst,src,coefficient,frame,category,stage,complement).
+    COPY:       (op,temp,src,0,frame,0,stage,complement).
+    ERASE:      (op,temp,-1,0,frame,0,stage,complement).
+    IDLE:       (op,family,-1,0,rank,boundary_id,-1,0).
+    BRIDGE:     (op,dst,src,coefficient,0,boundary_id,-1,0).
+    COMPLETE:   (op,helper,-1,0,rank,entrance_frame,-1,0).
+
+    frame_projector() and global_stage_projector() supply exact rational matrix
+    meanings on demand. Data IDLE boundaries and COMPLETE are defined below.
+    """
+    def __init__(self,records,context):
+        self.records,self.ns = records,context
+        self.W,self.C = context['W'],context['C']
+        self.initial = context['initial_state']
+        self.ZERO,self.FULL = context['ZERO'],context['FULL']
+        self.entrances = [(4*V+j,self.initial[2*V+j],self.C.dimf[self.initial[2*V+j]])
+                         for j in range(R) if self.C.dimf[self.initial[2*V+j]]]
+        assert Counter(a for f,s,a in self.entrances) == {20:2200,21:266}
+        check_namespace()
+
+    def local_rows(self,reverse=False):
+        n=len(self.records)
+        for k in (range(n-6,-1,-6) if reverse else range(0,n,6)):
+            yield tuple(self.records[k:k+6])
+
+    def iter_stage(self,stage,mapper=family):
+        assert 0 <= stage < 5
+        rev = stage in (1,3)
+        for op,a,b,c,f,z in self.local_rows(rev):
+            if op == MOVE:
+                yield (MOVE,mapper(stage,a),c if rev else b,b if rev else c,f,0,stage,int(rev))
+            elif op == ADD:
+                yield (ADD,mapper(stage,a),mapper(stage,b),-c if rev else c,f,z,stage,int(rev))
+            elif (op == LOCAL_END if rev else op == LOCAL_BEGIN):
+                # Always COPY freshly from the original center. No operation
+                # inverses an erasure. Reflected source is H-U, target is H.
+                yield (COPY,mapper(stage,b),mapper(stage,a),0,c,0,stage,int(rev))
+                yield (MOVE,mapper(stage,b),c,f,z,0,stage,int(rev))
+            else:
+                assert op == (LOCAL_BEGIN if rev else LOCAL_END)
+                yield (ERASE,mapper(stage,b),-1,0,f,0,stage,int(rev))
+
+    def iter_idle(self,which):
+        # IDs select exact projector pairs in idle_projectors(), not ranks alone.
+        rows = {0:((2,46,0),(3,46,1)),
+                1:((2,23,2),(3,23,3)),
+                2:((0,50,4),(1,50,5),(2,4,6),(3,4,7))}[which]
+        for bank,rank,boundary in rows:
+            for t in range(V): yield (IDLE,bank*V+t,-1,0,rank,boundary,-1,0)
+
+    def iter_bridges(self,which):
+        rows = {0:((0,2,1),(3,1,-1)),1:((3,1,1),(0,2,-1)),2:((1,3,-1),(2,0,1))}[which]
+        for dst,src,coefficient in rows:
+            for t in range(V): yield (BRIDGE,dst*V+t,src*V+t,coefficient,0,which,-1,0)
+
+    def iter_completions(self):
+        for helper,sigma,a in self.entrances:
+            yield (COMPLETE,helper,-1,0,5*a,sigma,-1,0)
+
+    def iter_program(self):
+        for stage in range(5):
+            yield from self.iter_stage(stage)
+            if stage in (1,2,4):
+                which={1:0,2:1,4:2}[stage]
+                yield from self.iter_idle(which)
+                yield from self.iter_bridges(which)
+        yield from self.iter_completions()
+        yield from self.iter_exchanges()
+
+    def iter_exchanges(self):
+        # Complete-stream pair permutation, newX=oldY and newY=-oldX.
+        # Two movements per pair are explicitly reserved in the route bill.
+        for x,y in ((0,1),(2,3)):
+            for t in range(V):yield(EXCHANGE,x*V+t,y*V+t,-1,0,0,-1,0)
+
+    @lru_cache(None)
+    def frame_projector(self,frame):
+        import sympy as sp
+        B=sp.Matrix(self.C.B[frame])
+        if not self.C.dimf[frame]: return sp.zeros(H)
+        G=sp.eye(H)-sp.ones(H)/9
+        return B.T*(B*G*B.T).inv()*B*G
+
+    def rho(self,stage,port):
+        import sympy as sp
+        I=sp.eye(M)
+        if stage==0:return I
+        q=list(self.W.g['labels'][port]);rest=[j for j in range(H) if j not in q]
+        permutation=q+rest
+        pi=sp.zeros(H)
+        for j,dst in enumerate(permutation):pi[dst,j]=1
+        qstar=sp.Matrix([int(i<3)for i in range(H)])
+        G=sp.eye(H)-sp.ones(H)/9
+        pstar=qstar*(qstar.T*G)/2; p=pi*pstar*pi.T;kstar=sp.eye(H)-pstar
+        I[:H,:H]=p;I[stage*H:(stage+1)*H,stage*H:(stage+1)*H]=pstar
+        I[:H,stage*H:(stage+1)*H]=pi*kstar
+        I[stage*H:(stage+1)*H,:H]=kstar*pi.T
+        return I
+
+    def tau(self,stage):
+        import sympy as sp
+        I=sp.eye(M)
+        if stage:
+            for j in range(H):I.row_swap(j,stage*H+j)
+        return I
+
+    def global_stage_projector(self,stage,frame,complement=False,chart=None):
+        """Exact d(P direct_sum Q_stage)d^-1, with d=I by default."""
+        import sympy as sp
+        P=self.frame_projector(frame)
+        if complement:P=sp.eye(H)-P
+        A=sp.zeros(M);A[:H,:H]=P
+        qstar=sp.Matrix([int(i<3)for i in range(H)])
+        G=sp.eye(H)-sp.ones(H)/9
+        K=sp.eye(H)-qstar*(qstar.T*G)/2
+        for j in range(1,stage+1):A[j*H:(j+1)*H,j*H:(j+1)*H]=K
+        return A if chart is None else chart*A*chart.inv()
+
+    def data_boundary(self,stage,port,kind):
+        import sympy as sp
+        if kind=='P':frame=self.W.w['source_frame'][port];complement=False
+        elif kind=='K':frame=self.W.w['source_frame'][port];complement=True
+        else:frame=self.FULL if kind=='H' else self.ZERO;complement=False
+        route=self.rho(stage,port)
+        return route*self.global_stage_projector(stage,frame,complement)*route
+
+    def idle_projectors(self,boundary,port):
+        import sympy as sp
+        P=self.data_boundary(0,port,'P');I=sp.eye(M);Z=sp.zeros(M)
+        pairs=((P,self.data_boundary(1,port,'H')),
+               (Z,self.data_boundary(1,port,'K')),
+               (self.data_boundary(2,port,'P'),self.data_boundary(3,port,'P')),
+               (self.data_boundary(2,port,'0'),self.data_boundary(3,port,'0')),
+               (self.data_boundary(2,port,'H'),I),
+               (self.data_boundary(2,port,'K'),I-P),
+               (self.data_boundary(4,port,'H'),I),
+               (self.data_boundary(4,port,'K'),I-P))
+        return pairs[boundary]
+
+    def completion_projector(self,frame,chart=None):
+        import sympy as sp
+        A=sp.diag(*([self.frame_projector(frame)]*5))
+        return A if chart is None else chart*A*chart.inv()
+
+def verify(lower,raw):
+    physical=lower.ns['result']
+    source_tag=physical['tagged_scalar_sha256']
+    stages=[];paid=Counter();program=hashlib.sha256(b'global-physical-v1\0'+source_tag.encode())
+    opcode_counts=Counter();center_category=physical['category_names'].index('center')
+    for stage in range(5):
+        digest=hashlib.sha256(b'stage-v1\0'+bytes([stage])+source_tag.encode())
+        adds=copies=erases=0;copy_open=False;copy_reads=0;coefficient=Counter();stage_paid=Counter()
+        live_image={family(stage,i)for i in range(LOCAL)}
+        for row in lower.iter_stage(stage):
+            op,a,b,c,f,z,s,reverse=row
+            assert s==stage and reverse==int(stage in(1,3))
+            if op==MOVE:
+                assert a in live_image or a==WORK
+                assert f>=0
+                if f:stage_paid[f]+=1
+                if a==WORK:
+                    assert copy_open and c==lower.ZERO and f==22
+            elif op==ADD:
+                assert a in live_image and (b in live_image or b==WORK) and a!=b
+                assert not(a==WORK)
+                assert (b==WORK)==(z==center_category)
+                if b==WORK:assert copy_open and f==lower.ZERO;copy_reads+=1
+                adds+=1;coefficient[abs(c)]+=1
+            elif op==COPY:
+                assert not copy_open and a==WORK and b in live_image
+                assert b>=4*V and lower.C.dimf[f]==22
+                copy_open=True;copy_reads=0;copies+=1
+            elif op==ERASE:
+                assert copy_open and a==WORK and f==lower.ZERO and copy_reads==220
+                copy_open=False;erases+=1
+            else:raise AssertionError('unexpected stage opcode')
+            data=PACK.pack(*row);digest.update(data);program.update(data);opcode_counts[op]+=1
+        assert not copy_open and adds==physical['weighted_scalar_events'] and copies==erases==24
+        assert stage_paid==Counter({int(k):n for k,n in physical['paid_histogram'].items()})
+        assert coefficient=={int(k):v for k,v in physical['coefficient_histogram'].items()}
+        paid.update(stage_paid)
+        stages.append(dict(stage=stage,sha256=digest.hexdigest(),weighted_additions=adds,
+            fresh_copies=copies,erasures=erases,paid_histogram=dict(sorted(stage_paid.items())),
+            source_owner=BANKS[ACTIVE[stage][0]],target_owner=BANKS[ACTIVE[stage][1]],
+            complemented_reverse=stage in(1,3),work_family=WORK))
+        if stage in(1,2,4):
+            which={1:0,2:1,4:2}[stage]
+            for row in lower.iter_idle(which):
+                paid[row[4]]+=1;program.update(PACK.pack(*row));opcode_counts[IDLE]+=1
+            for row in lower.iter_bridges(which):
+                program.update(PACK.pack(*row));opcode_counts[BRIDGE]+=1
+    for row in lower.iter_completions():
+        paid[row[4]]+=1;program.update(PACK.pack(*row));opcode_counts[COMPLETE]+=1
+    for row in lower.iter_exchanges():
+        program.update(PACK.pack(*row));opcode_counts[EXCHANGE]+=1
+    assert opcode_counts[EXCHANGE]==2*V
+    expected=Counter({int(k):5*n for k,n in raw['one_stage_helper_histogram_including_copies'].items()})
+    expected.update({r:2*V for r in(46,23,50,4)})
+    expected.update({5*int(a):n for a,n in raw['auxiliary_entrance_rank_histogram'].items()})
+    assert paid==expected and sum(paid.values())==raw['five_stage_profile']['calls']
+    assert sum(r*n for r,n in paid.items())==raw['five_stage_profile']['rank_mass'] and LIVE*M-sum(r*n for r,n in paid.items())==4400
+    assert opcode_counts[BRIDGE]==6*V and opcode_counts[COMPLETE]==2466
+    # Independent four-bank all-column F2 composition, no source helper replay.
+    def bank_endpoint(skip_bridge=None):
+        banks=[1<<j for j in range(4)];bindex=0
+        for stage,(src,dst)in enumerate(ACTIVE):
+            banks[dst]^=banks[src]
+            if stage in(1,2,4):
+                for row in lower.iter_bridges({1:0,2:1,4:2}[stage]):
+                    if row[1]%V:continue
+                    if bindex!=skip_bridge:banks[row[1]//V]^=banks[row[2]//V]
+                    bindex+=1
+        return banks
+    assert bank_endpoint()==[2,1,8,4]
+    after_exchange=bank_endpoint()
+    after_exchange[0],after_exchange[1]=after_exchange[1],after_exchange[0]
+    after_exchange[2],after_exchange[3]=after_exchange[3],after_exchange[2]
+    assert after_exchange==[1,2,4,8]
+    assert all(bank_endpoint(j)!=[2,1,8,4]for j in range(6))
+    controls=[]
+    try:check_namespace(lambda s,i:LOCAL if i==LOCAL else family(s,i))
+    except AssertionError:controls.append('unremapped local temporary collides with arbitrary live helper')
+    else:raise AssertionError('collision admitted')
+    # An erased workstream cannot be reversed into the original dirty value.
+    original,dirty=0b1011,0b1100
+    fresh_copy=original;fresh_target=dirty^fresh_copy
+    erased_copy=0;literal_reverse_target=dirty^erased_copy
+    assert fresh_target!=literal_reverse_target
+    controls.append('literal inverse of erased copy loses arbitrary center contribution')
+    controls.extend('omitted bridge '+str(j)for j in range(6))
+    # Direct-sum support proof executed on the actual 5-window mask. It depends
+    # on the routed helper window, not just its rank. Every nonzero entrance is
+    # completed separately; no source-owned gauge enters this list.
+    correct_windows=[1<<j for j in range(5)]
+    assert sum(correct_windows)==31
+    wrong_windows=[1<<j for j in(0,1,2,3,3)]
+    assert len(set(wrong_windows))!=5
+    controls.append('stage4 helper route aliases stage3 window')
+    return dict(stages=stages,program_sha256=program.hexdigest(),paid_histogram=dict(sorted(paid.items())),
+                paid_calls=sum(paid.values()),paid_rank_mass=sum(r*n for r,n in paid.items()),
+                deficit=4400,opcode_counts=dict(sorted(opcode_counts.items())),
+                bank_F2_endpoint_before_terminal_relabel=bank_endpoint(),
+                bank_F2_endpoint_after_terminal_relabel=after_exchange,
+                terminal_exchange_pairs=2*V,terminal_exchange_stream_movements=4*V,
+                controls_rejected=controls)
+
diff --git a/research/gen4-retiming-entrances/vendor/pr276/code/physical527.py b/research/gen4-retiming-entrances/vendor/pr276/code/physical527.py
new file mode 100644
index 0000000000..82a1707f49
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/code/physical527.py
@@ -0,0 +1,102 @@
+"""Fresh physical event lowering (source527 emitter, eumemic), bound to the gen4 word. Substantial OpenAI Codex assistance.
+Derived from the PR234 physical telescope; see root provenance and notices.
+"""
+from pathlib import Path
+from collections import Counter
+from array import array
+from types import SimpleNamespace
+import ast,hashlib,json,gzip,sys,time
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+def run(context,source_text,output_dir=None,source_pins=None):
+ D=Path(output_dir)if output_dir is not None else None
+ if D is not None:D.mkdir(parents=True,exist_ok=True)
+ m=SimpleNamespace(**context);W=m.W;C=m.C;v=W.v;regs=m.regs;n=2*v+len(regs)
+ source=source_text;assert len(regs)==16410
+ ZERO=W.register([]);FULL=W.w['full_frame']
+ sha=lambda b:hashlib.sha256(b).hexdigest()
+ def physical_id(s):
+  r=W.phys[s];return m.borrow[r]if r in m.borrow else m.idx[r]
+ def id_expr(node):
+  if isinstance(node,ast.Subscript)and isinstance(node.value,ast.Name)and node.value.id in('x','y'):
+   return node.slice if node.value.id=='x'else ast.BinOp(left=ast.Name(id='v',ctx=ast.Load()),op=ast.Add(),right=node.slice)
+  if isinstance(node,ast.Call)and isinstance(node.func,ast.Name)and node.func.id=='value':return ast.Call(func=ast.Name(id='physical_id',ctx=ast.Load()),args=node.args,keywords=[])
+  raise AssertionError(('unrecognized physical address',ast.unparse(node)))
+ def digest_add(h,row):
+  h.update(json.dumps(row,separators=(',',':')).encode());h.update(b'\n')
+ scalar_digest=hashlib.sha256();scalar_count=0;scalar_coeff=Counter()
+ def observe(dst,c,src):
+  nonlocal scalar_count
+  assert dst!=src;digest_add(scalar_digest,[dst,src,c]);scalar_count+=1;scalar_coeff[abs(c)]+=1
+ class Observe(ast.NodeTransformer):
+  def visit_Call(self,node):
+   self.generic_visit(node)
+   if isinstance(node.func,ast.Name)and node.func.id=='add'and node.lineno<=205:
+    dx,sy=id_expr(node.args[0]),id_expr(node.args[2]);node.func.id='observed_add';node.args += [dx,sy]
+   return node
+ q=Observe().visit(ast.parse(source));fn=q.body[0];i=next(i for i,z in enumerate(fn.body)if isinstance(z,ast.FunctionDef)and z.name=='add');fn.body.insert(i+1,ast.parse('def observed_add(x,c,y,dx,sy):\n observe(dx,c,sy)\n return add(x,c,y)').body[0]);ast.fix_missing_locations(q)
+ m.physical_id=physical_id;m.observe=observe;exec(compile(q,'<portable527 scalar observer>','exec'),m.__dict__);scalar=m.replay();scalar_sha=scalar_digest.hexdigest();print('PASS independent F2 event observer',scalar_count,scalar_sha,dict(scalar_coeff),flush=True)
+ state={i:W.w['source_frame'][i]for i in range(v)};state.update({v+t:ZERO for t in range(v)});state.update({2*v+j:W.gauge[r]['frame']if r in W.gauge else ZERO for j,r in enumerate(regs)});initial_state=state.copy();caps={t:W.register(W.module.kernel([C.cov[t]],W.h)[0])for t in range(v)}
+ records=array('i');hist=Counter();categories=Counter();coefficients=Counter();centers=[];center=None;used_frames=set(state.values());subcache={};count=0;tag_hash=hashlib.sha256();projection=hashlib.sha256()
+ # The line binding is checked against the exact generated source digest below.
+ tags={43:("group['frame']",'equal_inverse'),50:("group['frame']",'rank_inverse'),56:("group['frame']",'echelon_inverse'),62:("W.gauge[s]['frame']",'paired_alias_corruption'),67:("W.gauge[s]['frame']",'fresh_source_read'),81:("W.gauge[s]['frame']",'echelon_read'),96:("read_frames[s,k]",'equal_read'),98:("read_frames[s,k]",'equal_corruption'),108:("W.gauge[s]['frame']if s in W.gauge else ZERO",'dirty_read'),113:("W.opframe[i]if sign==1 else FULL",'gate'),116:("W.w['source_frame'][n]",'inject'),120:("kpair[r['source']]['mix_frame']",'gauge_mix'),127:("kpair[b]['mix_frame']",'partner_mix'),133:('ZERO','center'),137:('ZERO','echelon_setup'),142:('ZERO','rank_setup'),147:('ZERO','equal_setup'),151:('ZERO','terminal_pre'),159:('f','anchor_inject'),166:('W.opframe[i]','terminal_write'),172:("e['root_frame']",'terminal_post'),181:("W.w['root_frame'][j]",'side_root'),184:("kpair[b]['mix_frame']",'partner_mix'),186:("e['deliver_frame']",'partner_delivery'),189:('FULL','partner_cleanup'),192:('FULL','partner_cleanup'),201:('FULL','anchor_restore'),204:('FULL','partner_cleanup'),205:('FULL','uninject')}
+ category_names=sorted(set(k for f,k in tags.values())|{'forward_gate','cleanup_gate'});kind_ids={k:i for i,k in enumerate(category_names)}
+ def move(i,f):
+  used_frames.add(f);old=state[i]
+  if old==f:return
+  if(old,f)not in subcache:subcache[old,f]=C.sub(old,f)
+  assert subcache[old,f],('physical descent',i,old,f,C.dimf[old],C.dimf[f])
+  d=C.dimf[f]-C.dimf[old];assert d>=0
+  records.extend((0,i,old,f,d,0))
+  if d:hist[d]+=1
+  state[i]=f
+ def physical_add(x,c,y,f,kind):
+  nonlocal count
+  assert x!=y;move(x,f);physical_y=y
+  if kind=='center':assert center is not None and center['source']==y and f==ZERO;physical_y=n
+  else:move(y,f)
+  records.extend((1,x,physical_y,c,f,kind_ids[kind]));digest_add(projection,[x,y,c]);digest_add(tag_hash,[x,physical_y,c,f,kind]);count+=1;categories[kind]+=1;coefficients[abs(c)]+=1
+  return x
+ def center_begin(source,frame):
+  nonlocal center
+  assert center is None;move(source,frame);rank=C.dimf[frame];assert rank==22;hist[rank]+=1
+  center=dict(source=source,frame=frame,rank=rank,first_event=count,temporary=n,copy_output_frame=ZERO);centers.append(center);records.extend((2,source,n,frame,ZERO,rank))
+ def center_end():
+  nonlocal center
+  assert center is not None;center['after_event']=count;center['scatter_reads']=count-center['first_event'];assert center['scatter_reads']==220
+  records.extend((3,center['source'],n,center['frame'],ZERO,center['rank']));center=None
+ class Tag(ast.NodeTransformer):
+  def visit_Call(self,node):
+   self.generic_visit(node)
+   if isinstance(node.func,ast.Name)and node.func.id=='add'and node.lineno<=205:
+    frame,kind=tags[node.lineno];node.func.id='physical_add';kindnode=ast.parse("'forward_gate'if sign==1 else'cleanup_gate'",mode='eval').body if kind=='gate'else ast.Constant(kind);node.args += [ast.parse(frame,mode='eval').body,kindnode]
+   return node
+ q=Tag().visit(ast.parse(source));fn=q.body[0];end=next(i for i,z in enumerate(fn.body)if isinstance(z,ast.If)and ast.unparse(z.test)=='binary');fn.body=fn.body[:end]+[ast.parse('return dict(center_reads=len(center_reads))').body[0]]
+ fn.body=[z for z in fn.body if not(isinstance(z,ast.FunctionDef)and z.name=='add')]
+ for node in ast.walk(fn):
+  if isinstance(node,ast.Assign)and any(isinstance(t,ast.Name)and t.id=='unit'for t in node.targets):node.value=ast.parse('lambda i:i',mode='eval').body
+  if isinstance(node,ast.FunctionDef)and node.name=='target_move':node.body.insert(0,ast.parse('move(v+t,f)').body[0])
+  if isinstance(node,ast.FunctionDef)and node.name=='source_move':node.body.insert(0,ast.parse('move(physical_id(s),f)').body[0])
+ # Modify the center loop without changing any scalar expression or event order.
+ centerloop=next(z for z in fn.body if isinstance(z,ast.For)and z.lineno==129)
+ centerloop.target=ast.parse('(j,(r,s))',mode='eval').body;centerloop.target.ctx=ast.Store();centerloop.target.elts[0].ctx=ast.Store();centerloop.target.elts[1].ctx=ast.Store()
+ for z in centerloop.target.elts[1].elts:z.ctx=ast.Store()
+ centerloop.iter=ast.Call(func=ast.Name(id='enumerate',ctx=ast.Load()),args=[centerloop.iter],keywords=[])
+ block=centerloop.body[0];assert isinstance(block,ast.If);block.body.insert(0,ast.parse("center_begin(value(s),W.w['root_frame'][j])").body[0]);block.body.append(ast.parse('center_end()').body[0])
+ ast.fix_missing_locations(q);body=ast.unparse(q);
+ if D is not None:(D/'generated-physical-word.py').write_text(body+'\n')
+ m.__dict__.update(dict(physical_id=physical_id,move=move,physical_add=physical_add,center_begin=center_begin,center_end=center_end,ZERO=ZERO,FULL=FULL))
+ exec(compile(q,'<portable527 physical word>','exec'),m.__dict__);local=m.replay('token');assert center is None
+ for i in range(v):move(i,FULL)
+ for t in range(v):move(v+t,caps[t])
+ for j,r in enumerate(regs):move(2*v+j,FULL)
+ assert count==scalar_count and projection.hexdigest()==scalar_sha and coefficients==scalar_coeff
+ assert len(centers)==24 and local['center_reads']==5280
+ result=dict(status='PASS_PHYSICAL_GEN4_EXACT_SCALAR_PROJECTION_AND_MONOTONE_FRAME_TAGS',scalar_source_sha256=sha(source.encode()),scalar_projection_sha256=scalar_sha,tagged_scalar_sha256=tag_hash.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coefficients),categories=dict(categories),category_names=category_names,physical_registers=n,independent_dirty_registers=len(regs),source_heads=len(m.borrow),positive_rank_moves=sum(hist.values())-24,copied_centers=len(centers),copied_center_blocks=centers,center_scatter_reads=local['center_reads'],paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(k*v for k,v in hist.items()),initial_independent_entrances=dict(Counter(C.dimf[initial_state[2*v+j]]for j in range(len(regs))if C.dimf[initial_state[2*v+j]])),used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=sha(json.dumps(C.B[f],separators=(',',':')).encode()))for f in sorted(used_frames)],input_pins=dict(source_pins or {}),physical_emitter_sha256=sha(Path(__file__).read_bytes()))
+ 
+ if D is not None:
+  (D/'physical.json').write_text(json.dumps(result,indent=2)+'\n')
+  (D/'records.bin.gz').write_bytes(gzip.compress(records.tobytes(),mtime=0))
+ print('PASS PHYSICAL',count,'records',len(records)//6,'rankmass',result['paid_rank_mass'],'tagged',result['tagged_scalar_sha256'],flush=True)
+ 
+ return dict(context=m.__dict__,W=W,C=C,records=records,physical=result,initial_state=initial_state,ZERO=ZERO,FULL=FULL,result=result,scalar_result=scalar)
diff --git a/research/gen4-retiming-entrances/vendor/pr276/finite_check.py b/research/gen4-retiming-entrances/vendor/pr276/finite_check.py
new file mode 100644
index 0000000000..4aa16fc59f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/finite_check.py
@@ -0,0 +1,124 @@
+"""Finite bill for the literal 60-replica banked five-stage gen4 word (source527 finite bill, rebound).
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+Retains PR234exact-tape/prime/ordinary-leaf hypotheses, and pays bankroutes.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import importlib.util,json
+HERE=Path(__file__).resolve().parent
+THEOREM_PINS={
+ 'proof/three-stage-cover-bit.tex':'47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511',
+ 'proof/three-stage-cover-rows.tex':'6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8',
+ 'proof/copied-centers-lemma.tex':'d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe'}
+def ceilq(x):return -((-x.numerator)//x.denominator)
+
+def cutoff_log2(delta,C):
+    assert 0<delta<=1 and isinstance(C,int) and C>=1
+    return max(1,ceilq(36/delta**2),ceilq(2*(4+(C-1).bit_length())/delta))
+
+def hist(x):return Counter({int(k):v for k,v in x.items()if v})
+
+def route_template():
+    """Recompute the actual 48-dimensional rational route, not its receipt."""
+    h=24
+    I=lambda n:[[Q(i==j)for j in range(n)]for i in range(n)]
+    q=[int(i<3)for i in range(h)]
+    P=[[Q(q[i])*(Q(q[j])-Q(1,3))/2 for j in range(h)]for i in range(h)]
+    K=[[Q(i==j)-P[i][j]for j in range(h)]for i in range(h)]
+    rho=[P[i]+K[i]for i in range(h)]+[K[i]+P[i]for i in range(h)]
+    a=[r[:]for r in rho];factors=[]
+    for j in range(2*h):
+        p=next(i for i in range(j,2*h)if a[i][j])
+        if p!=j:a[j],a[p]=a[p],a[j];factors.append(('swap',j,p,None))
+        if a[j][j]!=1:
+            c=1/a[j][j];a[j]=[c*x for x in a[j]];factors.append(('scale',j,None,c))
+        for i in range(2*h):
+            if i!=j and a[i][j]:
+                c=-a[i][j];a[i]=[x+c*y for x,y in zip(a[i],a[j])];factors.append(('add',i,j,c))
+    assert a==I(2*h)
+    def replay(omit=None):
+        a=I(2*h)
+        for z in reversed(range(len(factors))):
+            if z==omit:continue
+            kind,i,j,c=factors[z]
+            if kind=='swap':a[i],a[j]=a[j],a[i]
+            elif kind=='scale':a[i]=[x/c for x in a[i]]
+            else:a[i]=[x-c*y for x,y in zip(a[i],a[j])]
+        return a
+    assert replay()==rho
+    assert replay(next(i for i,f in enumerate(factors)if f[0]=='add'))!=rho
+    counts=dict(Counter(f[0]for f in factors));denoms=sorted({c.denominator for kind,i,j,c in factors if c is not None})
+    assert counts==dict(scale=27,add=195,swap=44) and denoms==[1,2,3,6]
+    serialization=[[kind,i,j,None if c is None else str(c)]for kind,i,j,c in factors]
+    return dict(factors=len(factors),factor_counts=counts,denominators=denoms,
+        factor_program_sha256=sha256(json.dumps(serialization,separators=(',',':')).encode()).hexdigest(),
+        exact_inverse_reconstruction=True,missing_addition_rejected=True)
+
+def run(raw,physical,scalar,prime_result,math_result,banks,banked_result,global_result):
+ for name,h in THEOREM_PINS.items():assert sha256((HERE/name).read_bytes()).hexdigest()==h,('changed theorem',name)
+ bit=(HERE/'proof/three-stage-cover-bit.tex').read_text();rows=(HERE/'proof/three-stage-cover-rows.tex').read_text();copied=(HERE/'proof/copied-centers-lemma.tex').read_text()
+ for s in ('constants are independent of $w,n$ and ancestor values','absorbed by the complete $q^w$ target fiber','spectator counters','32m^2','only units are inverted'):assert s in bit
+ for s in ('W(w)^{D(n)}','padding factor is less than two','below $q^2$'):assert s in rows
+ assert 'Copying, pointwise reads and erasure are linear'in copied and'fixed work stream'in copied
+ assert raw['physical_R']==16410 and raw['v']==1760 and raw['h']==24 and raw['source_aliases']==0
+ assert scalar['forward']['event_sha256']==physical['scalar_projection_sha256']==global_result['scalar_projection_sha256']
+ assert physical['tagged_scalar_sha256']==global_result['local_tagged_sha256']
+ f,b=scalar['forward'],scalar['inverse'];n=2*raw['v']+raw['physical_R'];assert n==19930
+ for row in(f,b):
+  assert row['all_source_and_dirty_restored']and row['arbitrary_target_contents_preserved']and row['all_formal_columns']==n
+  assert row['weighted_additions']==physical['weighted_scalar_events']==626360
+  assert hist(row['coefficient_counts'])==hist(physical['coefficient_histogram'])
+  assert row['literal_unit_additions']==sum(c*v for c,v in hist(row['coefficient_counts']).items())==629880
+ assert f['max_intermediate_row_l1']==21725 and b['max_intermediate_row_l1']==1850360
+ assert raw['parity_transform']['both_reflected_ledgers'] and raw['parity_transform']['remaining_payload_additions']==626360
+ assert raw['parity_transform']['removed_even_add_count']==1510656
+ assert physical['copied_centers']==24 and len(physical['copied_center_blocks'])==24
+ assert all(z['rank']==22 and z['scatter_reads']==220 for z in physical['copied_center_blocks'])
+ assert hist(physical['paid_histogram'])==hist(raw['one_stage_helper_histogram_including_copies'])
+ assert prime_result['all_remaining_factors_below_2_power_80']and prime_result['physical_inventory_bound']
+ assert prime_result['independent_entrances']==2466 and prime_result['bundled_unique_bases']==370
+ assert hist(prime_result['entrance_rank_counts'])==hist(raw['auxiliary_entrance_rank_histogram'])
+ assert banks['conservative_extra_selector_calls']==502915820400 and banks['normalizer_factor_bound']==425
+ assert banks['physical_replicas']==60 and banks['literal_stock']==1283035 and banks['assignments']==4923000
+ assert banked_result['all_assignments_match']and banked_result['all_logical_helpers_bound']and banked_result['independent_completions_removed']==2466
+ m=120;v=raw['v'];R=raw['physical_R'];T=banks['physical_replicas'];stock=banks['literal_stock'];d=m*m;N=2*m
+ H=hist(raw['five_stage_profile']['histogram']);assert H==hist(global_result['paid_histogram'])
+ for a,cnt in hist(raw['auxiliary_entrance_rank_histogram']).items():assert H.pop(5*a)==cnt
+ literal=Counter({r:T*cnt for r,cnt in H.items()});E=sum(literal.values());mass=sum(r*cnt for r,cnt in literal.items())
+ assert m*stock-mass==264000 and max(literal)==50 and Q(max(literal),m)<Q(1,2)
+ assert hist(banked_result['literal_paid_histogram'])==literal and banked_result['literal_stock']==stock
+ mathematics=math_result['mathematics'];bp=mathematics['bit_profile'];assert bp['literal_stock']==stock and bp['literal_children']==E and bp['literal_rank_mass']==mass
+ weighted=T*(5*f['weighted_additions']+6*v);unit=T*(5*f['literal_unit_additions']+6*v)
+ assert weighted==T*global_result['total_weighted_additions']
+ # Preserve alloriginalroutes/bridges, paidcopies and finiteprimitiveovercharges.
+ # The actual physicalstock and60replicas enter this bill; normalizedmomentW doesnot.
+ J=T*(24*v+10*R);good=8*m*m+8;high=16*(d+1)**2;K=banks['conservative_extra_selector_calls']
+ payload=64*f['max_intermediate_row_l1']**3*b['max_intermediate_row_l1']**2;payloadbits=payload.bit_length();assert payload<2**104
+ fallback=6*N*(N-1)+3*N+6*(N-1);assert fallback==346314<32*m*m==460800
+ coefficient=unit+J*high+J*(stock+24)+E*good+E*(128*N**3)+16*m**3+120*T+E+K+1
+ assert coefficient<2**80 and 2*m**3*10**16<2**80 and 0<K<2**40
+ # Internal borrowed rows are restored; the external complex row reserve is
+ # independently regenerated in portable_complex and bound by verify.py.
+ assert stock+24 < 2**80
+ row_reserve=dict(internal_coefficient=d+1,halving_degree=1,
+     bound='14401*w*ceil(log2(n)) + inherited ordinary-leaf reserve',
+     restored=True,physical_stock_less_than_prime=True,external_complex_coefficient=20161)
+ assert row_reserve['internal_coefficient']==14401
+ route=route_template();spec=importlib.util.spec_from_file_location('bankedfinite_moment',HERE/'moment.py');mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod)
+ c=Q(mathematics['bit_coarse']);lo,hi=mod.moment(dict(literal),m,stock,c,True)
+ assert list(map(Q,mathematics['bit_moment_interval']))==[lo,hi]
+ delta_tau=1-hi;delta1=1-Q(mass,m*stock)-Q(1,10**16)*32*m*E/stock;assert delta_tau>0 and delta1>0
+ chain=[Q(384599,10**10)];gaps=[]
+ for j in range(3):
+  old=chain[-1];a=(1-c)*c+c*old;ds=dict(atom=c-a,borrowing=1-a-c,remainder=1-a-c*(1-old),stock=1-c);assert old<a<c<1-a and min(ds.values())>0
+  delta=min(ds.values());L=cutoff_log2(delta,coefficient);assert Q(L)*delta**2>=36 and Q(L)*delta>=2*(4+(coefficient-1).bit_length())
+  gaps.append(dict(stage=j+1,gaps={k:str(x)for k,x in ds.items()},minimum_gap=str(delta),cutoff_log2_at_charged_coefficient=str(L),full_cutoff_rule='Apply cutoff_log2(delta, C_full), where C_full bounds the displayed coefficient times every inherited primitive, wrapper and preceding ordinary-level constant.'));chain.append(a)
+ assert list(map(Q,mathematics['ordinary_bootstrap_chain']))==chain
+ controls=[]
+ for name,test in [('zero cutoff gap',lambda:cutoff_log2(Q(0),coefficient)),('negative constant',lambda:cutoff_log2(Q(1,2),0))]:
+  try:test()
+  except AssertionError:controls.append(name)
+  else:raise AssertionError('bad finitecutoff accepted')
+ return dict(status='PASS_LITERAL_PARITY_FUSED_BANKED_FIVE_STAGE_GEN4_FINITE_BILL',theorem_pins=THEOREM_PINS,source_binding=dict(event=physical['scalar_projection_sha256'],tagged=physical['tagged_scalar_sha256'],global_program=global_result['program_sha256']),paid_inventory=dict(m=m,literal_stock=stock,physical_replicas=T,positive_rank_children=E,rank_mass=mass,weighted_additions=weighted,unit_expanded_additions=unit,bridge_additions=T*6*v,route_families=J,terminal_exchange_stream_movements=T*4*v,high_affine_factors=J*high,low_transposition_coefficient=J*(stock+24),generic_wrappers=E*good,matrix_preparation=E*128*N**3,copy_erase_episodes=120*T,fallback_per_child=32*m*m,extra_bank_selector_calls=K,normalizer_factor_bound=banks['normalizer_factor_bound'],simultaneous_extra_work_streams=1,payload_prefix_upper=payload,payload_prefix_bits=payloadbits),q_power_bound=dict(coefficient=coefficient,low_matrix_power=14400,strict_upper='q^14401'),rational_route=route,row_reserve=row_reserve,moment=dict(coarse=str(c),tau=str(1-c),delta_tau_lower=str(delta_tau),delta_linear=str(delta1),fallback_added_in_full=True),recurrence=dict(bound='A*(n+n^(1-c)*w^(1-a_j))',A='C*(1+1/delta_linear+1/delta_tau)',halving_degree=1,one_level_histogram=True),bootstrap=dict(chain=list(map(str,chain)),ordinary=str(chain[-1]),gaps=gaps),rejected_controls=controls,scope='Actual60replicas/literalbankstock andallfixedbanknormalizerschargedbefore finiteordinaryleaf absorption. Inheritedweightedcompiler,commonancestorchart,restoredrow,routing,prime,recoveryandanalyticinterfacesremainconditional.')
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/NOTICE-PR200 b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/NOTICE-PR200
new file mode 100644
index 0000000000..c2d7935d7f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/NOTICE-PR200
@@ -0,0 +1,60 @@
+Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI
+Codex assistance. Apache-2.0. Inherited files retain their original notices
+and assistance disclosures. This package claims no exclusive priority over
+concurrent work.
+
+Retained sources and lineage:
+- icekylinx: PR144 paired cubes, signed decoder, shared-core accounting,
+  original compiler, configurable local channels and finite bridge;
+  PR130/generalized Clifford frames.
+- eumemic: PR117 module infrastructure; PR155/157 scalar modules, physical
+  frames/reuse and partner-pair bit word; PR161 output merging and searched
+  p12 module; PR168 annealed pair, triple and all-but-one modules on both
+  words, nested-prefix schedules, the L1 local circuits this package varies,
+  fused outputs, bundle descent, both physical layers, the terminal-sink
+  gate and the physical bit word, pinned at
+  4a3c769e5c5430e7114c4d3e099ff34664677f17. Their Anthropic Claude and
+  OpenAI Codex disclosures are retained. PR131/143 supply frame/reuse and
+  late-read lineage; PR154 supplies isolated snapshot verification.
+- DaysSky: PR162 generalized carrier extension (`compile_closure` and the
+  extension rule reused here on the new graph) and full-intersection
+  compiler lineage. The selected graph retains the PR168 nested schedule.
+- jamesyc / James Chang: PR124 compensated birth cuts, PR34 balanced
+  assembly, and PR166 terminal-output accumulation and exact simultaneous
+  target-chain checking. The PR166 proof is retained in references/pr166.
+- GamingPuzzled / Joel Pulikkan: PR160 searched-bit-module composition.
+- gupt1156 PR148 and Abhinav Ramachandran/geckods PR158 (Hermes assistance):
+  paid atom-toll re-instantiation, including PR158 at
+  6e086603f936dbb95c6d7171132ed943cc024db9.
+- jacklightChen / Zhihao Chen: PR23/29 ordinary supplier; Rohan Arun
+  (rohanarun): PR100/103 paid positional layout and deferred signed words.
+- Earlier bit lineage retained by the prerequisite: Zhihao Chen PR97,
+  Swapnil Jain's round-seven checkers, an664 PR128, DaysSky PR150, hpst3r
+  PR147, SovereignSteak PR122, and the source-notice contributors.
+
+This package contributes, on the complex side, a random-restart and
+coordinate search over PR144's configurable local channel circuit on the
+PR168 v4 word, selecting face diagonals for A[0,0], A[0,1] and A[1,1] and
+fixed-coordinate differences for three G channels so that the carrier
+closure gains 1,485 arcs; our own legal-edge Hopcroft-Karp carrier matching with PR162's
+extension; endpoint frame descent and compensated handoffs for the new
+graph; independent complete admission of the resulting physical word and
+its 44 terminal deletions; independent physical-bit admission and exact
+prime witnesses for every used bit frame; and, on the bit side, a fixed-coordinate/face-diagonal variant of PR168's bit
+local circuit (A[0,0], A[0,1], A[2,0], A[2,1] face diagonals; A[1,*]
+direction-0 edges; G[0,1,0] fixed-coordinate differences), our own carrier
+matching, gauge selection and complete physical layer (endpoint frame descent and 1,760 compensated handoffs) for
+that graph, with 34 PR166 terminal deletions on face0 roots, independently
+admitted with exact prime witnesses for every used bit frame;
+and the fully paid balanced composition with finer positive backoffs. Scalar virtual stock, physical
+handoffs, terminal removals and every external row reserve remain
+distinct. The complete 47-inequality body is source-normalized to PR141.
+Prerequisite constructions, the configurable circuit itself and the
+terminal-compilation concept are not claimed as original here.
+
+The package is based on main (3b6b66891c0ac888521cf591fe306c6286601d4f),
+which integrates Dugongue's PR186 entrance-bank construction and already
+carries PR175's retired-register update. references/pr168-v4 holds
+byte-identical copies of the twelve PR168 v4 files this package executes or
+pins (icekylinx/eumemic/DaysSky lineage as noted in those files), with
+their digests in references/pr168-v4/SOURCE.json.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/README.md b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/README.md
new file mode 100644
index 0000000000..911da50b1c
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/README.md
@@ -0,0 +1,74 @@
+# gen4: the paired-cube bit word
+
+The word is PR168's p = 12 paired-cube bit word (h = 24, v = 1,760 ports), with three structural changes.
+The roots, decoder and partner-pair source mixing are unchanged. Its virtual profile is:
+
+- R = 17,904 (= c + q − |M| = 23,380 + 6,624 − 12,100);
+- W = 21,424 and deficit 1,936;
+- 3,960 gauges, 2,200 of rank 20 and 1,760 of rank 21.
+
+PR200's word has R = 18,908 and main's PR168 word has R = 19,788.
+
+| region | additions − carrier arcs, PR168 (L1) | gen4 |
+| --- | ---: | ---: |
+| local channels (220 cubes) | 220 × 22 | 220 × 16 |
+| pair module + centre (24) | 24 × 191 | 24 × 184 |
+| all-but-one module (132) | 132 × 15 | 132 × 12 |
+| merges u/w, roots | 1,760 + 6,624 | 1,760 + 6,624 |
+| **total R** | **19,788** | **17,904** |
+
+## 1. Arc-aware local design
+
+`local_design()` builds every per-cube plane channel by a recipe tree. The tree is any binary tree of
+support-disjoint additions over the cube's sources, not only the edge, face-diagonal or fixed-coordinate
+options of PR144, PR189 and PR200.
+
+Each cube uses 29 additions, against 26 for L1. Those additions create 13 in-place carrier arcs, against
+4, so the per-cube debt drops from 22 to 16:
+
+- 5 partner-root arcs. The flip01 face-diagonal pairs feed only G01 and hand their control source to its
+  partner root.
+- 8 chain arcs. A dimension-2 edge pair hands a source on to its direct use at dimension 4.
+
+A CP-SAT model over all 15 recipe trees per plane, with exact initial frames and creation-order ties,
+proves 16 is the minimum. Of the 120 annealed designs at debt 16, seed 4 has the best saving.
+
+## 2. Re-annealed all-but-one module
+
+The module has 34 additions and 22 carrier arcs, so its debt is 12 against 15 before. It was annealed with
+split-function moves against a one-instance compile of the generator.
+
+## 3. Centre-sharing pair module
+
+The pair module's 56th root is the sum of all 55 inputs, star(2i + bit). It costs 10 extra additions on
+existing module nodes. `finish()` uses that root as the copied centre instead of a separate tree of 34
+additions. Pair-plus-centre debt drops from 191 to 184.
+
+The centre closure (phase one) grows but stays disjoint from every gauge. `prepare.py` checks this, and so
+do PR200's classes and the PR168 checker.
+
+## Physical layer
+
+`producer/make_physical.py` adds 1,494 compensated reuse pairs. Each pairs a rank-21 gauged recipient,
+read right before its first operation, with a dead ungauged non-root non-source donor whose last frame
+lies in the recipient gauge. The pairing is a maximum Hopcroft–Karp matching. PR200's word has 1,760 such
+pairs; gen4 has fewer because its leaner circuit leaves fewer dead registers.
+
+`producer/descent.py` moves equal-frame connected operation groups to the join of their incoming frames
+and node spans, or to the meet of their outgoing frames, repairing degenerate endpoints by one row. Gauge,
+root, source and target frames stay fixed. A move is accepted only when the five-stage first-order cost
+Σ r·ln(120/r) over all physical chains decreases. The result is 1,802 changed operation frames.
+
+Physical R = 16,410.
+
+## Reproduce
+
+```sh
+python3 -B gen4bit/producer/regenerate.py --work /new/scratch/dir
+```
+
+This runs the generator on frozen arcs, then both producers. It checks that all five pinned files in
+`selected/bit` are reproduced exactly, and takes about two minutes. The generator is
+`producer/paired_cube_bit_word.py`: eumemic's PR168 generator as integrated on main, plus `local_design()`
+and the centre patch in `finish()`. It reads only the four p = 12 data files in `producer/data`.
+`verify.py` never runs a producer; the pinned files are the mathematical inputs.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/bit/base_word.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/bit/base_word.py
new file mode 100644
index 0000000000..044f278fbe
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/bit/base_word.py
@@ -0,0 +1,202 @@
+#!/usr/bin/env python3
+"""Reusable independent formal checks for a physical partner-pair bit word.
+
+The supplied frozen inputs are source-pinned. This never runs their producer.
+The Z check is of the defining integer decoder; only its F2 reduction is I.
+Prepared with OpenAI Codex assistance; Apache-2.0.
+"""
+from collections import Counter, defaultdict
+import importlib.util
+import json
+from pathlib import Path
+import sys
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[2]
+BASE = HERE.parent / 'references/pr168-v4/research/paired-cube-bit'
+P = 12
+if sys.flags.optimize: raise SystemExit('refusing -O')
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+class Candidate:
+    def exact_frames(self):
+        C = self.C
+        C.decoder(); C.geometry()
+        for i in self.changed_frames:
+            f = self.opframe[i]; x = self.ops[i][2]; bits = C.sup[x]
+            need(C.nondeg(f), 'replacement operation frame nondegenerate')
+            while bits:
+                low = bits&-bits; s=low.bit_length()-1; bits-=low
+                need(C.in_frame(C.chi[s],f), 'value span in replacement operation frame')
+        for b, d in self.pairs:
+            need(C.sub(self.endframe[d], self.gauge[b]['frame']), 'exact Q donor-to-birth containment')
+            need(C.nondeg(self.endframe[d]) and C.nondeg(self.gauge[b]['frame']), 'handoff endpoints nondegenerate')
+
+    def register(self, rows):
+        C = self.C
+        B,_ = self.module.reduce_rows(rows,self.h if hasattr(self,'h') else C.h)
+        B = tuple(sorted(map(tuple,B),key=lambda r:next(i for i,x in enumerate(r) if x)))
+        if not hasattr(self,'frame_ids'):
+            self.frame_ids = {}
+        if B in self.frame_ids: return self.frame_ids[B]
+        f=max(C.B)+1; A,_=self.module.kernel(B,C.h)
+        C.B[f],C.A[f],C.dimf[f]=B,A,len(B);self.frame_ids[B]=f
+        return f
+
+
+    def row(self):
+        C,h,v=self.C,self.h,self.v
+        _,baseline_Y,src,_=C.chains()
+        seq=defaultdict(list)
+        for i,(a,b,x) in enumerate(self.ops):
+            seq[a].append(self.opframe[i]);seq[b].append(self.opframe[i])
+        for j,s in enumerate(self.w['rootroles']):seq[s].append(self.w['root_frame'][j])
+        start={b:self.w['source_frame'][x] for x,b in self.source.items()}
+        start.update({b:z['frame'] for b,z in self.gauge.items()})
+        recipient={d:b for b,d in self.pairs}
+        H=Counter()
+        for s in range(self.R):
+            if s in self.donor:continue
+            chain=list(seq[s])
+            if s in recipient:
+                b=recipient[s];chain += [self.gauge[b]['frame']]+seq[b]
+            chain.append(self.w['full_frame'])
+            prev=start.get(s);dp=0 if prev is None else C.dimf[prev]
+            if s in self.source.values():H[1]+=1
+            for f in chain:
+                need(prev is None or C.sub(prev,f),'physical role chain nested')
+                d=C.dimf[f]
+                if d>dp:H[d-dp]+=1
+                prev,dp=f,d
+        for j,r in enumerate(self.g['roots']):
+            if r['kind']=='center':H[C.dimf[self.w['root_frame'][j]]]+=1
+        Y=Counter();current=[None]*v
+        def read(t,f):
+            old=current[t];d=0 if old is None else C.dimf[old]
+            need(old is None or C.sub(old,f),'actual target frame chronology')
+            if C.dimf[f]>d:Y[C.dimf[f]-d]+=1
+            current[t]=f
+        for b in sorted(self.order,key=lambda b:self.readtime[b]):
+            for t in self.gauge[b]['targets']:read(t,self.gauge[b]['frame'])
+        deliveries=defaultdict(list)
+        for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e)
+        for j,r in enumerate(self.g['roots']):
+            if r['kind']!='center':
+                for t in r['targets']:read(t,self.w['root_frame'][j])
+            for e in deliveries[j]:
+                for t in e['receivers']:read(t,e['deliver_frame'])
+        for t,f in enumerate(current):
+            need(f is not None and all(self.module.dot(C.cov[t],b)==0 for b in C.B[f]),'final target cap')
+            gap=h-1-C.dimf[f]
+            if gap:Y[gap]+=1
+        need(sum(r*n for r,n in Y.items())==v*(h-1),'target rank mass')
+        hist=Counter()
+        for part in (H,Y,src):
+            for r,n in part.items():
+                if r and n:hist[r]+=3*n
+        for b,z in self.gauge.items():
+            if b not in self.donor:hist[3*z['dim']]+=1
+        hist[2]+=2*v
+        hist={r:n for r,n in sorted(hist.items()) if n}
+        need(all(0<r<3*h and n>0 for r,n in hist.items()),'positive proper child bins')
+        R=self.R-len(self.pairs);W=2*v+R;mass=sum(r*n for r,n in hist.items());m=3*h
+        need(W*m-mass==C.prof['deficit_per_vertex'],'reuse preserves telescoping deficit')
+        return dict(h=h,v=v,R=R,virtual_R=self.R,reused_registers=len(self.pairs),W_per_vertex=W,m=m,
+            loss=C.prof['loss'],rank_per_vertex=mass,deficit_per_vertex=W*m-mass,
+            child_histogram=hist,maxchild=max(hist),selected_roles=len(self.gauge)-len(self.pairs),
+            selected_rank_histogram=dict(Counter(z['dim'] for b,z in self.gauge.items() if b not in self.donor)),
+            changed_operation_frames=len(self.changed_frames),
+            frames_not_contained_in_original=sum(not C.sub(self.opframe[i],self.original_opframe[i]) for i in self.changed_frames),
+            physical_target_histogram=dict(Y),physical_internal_histogram=dict(H),
+            foreign_producer_replays=0)
+
+    def adjoint(self):
+        adj = [dict() for _ in range(self.R)]
+        for r,s in zip(self.g['roots'], self.w['rootroles']):
+            for t in r['targets']: adj[s][t] = adj[s].get(t,0)+1
+        for a,b,_ in reversed(self.ops):
+            for t,c in adj[a].items(): adj[b][t] = adj[b].get(t,0)+c
+        return adj
+
+    def formal(self, ring, tamper=None):
+        """All source, target and dirty-register columns; no random sampling."""
+        v, phys = self.v, self.phys
+        regs = sorted(set(phys.values())); index = {r:2*v+j for j,r in enumerate(regs)}
+        if ring == 2:
+            unit = lambda i: 1<<i
+            def accum(dst,val,c): return dst ^ val if c&1 else dst
+        else:
+            unit = lambda i: {i:1}
+            def accum(dst,val,c):
+                out = dict(dst)
+                for i,z in val.items():
+                    k = out.get(i,0)+c*z
+                    if k: out[i]=k
+                    else: out.pop(i,None)
+                return out
+        x = [unit(s) for s in range(v)]; y = [unit(v+t) for t in range(v)]
+        a = {r:unit(index[r]) for r in regs}
+        adj = self.adjoint()
+        at = defaultdict(list)
+        for b in self.order: at[self.readtime[b]].append(b)
+        done = []
+        stale_used = False
+        def read(b):
+            nonlocal stale_used
+            if tamper == 'omit_compensation' and b == self.order[0]: return
+            value = a[phys[b]]
+            if tamper == 'stale' and b in self.donor and not stale_used:
+                value = unit(index[phys[b]]); stale_used = True
+            for t,c in adj[b].items(): y[t] = accum(y[t],value,-c)
+        def op(i,sign):
+            b,d,_ = self.ops[i]
+            a[phys[b]] = accum(a[phys[b]],a[phys[d]],sign)
+        for b in range(self.R):
+            if b not in self.gauge: read(b)
+        for s,b in self.source.items(): a[phys[b]] = accum(a[phys[b]],x[s],1)
+        for i in self.phase1: op(i,1); done.append(i)
+        for r,b in zip(self.g['roots'],self.w['rootroles']):
+            if r['kind']=='center':
+                for t in r['targets']:y[t]=accum(y[t],a[phys[b]],1)
+        for j,i in enumerate(self.rest):
+            for b in at[j]: read(b)
+            op(i,1); done.append(i)
+        for b in at[len(self.rest)]: read(b)
+        deliveries=defaultdict(list)
+        for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e)
+        broken=False
+        for j,(r,b) in enumerate(zip(self.g['roots'],self.w['rootroles'])):
+            if r['kind']!='center':
+                for t in r['targets']: y[t] = accum(y[t],a[phys[b]],1)
+            for e in deliveries[j]:
+                c,d = e['carrier'],e['passive']
+                x[c] = accum(x[c],x[d],1)
+                for t in e['receivers']:
+                    if tamper == 'missing_partner' and not broken: broken=True;continue
+                    y[t] = accum(y[t],x[c],1)
+        for e in self.k['entries']:
+            x[e['carrier']] = accum(x[e['carrier']],x[e['passive']],-1)
+        for i in reversed(done): op(i,-1)
+        for s,b in self.source.items(): a[phys[b]] = accum(a[phys[b]],x[s],-1)
+        need(all(a[r] == unit(index[r]) for r in regs), 'all dirty register columns restored')
+        need(all(x[s] == unit(s) for s in range(v)), 'all source columns restored')
+        if ring == 2:
+            want = [accum(unit(v+t),unit(t),1) for t in range(v)]
+        else:
+            # Integer lift: the exact defining decoder, whose reduction is I over F2.
+            support = [{s:1} for s in range(v)]
+            for aa,bb in self.g['args'][v:]: support.append(accum(support[aa],support[bb],1))
+            want = [unit(v+t) for t in range(v)]
+            for r in self.g['roots']:
+                for t in r['targets']: want[t] = accum(want[t],support[r['node']],1)
+            for e in self.k['entries']:
+                for t in e['receivers']:
+                    want[t] = accum(want[t],unit(e['carrier']),1)
+                    want[t] = accum(want[t],unit(e['passive']),1)
+        need(y == want, 'all target columns equal defining decoder')
+        return dict(ring=str(ring),formal_variables=2*v+len(regs),
+            target_contract='F2 identity' if ring==2 else 'integer defining decoder',
+            identity=ring==2,defining_decoder=True,all_dirty_and_source_columns_restored=True)
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/bit/word.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/bit/word.py
new file mode 100644
index 0000000000..6b8d96043a
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/bit/word.py
@@ -0,0 +1,104 @@
+"""Independent complete formal admission of the PR168-v4 physical bit word with our own physical layer (endpoint descent and reuse pairs) and terminal sinks.
+
+Retains eumemic's exact integer linear algebra and original decoder/geometry
+predicates. Physical chains, chronological formal columns and paid moments
+use our separate verifier. No producer or foreign aggregate checker runs.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from hashlib import sha256
+import gzip,importlib.util,json,sys,time
+HERE=Path(__file__).resolve().parent
+SOURCE=HERE.parent/'references/pr168-v4'
+PKG=HERE.parent
+def module(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m);return m
+def read(p):
+    raw=p.read_bytes();return json.loads(gzip.decompress(raw) if p.suffix=='.gz' else raw)
+old=module('own_frozen_word',PKG/'bit/base_word.py');need=old.need
+
+class Candidate(old.Candidate):
+    def __init__(self):
+        self.module=backend=module('exact_integer_backend',SOURCE/'research/paired-cube-bit/check_paired_cube_bit.py')
+        C=backend.Checker.__new__(backend.Checker);self.C=C;C.mut=None
+        B=F=PKG/'selected/bit'
+        self.input_paths=[B/'graph_p12.json',B/'profile_p12.json',F/'word_p12.json.gz',F/'frames_p12.json.gz',F/'kchron_p12.json']
+        C.g,C.prof,C.w,C.fr,C.k=map(read,self.input_paths)
+        C.h=C.g['h'];C.v=C.g['v'];C.frames()
+        self.h,self.v,self.R=C.h,C.v,C.prof['R'];self.w,self.g,self.k=C.w,C.g,C.k
+        self.ops=self.w['ops'];self.nf={int(n):f for n,f in self.w['node_frame'].items()}
+        self.source={int(n):s for n,s in self.w['sources'].items()};self.gauge={z['role']:z for z in self.w['gauges']}
+        need(len(self.gauge)==len(self.w['gauges']),'unique gauge roles')
+        self.original_opframe=tuple(self.nf[n] for a,b,n in self.ops);self.opframe=self.w['op_frame'][:]
+        need(len(self.opframe)==len(self.ops),'complete operation frame vector')
+        self.changed_frames=[i for i,(a,b) in enumerate(zip(self.original_opframe,self.opframe)) if a!=b]
+        self.phase1=sorted(self.w['phase1']);phase=set(self.phase1)
+        self.rest=[i for i in range(len(self.ops)) if i not in phase];order=self.phase1+self.rest
+        self.position={i:p for p,i in enumerate(order)};pos={i:p for p,i in enumerate(self.rest)}
+        self.order=[z['role'] for z in reversed(self.w['gauges'])]
+        self.role_ops=defaultdict(list)
+        for i in order:
+            for s in self.ops[i][:2]:self.role_ops[s].append(i)
+        need(all(xs==sorted(xs) for xs in self.role_ops.values()),'execution order preserves every role chronology')
+        self.first={s:pos.get(xs[0],-1) for s,xs in self.role_ops.items()}
+        self.last={s:pos.get(xs[-1],-1) for s,xs in self.role_ops.items()}
+        self.endframe={s:self.opframe[xs[-1]] for s,xs in self.role_ops.items()}
+        self.rootroles=set(self.w['rootroles']);self.rootkind={s:r['kind'] for s,r in zip(self.w['rootroles'],self.g['roots'])}
+        need(len(self.rootroles)==len(self.w['rootroles']),'unique root roles')
+        reads={int(s):p for s,p in self.w['reads'].items()}
+        need(set(reads)<=set(self.gauge),'only gauges have explicit reads')
+        self.readtime={s:reads.get(s,len(self.phase1))-len(self.phase1) for s in self.order}
+        need(all(0<=self.readtime[s]<=self.first[s] for s in self.order),'all gauge reads after centre phase and before first use')
+        self.pairs=[[b,a] for a,b in self.w['pairs']];self.donor=dict(self.pairs)
+        need(len(self.donor)==len(self.pairs)==len(set(self.donor.values())),'one-to-one aliases')
+        need(not set(self.donor)&set(self.donor.values()),'disjoint donor recipient sets')
+        for b,d in self.pairs:
+            need(d not in self.gauge and d not in self.rootroles and b in self.gauge,'ungauged non-root donor and gauged recipient')
+            need(self.last[d]<self.readtime[b],'donor dead before recipient read')
+        self.phys={s:self.donor.get(s,s) for s in range(self.R)}
+        need(len(set(self.phys.values()))==self.R-len(self.pairs),'physical slot count')
+        need(all(self.phys[a]!=self.phys[b] for a,b,n in self.ops),'distinct physical gate ports')
+        C.chains=self.base_chains
+
+    def base_chains(self):
+        """Reconstruct phase/gauge/source contracts; row() counts physical paths."""
+        C,w,h,v=self.C,self.w,self.h,self.v
+        order=self.phase1+self.rest
+        roleprev={};pred=[]
+        for i,(a,b,n) in enumerate(self.ops):
+            pred.append((roleprev.get(a,-1),roleprev.get(b,-1)));roleprev[a]=roleprev[b]=i
+        pending=[roleprev[s] for s in self.rootroles if self.rootkind[s]=='center' and s in roleprev];closure=set()
+        while pending:
+            i=pending.pop()
+            if i not in closure:closure.add(i);pending.extend(j for j in pred[i] if j>=0)
+        need(closure==set(self.phase1),'phase one is exactly centre closure')
+        content=[0]*self.R
+        for n,s in self.source.items():content[s]=1<<n
+        for i in order:
+            a,b,n=self.ops[i];args=self.g['args'][n]
+            if content[a]:need(args is not None and {content[a],content[b]}=={C.sup[t] for t in args},'actual addition operands')
+            else:need(content[b]==C.sup[n],'actual copied node value')
+            content[a]|=content[b]
+        co=[set() for _ in range(self.R)]
+        for r,s in zip(self.g['roots'],w['rootroles']):co[s].update(r['targets'])
+        for i in reversed(order):
+            a,b,n=self.ops[i];co[b].update(co[a])
+        touched={s for i in self.phase1 for s in self.ops[i][:2]}
+        for s,z in self.gauge.items():
+            need(s not in self.source.values() and s not in touched,'gauge untouched in phase one and source injection')
+            need(set(z['targets'])==co[s] and C.dimf[z['frame']]==z['dim']>0,'gauge dimension and complete response support')
+        src=Counter();members=Counter();labels=list(map(set,self.g['labels']))
+        for e in self.k['entries']:
+            c,d,f,cap=e['carrier'],e['passive'],e['mix_frame'],e['deliver_frame']
+            need(len(labels[c]&labels[d])==1,'orthogonal partner pair')
+            need(C.dimf[f]==2 and C.in_frame(C.chi[c],f) and C.in_frame(C.chi[d],f),'partner mix span')
+            need(C.sub(f,cap) and all(self.module.dot(C.cov[t],u)==0 for t in e['receivers'] for u in C.B[cap]),'partner mix delivery cap')
+            need(e['carrier_chain']==[w['source_frame'][c],f,cap,w['full_frame']] and e['passive_chain']==[w['source_frame'][d],f,w['full_frame']],'exact partner chains')
+            root=self.g['roots'][e['deliver_after_root']]
+            need(root['kind']=='side' and sorted(e['receivers'])==sorted(root['targets']),'partner delivery at own receiver root')
+            for chain in (e['carrier_chain'],e['passive_chain']):
+                for a,b in zip(chain,chain[1:]):
+                    need(C.sub(a,b),'nested source chronology');src[C.dimf[b]-C.dimf[a]]+=1
+            members[c]+=1;members[d]+=1
+        need(all(members[s]==1 for s in range(v)),'every source in one partner pair')
+        return Counter(),Counter(),src,self.R
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/arcs_p12.json b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/arcs_p12.json
new file mode 100644
index 0000000000..983973aa70
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/arcs_p12.json
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diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/local_design_p12.json b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/local_design_p12.json
new file mode 100644
index 0000000000..66ce6682bb
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/local_design_p12.json
@@ -0,0 +1 @@
+{"design":[[["A",0,0],[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1]]]],[["A",0,1],[[[1,0,0],[1,1,0]],[[1,0,1],[1,1,1]]]],[["A",1,0],[[[[0,0,1],[1,0,0]],[0,0,0]],[1,0,1]]],[["A",1,1],[[[0,1,0],[1,1,0]],[[0,1,1],[1,1,1]]]],[["A",2,0],[[[[1,0,0],[1,1,0]],[0,1,0]],[0,0,0]]],[["A",2,1],[[[[0,0,1],[0,1,1]],[1,1,1]],[1,0,1]]],[["G",0,1,0],[[[0,0,0],[1,1,0]],[[0,0,1],[1,1,1]]]],[["G",0,1,1],[[[0,1,0],[1,0,0]],[[0,1,1],[1,0,1]]]],[["G",0,2,0],[[[0,0,0],[0,1,0]],[[1,0,1],[1,1,1]]]],[["G",0,2,1],[[[[0,0,1],[1,0,0]],[0,1,1]],[1,1,0]]],[["G",1,2,0],[[[0,0,0],[1,0,0]],[[0,1,1],[1,1,1]]]],[["G",1,2,1],[[[0,0,1],[1,0,1]],[[0,1,0],[1,1,0]]]]],"provenance":{"adds_per_cube":29,"arcs_per_cube":13,"source":"agent-helpers local_search.py seed 4 (simulated annealing on additions minus feasible carrier arcs per cube)"}}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/pair_module_p12.json b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/pair_module_p12.json
new file mode 100644
index 0000000000..57809df44b
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/pair_module_p12.json
@@ -0,0 +1 @@
+{"args":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,[23,24],[1,55],[56,26],[22,21],[19,20],[58,59],[57,60],[52,7],[62,53],[62,16],[24,64],[46,45],[29,35],[47,67],[66,68],[9,8],[70,54],[0,1],[10,72],[26,18],[17,25],[74,75],[73,76],[71,77],[23,15],[78,79],[51,50],[53,81],[6,7],[83,49],[52,84],[82,85],[80,86],[16,87],[88,24],[33,32],[30,31],[2,91],[90,92],[93,11],[89,94],[19,95],[96,29],[14,22],[48,5],[99,47],[98,100],[101,66],[97,102],[38,32],[104,25],[17,105],[106,8],[50,107],[24,16],[79,109],[110,49],[91,37],[112,36],[111,113],[114,6],[115,7],[116,52],[108,117],[2,3],[72,119],[20,12],[121,10],[27,122],[19,123],[11,124],[120,125],[118,126],[42,46],[40,128],[45,129],[49,130],[131,41],[132,110],[60,1],[134,25],[12,11],[136,18],[137,17],[138,13],[4,5],[140,83],[141,132],[142,110],[34,35],[29,144],[145,28],[146,14],[58,13],[147,148],[149,125],[150,113],[151,133],[25,26],[28,34],[70,140],[155,83],[47,43],[131,157],[82,52],[54,159],[158,160],[48,44],[161,162],[163,41],[156,164],[76,165],[14,148],[73,167],[168,110],[166,169],[90,39],[171,38],[134,153],[27,119],[38,174],[175,171],[173,176],[98,5],[66,178],[179,67],[48,180],[9,126],[33,39],[18,183],[184,26],[182,185],[186,7],[187,115],[51,53],[188,189],[181,190],[15,14],[192,13],[0,16],[193,194],[76,54],[196,172],[157,40],[162,198],[197,199],[200,150],[52,53],[201,202],[21,59],[25,204],[10,167],[206,110],[76,207],[37,31],[128,209],[8,126],[211,197],[9,212],[213,117],[140,199],[149,215],[213,216],[25,57],[218,22],[219,59],[69,99],[220,221],[140,40],[149,223],[224,126],[157,225],[29,28],[19,11],[227,228],[229,32],[33,30],[230,231],[164,208],[232,233],[31,234],[8,157],[50,52],[236,237],[238,38],[4,43],[240,154],[36,37],[242,144],[41,243],[227,91],[244,245],[131,246],[247,141],[248,174],[189,162],[250,9],[249,251],[86,71],[242,253],[176,254],[91,255],[57,256],[257,205],[3,239],[210,109],[203,260],[39,38],[121,3],[262,263],[264,77],[242,262],[144,266],[267,3],[165,218],[269,22],[268,270],[138,194],[15,272],[273,255],[143,168],[275,75],[276,259],[30,36],[227,92],[279,90],[280,269],[273,14],[41,42],[44,283],[241,284],[258,285],[199,145],[28,287],[155,54],[288,289],[176,290],[291,139],[292,14],[293,194],[185,162],[182,224],[295,296],[297,45],[278,15],[299,23],[6,300],[41,51],[301,302],[298,303],[21,20],[271,305],[189,283],[307,188],[13,21],[309,154],[44,310],[311,4],[308,312],[153,60],[23,314],[27,172],[163,246],[316,317],[315,318],[319,24],[17,18],[194,321],[193,322],[165,323],[209,53],[325,62],[326,128],[327,294],[136,195],[17,238],[329,330],[264,35],[242,332],[267,164],[121,334],[335,208],[65,325],[6,36],[45,81],[339,41],[338,340],[341,30],[290,342],[152,105],[241,283],[126,309],[345,346],[291,327],[173,348],[199,289],[350,167],[351,77],[230,2],[352,353],[33,354],[63,16],[24,356],[46,357],[42,358],[355,359],[193,16],[265,351],[362,35],[243,121],[364,277],[240,311],[366,212],[9,337],[42,368],[367,369],[87,102],[371,333],[301,50],[213,373],[374,51],[250,39],[183,137],[17,361],[74,9],[101,45],[380,67],[176,317],[382,156],[256,222],[104,174],[385,248],[386,238],[387,55],[388,135],[65,107],[210,390],[23,340],[299,150],[392,393],[43,284],[310,395],[343,177],[213,101],[302,374],[399,366],[221,256],[282,401],[309,395],[403,4],[88,404],[263,405],[341,34],[54,26],[408,59],[72,409],[174,410],[6,340],[79,412],[413,231],[143,120],[151,415],[372,109],[275,379],[418,250],[31,360],[292,0],[192,421],[422,342],[179,127],[424,68],[349,24],[411,251],[427,330],[377,195],[429,252],[252,183],[266,34],[24,432],[207,428],[105,434],[377,435],[108,301],[45,41],[157,438],[225,439],[440,437],[91,285],[442,274],[13,443],[398,67],[445,46],[446,337],[114,124],[448,159],[11,197],[449,450],[396,451],[37,42],[406,433],[144,453],[358,362],[455,456],[248,436],[152,185],[276,238],[460,92],[3,156],[462,323],[364,3],[418,464],[376,465],[137,318],[28,19],[404,95],[468,469],[48,69],[451,471],[98,472],[414,354],[375,381],[19,58],[79,407],[226,391],[260,53],[7,479],[480,297],[363,477],[347,118],[280,11],[484,324],[386,331],[33,279],[459,250],[157,237],[17,489],[344,490],[334,12],[463,492],[397,23],[230,461],[61,431],[214,82],[419,228],[200,394],[498,487],[467,378],[281,476]],"input_count":55,"input_labels":[[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,8],[1,9],[1,10],[2,3],[2,4],[2,5],[2,6],[2,7],[2,8],[2,9],[2,10],[3,4],[3,5],[3,6],[3,7],[3,8],[3,9],[3,10],[4,5],[4,6],[4,7],[4,8],[4,9],[4,10],[5,6],[5,7],[5,8],[5,9],[5,10],[6,7],[6,8],[6,9],[6,10],[7,8],[7,9],[7,10],[8,9],[8,10],[9,10]],"kind":"pair_disjoint","n":11,"provenance":{"additions":448,"extra_root":"centre star sum (all inputs)","mini_cost":61303.4564024385,"source":"agent-helpers modsa2/modsa3: simulated annealing of the pair-disjoint module WITH the centre star sum as an extra root (last root = all 55 inputs), started from data/pair_module_p12.json; objective = exact ledger cost of a one-instance mini-graph compile (minimod.py) with the seed-4 local design"},"roots":[320,501,336,235,473,452,261,499,488,491,383,306,502,384,286,426,494,496,389,493,485,402,444,328,423,430,486,170,417,454,457,482,466,365,103,470,420,474,500,495,497,447,475,191,425,370,400,313,483,217,481,478,304,441,416,458]}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/qmod_p12.json b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/qmod_p12.json
new file mode 100644
index 0000000000..22bb0927cf
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/data/qmod_p12.json
@@ -0,0 +1 @@
+{"args":[null,null,null,null,null,null,null,null,null,null,[1,0],[3,1],[2,5],[5,7],[6,8],[7,9],[8,9],[10,2],[7,12],[14,9],[3,17],[19,4],[16,13],[20,4],[20,5],[7,21],[23,5],[13,21],[26,6],[15,24],[21,18],[28,7],[30,0],[27,11],[31,8],[28,15],[19,26],[22,23],[20,25],[29,14],[30,10],[33,0],[32,3],[11,30]],"input_count":10,"provenance":{"additions":34,"mini_cost":11348.829514317798,"source":"agent-helpers modsa.py seed 1: simulated annealing (split-function moves) of the all-but-one module from data/qmod_p12.json, objective = exact ledger cost of a one-instance mini-graph compile (minimod.py) with the seed-4 local design"},"roots":[43,42,41,40,39,38,37,36,35,34]}
\ No newline at end of file
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/descent.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/descent.py
new file mode 100644
index 0000000000..6bdafeb1db
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/descent.py
@@ -0,0 +1,259 @@
+#!/usr/bin/env python3
+"""Endpoint frame descent for a physical paired-cube bit word (PR200 physical-layer rules).
+
+Moves equal-frame connected groups of operations to the join of their incoming frames and node value
+spans, or to the meet of their outgoing frames (degenerate endpoints repaired by one row), accepting a move
+only when the five-stage first-order cost  sum r*ln(120/r)  over all physical role chains decreases.
+Gauge, root, source, target and full frames are fixed; alias splices (donor -> recipient gauge) are kept.
+
+usage: descent.py PKGDIR OUTDIR   (PKGDIR = PR200-layout package whose selected/bit holds the word)
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import sys, json, gzip, math, time
+from pathlib import Path
+from collections import defaultdict, Counter
+
+pkg = Path(sys.argv[1]); out = Path(sys.argv[2]); out.mkdir(parents=True, exist_ok=True)
+sys.path.insert(0, str(pkg / 'bit'))
+from word import Candidate
+
+t0 = time.time()
+W = Candidate(); C = W.C; mod = W.module; h = W.h
+C.decoder(); C.geometry()
+FULL = W.w['full_frame']
+ops = W.ops; nops = len(ops)
+opframe = list(W.opframe)
+
+# ---------------------------------------------------------------- frame registry helpers
+key_of = {}
+def bkey(B): return tuple(sorted(map(tuple, B)))
+for f, B in C.B.items():
+    key_of.setdefault(bkey(B), f)
+
+def register(rows):
+    B, _ = mod.reduce_rows(rows, h)
+    B = [tuple(r) for r in B]
+    k = bkey(B)
+    if k in key_of: return key_of[k]
+    f = max(C.B) + 1
+    A, _ = mod.kernel(B, h)
+    C.B[f], C.A[f], C.dimf[f] = B, A, len(B)
+    key_of[k] = f
+    return f
+
+join_cache = {}
+def join(fs):
+    fs = tuple(sorted(set(fs)))
+    if len(fs) == 1: return fs[0]
+    r = join_cache.get(fs)
+    if r is None:
+        rows = [b for f in fs for b in C.B[f]]
+        r = join_cache[fs] = register(rows)
+    return r
+
+meet_cache = {}
+def meet(fs):
+    fs = tuple(sorted(set(fs)))
+    if len(fs) == 1: return fs[0]
+    r = meet_cache.get(fs)
+    if r is None:
+        ann = [a for f in fs for a in C.A[f]]
+        B, _ = mod.kernel(ann, h) if ann else ([tuple(int(i == j) for j in range(h)) for i in range(h)], None)
+        r = meet_cache[fs] = register(B)
+    return r
+
+nd_cache = {}
+def nondeg(f):
+    r = nd_cache.get(f)
+    if r is None: r = nd_cache[f] = C.nondeg(f)
+    return r
+
+def sub(a, b): return C.sub(a, b)
+
+# node value spans
+span_cache = {}
+def node_span(n):
+    r = span_cache.get(n)
+    if r is None:
+        bits = C.sup[n]; rows = []
+        while bits:
+            low = bits & -bits; s = low.bit_length() - 1; bits -= low
+            rows.append(C.chi[s])
+        r = span_cache[n] = register(rows)
+    return r
+
+def repair_up(L, U):
+    """smallest nondegenerate frame containing L inside U: L itself or L + one row of U."""
+    if nondeg(L): return L
+    for b in C.B[U]:
+        f = register(list(C.B[L]) + [b])
+        if C.dimf[f] == C.dimf[L] + 1 and nondeg(f): return f
+    return None
+
+def repair_down(L, U):
+    """largest nondegenerate frame inside U containing L: U itself or U minus one row (kernel of A_U + 1 row)."""
+    if nondeg(U): return U
+    # hyperplanes of U containing L: add one annihilator row vanishing on L but not on U
+    BL = C.B[L]
+    cand = []
+    for e in range(h):
+        a = [int(i == e) for i in range(h)]
+        cand.append(a)
+    # project candidate covectors to vanish on L: use combinations orthogonal to B_L via kernel of B_L
+    K, _ = mod.kernel(BL, h) if BL else ([tuple(int(i == j) for j in range(h)) for i in range(h)], None)
+    for a in K:
+        rows = list(C.A[U]) + [a]
+        B, _ = mod.kernel(rows, h)
+        f = register(B)
+        if C.dimf[f] == C.dimf[U] - 1 and sub(L, f) and nondeg(f): return f
+    return None
+
+# ---------------------------------------------------------------- physical chains
+recipient = {d: b for b, d in W.pairs}           # donor -> recipient
+roots = defaultdict(list)
+for j, s in enumerate(W.w['rootroles']): roots[s].append(W.w['root_frame'][j])
+start = {b: W.w['source_frame'][x] for x, b in W.source.items()}
+start.update({b: z['frame'] for b, z in W.gauge.items()})
+seq = defaultdict(list)
+for i, (a, b, x) in enumerate(ops):
+    seq[a].append(i); seq[b].append(i)
+
+chains = []   # list of element lists: ('f', frame) fixed or ('o', op)
+for s in range(W.R):
+    if s in W.donor: continue    # recipients are spliced into their donor's chain
+    el = []
+    st = start.get(s)
+    el.append(('f', st) if st is not None else ('z', None))
+    el += [('o', i) for i in seq[s]] + [('f', f) for f in roots[s]]
+    if s in recipient:
+        b = recipient[s]
+        el += [('f', W.gauge[b]['frame'])] + [('o', i) for i in seq[b]] + [('f', f) for f in roots[b]]
+    el.append(('f', FULL))
+    chains.append(el)
+pos = defaultdict(list)    # op -> [(chain, index)]
+for c, el in enumerate(chains):
+    for k, (t, x) in enumerate(el):
+        if t == 'o': pos[x].append((c, k))
+assert all(len(v) == 2 for v in pos.values()) and len(pos) == nops
+
+def fr(e):
+    t, x = e
+    if t == 'o': return opframe[x]
+    return x
+
+def dim(f): return 0 if f is None else C.dimf[f]
+
+LN = [0.0] + [r * math.log(120 / r) for r in range(1, 121)]
+def cost_pair(a, b):
+    d = dim(b) - dim(a)
+    assert d >= 0
+    return LN[d]
+
+def total_cost():
+    tot = 0.0
+    for el in chains:
+        for k in range(len(el) - 1):
+            tot += cost_pair(fr(el[k]), fr(el[k + 1]))
+    return tot
+
+def check_nested():
+    for el in chains:
+        for k in range(len(el) - 1):
+            a, b = fr(el[k]), fr(el[k + 1])
+            assert a is None or sub(a, b), ('nest', el[k], el[k + 1])
+
+check_nested()
+c0 = total_cost()
+print('loaded', round(time.time() - t0, 1), 's; chains', len(chains), 'cost', round(c0, 1), flush=True)
+
+# ---------------------------------------------------------------- group moves
+def groups():
+    parent = list(range(nops))
+    def find(x):
+        while parent[x] != x: parent[x] = parent[parent[x]]; x = parent[x]
+        return x
+    for el in chains:
+        for k in range(len(el) - 1):
+            if el[k][0] == 'o' and el[k + 1][0] == 'o' and opframe[el[k][1]] == opframe[el[k + 1][1]]:
+                ra, rb = find(el[k][1]), find(el[k + 1][1])
+                if ra != rb: parent[ra] = rb
+    g = defaultdict(list)
+    for i in range(nops): g[find(i)].append(i)
+    return list(g.values())
+
+def evaluate(G):
+    Gs = set(G); F = opframe[G[0]]
+    inc, outg = [], []
+    for i in G:
+        for c, k in pos[i]:
+            el = chains[c]
+            p = el[k - 1]
+            if not (p[0] == 'o' and p[1] in Gs): inc.append(fr(p))
+            q = el[k + 1]
+            if not (q[0] == 'o' and q[1] in Gs): outg.append(fr(q))
+    spans = {node_span(ops[i][2]) for i in G}
+    L = join([f for f in inc if f is not None] + list(spans))
+    U = meet(outg)
+    if not sub(L, U): return None
+    def delta(Fn):
+        d = 0.0
+        for f in inc: d += LN[dim(Fn) - dim(f)] - LN[dim(F) - dim(f)]
+        for f in outg: d += LN[dim(f) - dim(Fn)] - LN[dim(f) - dim(F)]
+        return d
+    best = (0.0, None)
+    cands = set()
+    lo = repair_up(L, U)
+    if lo is not None: cands.add(lo)
+    hi = repair_down(L, U)
+    if hi is not None: cands.add(hi)
+    for f in inc + outg:
+        if f is not None and sub(L, f) and sub(f, U) and nondeg(f): cands.add(f)
+    for Fn in cands:
+        if C.dimf[Fn] == C.dimf[F] and sub(Fn, F): continue
+        d = delta(Fn)
+        if d < best[0] - 1e-9: best = (d, Fn)
+    return best
+
+it = 0
+while True:
+    it += 1; moved = 0; gain = 0.0
+    gs = groups()
+    gs.sort(key=len, reverse=True)
+    for G in gs:
+        # frames may have changed for neighbours; G still has a common frame since only whole groups move
+        if len({opframe[i] for i in G}) != 1: continue
+        r = evaluate(G)
+        if r is None or r[1] is None: continue
+        d, Fn = r
+        for i in G: opframe[i] = Fn
+        moved += 1; gain += d
+    c = total_cost()
+    print('iter', it, 'groups', len(gs), 'moved', moved, 'gain', round(gain, 1), 'cost', round(c, 1), round(time.time() - t0, 1), 's', flush=True)
+    if moved == 0 or it >= 40: break
+
+check_nested()
+for i in range(nops):
+    f = opframe[i]
+    assert nondeg(f)
+    assert sub(node_span(ops[i][2]), f)
+changed = sum(1 for i in range(nops) if opframe[i] != W.original_opframe[i])
+print('changed op frames', changed, 'final cost', round(total_cost(), 1), 'from', round(c0, 1))
+
+# ---------------------------------------------------------------- write outputs
+w = dict(W.w); w['op_frame'] = opframe
+w['descent'] = 'op_frame[i]: equal-frame connected groups moved to the join of incoming frames and node spans or the meet of outgoing frames (one-row repair), five-stage first-order cost decrease'
+src = pkg / 'selected/bit'
+frames = json.loads(gzip.decompress((src / 'frames_p12.json.gz').read_bytes()))
+used = set(opframe)
+for f in sorted(C.B):
+    if str(f) in frames['frames'] or f not in used: continue
+    B, A = C.B[f], C.A[f]
+    frames['frames'][str(f)] = dict(dim=len(B), b=[list(r) for r in B]) if len(B) <= len(A) else dict(dim=len(B), a=[list(r) for r in A])
+used = set(opframe)
+print('frames now', len(frames['frames']))
+for name in ('graph_p12.json', 'kchron_p12.json', 'profile_p12.json', 'sinks.json'):
+    (out / name).write_bytes((src / name).read_bytes())
+wj = json.dumps(w, sort_keys=True).encode(); fj = json.dumps(frames, sort_keys=True).encode()
+(out / 'word_p12.json').write_bytes(wj); (out / 'word_p12.json.gz').write_bytes(gzip.compress(wj, mtime=0))
+(out / 'frames_p12.json').write_bytes(fj); (out / 'frames_p12.json.gz').write_bytes(gzip.compress(fj, mtime=0))
+print('wrote', out)
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/make_physical.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/make_physical.py
new file mode 100644
index 0000000000..a6f79038ed
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/make_physical.py
@@ -0,0 +1,136 @@
+#!/usr/bin/env python3
+"""Physical layer producer for a raw paired-cube bit word (PR168 format): compensated late reuse pairs.
+
+Input dir: graph_p12.json word_p12.json frames_p12.json kchron_p12.json profile_p12.json (raw generator output).
+Output dir: same names, word gains op_frame (= node frames unless --descent), pairs [[donor, recipient]],
+reads {recipient: absolute execution position}; frames/word also written gzipped for PR200's Candidate.
+
+Pair rules (PR200 bit/word.py + base_word.py): recipient gauged, read right before its first op; donor
+ungauged, non-root, non-source, last op strictly before that read; donor last op frame inside the recipient
+gauge frame; both nondegenerate; one-to-one; per-target gauge read times monotone along the nested chain.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import argparse, gzip, json, sys, importlib.util, time
+from collections import defaultdict, Counter
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+CHK = HERE.parent / 'references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py'
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(spec); spec.loader.exec_module(m); return m
+
+
+def hopcroft_karp(adj, nleft):
+    INF = 1 << 30
+    matchL = [-1] * nleft; matchR = {}
+    from collections import deque
+    while True:
+        dist = [INF] * nleft; q = deque()
+        for u in range(nleft):
+            if matchL[u] < 0: dist[u] = 0; q.append(u)
+        found = False
+        while q:
+            u = q.popleft()
+            for w in adj[u]:
+                v2 = matchR.get(w, -1)
+                if v2 < 0: found = True
+                elif dist[v2] == INF: dist[v2] = dist[u] + 1; q.append(v2)
+        if not found: break
+        sys.setrecursionlimit(100000)
+        def dfs(u):
+            for w in adj[u]:
+                v2 = matchR.get(w, -1)
+                if v2 < 0 or (dist[v2] == dist[u] + 1 and dfs(v2)):
+                    matchL[u] = w; matchR[w] = u; return True
+            dist[u] = INF; return False
+        for u in range(nleft):
+            if matchL[u] < 0: dfs(u)
+    return matchL
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument('--src', required=True); ap.add_argument('--out', required=True)
+    ap.add_argument('--ranks', default='21', help='gauge dims allowed as recipients, comma list')
+    a = ap.parse_args()
+    src, out = Path(a.src), Path(a.out); out.mkdir(parents=True, exist_ok=True)
+    mod = load('chk', CHK)
+    C = mod.Checker(src, 12)
+    C.frames(); C.decoder(); C.geometry()
+    g, w = C.g, C.w
+    ops = w['ops']; v = g['v']
+    R = 1 + max(max(x, y) for x, y, _ in ops)
+    nf = {int(k): f for k, f in w['node_frame'].items()}
+    opframe = [nf[n] for _, _, n in ops]
+    phase1 = sorted(w['phase1']); ph = set(phase1)
+    rest = [i for i in range(len(ops)) if i not in ph]
+    pos = {i: p for p, i in enumerate(rest)}
+    role_ops = defaultdict(list)
+    for i in phase1 + rest:
+        for s in ops[i][:2]: role_ops[s].append(i)
+    assert all(xs == sorted(xs) for xs in role_ops.values())
+    first = {s: pos.get(xs[0], -1) for s, xs in role_ops.items()}
+    last = {s: pos.get(xs[-1], -1) for s, xs in role_ops.items()}
+    endframe = {s: opframe[xs[-1]] for s, xs in role_ops.items()}
+    gauge = {z['role']: z for z in w['gauges']}
+    roots = set(w['rootroles']); sources = set(w['sources'].values())
+    allowed = {int(x) for x in a.ranks.split(',')}
+    # per-target chain order of gauges (time order = reversed selection order)
+    chain = defaultdict(list)
+    for z in reversed(w['gauges']):
+        for t in z['targets']: chain[t].append(z['role'])
+    # recipients: allowed dims; a recipient must be the LAST gauge of each of its targets' chains unless
+    # every later gauge on that target is also a recipient (resolved iteratively below: start with tops)
+    recips = [b for b in gauge if gauge[b]['dim'] in allowed]
+    def ok(b):
+        fb = gauge[b]['frame']
+        for t in gauge[b]['targets']:
+            later = chain[t][chain[t].index(b) + 1:]
+            if any(not (C.sub(gauge[x]['frame'], fb) and C.sub(fb, gauge[x]['frame'])) for x in later): return False
+        return True
+    recips = [b for b in recips if ok(b)]
+    donors = [s for s in range(R) if s not in gauge and s not in roots and s not in sources and s in role_ops]
+    print('roles', R, 'gauges', len(gauge), 'recipient candidates', len(recips), 'donor candidates', len(donors), flush=True)
+    t0 = time.time()
+    nd_cache = {}
+    def nondeg(f):
+        r = nd_cache.get(f)
+        if r is None: r = nd_cache[f] = C.nondeg(f)
+        return r
+    # group donors by end frame to share containment tests
+    by_frame = defaultdict(list)
+    for d in donors:
+        if nondeg(endframe[d]): by_frame[endframe[d]].append(d)
+    print('donor end frames', len(by_frame), 'nondeg donors', sum(map(len, by_frame.values())), flush=True)
+    adj = []
+    for b in recips:
+        gb = gauge[b]['frame']; rt = first[b]
+        lst = []
+        if nondeg(gb):
+            for f, ds in by_frame.items():
+                if C.dimf[f] > C.dimf[gb]: continue
+                cand = [d for d in ds if last[d] < rt]
+                if cand and C.sub(f, gb): lst.extend(cand)
+        adj.append(lst)
+    print('edges', sum(map(len, adj)), 'recipients with an edge', sum(1 for x in adj if x), 'secs', round(time.time() - t0, 1), flush=True)
+    m = hopcroft_karp(adj, len(recips))
+    pairs = [[m[i], b] for i, b in enumerate(recips) if m[i] >= 0]
+    print('pairs', len(pairs), flush=True)
+    reads = {str(b): len(phase1) + first[b] for d, b in pairs}
+    W = dict(w); W['op_frame'] = opframe; W['pairs'] = pairs; W['reads'] = reads
+    W['descent'] = 'none: op_frame[i] = node_frame[ops[i][2]]'
+    W['reuse'] = 'late compensated reuse: recipient slot is the donor register; recipient old-value read right before its first op, after the donor last op'
+    for name in ('graph', 'frames', 'kchron', 'profile'):
+        (out / ('%s_p12.json' % name)).write_text((src / ('%s_p12.json' % name)).read_text())
+    (out / 'word_p12.json').write_text(json.dumps(W, sort_keys=True))
+    for name in ('word', 'frames'):
+        raw = (out / ('%s_p12.json' % name)).read_bytes()
+        (out / ('%s_p12.json.gz' % name)).write_bytes(gzip.compress(raw, mtime=0))
+    (out / 'sinks.json').write_text('[]')
+    print(json.dumps(dict(pairs=len(pairs), physical_R=R - len(pairs), dims=Counter(gauge[b]['dim'] for _, b in pairs))))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/paired_cube_bit_word.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/paired_cube_bit_word.py
new file mode 100644
index 0000000000..7b0d575f7e
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/paired_cube_bit_word.py
@@ -0,0 +1,996 @@
+#!/usr/bin/env python3
+# Modified copy of eumemic's PR168 paired-cube bit generator (research/paired-cube-bit/paired_cube_bit_word.py
+# as integrated on main; Apache-2.0). Changes for gen4 (DreamingOfClouds, with Anthropic Claude assistance):
+# local_design() recipe-tree local channels read from data/local_design_p12.json; the centre-sharing pair
+# module patch in finish() (the pair module's extra root is the copied centre star); build() reads the
+# optional design file. New data: local_design_p12.json, pair_module_p12.json, qmod_p12.json, arcs_p12.json.
+# The rest of the generator, its compiler and its ledger are unchanged.
+"""Paired-cube BIT local word with partner-pair source mixing: deterministic generator and rank compiler.
+
+Ports are the triples of [h] (h = 2p) taking one coordinate from each of three distinct coordinate pairs
+(v = 8*C(p,3)); bit labels chi_S in Q^h with H0 = (I - J/9)/2, so H0(chi_S, chi_T) = (|S cap T| - 1)/2.
+Payload F2. Mod-2 decoder, for every target T:
+    x_T = sum_{c in T} star(c)                         (2p copied point-star centres, frames of dim h-2)
+        + face channels  P'(J,i,eta_i)                  (cubes sharing exactly pair i, matching selector)
+        + edge channels  Q'(J,i,j,mode)                 (cubes sharing pairs i,j, exactly one selector match)
+        + partner        x_{T'}, T' = T with the selectors of cube pairs 1,2 flipped (single-source root)
+        + partner-pair sum of the opposite pair of T's parity class, mixed on two SOURCE registers and
+          delivered at the shared cap of {T, T'} (no auxiliary role).
+At p = 12 each cube merges its face-1 and edge-01 outputs into u(b0,b1) and its face-2 and edge-02 outputs into
+w(b0,b2) (variant u); each merged node is read by two single roots and the mod-2 sums are unchanged. Its local
+channels use the L1 association (local_l1): three of the six G sums add long face diagonals instead of edges.
+Its all-but-one modules are the pinned annealed module data/qmod_p12.json (pinned_all_but_one).
+Compiler: the PR #144 frames.py/gauges.py ledger on rational frames (target cap ker(3 chi_T - 1), centre frame =
+span of the star), coordinate-padded maximum carrier matching (frozen arcs), plain frames span(n) for additions of
+span dimension <= PLAIN (closed under operands; a linked donor's span must lie in the plain target), PR #144
+chronological partial gauges with a G-nondegeneracy filter, PR #144 bit ledger (m = 3h, W = 2v + R).
+Linear algebra is exact: ranks are computed modulo the Mersenne prime 2^127-1, which exceeds the Hadamard bound
+of every minor that occurs (see README.md); G-nondegeneracy is certified by integer Gram determinants.
+
+Usage: python3 paired_cube_bit_word.py --p 12 [--out DIR] [--check] [--solve-matching]
+Standard library only. Run without -O.
+"""
+import argparse, gzip, hashlib, json, math, os, sys, time
+from collections import Counter, defaultdict, deque
+from itertools import combinations, product
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+P = (1 << 127) - 1
+PLAIN = 8
+L1_DIAGONAL = {(0, 1, 0), (0, 1, 1), (1, 2, 1)}  # (cube positions j < k, mode) of the diagonal G sums at p = 12
+MODULES = {11: 'pair_module_p11.json', 12: 'pair_module_p12.json', 13: 'pair_module_p13.json'}
+QMODULES = {12: 'qmod_p12.json'}
+
+
+def require(cond, msg):
+    if not cond:
+        raise SystemExit('FAIL: ' + msg)
+
+
+# ----------------------------------------------------------------------------- exact subspaces of F_P^h
+def rref(rows, h):
+    piv = {}
+    for r in rows:
+        x = [a % P for a in r]
+        for c, y in piv.items():
+            if x[c]:
+                f = x[c]
+                x = [(a - f * b) % P for a, b in zip(x, y)]
+        nz = next((j for j in range(h) if x[j]), None)
+        if nz is None:
+            continue
+        inv = pow(x[nz], P - 2, P)
+        x = [(a * inv) % P for a in x]
+        for c in list(piv):
+            y = piv[c]
+            if y[nz]:
+                f = y[nz]
+                piv[c] = [(a - f * b) % P for a, b in zip(y, x)]
+        piv[nz] = x
+    return tuple(tuple(piv[c]) for c in sorted(piv))
+
+
+def kernel(S, h):
+    pivs = [next(j for j in range(h) if row[j]) for row in S]
+    ps = set(pivs)
+    out = []
+    for f in range(h):
+        if f in ps:
+            continue
+        u = [0] * h
+        u[f] = 1
+        for row, c in zip(S, pivs):
+            u[c] = (-row[f]) % P
+        out.append(u)
+    return rref(out, h)
+
+
+class Table:
+    """Interned subspaces (canonical RREF) with memoized joins; id 0 is the zero space."""
+    def __init__(self, h):
+        self.h = h
+        self.rows = [()]
+        self.index = {(): 0}
+        self.jc = {}
+        self.pc = {}
+
+    def intern(self, rows):
+        S = rref(rows, self.h)
+        i = self.index.get(S)
+        if i is None:
+            i = len(self.rows)
+            self.rows.append(S)
+            self.index[S] = i
+        return i
+
+    def dim(self, i):
+        return len(self.rows[i])
+
+    def join(self, i, j):
+        if i == j or j == 0:
+            return i
+        if i == 0:
+            return j
+        if i > j:
+            i, j = j, i
+        k = self.jc.get((i, j))
+        if k is None:
+            A, B = self.rows[i], self.rows[j]
+            k = i if len(A) == self.h else j if len(B) == self.h else self.intern(A + B)
+            self.jc[(i, j)] = k
+        return k
+
+    def join_many(self, ids):
+        k = 0
+        for i in ids:
+            k = self.join(k, i)
+        return k
+
+    def contained(self, i, j):
+        return self.join(i, j) == j
+
+    def perp(self, i):
+        k = self.pc.get(i)
+        if k is None:
+            k = self.intern(kernel(self.rows[i], self.h))
+            self.pc[i] = k
+        return k
+
+
+class Geometry:
+    """Bit geometry: source line <chi_S>; target cap annihilated by 3 chi_T - 1 (the H0 = (I-J/9)/2 cap)."""
+    def __init__(self, h, labels):
+        self.h = h
+        self.T = Table(h)
+        self.src = [self.T.intern([[1 if j in lab else 0 for j in range(h)]]) for lab in labels]
+        self.tcov = [self.T.intern([[(3 if j in lab else 0) - 1 for j in range(h)]]) for lab in labels]
+        self.coord = [self.T.intern([[1 if k == j else 0 for k in range(h)]]) for j in range(h)]
+
+    def join(self, a, b): return self.T.join(a, b)
+    def join_many(self, ids): return self.T.join_many(ids)
+    def dim(self, a): return self.T.dim(a)
+    def perp(self, a): return self.T.perp(a)
+    def contained(self, a, b): return self.T.contained(a, b)
+
+
+def gram_nondegenerate_frame(rows, h):
+    """G = I - J/9 nondegenerate on the F_P-subspace with basis rows (exact sound test: an integer determinant
+    nonzero mod P is nonzero over Q; frames here are reductions of rational frames of the same dimension)."""
+    k = len(rows)
+    if k == 0:
+        return True
+    inv9 = pow(9, P - 2, P)
+    sums = [sum(s) % P for s in rows]
+    M = [[(sum(a * b for a, b in zip(rows[i], rows[j])) - inv9 * sums[i] * sums[j]) % P for j in range(k)] for i in range(k)]
+    return len(rref(M, k)) == k
+
+
+# ----------------------------------------------------------------------------- graph
+class BitGraph:
+    def __init__(self, p):
+        self.p, self.h = p, 2 * p
+        self.cubes = list(combinations(range(p), 3))
+        self.labels = [tuple(2 * i + b for i, b in zip(I, bits)) for I in self.cubes for bits in product(range(2), repeat=3)]
+        self.a = [None] * len(self.labels)
+        self.s = [1 << i for i in range(len(self.labels))]
+        self.intern = {}
+        self.source = {(I, bits): 8 * j + k for j, I in enumerate(self.cubes) for k, bits in enumerate(product(range(2), repeat=3))}
+        self.A, self.G = {}, {}
+        self.root, self.centers, self.mix = [], [], []
+
+    def add(self, a, b):
+        if a is None:
+            return b
+        if b is None:
+            return a
+        if a > b:
+            a, b = b, a
+        if (a, b) not in self.intern:
+            require(not self.s[a] & self.s[b], 'support-disjoint addition')
+            self.intern[a, b] = len(self.a)
+            self.a.append([a, b])
+            self.s.append(self.s[a] | self.s[b])
+        return self.intern[a, b]
+
+    def sum(self, xs):
+        xs = [x for x in xs if x is not None]
+        while len(xs) > 1:
+            xs = [self.add(xs[i], xs[i + 1]) if i + 1 < len(xs) else xs[i] for i in range(0, len(xs), 2)]
+        return xs[0] if xs else None
+
+    def module(self, data, inputs):
+        image = list(inputs)
+        n = data['input_count']
+        require(len(image) == n, 'module arity')
+        for pair in data['args'][n:]:
+            image.append(self.add(image[pair[0]], image[pair[1]]))
+        return [image[x] for x in data['roots']]
+
+    def local_channels(self):
+        for I in self.cubes:
+            src = lambda bits: self.source[I, tuple(bits)]
+            edges = {}
+            for ii, jj in combinations(range(3), 2):
+                kk = 3 - ii - jj
+                for a, b in product(range(2), repeat=2):
+                    b0 = [0] * 3
+                    b0[ii], b0[jj] = a, b
+                    b1 = b0[:]
+                    b1[kk] = 1
+                    edges[ii, jj, a, b] = self.add(src(b0), src(b1))
+                self.G[I, I[ii], I[jj], 0] = self.add(edges[ii, jj, 0, 0], edges[ii, jj, 1, 1])
+                self.G[I, I[ii], I[jj], 1] = self.add(edges[ii, jj, 0, 1], edges[ii, jj, 1, 0])
+            for ii in range(3):
+                jj = next(j for j in range(3) if j != ii)
+                for a in range(2):
+                    ids = [edges[(ii, jj, a, b) if ii < jj else (jj, ii, b, a)] for b in range(2)]
+                    self.A[I, I[ii], a] = self.add(*ids)
+
+    def local_l1(self):
+        """L1 local-channel association (eumemic, Claude assistance): the G sums listed in L1_DIAGONAL add the two
+        long diagonals of their cube face, the other G sums and the A sums add two edges; same supports as
+        local_channels, with the nodes created in channel order."""
+        for I in self.cubes:
+            def at(bits):
+                b = [0] * 3
+                for q, x in bits.items():
+                    b[q] = x
+                return self.source[I, tuple(b)]
+
+            def edge(d, fixed):
+                return self.add(at({**fixed, d: 0}), at({**fixed, d: 1}))
+            for j, k in combinations(range(3), 2):
+                r = 3 - j - k
+                for mode in range(2):
+                    if (j, k, mode) in L1_DIAGONAL:
+                        node = self.add(self.add(at({j: 0, k: mode, r: 0}), at({j: 1, k: 1 - mode, r: 1})),
+                                        self.add(at({j: 0, k: mode, r: 1}), at({j: 1, k: 1 - mode, r: 0})))
+                    else:
+                        node = self.add(edge(r, {j: 0, k: mode}), edge(r, {j: 1, k: 1 - mode}))
+                    self.G[I, I[j], I[k], mode] = node
+            for i in range(3):
+                j, k = [q for q in range(3) if q != i]
+                for a in range(2):
+                    self.A[I, I[i], a] = self.add(edge(k, {i: a, j: 0}), edge(k, {i: a, j: 1}))
+
+    def local_design(self, design):
+        """Design-driven local channels (agent-helpers search): every plane channel of every cube is built by the
+        recipe tree of `design` (a list of [plane key, tree] in creation order; a plane key is ['A', i, a] for the
+        sources with selector a at cube position i, or ['G', j, k, m] for the sources with s_j ^ s_k = m; a tree is a
+        3-bit selector (leaf) or a pair of trees).  Equal supports must have equal recipes (checked)."""
+        def members(key):
+            allb = list(product(range(2), repeat=3))
+            if key[0] == 'A':
+                return {b for b in allb if b[key[1]] == key[2]}
+            return {b for b in allb if b[key[1]] ^ b[key[2]] == key[3]}
+        for I in self.cubes:
+            def build(t):
+                if isinstance(t[0], int):
+                    return self.source[I, tuple(t)], {tuple(t)}
+                (a, sa), (b, sb) = build(t[0]), build(t[1])
+                require(not sa & sb, 'design support-disjoint')
+                return self.add(a, b), sa | sb
+            for key, tree in design:
+                node, sup = build(tree)
+                require(sup == members(key), 'design plane support')
+                if key[0] == 'A':
+                    self.A[I, I[key[1]], key[2]] = node
+                else:
+                    self.G[I, I[key[1]], I[key[2]], key[3]] = node
+
+    def finish(self, pair, allbut, merge=False, l1=False, design=None):
+        p = self.p
+        if design is not None:
+            self.local_design(design)
+        else:
+            self.local_l1() if l1 else self.local_channels()
+        Pm, Qm = {}, {}
+        cen = {}
+        for i in range(p):
+            pairs = list(combinations([a for a in range(p) if a != i], 2))
+            for bit in range(2):
+                outs = self.module(pair, [self.A[tuple(sorted((i, *K))), i, bit] for K in pairs])
+                for K, node in zip(pairs, outs):
+                    Pm[tuple(sorted((i, *K))), i, bit] = node
+                if len(outs) == len(pairs) + 1:
+                    # centre-sharing pair module (agent-helpers): the extra root sums all inputs = star(2i+bit)
+                    cen[2 * i + bit] = outs[-1]
+        for i, j in combinations(range(p), 2):
+            others = [a for a in range(p) if a not in (i, j)]
+            for mode in range(2):
+                for k, node in zip(others, self.module(allbut, [self.G[tuple(sorted((i, j, k))), i, j, mode] for k in others])):
+                    Qm[tuple(sorted((i, j, k))), i, j, mode] = node
+        allb = list(product(range(2), repeat=3))
+
+        def emit(I, bl, node, channel):
+            self.root.append(dict(node=node, targets=[self.source[I, b] for b in bl], kind='side', channel=channel))
+        for I in self.cubes:
+            for a in range(2):
+                emit(I, [b for b in allb if b[0] == a], Pm[I, I[0], a], 'face0')
+            for a in range(2):
+                for m12 in range(2):
+                    emit(I, [b for b in allb if b[0] == a and (b[1] ^ b[2]) == m12], Qm[I, I[1], I[2], 1 - m12], 'edge12')
+            if merge:
+                # variant u output merge (eumemic, Claude assistance): u(b0,b1) = face1 + edge01 and
+                # w(b0,b2) = face2 + edge02, each read by two single roots, replace the four single reads
+                u = {(b0, b1): self.add(Pm[I, I[1], b1], Qm[I, I[0], I[1], 1 - (b0 ^ b1)]) for b0 in range(2) for b1 in range(2)}
+                w = {(b0, b2): self.add(Pm[I, I[2], b2], Qm[I, I[0], I[2], 1 - (b0 ^ b2)]) for b0 in range(2) for b2 in range(2)}
+            for b in allb:
+                if merge:
+                    emit(I, [b], u[b[0], b[1]], 'u01')
+                    emit(I, [b], w[b[0], b[2]], 'w02')
+                else:
+                    emit(I, [b], Pm[I, I[1], b[1]], 'face1')
+                    emit(I, [b], Qm[I, I[0], I[1], 1 - (b[0] ^ b[1])], 'edge01')
+                    emit(I, [b], Pm[I, I[2], b[2]], 'face2')
+                    emit(I, [b], Qm[I, I[0], I[2], 1 - (b[0] ^ b[2])], 'edge02')
+                emit(I, [b], self.source[I, (b[0], 1 - b[1], 1 - b[2])], 'partner')
+            # partner-pair source mixing: in each parity class the pair with selector a on cube pair 0
+            # (carrier = smaller bits, passive = its partner) is delivered to the opposite pair of the class.
+            for par in range(2):
+                for a in range(2):
+                    pair_ = sorted(b for b in allb if sum(b) % 2 == par and b[0] == a)
+                    recv = sorted(b for b in allb if sum(b) % 2 == par and b[0] == 1 - a)
+                    self.mix.append(dict(carrier=self.source[I, pair_[0]], passive=self.source[I, pair_[1]],
+                                         receivers=[self.source[I, r] for r in recv]))
+        for i in range(p):
+            for e in range(2):
+                if 2 * i + e in cen:
+                    self.centers.append(cen[2 * i + e])
+                else:
+                    self.centers.append(self.sum(self.A[I, i, e] for I in self.cubes if i in I))
+        for coordinate, node in enumerate(self.centers):
+            self.root.append(dict(node=node, targets=[t for t, lab in enumerate(self.labels) if coordinate in lab],
+                                  kind='center', coordinate=coordinate))
+        return dict(p=p, h=self.h, v=len(self.labels), labels=[list(l) for l in self.labels], args=self.a,
+                    roots=self.root, partner_mix=self.mix)
+
+
+def check_decoder(g):
+    v, args = g['v'], g['args']
+    sup = [1 << i for i in range(v)] + [0] * (len(args) - v)
+    for x in range(v, len(args)):
+        a, b = args[x]
+        require(not sup[a] & sup[b], 'disjoint supports')
+        sup[x] = sup[a] | sup[b]
+    acc = [0] * v
+    for r in g['roots']:
+        for t in r['targets']:
+            acc[t] ^= sup[r['node']]
+    for mx in g['partner_mix']:
+        for t in mx['receivers']:
+            acc[t] ^= (1 << mx['carrier']) | (1 << mx['passive'])
+    return sum(acc[t] != 1 << t for t in range(v))
+
+
+# ----------------------------------------------------------------------------- matching
+def hopcroft_karp(adj, nleft, nright):
+    INF = 1 << 30
+    mL, mR = [-1] * nleft, [-1] * nright
+    while True:
+        dist = [INF] * nleft
+        dq = deque(u for u in range(nleft) if mL[u] < 0)
+        for u in dq:
+            dist[u] = 0
+        found = False
+        while dq:
+            u = dq.popleft()
+            for w in adj[u]:
+                m = mR[w]
+                if m < 0:
+                    found = True
+                elif dist[m] == INF:
+                    dist[m] = dist[u] + 1
+                    dq.append(m)
+        if not found:
+            return mL
+        it = [0] * nleft
+        for u0 in range(nleft):
+            if mL[u0] >= 0:
+                continue
+            stack = [u0]
+            while stack:
+                u = stack[-1]
+                if it[u] < len(adj[u]):
+                    w = adj[u][it[u]]
+                    it[u] += 1
+                    m = mR[w]
+                    if m < 0:
+                        ws = w
+                        for uu in reversed(stack):
+                            prev = mL[uu]
+                            mL[uu], mR[ws] = ws, uu
+                            ws = prev
+                        break
+                    if dist[m] == dist[u] + 1:
+                        stack.append(m)
+                else:
+                    dist[u] = INF
+                    stack.pop()
+
+
+# ----------------------------------------------------------------------------- compiler
+def compile_word(g, frozen=None, plain_k=PLAIN, log=lambda *a: None):
+    h, v = g['h'], g['v']
+    geo = Geometry(h, [tuple(l) for l in g['labels']])
+    args = [None] + [None if a is None else [x + 1 for x in a] for a in g['args']]  # node 0 reserved
+    roots = [dict(r, node=r['node'] + 1) for r in g['roots']]
+    n, q = len(args), len(roots)
+    sup = [0] * n
+    for i in range(v):
+        sup[i + 1] = 1 << i
+    spans = [0] * n
+    for i in range(v):
+        spans[i + 1] = geo.src[i]
+    for x in range(v + 1, n):
+        a, b = args[x]
+        spans[x] = geo.join(spans[a], spans[b])
+        sup[x] = sup[a] | sup[b]
+    rframe, rann, ell = [], [], 0
+    Y, targetH = [0] * v, Counter()
+    for r in roots:
+        x = r['node']
+        if r['kind'] == 'center':
+            U = spans[x]; A = geo.perp(U); ell += geo.dim(U)
+        else:
+            A = geo.join_many(geo.tcov[t] for t in r['targets']); U = geo.perp(A)
+            for t in r['targets']:
+                require(geo.contained(Y[t], U), 'target retreat')
+                targetH[geo.dim(U) - geo.dim(Y[t])] += 1
+                Y[t] = U
+        require(geo.contained(spans[x], U), 'root physical compatibility')
+        rframe.append(U); rann.append(A)
+    for t in range(v):
+        require(geo.contained(Y[t], geo.perp(geo.tcov[t])), 'target cap')
+        targetH[h - 1 - geo.dim(Y[t])] += 1
+    active, todo = set(range(1, v + 1)), [r['node'] for r in roots]
+    while todo:
+        x = todo.pop()
+        if x not in active:
+            active.add(x)
+            if args[x]:
+                todo.extend(args[x])
+    succ0, cons = [[] for _ in args], [[] for _ in args]
+    for x in sorted(active):
+        if args[x]:
+            for y in args[x]:
+                succ0[y].append(x)
+    for j, r in enumerate(roots):
+        cons[r['node']].append(rann[j])
+    preann, initial = [0] * n, [0] * n
+    for x in sorted(active, reverse=True):
+        preann[x] = geo.join_many(cons[x] + [preann[y] for y in succ0[x]])
+        cover = 0
+        s = sup[x]
+        while s:
+            b = s & -s; s ^= b
+            for j in g['labels'][b.bit_length() - 1]:
+                cover |= 1 << j
+        initial[x] = geo.join_many([preann[x]] + [geo.coord[j] for j in range(h) if not cover >> j & 1])
+    order = sorted(active, key=lambda x: (h - geo.dim(initial[x]), x))
+    position = {x: i for i, x in enumerate(order)}
+    uses, usevalue, usetarget, useann, usecode = [[] for _ in args], [], [], [], []
+    for x in order:
+        if args[x]:
+            for j, y in enumerate(args[x]):
+                uses[y].append(len(usevalue)); usevalue.append(y); usetarget.append(x); useann.append(initial[x]); usecode.append(['op', x - 1, j])
+    for j, r in enumerate(roots):
+        x = r['node']
+        uses[x].append(len(usevalue)); usevalue.append(x); usetarget.append(n + j); useann.append(rann[j]); usecode.append(['root', j])
+    donors = [x for x in order if args[x]]
+    code_index = {tuple(c): u for u, c in enumerate(usecode)}
+    if frozen is not None:
+        arcs = {d + 1: code_index[tuple(c)] for d, c in frozen}
+    else:
+        dindex = {x: i for i, x in enumerate(donors)}
+        adj = [[] for _ in donors]
+        for x in donors:
+            for y in args[x]:
+                for u in uses[y]:
+                    t = usetarget[u]
+                    if t == x or (t < n and position[t] <= position[x]):
+                        continue
+                    if geo.contained(useann[u], initial[x]):
+                        adj[dindex[x]].append(u)
+        mL = hopcroft_karp(adj, len(donors), len(usevalue))
+        arcs = {donors[i]: u for i, u in enumerate(mL) if u >= 0}
+    for x, u in arcs.items():
+        t = usetarget[u]
+        require(usevalue[u] in args[x] and (t >= n or position[t] > position[x]), 'arc order')
+        require(geo.contained(useann[u], initial[x]), 'arc frame')
+    succ, direct = [[] for _ in args], [[] for _ in args]
+    for x in order:
+        if args[x]:
+            for y in args[x]:
+                succ[y].append(x)
+    for j, r in enumerate(roots):
+        direct[r['node']].append(rann[j])
+    for x, u in arcs.items():
+        t = usetarget[u]
+        (succ[x].append(t) if t < n else direct[x].append(rann[t - n]))
+    ann, rank = [0] * n, [0] * n
+    for x in reversed(order):
+        ann[x] = geo.join_many(direct[x] + [ann[y] for y in succ[x]])
+        rank[x] = h - geo.dim(ann[x])
+        require(geo.contained(ann[x], geo.perp(spans[x])), 'span inside frame')
+    # plain frames span(n): leaves and small additions, closed under operands; a linked donor must be plain and
+    # its span must lie in the plain target's span
+    cand = set(x for x in active if not args[x])
+    for x in sorted(active):
+        if args[x] and geo.dim(spans[x]) <= plain_k and all(y in cand for y in args[x]):
+            cand.add(x)
+    arcin, users = defaultdict(list), defaultdict(list)
+    for x, u in arcs.items():
+        if usetarget[u] < n:
+            arcin[usetarget[u]].append(x)
+    for x in active:
+        if args[x]:
+            for y in args[x]:
+                users[y].append(x)
+    changed = True
+    while changed:
+        changed = False
+        for t in sorted(cand):
+            if t in cand and any(x not in cand or not geo.contained(spans[x], spans[t]) for x in arcin[t]):
+                cand.discard(t); changed = True
+                st = [t]
+                while st:
+                    z = st.pop()
+                    for w in users[z]:
+                        if w in cand:
+                            cand.discard(w); st.append(w)
+    plain = sorted(cand)
+    for x in plain:
+        ann[x] = geo.perp(spans[x]); rank[x] = h - geo.dim(ann[x])
+    H = Counter()
+    for x in order:
+        r, deg = rank[x], len(uses[x])
+        require(deg > 0, 'unused node')
+        H[r] += deg - 1
+        if args[x]:
+            H[h - r] += 1
+            for y in args[x]:
+                require(geo.contained(ann[x], ann[y]), 'operand nesting')
+                H[r - rank[y]] += 1
+        else:
+            H[1] += 1; H[r - 1] += 1
+    for j, root in enumerate(roots):
+        x = root['node']; r = rank[x]; rt = geo.dim(rframe[j])
+        require(r <= rt, 'root climb')
+        if root['kind'] == 'center':
+            require(r == rt, 'centre frame')
+            H[r] += 1; H[h - r] += 1
+        else:
+            H[rt - r] += 1; H[h - rt] += 1
+    for x, u in arcs.items():
+        val, t = usevalue[u], usetarget[u]
+        rv, rd = rank[val], rank[x]
+        rt = rank[t] if t < n else geo.dim(rframe[t - n])
+        require(rt >= rd >= rv, 'arc ranks')
+        H[h - rd] -= 1; H[rv] -= 1; H[rt - rv] -= 1; H[rt - rd] += 1
+    require(min(H.values()) >= 0, 'nonnegative ledger')
+    R = len(donors) + q - len(arcs)
+    require(sum(r * c for r, c in H.items()) == h * R + ell, 'mass identity')
+    prof = dict(h=h, v=v, R=R, q=q, c=len(donors), matched=len(arcs), loss=ell, plain=len(plain))
+    wit = dict(geo=geo, args=args, roots=roots, n=n, order=order, arcs=arcs, ann=ann, rank=rank, uses=uses,
+               usevalue=usevalue, usetarget=usetarget, usecode=usecode, rframe=rframe, rann=rann, spans=spans,
+               plain=plain, H=H, targetH=targetH)
+    return prof, wit
+
+
+def nondeg_id(geo, f, cache):
+    if f not in cache:
+        cache[f] = gram_nondegenerate_frame(list(geo.T.rows[f]), geo.h)
+    return cache[f]
+
+
+def select_gauges(g, prof, wit, trial_a=0.00065):
+    """PR #144 gauges.select, exactly, plus the bit G-nondegeneracy filter on sigma."""
+    geo = wit['geo']; h, v = prof['h'], prof['v']
+    args, roots, n, order, ann, arcs = wit['args'], wit['roots'], wit['n'], wit['order'], wit['ann'], wit['arcs']
+    usevalue, usetarget = wit['usevalue'], wit['usetarget']
+    incoming = set(arcs.values())
+    uses, opuse, rootuse = [[] for _ in args], {}, {}
+    for u, (val, t) in enumerate(zip(usevalue, usetarget)):
+        uses[val].append(u)
+        if t < n:
+            opuse[t, 0 if args[t][0] == val else 1] = u
+        else:
+            rootuse[t - n] = u
+    assign, sources, ops, R = {}, {}, [], 0
+    for x in order:
+        if args[x]:
+            aa, bb = args[x]
+            dest, control = assign[opuse[x, 0]], assign[opuse[x, 1]]
+            if x in arcs:
+                u = arcs[x]
+                if usevalue[u] == aa:
+                    dest, control = control, dest
+                require(u not in assign, 'arc use assigned once')
+                assign[u] = control
+            ops.append((dest, control, x))
+        else:
+            dest = R; R += 1; sources[x] = dest
+        free = [u for u in uses[x] if u not in incoming]
+        require(free, 'free use')
+        for j, u in enumerate(free):
+            if j == 0:
+                assign[u] = dest
+            else:
+                t = R; R += 1; assign[u] = t; ops.append((t, dest, x))
+    require(R == prof['R'], 'role count')
+    rootroles = [assign[rootuse[j]] for j in range(len(roots))]
+    prev, pred, first = [-1] * R, [], [None] * R
+    for i, (a, b, x) in enumerate(ops):
+        pred.append((prev[a], prev[b])); prev[a] = prev[b] = i
+        if first[a] is None:
+            first[a] = x
+        if first[b] is None:
+            first[b] = x
+    stack = [prev[s] for r, s in zip(roots, rootroles) if r['kind'] == 'center' and prev[s] >= 0]
+    phase = set()
+    while stack:
+        i = stack.pop()
+        if i not in phase:
+            phase.add(i); stack.extend(j for j in pred[i] if j >= 0)
+    touched = set(sources.values())
+    for i in phase:
+        touched.update(ops[i][:2])
+    co = [0] * R
+    for r, s in zip(roots, rootroles):
+        co[s] |= sum(1 << t for t in r['targets'])
+    for a, b, x in reversed(ops):
+        co[b] |= co[a]
+    limit = [None] * v
+    for r in roots:
+        if r['kind'] != 'center':
+            A = geo.join_many(geo.tcov[t] for t in r['targets'])
+            for t in r['targets']:
+                if limit[t] is None:
+                    limit[t] = A
+    for t in range(v):
+        if limit[t] is None:
+            limit[t] = geo.tcov[t]
+    H = Counter(wit['H'])
+    gauges, selected, cache = Counter(), [], {}
+    cands = sorted((s for s in range(R) if s not in touched and first[s] is not None),
+                   key=lambda s: (geo.dim(ann[first[s]]), bin(co[s]).count('1'), s))
+
+    def excess(t):
+        return t * math.expm1(trial_a * math.log(3 * h / t)) if t else 0.
+    for s in cands:
+        A, targets, bits = ann[first[s]], [], co[s]
+        while bits:
+            low = bits & -bits; t = low.bit_length() - 1; bits ^= low; targets.append(t)
+            A = geo.join(A, limit[t])
+            if geo.dim(A) == h:
+                break
+        if geo.dim(A) == h:
+            continue
+        r, d = h - geo.dim(ann[first[s]]), h - geo.dim(A)
+        delta = 3 * (excess(r - d) - excess(r)) + excess(3 * d)
+        delta += 3 * math.fsum(excess(d) + excess(h - geo.dim(limit[t]) - d) - excess(h - geo.dim(limit[t])) for t in targets)
+        if delta >= -1e-12 or not nondeg_id(geo, geo.perp(A), cache):
+            continue
+        H[r] -= 1; H[r - d] += 1; gauges[d] += 1
+        require(H[r] >= 0, 'gauge ledger')
+        for t in targets:
+            limit[t] = A
+        selected.append(dict(role=s, first=first[s] - 1, targets=targets, dim=d, ann=A))
+    Yh, cur = Counter(), [0] * v
+    for z in reversed(selected):
+        U = geo.perp(z['ann'])
+        for t in z['targets']:
+            require(geo.contained(cur[t], U), 'gauge target chain')
+            Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U
+    for r in roots:
+        if r['kind'] != 'center':
+            U = geo.perp(geo.join_many(geo.tcov[t] for t in r['targets']))
+            for t in r['targets']:
+                require(geo.contained(cur[t], U), 'side target chain')
+                Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U
+    for t in range(v):
+        Yh[h - 1 - geo.dim(cur[t])] += 1
+    word = dict(ops=[[a, b, x - 1] for a, b, x in ops], sources={str(x - 1): s for x, s in sources.items()},
+                rootroles=rootroles, phase1=sorted(phase), gauges=[{k: z[k] for k in ('role', 'first', 'targets', 'dim')} for z in selected],
+                _gauge_ann=[z['ann'] for z in selected])
+    return gauges, H, Yh, word
+
+
+def profile(prof, gauges, H, Y):
+    h, v, R, ell = prof['h'], prof['v'], prof['R'], prof['loss']
+    m, W = 3 * h, 2 * v + R
+    source = Counter({1: v, h - 4: v // 2, 2: v // 2, h - 2: v // 2})
+    C = Counter()
+    for part in (H, source, Y):
+        for r, c in part.items():
+            if r and c:
+                C[r] += 3 * c
+    for d, c in gauges.items():
+        C[3 * d] += c
+    C[2] += 2 * v
+    mass = sum(r * c for r, c in C.items())
+    require(W * m - mass == 2 * v - 3 * ell, 'shared-core telescoping deficit')
+    srt = lambda c: {str(k): c[k] for k in sorted(c) if c[k]}
+    return dict(h=h, v=v, R=R, c=prof['c'], q=prof['q'], matched=prof['matched'], loss=ell, plain_frames=prof['plain'],
+                m=m, W_per_vertex=W, rank_per_vertex=mass, deficit_per_vertex=W * m - mass,
+                selected_roles=sum(gauges.values()), selected_rank_histogram=srt(gauges),
+                remaining_internal_histogram=srt(H), source_data_histogram=srt(source), target_data_histogram=srt(Y),
+                child_histogram=srt(C), maxchild=max(C))
+
+
+def float_root(child, W, m):
+    items = [(int(t), c) for t, c in child.items()]
+    lo, hi = 0., .1
+    for _ in range(80):
+        a = (lo + hi) / 2
+        if math.fsum(c * (t / m) ** (1 - a) for t, c in items) < W:
+            lo = a
+        else:
+            hi = a
+    return lo
+
+
+def ratrec(r):
+    """Rational reconstruction a/b of a residue mod P with |a|, b < sqrt(P/2)."""
+    r %= P
+    if r == 0:
+        return 0, 1
+    bound = math.isqrt(P // 2)
+    r0, r1, s0, s1 = P, r, 0, 1
+    while r1 > bound:
+        qq = r0 // r1
+        r0, r1 = r1, r0 - qq * r1
+        s0, s1 = s1, s0 - qq * s1
+    require(abs(s1) <= bound and s1 != 0, 'rational reconstruction')
+    a, b = (r1, s1) if s1 > 0 else (-r1, -s1)
+    require((a - r * b) % P == 0, 'reconstruction residue')
+    return a, b
+
+
+def primitive(row):
+    from fractions import Fraction
+    fr = [Fraction(*ratrec(x)) for x in row]
+    den = 1
+    for f in fr:
+        den = den * f.denominator // math.gcd(den, f.denominator)
+    ints = [int(f * den) for f in fr]
+    gg = 0
+    for x in ints:
+        gg = math.gcd(gg, abs(x))
+    ints = [x // gg for x in ints] if gg else ints
+    first = next((x for x in ints if x), 1)
+    return [-x for x in ints] if first < 0 else ints
+
+
+def frame_record(geo, ann_id):
+    """Exact integer description of the frame perp(ann): 'a' = integer annihilator rows (frame = common kernel)
+    when codim <= dim, else 'b' = integer basis rows. Both are primitive rows of the rational RREF."""
+    h = geo.h
+    A = geo.T.rows[ann_id]
+    codim = len(A)
+    if codim <= h - codim:
+        rows = [primitive(r) for r in A]
+        return dict(dim=h - codim, a=rows)
+    B = geo.T.rows[geo.perp(ann_id)]
+    return dict(dim=h - codim, b=[primitive(r) for r in B])
+
+
+def dumps(obj):
+    return json.dumps(obj, sort_keys=True, separators=(',', ':')) + '\n'
+
+
+def build(p, frozen_arcs=None, log=print):
+    mod = json.loads((HERE / 'data' / MODULES[p]).read_text())
+    abo = pinned_all_but_one(QMODULES[p], p - 2) if p in QMODULES else all_but_one(p - 2)
+    dpath = HERE / 'data' / ('local_design_p%d.json' % p)
+    design = json.loads(dpath.read_text())['design'] if dpath.exists() else None
+    g = BitGraph(p).finish(mod, abo, merge=p == 12, l1=p == 12, design=design)
+    require(check_decoder(g) == 0, 'mod-2 decoder identity')
+    t0 = time.time()
+    prof, wit = compile_word(g, frozen=frozen_arcs)
+    log('compiled p=%d in %.1fs: R=%d arcs=%d plain=%d' % (p, time.time() - t0, prof['R'], prof['matched'], prof['plain']))
+    gauges, H, Y, word = select_gauges(g, prof, wit)
+    prf = profile(prof, gauges, H, Y)
+    arcs = sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items())
+    cache = {}
+    geo = wit['geo']
+    deg = sum(1 for x in wit['order'] if not nondeg_id(geo, geo.perp(wit['ann'][x]), cache))
+    deg += sum(1 for U in wit['rframe'] if not nondeg_id(geo, U, cache))
+    require(deg == 0, 'G-nondegenerate node and root frames')
+    out = dict(graph=dict(p=p, h=g['h'], v=g['v'], labels=g['labels'], args=g['args'], roots=g['roots'],
+                          partner_mix=g['partner_mix'], pair_module_sha256=hashlib.sha256((HERE / 'data' / MODULES[p]).read_bytes()).hexdigest()),
+               compile=dict(plain_threshold=PLAIN, order=[x - 1 for x in wit['order']], plain=[x - 1 for x in wit['plain']], arcs=arcs),
+               word={k: v for k, v in word.items() if not k.startswith('_')})
+    exp = export(p, g, prof, wit, word, prf)
+    return out, prf, arcs, exp
+
+
+def export(p, g, prof, wit, word, prf):
+    """Plain-JSON gate files: graph, word (selection.json shape), exact frames, partial-K chronology."""
+    geo, h, v = wit['geo'], g['h'], g['v']
+    n, roots = wit['n'], wit['roots']
+    ann = wit['ann']
+    frames = {}
+
+    def fid(a):
+        if a not in frames:
+            frames[a] = None
+        return a
+    node_frame = {str(x - 1): fid(ann[x]) for x in wit['order']}
+    root_frame = [fid(a) for a in wit['rann']]
+    gauges = []
+    for z, A in zip(word['gauges'], word['_gauge_ann']):
+        gauges.append(dict(z, frame=fid(A)))
+    lab = g['labels']
+    src_ann = [fid(geo.perp(geo.src[i])) for i in range(v)]
+    full = fid(0)
+    level2 = {}
+    for j, r in enumerate(g['roots']):
+        if r['kind'] == 'side' and len(r['targets']) == 2:
+            level2[tuple(sorted(r['targets']))] = j
+    kchron = []
+    for mx in g['partner_mix']:
+        c, d = mx['carrier'], mx['passive']
+        mixf = fid(geo.perp(geo.join(geo.src[c], geo.src[d])))
+        j = level2[tuple(sorted(mx['receivers']))]
+        capf = root_frame[j]
+        require(geo.contained(capf, mixf), 'mix frame inside receivers cap')
+        kchron.append(dict(carrier=c, passive=d, receivers=mx['receivers'], mix_frame=mixf, deliver_frame=capf,
+                           deliver_after_root=j, undo_frame=full,
+                           carrier_chain=[src_ann[c], mixf, capf, full], passive_chain=[src_ann[d], mixf, full],
+                           carrier_ranks=[1, h - 4, 2], passive_ranks=[1, h - 2]))
+    table = {str(a): frame_record(geo, a) for a in sorted(frames)}
+    conv = dict(target_covector='3*chi_T - 1 (target cap = {u : (3 chi_T - 1).u = 0} = H0-orthogonal complement of chi_T)',
+                gram='G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested for G',
+                frame_ids='frame id = id of the canonical annihilator; record "a" lists integer annihilator rows (frame ='
+                          ' common kernel), record "b" lists integer basis rows; id 0 (empty "a") is the full space Q^h',
+                ops='[dest, control, node]: dest ^= control at the frame of node (copies: dest is the fresh role)',
+                nodes='zero-based graph nodes; nodes < v are the source leaves (port index)')
+    graph = dict(p=p, h=h, v=v, labels=g['labels'], args=g['args'],
+                 roots=[dict(r, coefficient=1) for r in g['roots']], partner_mix=g['partner_mix'],
+                 decoder='mod 2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T;'
+                         ' side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T;'
+                         ' equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} x_S')
+    wordj = dict(ops=word['ops'], sources=word['sources'], rootroles=word['rootroles'], phase1=word['phase1'],
+                 gauges=gauges, order=[x - 1 for x in wit['order']], arcs=sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items()),
+                 plain=[x - 1 for x in wit['plain']], node_frame=node_frame, root_frame=root_frame,
+                 source_frame=src_ann, full_frame=full, conventions=conv,
+                 schedule='old-value reads of non-gauged roles (frame 0); V injections at <chi_S>; ops in order (phase1 ops'
+                          ' are those listed); centre copies read at 0; gauged old-value reads at their gauge frames'
+                          ' (ascending per target); side root reads in root order; partial-K deliveries right after'
+                          ' root deliver_after_root; undo at full frame; inverse ops; V removal')
+    return dict(graph=graph, word=wordj, frames=dict(h=h, P_used_for_ranks='2^127-1', conventions=conv, frames=table),
+                kchron=dict(h=h, entries=kchron, conventions=conv))
+
+
+def nested_prefix(n):
+    """Nested-prefix all-but-one module (QMOD lane; eumemic, Claude assistance): prefix p_{k+1} = p_k + x_k, suffix
+    s_k = x_k + s_{k+1}; y_0 = s_1, y_{n-1} = p_{n-1}, y_{i+1} = p_i + (x_i + s_{i+2}). Each prefix is used twice with
+    nested supports, which gives the carrier matching more links than the balanced tree. Contract-checked. It is the
+    seed of the pinned p = 12 module data/qmod_p12.json."""
+    args = [None] * n
+
+    def add(a, b):
+        args.append([a, b])
+        return len(args) - 1
+    pre = {1: 0}
+    for k in range(1, n - 1):
+        pre[k + 1] = add(pre[k], k)
+    suf = {n - 1: n - 1}
+    for k in range(n - 2, 0, -1):
+        suf[k] = add(k, suf[k + 1])
+    roots = [None] * n
+    roots[0], roots[n - 1] = suf[1], pre[n - 1]
+    roots[1] = add(0, suf[2])
+    for i in range(1, n - 2):
+        roots[i + 1] = add(pre[i], add(i, suf[i + 2]))
+    support = []
+    for x, a in enumerate(args):
+        if a is None:
+            support.append(1 << x)
+        else:
+            require(0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'nested prefix disjoint')
+            support.append(support[a[0]] | support[a[1]])
+    full = (1 << n) - 1
+    require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'nested prefix all-but-one roots')
+    return dict(input_count=n, args=args, roots=roots)
+
+
+def pinned_all_but_one(name, n):
+    """Pinned all-but-one module {input_count, args, roots} in data/ (eumemic, Claude assistance). The p = 12
+    module was annealed from nested_prefix(10) by split-function moves, scored by the p = 12 bit word.
+    Contract-checked: disjoint supports, root i sums every input but i."""
+    mod = json.loads((HERE / 'data' / name).read_text())
+    args, roots = mod['args'], mod['roots']
+    require(mod['input_count'] == n == len(roots) and args[:n] == [None] * n, 'pinned all-but-one arity')
+    support = [1 << x for x in range(n)]
+    for x, a in enumerate(args[n:], n):
+        require(a and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'pinned all-but-one disjoint')
+        support.append(support[a[0]] | support[a[1]])
+    full = (1 << n) - 1
+    require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'pinned all-but-one roots')
+    return dict(input_count=n, args=args, roots=roots)
+
+
+def all_but_one(n):
+    """PR #144 modules.all_but_one (balanced binary tree upward sums and complementary downward sums)."""
+    args, support = [None] * n, [1 << i for i in range(n)]
+    by = {s: i for i, s in enumerate(support)}
+
+    def add(a, b):
+        if a is None:
+            return b
+        if b is None:
+            return a
+        s = support[a] | support[b]
+        if s not in by:
+            by[s] = len(args); args.append([a, b]); support.append(s)
+        return by[s]
+
+    def tree(lo, hi):
+        if hi - lo == 1:
+            return (lo, None, None)
+        mid = (lo + hi) // 2
+        L, Rr = tree(lo, mid), tree(mid, hi)
+        return (add(L[0], Rr[0]), L, Rr)
+    roots = [None] * n
+
+    def walk(t, outside):
+        x, L, Rr = t
+        if L is None:
+            roots[x] = outside
+            return
+        walk(L, add(outside, Rr[0])); walk(Rr, add(outside, L[0]))
+    walk(tree(0, n), None)
+    active, stack = set(range(n)), list(roots)
+    while stack:
+        x = stack.pop()
+        if x not in active:
+            active.add(x)
+            if args[x] is not None:
+                stack.extend(args[x])
+    ids = sorted(active); ren = {x: i for i, x in enumerate(ids)}
+    return dict(input_count=n, args=[None if args[x] is None else [ren[y] for y in args[x]] for x in ids], roots=[ren[x] for x in roots])
+
+
+def main():
+    require(not sys.flags.optimize, 'run without -O')
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--p', type=int, default=12)
+    ap.add_argument('--out', type=Path, default=HERE / 'out')
+    ap.add_argument('--check', action='store_true', help='regenerate from frozen arcs and compare byte-identically')
+    ap.add_argument('--solve-matching', action='store_true', help='recompute the carrier matching (Hopcroft-Karp)')
+    a = ap.parse_args()
+    a.out.mkdir(parents=True, exist_ok=True)
+    arcs_path = HERE / 'data' / ('arcs_p%d.json' % a.p)
+    frozen = None if a.solve_matching or not arcs_path.exists() else json.loads(arcs_path.read_text())
+    out, prf, arcs, exp = build(a.p, frozen)
+    root = float_root(prf['child_histogram'], prf['W_per_vertex'], prf['m'])
+    word_bytes = gzip.compress(dumps(out).encode(), mtime=0)
+    prof_bytes = dumps(prf).encode()
+    names = {'word_p%d.json.gz' % a.p: word_bytes, 'profile_p%d.json' % a.p: prof_bytes}
+    for k, obj in exp.items():
+        names['%s_p%d.json' % (k, a.p)] = dumps(obj).encode()
+    if a.check:
+        for name, data in names.items():
+            old = (a.out / name).read_bytes()
+            if name.endswith('.gz'):  # gzip bytes depend on the zlib build; compare the compressed content
+                old, data = gzip.decompress(old), gzip.decompress(data)
+            require(old == data, 'byte-identical regeneration of ' + name)
+        require(frozen is not None, 'frozen arcs present')
+        print('PASS p=%d: word and profile regenerate byte-identically (sha256 %s, %s)' % (
+            a.p, hashlib.sha256(word_bytes).hexdigest()[:16], hashlib.sha256(prof_bytes).hexdigest()[:16]))
+    else:
+        for name, data in names.items():
+            (a.out / name).write_bytes(data)
+        if frozen is None:
+            arcs_path.write_text(dumps(arcs))
+        print('wrote p=%d: R=%d R/v=%.3f loss=%d deficit=%d W=%d gauges=%d float a_b=%.7e' % (
+            a.p, prf['R'], prf['R'] / prf['v'], prf['loss'], prf['deficit_per_vertex'], prf['W_per_vertex'],
+            prf['selected_roles'], root))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/regenerate.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/regenerate.py
new file mode 100644
index 0000000000..aacaae266f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/producer/regenerate.py
@@ -0,0 +1,38 @@
+#!/usr/bin/env python3
+"""Rebuild gen4bit/selected/bit from the generator and the two physical-layer producers, and compare.
+
+    python3 -B gen4bit/producer/regenerate.py --work /new/scratch/dir      (about 2 minutes)
+
+1. paired_cube_bit_word.py --p 12 (frozen arcs data/arcs_p12.json) writes the virtual word;
+2. make_physical.py adds the compensated reuse pairs and late recipient reads;
+3. descent.py moves operation frames (PR200 physical-layer rules) and writes the physical word.
+The five pinned files must be reproduced exactly (gzip members compared after decompression).
+This is provenance only: verify.py admits the pinned files themselves and never runs a producer.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+import argparse, gzip, shutil, subprocess, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+BIT = HERE.parent
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__); ap.add_argument('--work', type=Path, required=True)
+    a = ap.parse_args(); work = a.work.resolve(); assert not work.exists(), 'work dir must be new'
+    raw, phys, pkg, final = work/'raw', work/'phys', work/'pkg', work/'final'
+    py = [sys.executable, '-B']
+    subprocess.run(py + [str(HERE/'paired_cube_bit_word.py'), '--p', '12', '--out', str(raw)], check=True)
+    subprocess.run(py + [str(HERE/'make_physical.py'), '--src', str(raw), '--out', str(phys)], check=True)
+    (pkg/'selected').mkdir(parents=True)
+    shutil.copytree(BIT/'bit', pkg/'bit'); shutil.copytree(BIT/'references', pkg/'references')
+    shutil.copytree(phys, pkg/'selected/bit')
+    subprocess.run(py + [str(HERE/'descent.py'), str(pkg), str(final)], check=True)
+    pinned = BIT/'selected/bit'
+    for name in ('graph_p12.json', 'kchron_p12.json', 'profile_p12.json'):
+        assert (final/name).read_bytes() == (pinned/name).read_bytes(), name
+    for name in ('word_p12.json.gz', 'frames_p12.json.gz'):
+        assert gzip.decompress((final/name).read_bytes()) == gzip.decompress((pinned/name).read_bytes()), name
+    print('PASS gen4 regeneration: all five pinned bit-word files reproduced exactly')
+
+if __name__ == '__main__':
+    main()
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/references/pr168-v4/SOURCE.json b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/references/pr168-v4/SOURCE.json
new file mode 100644
index 0000000000..c57edcae25
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/references/pr168-v4/SOURCE.json
@@ -0,0 +1,20 @@
+{
+  "commit": "4a3c769e5c5430e7114c4d3e099ff34664677f17",
+  "files": {
+    "certificates/paired-cube-network.json": "05b253a21dc526b6039f56d1068162a19a8a4f29291ad94eb892656b88e9142d",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "research/paired-cube-bit/check_paired_cube_bit.py": "4d7c86cd999a1519e0dfb6dcf33a8f26e442a353c3665a0f06881216a260fbf3",
+    "scripts/certify.py": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e",
+    "scripts/paired_cube/__init__.py": "b5fb17c79fd41a75c0648e7a5f99076f9f42a619857d5e34e71699bf00ef0c91",
+    "scripts/paired_cube/closure.py": "e4b3086f4b5663297fe06f4646e1349f10d8647997989f17eef6ec4e84aec693",
+    "scripts/paired_cube/frames.py": "7d897418dbfee47de0723ea4983098a982610ccba45e1bac9000a79626d8421c",
+    "scripts/paired_cube/gauges.py": "8a501c66e1330f054e0e11a35e9321d2deea7b51cd03ca56b6a41765e43fe061",
+    "scripts/paired_cube/graph.py": "d10478ba509c7d8abcefcaaf7c5e0b580b9cd9cbe7777b3e49b2fe24620985c8",
+    "scripts/paired_cube/modules.py": "6c134f3d24c6cd9aca03763050aaf600005c126c09b35ac0ff5f040e0e29db87",
+    "scripts/paired_cube/verify.py": "b1eb42a91381ae031d97879f7c43e6c00fc4787e132ed60eb3e124994bdb7d35",
+    "scripts/paired_cube_physical.py": "9c9ea1ea29e551ab6116d7c8ca09f4703ff9e2fa102032d5055327fde07ba319"
+  },
+  "pr": 168,
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "scope": "Byte-identical copies of the PR168 v4 files this package executes or pins (compiler frames/closure/gauges/graph/modules, physical checkers, package bit checker, parent certificate, frame theorem note), so the package is self-contained on main."
+}
diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py
new file mode 100644
index 0000000000..69d535a6c2
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py
@@ -0,0 +1,465 @@
+#!/usr/bin/env python3
+"""Standalone checker for subset-port bit words with broadcast roots (paired-cube bit word with partner-pair
+source mixing).  Standard library only; independent of the generator (own exact integer linear algebra, own
+register simulation).  Refuses to run under python -O.
+
+Inputs (plain JSON written by paired_cube_bit_word.py): graph_pP.json, word_pP.json, frames_pP.json,
+kchron_pP.json, profile_pP.json.  Checks:
+  1. exact frames: every frame record (integer annihilator rows 'a' or integer basis rows 'b') is completed to
+     the other representation by exact integer elimination; A.B^T = 0 exactly and rank A + rank B = h;
+  2. the mod-2 decoder: supports of all additions are disjoint; for every target the deliveries (star roots,
+     side roots, partner singles, partner-pair sums) XOR to {T}; stars read are exactly the c in T and the
+     side part is exactly sum_{|S cap T|=1} x_S;
+  3. geometry: source frames are the lines <chi_S>; side root frames lie in every receiver's cap
+     ker(3 chi_T - 1) and equal the common cap of the group; centre frames are the star spans; the frame of
+     every addition contains its operands' frames; every root node's frame lies in its root frame;
+  4. every role chain (start -> each op frame -> root frame -> full) is nested, including gauged starts
+     (sigma inside the first op frame, gauged roles untouched in phase one); every target chain (gauge reads
+     ascending, side root caps in root order, partner-pair delivery at the level-2 cap, final cap) is nested;
+     the partner-pair chronology: mix frame span{chi_c,chi_d} with H0-Gram I_2, contained in the receivers'
+     level-2 cap, carrier chain [<chi_c>, mix, cap, full] and passive chain [<chi_d>, mix, full] nested;
+  5. G = I - J/9 nondegenerate on every frame used (exact integer determinant test);
+  6. literal F2 replay with arbitrary dirty scratch: y = y0 + x, scratch and sources restored;
+  7. independent ledger recount from the role chains equals the saved child histogram (PR #144 bit ledger);
+  8. mutation controls (must all be REJECTED): broken partner mix, delivery outside the shared cap (full
+     frame), delivery below the level (face cap without span{chi_c,chi_d}), dropped star, non-nested role chain.
+Usage: python3 check_paired_cube_bit.py --dir out --p 12
+"""
+import argparse, json, random, sys
+from collections import Counter, defaultdict
+from math import gcd
+from operator import mul
+from pathlib import Path
+
+if sys.flags.optimize:
+    raise SystemExit('refusing to run under python -O: assertions are part of the check')
+
+
+class Fail(Exception):
+    pass
+
+
+def need(cond, msg):
+    if not cond:
+        raise Fail(msg)
+
+
+# ------------------------------------------------------------------ exact integer linear algebra
+def prim(v):
+    g = 0
+    for x in v:
+        g = gcd(g, abs(x))
+    if g > 1:
+        v = [x // g for x in v]
+    f = next((x for x in v if x), 0)
+    return tuple(-x for x in v) if f < 0 else tuple(v)
+
+
+def reduce_rows(rows, h):
+    """Integer reduced echelon form: returns (rows, pivot columns); each pivot column is zero outside its row."""
+    rows = [list(r) for r in rows]
+    out, pivs = [], []
+    for r in rows:
+        for pr, pc in zip(out, pivs):
+            if r[pc]:
+                a, b = pr[pc], r[pc]
+                r = [x * a - y * b for x, y in zip(r, pr)]
+        r = list(prim(r))
+        c = next((j for j in range(h) if r[j]), None)
+        if c is None:
+            continue
+        for i, (pr, pc) in enumerate(zip(out, pivs)):
+            if pr[c]:
+                a, b = r[c], pr[c]
+                out[i] = list(prim([x * a - y * b for x, y in zip(pr, r)]))
+        out.append(r); pivs.append(c)
+    return out, pivs
+
+
+def kernel(rows, h):
+    red, pivs = reduce_rows(rows, h)
+    ps = set(pivs)
+    basis = []
+    for f in range(h):
+        if f in ps:
+            continue
+        D = 1
+        for r, c in zip(red, pivs):
+            if r[f]:
+                D = D * abs(r[c]) // gcd(D, abs(r[c]))
+        v = [0] * h
+        v[f] = D
+        for r, c in zip(red, pivs):
+            if r[f]:
+                v[c] = -r[f] * D // r[c]
+        basis.append(prim(v))
+    return basis, len(red)
+
+
+def rank(rows, h):
+    return len(reduce_rows(rows, h)[0])
+
+
+def dot(a, b):
+    return sum(map(mul, a, b))
+
+
+# ------------------------------------------------------------------ checker
+class Checker:
+    def __init__(self, d, p, mutate=None):
+        self.mut = mutate
+        rd = lambda name: json.loads((d / ('%s_p%d.json' % (name, p))).read_text())
+        self.g, self.w, self.fr, self.k, self.prof = rd('graph'), rd('word'), rd('frames'), rd('kchron'), rd('profile')
+        self.h, self.v = self.g['h'], self.g['v']
+        if mutate == 'dropped_star':
+            j = next(i for i, r in enumerate(self.g['roots']) if r['kind'] == 'center')
+            self.g['roots'][j]['targets'] = []
+        if mutate == 'broken_mix':
+            self.k['entries'][0]['skip_mix'] = True
+        if mutate == 'outside_cap':
+            # raise the mixed carrier past the receivers' shared cap (to the full frame) and deliver there
+            e = self.k['entries'][0]
+            e['deliver_frame'] = self.w['full_frame']
+            e['carrier_chain'][2] = e['deliver_frame']
+        if mutate == 'below_level':
+            # deliver at the receivers' level-1 (face) cap, which does not contain span{chi_c, chi_d}
+            e = self.k['entries'][0]
+            face = next(j for j, r in enumerate(self.g['roots']) if r['kind'] == 'side' and set(e['receivers']) < set(r['targets']))
+            e['deliver_frame'] = self.w['root_frame'][face]
+            e['carrier_chain'][2] = e['deliver_frame']
+        if mutate == 'non_nested':
+            # move one addition's frame down to the frame of its smallest operand's source line
+            x = next(int(k) for k, f in sorted(self.w['node_frame'].items(), key=lambda kv: int(kv[0])) if int(k) >= self.v and str(int(k)) not in set(map(str, self.w['plain'])))
+            self.w['node_frame'][str(x)] = self.w['source_frame'][0]
+
+    # ---------------- frames
+    def frames(self):
+        h = self.h
+        self.A, self.B, self.dimf = {}, {}, {}
+        for key, rec in self.fr['frames'].items():
+            f = int(key)
+            if 'a' in rec:
+                A = [tuple(r) for r in rec['a']]
+                need(rank(A, h) == len(A), 'independent annihilator rows %d' % f)
+                B, _ = kernel(A, h)
+            else:
+                B = [tuple(r) for r in rec['b']]
+                need(rank(B, h) == len(B), 'independent basis rows %d' % f)
+                A, _ = kernel(B, h)
+            need(len(A) + len(B) == h and len(B) == rec['dim'], 'dimensions of frame %d' % f)
+            need(all(dot(a, b) == 0 for a in A for b in B), 'A.B = 0 for frame %d' % f)
+            self.A[f], self.B[f], self.dimf[f] = A, B, len(B)
+        self.cc = {}
+        return len(self.A)
+
+    def sub(self, f1, f2):
+        """frame f1 contained in frame f2 (exact)"""
+        if f1 == f2:
+            return True
+        key = (f1, f2)
+        r = self.cc.get(key)
+        if r is None:
+            B1, A2 = self.B[f1], self.A[f2]
+            r = len(B1) <= len(self.B[f2]) and all(dot(a, b) == 0 for a in A2 for b in B1)
+            self.cc[key] = r
+        return r
+
+    def in_frame(self, vec, f):
+        return all(dot(a, vec) == 0 for a in self.A[f])
+
+    def nondeg(self, f):
+        h = self.h
+        B, A = self.B[f], self.A[f]
+        if not B or len(B) == h:
+            return True
+        if len(B) <= len(A):
+            s = [sum(b) for b in B]
+            M = [[9 * dot(B[i], B[j]) - s[i] * s[j] for j in range(len(B))] for i in range(len(B))]
+            return rank(M, len(B)) == len(B)
+        s = [sum(a) for a in A]
+        M = [[(9 - h) * dot(A[i], A[j]) + s[i] * s[j] for j in range(len(A))] for i in range(len(A))]
+        return rank(M, len(A)) == len(A)
+
+    # ---------------- decoder
+    def decoder(self):
+        g, v = self.g, self.v
+        args = g['args']
+        lab = [frozenset(l) for l in g['labels']]
+        sup = [1 << i for i in range(v)] + [0] * (len(args) - v)
+        for x in range(v, len(args)):
+            a, b = args[x]
+            need(not sup[a] & sup[b], 'support-disjoint addition %d' % x)
+            sup[x] = sup[a] | sup[b]
+        self.sup = sup
+        acc, stars, side = [0] * v, [set() for _ in range(v)], [0] * v
+        for r in g['roots']:
+            need(r.get('coefficient', 1) == 1, 'mod-2 unit coefficients')
+            for t in r['targets']:
+                acc[t] ^= sup[r['node']]
+                if r['kind'] == 'center':
+                    stars[t].add(r['coordinate'])
+                else:
+                    side[t] ^= sup[r['node']]
+        for e in self.k['entries']:
+            for t in e['receivers']:
+                acc[t] ^= (1 << e['carrier']) | (1 << e['passive'])
+                side[t] ^= (1 << e['carrier']) | (1 << e['passive'])
+        for t in range(v):
+            need(acc[t] == 1 << t, 'decoder identity at target %d' % t)
+            need(stars[t] == set(lab[t]), 'stars read by target %d' % t)
+            orth = sum(1 << s for s in range(v) if len(lab[s] & lab[t]) == 1)
+            need(side[t] == orth, 'side part = sum over |S cap T| = 1 at target %d' % t)
+        for r in g['roots']:
+            if r['kind'] == 'center':
+                c = r['coordinate']
+                need(sup[r['node']] == sum(1 << s for s in range(v) if c in lab[s]), 'star support %d' % c)
+
+    # ---------------- geometry and chains
+    def geometry(self):
+        g, w, h, v = self.g, self.w, self.h, self.v
+        lab = g['labels']
+        chi = [tuple(1 if j in l else 0 for j in range(h)) for l in lab]
+        cov = [tuple((3 if j in l else 0) - 1 for j in range(h)) for l in lab]
+        nf = {int(k): f for k, f in w['node_frame'].items()}
+        rf = w['root_frame']
+        full = w['full_frame']
+        need(self.dimf[full] == h, 'full frame')
+        for s in range(v):
+            f = w['source_frame'][s]
+            need(self.dimf[f] == 1 and self.in_frame(chi[s], f), 'source line <chi_S>')
+        args = g['args']
+        for x, f in nf.items():
+            if x < v:
+                need(self.in_frame(chi[x], f), 'leaf label inside its frame')
+            else:
+                for y in args[x]:
+                    need(self.sub(nf[y], f), 'operand frame inside node frame (%d <- %d)' % (x, y))
+        loss = 0
+        for j, r in enumerate(g['roots']):
+            f = rf[j]
+            need(self.sub(nf[r['node']], f), 'root node frame inside root frame %d' % j)
+            if r['kind'] == 'center':
+                c = r['coordinate']
+                S = [chi[s] for s in range(v) if c in lab[s]]
+                need(all(self.in_frame(x, f) for x in S) and rank(S, h) == self.dimf[f], 'centre frame = star span')
+                loss += self.dimf[f]
+            else:
+                need(all(dot(cov[t], b) == 0 for t in r['targets'] for b in self.B[f]), 'root frame inside caps')
+                need(self.dimf[f] == h - rank([cov[t] for t in r['targets']], h), 'root frame = common cap')
+        need(loss == self.prof['loss'], 'copied-centre loss')
+        self.chi, self.cov, self.nf, self.rf = chi, cov, nf, rf
+
+    def chains(self):
+        """Role chains of the physical word and target chains; returns the recounted child histogram."""
+        g, w, h, v = self.g, self.w, self.h, self.v
+        nf, rf, full = self.nf, self.rf, w['full_frame']
+        ops, rootroles = w['ops'], w['rootroles']
+        R = 1 + max(max(a, b) for a, b, _ in ops)
+        R = max(R, 1 + max(rootroles), 1 + max(w['sources'].values()))
+        need(R == self.prof['R'], 'role count')
+        start = {}
+        for leaf, s in w['sources'].items():
+            start[s] = w['source_frame'][int(leaf)]
+        phase1 = set(w['phase1'])
+        touched_p1 = set()
+        for i in phase1:
+            touched_p1.update(ops[i][:2])
+        # phase one = closure of the centre roots' last ops under per-role precedence (recomputed)
+        prev_op, pred = {}, []
+        for i, (a, b, _) in enumerate(ops):
+            pred.append((prev_op.get(a, -1), prev_op.get(b, -1)))
+            prev_op[a] = prev_op[b] = i
+        stack = [prev_op[s] for r, s in zip(g['roots'], rootroles) if r['kind'] == 'center' and s in prev_op]
+        closure = set()
+        while stack:
+            i = stack.pop()
+            if i not in closure:
+                closure.add(i); stack.extend(j for j in pred[i] if j >= 0)
+        need(closure == phase1, 'phase one is the centre closure')
+        # conservative response support of every role (union incidence through the XOR word)
+        co = [0] * R
+        for j, (r, s) in enumerate(zip(g['roots'], rootroles)):
+            for t in r['targets']:
+                co[s] |= 1 << t
+        for a, b, _ in reversed(ops):
+            co[b] |= co[a]
+        gauge_of = {}
+        for z in w['gauges']:
+            need(sum(1 << t for t in z['targets']) == co[z['role']], 'gauge targets = response support of its role')
+            s = z['role']
+            need(s not in start, 'gauged role is not a source role')
+            need(s not in touched_p1, 'gauged role untouched in phase one')
+            need(self.dimf[z['frame']] == z['dim'] and z['dim'] > 0, 'gauge dimension')
+            need(self.nondeg(z['frame']), 'gauge frame nondegenerate')
+            start[s] = z['frame']; gauge_of[s] = z
+        seq = defaultdict(list)
+        for i, (a, b, x) in enumerate(ops):
+            f = nf[x]
+            seq[a].append(f); seq[b].append(f)
+        for j, s in enumerate(rootroles):
+            seq[s].append(rf[j])
+        H = Counter()
+        for s in range(R):
+            chain = [start.get(s)] + seq[s] + [full]
+            prev = chain[0]
+            dprev = 0 if prev is None else self.dimf[prev]
+            if prev is not None and s not in gauge_of:
+                H[1] += 1          # source role: injection frame <chi_S> (entrance child of width 1)
+            for f in chain[1:]:
+                if prev is not None:
+                    need(self.sub(prev, f), 'nested role chain (role %d)' % s)
+                d = self.dimf[f]
+                need(d >= dprev, 'ascending role chain (role %d)' % s)
+                if d > dprev:
+                    H[d - dprev] += 1
+                prev, dprev = f, d
+        for j, r in enumerate(g['roots']):
+            if r['kind'] == 'center':
+                H[self.dimf[rf[j]]] += 1   # copied-centre transform
+        # partner-pair chronology
+        src = Counter()
+        lab = [set(l) for l in g['labels']]
+        for e in self.k['entries']:
+            c, d = e['carrier'], e['passive']
+            need(len(lab[c] & lab[d]) == 1, 'carrier and passive orthogonal (H0-Gram I_2)')
+            mf, cf = e['mix_frame'], e['deliver_frame']
+            need(self.dimf[mf] == 2 and self.in_frame(self.chi[c], mf) and self.in_frame(self.chi[d], mf), 'mix frame = span{chi_c, chi_d}')
+            need(self.nondeg(mf), 'mix frame nondegenerate')
+            need(self.sub(mf, cf), 'mix frame inside the receivers shared cap')
+            need(all(dot(self.cov[t], b) == 0 for t in e['receivers'] for b in self.B[cf]), 'delivery frame inside receiver caps')
+            need(e['carrier_chain'][0] == w['source_frame'][c] and e['passive_chain'][0] == w['source_frame'][d], 'chains start at source lines')
+            need(e['carrier_chain'][1:] == [mf, cf, w['full_frame']] and e['passive_chain'][1:] == [mf, w['full_frame']], 'chain shape')
+            for ch in (e['carrier_chain'], e['passive_chain']):
+                for f1, f2 in zip(ch, ch[1:]):
+                    need(self.sub(f1, f2), 'nested source-register chain')
+                for f1, f2 in zip(ch, ch[1:]):
+                    src[self.dimf[f2] - self.dimf[f1]] += 1
+        # target chains: gauge reads (time order = reverse selection order), side caps in root order,
+        # partner-pair delivery at the level-2 cap right after its root, final cap
+        events = defaultdict(list)
+        for z in reversed(w['gauges']):
+            for t in z['targets']:
+                events[t].append(z['frame'])
+        deliveries = defaultdict(list)
+        for e in self.k['entries']:
+            deliveries[e['deliver_after_root']].append(e)
+        for j, r in enumerate(g['roots']):
+            if r['kind'] == 'center':
+                continue
+            for t in r['targets']:
+                events[t].append(rf[j])
+            for e in deliveries.get(j, []):
+                need(sorted(e['receivers']) == sorted(r['targets']), 'delivery after the receivers own level-2 root')
+                for t in e['receivers']:
+                    events[t].append(e['deliver_frame'])
+        Y = Counter()
+        cap = {}
+        for t in range(v):
+            capf = None
+            prev, dprev = None, 0
+            for f in events[t]:
+                if prev is not None:
+                    need(self.sub(prev, f), 'nested target chain (target %d)' % t)
+                need(all(dot(self.cov[t], b) == 0 for b in self.B[f]), 'target frame inside cap (target %d)' % t)
+                if self.dimf[f] > dprev:
+                    Y[self.dimf[f] - dprev] += 1
+                prev, dprev = f, self.dimf[f]
+            need(dprev <= h - 1, 'target chain below the cap')
+            Y[h - 1 - dprev] += 1 if h - 1 - dprev else 0
+        # every source register is in exactly one mixing pair
+        members = Counter()
+        for e in self.k['entries']:
+            members[e['carrier']] += 1; members[e['passive']] += 1
+        need(all(members[s] == 1 for s in range(v)), 'each source in exactly one partner pair')
+        for f in set(self.nf.values()) | set(self.rf):
+            need(self.nondeg(f), 'G-nondegenerate frame %d' % f)
+        return H, Y, src, R
+
+    # ---------------- replay
+    def replay(self, seeds=3):
+        g, w, v = self.g, self.w, self.v
+        ops, rootroles = w['ops'], w['rootroles']
+        R = self.prof['R']
+        srcmap = {int(k): s for k, s in w['sources'].items()}
+        roots = g['roots']
+        for seed in range(seeds):
+            rng = random.Random(1000 + seed)
+            x = [rng.getrandbits(1) for _ in range(v)]
+            y0 = [rng.getrandbits(1) for _ in range(v)]
+            z0 = [rng.getrandbits(1) for _ in range(R)]
+            X, Yv, z = x[:], y0[:], z0[:]
+            # y <- y - J M z (old-value response of the dirty scratch)
+            zd = z0[:]
+            for a, b, _ in ops:
+                zd[a] ^= zd[b]
+            for j, r in enumerate(roots):
+                for t in r['targets']:
+                    Yv[t] ^= zd[rootroles[j]]
+            for leaf, s in srcmap.items():      # z <- z + V x  (at the rank-one source lines)
+                z[s] ^= X[leaf]
+            for a, b, _ in ops:                  # z <- M z
+                z[a] ^= z[b]
+            for j, r in enumerate(roots):        # y <- y + J z
+                for t in r['targets']:
+                    Yv[t] ^= z[rootroles[j]]
+            for e in self.k['entries']:          # partner-pair sums on the source registers
+                if not e.get('skip_mix'):
+                    X[e['carrier']] ^= X[e['passive']]
+                for t in e['receivers']:
+                    Yv[t] ^= X[e['carrier']]
+            for e in self.k['entries']:          # undo at the full frame
+                if not e.get('skip_mix'):
+                    X[e['carrier']] ^= X[e['passive']]
+            for a, b, _ in reversed(ops):        # z <- M^-1 z
+                z[a] ^= z[b]
+            for leaf, s in srcmap.items():       # z <- z - V x
+                z[s] ^= X[leaf]
+            need(all(Yv[t] == y0[t] ^ x[t] for t in range(v)), 'replay: y = y0 + x (seed %d)' % seed)
+            need(z == z0 and X == x, 'replay: scratch and sources restored (seed %d)' % seed)
+
+    def run(self):
+        nfr = self.frames()
+        self.decoder()
+        self.geometry()
+        H, Y, src, R = self.chains()
+        self.replay()
+        h, v = self.h, self.v
+        m, W = 3 * h, 2 * v + R
+        C = Counter()
+        for part in (H, Y, src):
+            for r, c in part.items():
+                if r and c:
+                    C[r] += 3 * c
+        for z in self.w['gauges']:
+            C[3 * z['dim']] += 1
+        C[2] += 2 * v
+        saved = {int(k): c for k, c in self.prof['child_histogram'].items()}
+        need(dict(C) == saved, 'independent recount equals the saved child histogram')
+        mass = sum(r * c for r, c in C.items())
+        need(W == self.prof['W_per_vertex'] and W * m - mass == 2 * v - 3 * self.prof['loss'] == self.prof['deficit_per_vertex'],
+             'W = 2v + R and deficit 2v - 3 ell')
+        return dict(frames=nfr, roles=R, W=W, m=m, deficit=W * m - mass, children=sum(C.values()))
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--dir', type=Path, default=Path(__file__).resolve().parent / 'out')
+    ap.add_argument('--p', type=int, default=12)
+    ap.add_argument('--no-controls', action='store_true')
+    a = ap.parse_args()
+    res = Checker(a.dir, a.p).run()
+    print('PASS p=%d: %s' % (a.p, res))
+    if a.no_controls:
+        return
+    for m in ('broken_mix', 'outside_cap', 'below_level', 'dropped_star', 'non_nested'):
+        try:
+            Checker(a.dir, a.p, mutate=m).run()
+        except Fail as e:
+            print('control %-13s REJECTED: %s' % (m, e))
+            continue
+        raise SystemExit('FAIL: control %s was accepted' % m)
+    print('PASS: all 5 mutation controls rejected')
+
+
+if __name__ == '__main__':
+    main()
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+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/selected/bit/graph_p12.json
@@ -0,0 +1 @@
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2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T; side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T; equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} 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diff --git a/research/gen4-retiming-entrances/vendor/pr276/gen4bit/selected/bit/kchron_p12.json b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/selected/bit/kchron_p12.json
new file mode 100644
index 0000000000..f39b02e3f7
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/selected/bit/kchron_p12.json
@@ -0,0 +1 @@
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new file mode 100644
index 0000000000..da422014b7
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/selected/bit/profile_p12.json
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Binary files /dev/null and b/research/gen4-retiming-entrances/vendor/pr276/gen4bit/selected/bit/word_p12.json.gz differ
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/LICENSE b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/LICENSE
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+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
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+      institute patent litigation against any entity (including a
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+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
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+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
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+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
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+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
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+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
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+   Copyright [yyyy] [name of copyright owner]
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+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
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diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/NOTICE b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/NOTICE
new file mode 100644
index 0000000000..63aa295646
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/NOTICE
@@ -0,0 +1,290 @@
+Walsh-Hadamard power saving (wht-power-saving-lean)
+Copyright 2026 Jacob Sussman
+
+Repository: https://github.com/jacobalansussman/wht-power-saving-lean
+
+This repository is not a project of OpenAI. OpenAI did not write, review or
+endorse it. The package name "OAI" and the namespace "OAI.PowerSaving" are
+those of openai/math and are kept only because the new files extend that
+development.
+
+This repository is not a project of CrocSwap/integer-mult-bounds either. Its
+authors did not write, review or endorse it. Section 6 says what is taken
+from their repository.
+
+This repository contains files from, and files derived from, the repository
+"openai/math" (https://github.com/openai/math), family 130, "Exact Fourier
+transforms below n log n", at commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.
+That repository is published under the Apache License, Version 2.0. A copy of
+the licence is in the file LICENSE. The upstream repository has no NOTICE file
+and its licence text names no copyright holder; the files are attributed here
+to the authors of openai/math (OpenAI).
+
+1. Unmodified upstream files.
+   The 89 files under OAI/Computability/ are byte-for-byte copies of the files
+   with the same paths under lean/ in openai/math at the commit above. They
+   have not been changed. Modified copies of some of them are under
+   Work/Fourier/ and are listed in section 7.
+   One more file of openai/math is here unchanged, outside the Lean build:
+   third-party/openai-math/lean/ComparatorChallenges/UniformFourier.lean is a
+   byte-for-byte copy of lean/ComparatorChallenges/UniformFourier.lean at the
+   commit above (the statement of OpenAI's Fourier challenge). It is included
+   so that the modified copy named in section 2 can be compared with it.
+
+2. Files that contain upstream text.
+   - Work/CarrierCheck/ChallengeB2Ke16x.lean,
+     Work/CarrierCheck/ChallengeB2Ke16xR.lean,
+     Work/GCert/Data/ChallengeB2Gp193x.lean and the text template
+     tools/gen/templates/ChallengeB2L16x.lean.txt each contain, as their
+     lines 22-270, lines 9-257 of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the RAM cost
+     model), unchanged. Everything else in these files was written for this
+     repository.
+   - Work/Fourier/UniformFourierChallenge.lean is a modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean of openai/math (the
+     statement of OpenAI's Fourier challenge, 336 lines). Changes: a comment
+     was added at the top; the exponent 1 - 1/(10^(13:ℕ)) was replaced by
+     1 - 7474546/(10^(10:ℕ)); seven names received the suffix "Z"
+     (decimalExponent, decimalTime, TimeBounds, DFTGoal, ConvGoal,
+     transform_main, convolution_main). Everything else in the file is the
+     upstream text, unchanged. See section 7.
+   - Work/Scratch/Engine.lean and Work/Block/Engine.lean contain copies of
+     proofs of openai/math, changed for this repository: sections 1, 2 and 5
+     of Work/Scratch/Engine.lean are upstream proofs with the batch layout
+     renamed, and both files contain a copy of the private upstream theorem
+     "hills_project" (lean/OAI/Computability/FourierTransform/
+     TensorProgram.lean) with its envelope generalised. The comments in the
+     two files mark these places.
+   - lakefile.lean is adapted from lean/lakefile.lean of openai/math: the same
+     package name, toolchain, package option and Mathlib pin; every other
+     dependency was removed and the libraries of this repository were added.
+     lean-toolchain is a byte-for-byte copy of lean/lean-toolchain.
+     lake-manifest.json lists Mathlib and its dependencies at the revisions of
+     lean/lake-manifest.json.
+   - RELATED-WORK.md reproduces the BibTeX entries of two manuscripts of
+     openai/math.
+
+3. New files that build on upstream proofs.
+   The other files under WHTCheck/ and Work/ were written for this
+   repository. They import the upstream files, and several of them generalise
+   or adapt proofs of upstream files (for example Work/Block/Recursion.lean,
+   which says so in its header). They are changes and additions made for this
+   repository and are not part of openai/math.
+
+4. How the new files were made.
+   Jacob Sussman made the new files on 2026-10-08 and 2026-10-09 by directing
+   a team of AI agents (Claude). The agents wrote the new Lean files, the
+   certificate data and the generator scripts. See README.md, section 4.
+
+5. Ideas taken from other public work.
+   The network of the first result uses ideas published by others, among them
+   the helper circuit "NStar3" (Swapnil-jain/integer-mult-kappa, which credits
+   CrocSwap pull request #36 and Paureel for parts of it), its transfer to
+   family 130 (shea256/fourier-transform-below-nlogn), and "carrier links" and
+   "whole-residual batching" (pull requests to CrocSwap/integer-mult-bounds).
+   No file of Swapnil-jain/integer-mult-kappa or of
+   shea256/fourier-transform-below-nlogn is included here. One comment in
+   Work/Scratch/Engine.lean quotes three counts reported in
+   Swapnil-jain/integer-mult-kappa and names that source. The general frame
+   lemma that Work/GFrame proves is stated in
+   notes/general-clifford-frames.tex of CrocSwap/integer-mult-bounds; its Lean
+   proof was written for this repository. The credits, with links, are in
+   RELATED-WORK.md.
+
+6. Data derived from CrocSwap/integer-mult-bounds (second result).
+   The helper circuit of the second result is the paired-cube circuit of the
+   repository "CrocSwap/integer-mult-bounds"
+   (https://github.com/CrocSwap/integer-mult-bounds), in the state of its pull
+   request #193. It is the design of that community: icekylinx (pull requests
+   #144 and #184), eumemic (#168, and #117 behind its modules), ikeboy /
+   Avi Eisenberg (#191 and #193), with an664 (#128) credited there for the
+   workspace-sharing principle. That repository is published under the Apache
+   License, Version 2.0 (the same licence text as the file LICENSE). Its
+   NOTICE file begins "A sharper exponent for integer multiplication /
+   Copyright 2026 Douglas Colkitt" and says that the community release "is
+   not solely Douglas Colkitt's work". A complete copy of that NOTICE file, as
+   it is at the head of pull request #193, is in
+   third-party/CrocSwap-integer-mult-bounds/NOTICE.
+
+   The data were taken from these files of that repository. They were loaded
+   as data by programs written for this repository; no program of that
+   repository was run, and none is included here.
+   - at the head of pull request #168 (eumemic),
+     4a3c769e5c5430e7114c4d3e099ff34664677f17:
+       references/paired-cube/sources/local_L1.json
+       references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json
+       references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json
+       references/paired-cube/sources/qmod_climb3u_best.json
+       references/paired-cube/selected-module/matching-arcs.json
+       references/paired-cube/physical/frames.json
+   - at the head of pull request #193 (ikeboy),
+     187e1010ac8b259af8e9b5166f68b64bc27b4b47:
+       research/source-assisted-v4/data/physical-pairs.json
+
+   Files of this repository that contain data derived from them:
+   tools/certificate/gcert1-p11-pr193.json.gz and the Lean data modules
+   generated from it, Work/GCert/Data/Gen/P193*.lean and the files they import
+   from Work/GCert/Data/Gen/P193/; its block counts are also in the generated
+   modules Work/GCert/Data/P193Price.lean, RateB2Gp193.lean, RateB2Gp193x.lean
+   and InstB2Gp193.lean.
+   Changes made: the circuit was rebuilt from those data as one explicit,
+   renumbered list of additions with a table of frames, in the certificate
+   format "gcert/1" of this repository; its 1,980 in-place steps were written
+   as pairs of additions with rescaled coefficients; the Lean data modules
+   were generated from that list. No file of that repository is included
+   unchanged, except the copy of its NOTICE file named above.
+
+   Notices of that NOTICE file that pertain to these data, quoted:
+
+     Paired-cube and shared-core extension, 9 October 2026
+     Copyright 2026 icekylinx
+
+     Source-assisted common-frame extension (2026-10-09)
+     Copyright 2026 icekylinx. Apache-2.0.
+     Substantial dependency: eumemic PR168,
+     fd25adb7fbaa12ee761d02c733c54d1d2a7687ee
+
+   The full text of both notices, and the notices of the work they build on,
+   are in the copy named above. The credits, with links and with the words of
+   pull request #193 about its own sources, are in README.md ("Whose circuit
+   this is") and in RELATED-WORK.md, section 1.
+
+7. Modified copies of upstream files (third result).
+   The files listed below are copies of files of openai/math at the commit
+   above, changed for this repository. Each begins with a comment that names
+   the upstream file it is derived from and states what was changed. The
+   upstream originals under lean/OAI/Computability/ are in this repository
+   as well, unchanged (section 1), and the copies import them. The upstream
+   challenge file lean/ComparatorChallenges/UniformFourier.lean is in this
+   repository in both forms: unchanged under third-party/openai-math/
+   (section 1) and modified (section 2).
+
+   - Work/Fourier/ArbitraryLength.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ArbitraryLength.lean (224
+     lines; 159 of them unchanged in the copy). Changes: identifiers renamed
+     on 64 lines (18 names: 15 with the suffix Z, 3 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Asymptotics.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Asymptotics.lean (187 lines;
+     112 of them unchanged in the copy). Changes: identifiers renamed on 74
+     lines (32 names: 26 with the suffix Z, 6 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/Axioms.lean: written for this repository (not a copy of an
+     upstream file).
+   - Work/Fourier/ConvolutionProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/ConvolutionProgram.lean (100
+     lines; 77 of them unchanged in the copy). Changes: identifiers renamed
+     on 22 lines (10 names: 9 with the suffix Z, 1 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/Goal.lean: written for this repository; contains lines of
+     upstream files: of its 7 code lines, 6 are lines of
+     lean/OAI/Computability/FourierTransform/Goal.lean (original lines 35,
+     75-77, 79, 81): unchanged: its lines 25; with identifiers renamed: its
+     lines 21, 24, 26, 28, 30.
+   - Work/Fourier/Main.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/Main.lean (151 lines; 90 of
+     them unchanged in the copy). Changes: identifiers renamed on 59 lines
+     (40 names: 35 with the suffix Z, 5 with Z inserted); 1 import line
+     replaced by 2; 24 comment lines added; other code lines changed: 1 of
+     the original, 1 of the copy (copy line 59).
+   - Work/Fourier/Seam.lean: written for this repository; contains lines of
+     upstream files: of its 122 code lines, 15 are lines of
+     lean/OAI/Computability/FourierTransform/TensorProgram.lean (original
+     lines 36-37, 95-96): unchanged: its lines 93-94, 113-114, 141-142,
+     163-164, 185-187, 194-196; with identifiers renamed: its lines 184; 3
+     are lines of lean/OAI/Computability/FourierTransform/TensorSaving.lean
+     (original lines 83-84, 114): with identifiers renamed: its lines 45-46,
+     59; 1 is a line of lean/OAI/Computability/FourierTransform/Main.lean
+     (original line 60): with identifiers renamed: its lines 213.
+   - Work/Fourier/SectorAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SectorAlgorithm.lean (224
+     lines; 162 of them unchanged in the copy). Changes: identifiers renamed
+     on 61 lines (17 names: 13 with the suffix Z, 4 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/SynchronizedAlgorithm.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/SynchronizedAlgorithm.lean (126
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 31 lines (12 names: 10 with the suffix Z, 1 with Z inserted, 1
+     other), the other being "canopy" to "Grove.canopy" (5 lines); 1 import
+     line replaced by 1; 16 comment lines added; no other change to the
+     code.
+   - Work/Fourier/TransformProgram.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/TransformProgram.lean (146
+     lines; 94 of them unchanged in the copy). Changes: identifiers renamed
+     on 51 lines (21 names: 19 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/UniformBounds.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/UniformBounds.lean (183 lines;
+     115 of them unchanged in the copy). Changes: identifiers renamed on 67
+     lines (29 names: 25 with the suffix Z, 4 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+   - Work/Fourier/UniformFourierChallenge.lean: modified copy of
+     lean/ComparatorChallenges/UniformFourier.lean (336 lines; 328 of them
+     unchanged in the copy). Changes: identifiers renamed on 7 lines (7
+     names: 7 with the suffix Z); 12 comment lines added; other code lines
+     changed: 1 of the original, 1 of the copy (copy line 281).
+   - Work/Fourier/WorkingCompiler.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingCompiler.lean (153
+     lines; 104 of them unchanged in the copy). Changes: identifiers renamed
+     on 48 lines (14 names: 14 with the suffix Z); 1 import line replaced by
+     1; 15 comment lines added; no other change to the code.
+   - Work/Fourier/WorkingPreparation.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingPreparation.lean (212
+     lines; 156 of them unchanged in the copy). Changes: identifiers renamed
+     on 55 lines (30 names: 28 with the suffix Z, 2 with Z inserted); 1
+     import line replaced by 1; 15 comment lines added; no other change to
+     the code.
+   - Work/Fourier/WorkingTransform.lean: modified copy of
+     lean/OAI/Computability/FourierTransform/WorkingTransform.lean (119
+     lines; 91 of them unchanged in the copy). Changes: identifiers renamed
+     on 27 lines (9 names: 8 with the suffix Z, 1 with Z inserted); 1 import
+     line replaced by 1; 15 comment lines added; no other change to the
+     code.
+
+   Changes made to the eleven copied proof files: every declaration received
+   the letter "Z" in its name (as a suffix of its own name, or of the name
+   of the declaration it belongs to), so that it does not collide with the
+   upstream declaration of the same name; the upstream exponent "alpha"
+   (1 - 2/10^11) and the bound "hills" defined from it were replaced by
+   "alphaZ" (1 - 7474547/10^10) and "hillsZ", which are defined in
+   Work/Fourier/Seam.lean, and the single use of the upstream theorem
+   "hills_program" by "hillsZ_program"; the five definitions of the upstream
+   statement that contain its exponent (decimalExponent, decimalTime,
+   TimeBounds, DFTGoal, ConvGoal) were replaced by the versions of
+   Work/Fourier/Goal.lean, whose exponent is 1 - 7474546/(10^(10:ℕ));
+   the import lines point to the copies; a header comment was added.
+      Two further changes: in the copy of Main.lean the same constant stands
+   once as the literal 2/10^11 and was replaced there too, and the two
+   final theorems of that copy received a documentation comment; in the
+   copy of SynchronizedAlgorithm.lean the name "canopy" was written out as
+   "Grove.canopy" in 5 places, because the short name is shadowed in the
+   larger environment of the copy. The script also renamed three names
+   inside upstream comments; the comments are otherwise the upstream ones
+   and describe the upstream network.
+   The proofs are those of openai/math. The copies were made by the script
+   tools/fourier/mkchain.py of this repository.
+
+   Work/Fourier/Goal.lean contains copies of those five definitions of
+   lean/OAI/Computability/FourierTransform/Goal.lean, with the exponent
+   replaced and the suffix "Z" on the five names.
+
+   Work/Fourier/Seam.lean was written for this repository. It repeats the
+   statement of the upstream theorem "hills_program" (TensorProgram.lean) and
+   the definition of "hills" (TensorSaving.lean) with the two names replaced;
+   its header says so.
+
+   The work of others that the third result follows (danadran01, shea256,
+   eumemic) is credited in README.md ("Whose reduction this is") and in
+   RELATED-WORK.md, section 1. No file of their repositories is included
+   here.
+
+Not included in this repository and fetched by the build: Mathlib
+(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its
+dependencies. The comparator (https://github.com/leanprover/comparator) is a
+separate tool and is not included.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/gcert1-p11-pr193.json.gz b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/gcert1-p11-pr193.json.gz
new file mode 100644
index 0000000000..a98026a72f
Binary files /dev/null and b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/gcert1-p11-pr193.json.gz differ
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/FINITE_BRIDGE.txt b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/FINITE_BRIDGE.txt
new file mode 100644
index 0000000000..c1a8843611
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/FINITE_BRIDGE.txt
@@ -0,0 +1,141 @@
+FINITE ROUTER, ROW-STOCK, AND SEMANTIC BRIDGE FOR ROUND 13
+
+Prepared for icekylinx by GPT-6 Astra, 9 October 2026. Apache-2.0.
+
+This bridge applies to a completed, physically proved round-13 profile.
+It cannot make a numerically attractive but unconstructed profile valid.
+The local source/target flags, controlled injections, old-response
+subtraction, inverse cleanup, and retained alias boundaries are separate
+construction obligations. assemble_profiles.py records their role as
+proof dependencies and independently checks the exact arithmetic.
+
+1. The inherited uniform interfaces
+
+Retain the three completed-core cover of PR144/PR168 and all of its
+analytic and fixed-tape assumptions. The complex cover is O(m,2), m<=72,
+with order V<2^(m*m)<=2^5184. No new independent cover coordinates are
+introduced by common-frame scalar lifts or source-controlled local
+rewrites. Every stage still uses one completed invocation at each vertex.
+
+For a supplied profile with W0<10^7 roles per cover vertex, the full
+physical stock W=V W0 is less than2^5208. Its total rank s is less
+than mW<2^5215. The profile's actual proper-child maximum is retained;
+the selected complex maximum must be less than m/2. The script checks
+these inequalities rather than assuming that fewer auxiliary rows imply
+a better contraction or a shorter recursion.
+
+The bit word uses the same weighted q-adic frame interface and the same
+internally borrowed selectors as its pinned parent. New source controls
+must use existing nondegenerate source-meeting planes or separately
+certified new frames. All zero-rank adapters remain charged scalar work.
+The group-size factor is not omitted and is not inserted into an external
+polynomial row reserve. The inherited ordinary leaf saving is exactly
+384599/10^10. The bad-row allowance is1/10^16; the charged fallback per
+edge is32m^2. Its inequality2m^3/2^80<1/10^16 is checked explicitly.
+
+2. A deliberately loose finite scalar bound
+
+The pinned words and round-13 modifications are finite straight-line
+programs with fewer than2^40 stored nodes, roles, coefficients, and
+boundary entries. Scalar sum/difference lifts use actual invertible
+matrices and are executed pointwise at common frame representatives.
+For the selected dyadic rewrite, new elementary coefficients are
+dyadic; the inherited center scatters retain their fixed odd divisor3.
+No unrecorded new odd denominator may be included under this bridge.
+
+Fixed integer multipliers can be expanded into scalar doublings and
+additions; dyadic divisions can be expanded into halvings. The explicit
+low words and full-frame inverses are much smaller than2^4096 primitive
+scalar/movement groups per invocation. Even constructing their fixed
+old-response matrices by exact elimination is dominated by this bound:
+matrix order is below2^40, original finite-word coefficient bit lengths
+are below2^80, and the elementary elimination and coefficient expansion
+bounds are below2^1024. No input-size-dependent dense elimination is
+being performed. These are constants of the chosen finite construction.
+
+Consequently all3V invocation words, endpoint adapters, and finite role
+bookkeeping fit within K<2^9300 logical groups. The retained universal
+router is overcharged by a full W-role permutation for every group:
+
+    64 (m+1)^3 (K+1) (W+1)^2 < 2^20000.
+
+Choose the exact dominating scalar/router budget G=2^30000. This also
+dominates the primitive arithmetic required to realize the fixed scalar
+coefficients and source-controlled inverse cleanup. The router still
+uses a fixed number of tapes, with sequential reuse of row stock.
+
+3. Explicit semantic constants
+
+Choose the exact integer E=2^100000 and put B=s+E. Then
+
+    2 G W^2 + 8s + 4W + 4 + 32m < 2^40500 < E,
+    E <= B < 2^100001.
+
+For the actual maximum child r<m, the induction gap obeys
+
+    2B(m-r)-s-E >= s+E >= 1.
+
+Choose C0=2^210000 and C1=1. These dominate both the retained semantic
+requirement32m B^2 and2B+18. The reported strict_literal_gap=1 and
+induction_gap_lower=1 are proved lower bounds on the positive actual
+integer gaps; they are not claims that those gaps equal one.
+
+Use the inherited common dyadic grid with fixed3^(-K') exposure and
+retain its precision/rounding contract. No child receives an independent
+rounding allowance and no source-controlled injection is treated as an
+unpaid numerical operation.
+
+4. External rows and stopping
+
+The complex child maximum below m/2 gives halving degree1, while
+log2 W<5208<10000. Keep the deliberately conservative inherited bit
+coarse reserve9909 and ordinary-leaf reserve252. Thus the external
+row coefficient is bounded by
+
+    A=10000+9909+252=20161.
+
+Choose degree D=1000000 and suffix slope4D. The exact row gap is
+
+    D - (51/25)A > 0.
+
+The q-adic selector fields and source-control labels remain internally
+borrowed and restored. Increasing these finite overcharges changes
+constants and the all-size bridge, not the selected exponent saving.
+
+5. Exact supplier moments and balanced assembly
+
+For each actual histogram, assemble_profiles.py proves
+
+    sum_r n_r r exp(a log(m/r))/(mW0) + bad_allowance < 1
+
+using rational upper bounds, with upward rounding on the2^120 grid.
+The bit atom stop is the first10^(-12) grid point above
+a/(1+a-old), which implies both required strict toll inequalities.
+Its effective saving is(1-beta)a+beta*old. This stopping rule is the
+already reviewed PR158 edge rule, not a new local-word contribution.
+
+The final assembly uses the substantial PR168 balanced-prefix adapter,
+with eta=10^(-8) and phase stop10^(-9), retaining all47 strict
+constraints and all7 margins. The selected final kappa is rounded
+down on the10^(-10) grid below the minimum complete margin. The
+script checks every constraint exactly and reports whether the fixed
+target0.0009218338 is reached.
+
+This is a conditional bound of the retained theorem form
+
+    T(n)=O(n (log n)^(1-kappa)).
+
+The improvement ratio refers to kappa, the logarithmic exponent saving.
+It is not a measurement of practical multiplication throughput.
+
+Credits
+
+The base supplier, scalar/frame verification, and actual profiles are
+pinned to PR168 fd25adb7fbaa12ee761d02c733c54d1d2a7687ee, eumemic
+(Anthropic Claude assistance), building on icekylinx's PR144. The
+balanced prefix is RaD/hipotures; the semantic constraints are retained
+from the reviewed PR23 line; completed-core sharing is credited to
+an664 PR128; the atom-edge stop is credited to geckods PR158. Existing
+source notices retain their more detailed upstream attributions.
+The new source-controlled boundary construction, this conservative
+bridge, and its integration are GPT-6 Astra's round-13 work.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/compact-control-layout.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/compact-control-layout.tex
new file mode 100644
index 0000000000..16f4d23347
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/compact-control-layout.tex
@@ -0,0 +1,118 @@
+\paragraph{Rows and complete compact fields.}
+Let $m,W,s$ denote the complex network constants and keep the layer's global
+$p,d,K$ at every node. Put
+\[
+ G=4\lceil\log_2p\rceil+6,\quad H=dG,\quad
+ q_F=\left\lceil\frac{2H}{K}\right\rceil,\quad
+ q_B=\left\lceil\frac{H}{K}\right\rceil,
+\]
+\[
+ q_0=\lceil\log_2W\rceil\lceil\log_m(2d)\rceil,
+ \quad k_0=\lceil\log_m d\rceil,\quad Q_0=q_0+q_F+q_B.
+\]
+If $D\le Q_0$, apply all $D$ selected kernels individually. Otherwise,
+process individually the first $q_0+q_F$ and last $q_B$ selected axes.
+This uses existing coordinates only. The remaining active axes are a
+consecutive middle block of length $D-Q_0$.
+
+Regard the first $q_0$ chunks as the row index. Immediately after it, the
+next $q_F$ chunks have at least $2H$ bits. Reinterpret these consecutive
+bits as two $H$-bit front fields and a spectator remainder; a remainder
+of length zero is omitted. The last $q_B$ chunks similarly supply one
+$H$-bit back field and a spectator remainder. These reinterpretations move
+no records and preserve the total address space. For a call with $f$ axes
+per slot, carve $nG=(f-1)G\le H$ consecutive bits from each of these
+fields; collapse their unused bits into spectators. The resulting field
+list has a fixed number of entries. Both front fields precede all active
+slots and the back field follows them, so the compact-control proposition
+applies to every ordered pair of slots. For $f=1$ no compact fields are used.
+
+The original row range has length $R_{\rm row}=2^{q_0K}\ge W^{k_0}$.
+For each original prefix, pad this row range to the next multiple of
+$W^{k_0}$ by adding zero rows. A row includes the entire complete front
+fields, active middle block, back field, all spectator coordinates and
+polynomial record suffix. Padding adds whole such rows, so increases total
+volume by at most two and does not change any within-row range.
+
+At a node write the row index as $u=Wg+w$, $0\le w<W$, and send the entire
+row to role $w$. The index $u$ consists solely of the first row region:
+\emph{no compact-field bit is included in it}. Each role therefore has
+the same complete within-row address set and exactly $1/W$ of the parent
+volume. At depth $j$ the remaining row count is divisible by $W^{k_0-j}$.
+This invariant survives further splits, padding, and reassembly. Pointwise
+gates on different roles have aligned $g$ and every remaining coordinate.
+All compact operations restore the temporary fields before a scalar gate,
+recursive child, or returned result uses that layout.
+
+The fixed-tape scheduler is unchanged: park only the other role streams at
+the active stack top, execute the child on a complete role stream, and restore
+the parked streams on return. Every child has its own current logical volume;
+copying, parking, rewinds and clearing cost a fixed multiple of that volume.
+The constant number of compact operations per edge use fixed work areas.
+Descriptors include the global $p,d,K,G,H$ and the carved field lengths;
+all have $O(p)$ bits and there are a fixed number of fields. The existing
+record suffix absorbs polynomial setup at every node and per record.
+
+Each completed invocation acts as the desired $C$ tensor on its active axes
+and as identity on the reserved and spectator coordinates. It therefore
+commutes with the earlier individual kernels, including those on bits now
+interpreted as compact fields. Restoring the row permutation returns the
+result to each original row separately. A padded zero row is consequently
+zero at completion and can be deleted exactly as before. Neither temporary
+field contents nor intermediate scratch payloads were assumed to be zero.
+
+The number of individually processed axes is at most $Q_0$, including the
+fallback $D\le Q_0$. For large $p$, $K\ge d^c/2$ and
+\[
+ q_F+q_B\le\frac{3dG}{K}+2\le6d^{1-c}G+2.
+\]
+Thus preprocessing, padding and reservation cost
+\[
+ O\bigl(V(\log(2d)+d^{\max\{1-c,0\}}\log p+1)\bigr).
+\]
+All reserved axes lie within the original $D$ axes; in particular their
+total number never exceeds $d$. This fact also bounds their coefficient
+dependency depth by the same $8d$ allowance used in the guard proof.
+
+\paragraph{Unrolling the compact-control recurrence.}
+Fix rational $0<\beta<1$. Choose $0<\tau<1$ and
+$\max\{0,\log_m(s/W)\}<\sigma<1$. Stop when $e<d^\beta$ and apply
+the remaining kernels individually. With $F(e)$ denoting time per current
+logical volume, the exact row split gives
+\[
+ F(e)\le(s/W)F(e/m)+O(G^\tau e^\tau+1),\qquad
+ F(e)=O(e)\quad(e<d^\beta).
+\]
+Here $G$ and the compact reservations are global parameters, not rebuilt
+at each node. This is why no factor $K^\tau$ appears in the overhead.
+Repair costs are already included in the node overhead.
+
+Write $b=s/W$. At level $j$ the internal contribution is bounded by
+$O(G^\tau e^\tau(b/m^\tau)^j)$. Summing through the stopping depth gives
+\[
+ O(G^\tau\log(2d)d^\chi),\qquad
+ \chi=\tau+(1-\beta)\max\{\sigma-\tau,0\}.
+\]
+Indeed if $\sigma\le\tau$ the root bounds every summand; otherwise the
+last internal level costs at most the root bound times a fixed constant
+and $d^{(1-\beta)(\sigma-\tau)}$. The additive $1$ is absorbed by
+$G^\tau e^\tau$ at internal nodes. The leaf contribution is at most
+$O(d^{\sigma+\beta(1-\sigma)})$, by the original volume-weighted argument.
+
+Partition $D-Q_0$ into consecutive powers of $m$, using its base-$m$
+expansion. There are $O(\log(2d))$ pieces. Include their costs and the
+reservation cost to obtain, per original volume,
+\[
+ O\!\left((\log p)^3
+ [d^\chi+d^{\sigma+\beta(1-\sigma)}+d^{\max\{1-c,0\}}+1]\right).
+\]
+We used $\log d=\Theta(\log p)$ and $G=O(\log p)$ for each fixed
+$d=\Theta(p^\epsilon)$ family. Any fixed rational exponents satisfying
+\[
+ \max\{\tau,\sigma,\chi\}<\lambda<\lambda'<1,\qquad
+ \max\{\sigma+\beta(1-\sigma),1-c,0\}<\lambda'
+\]
+therefore give the complete $O(Vd^{\lambda'})$ layer bound. The strict gaps
+absorb the logarithms. The small-$D$ fallback obeys the same bound.
+For fixed rational $\beta=u/v$, implement stopping by the integer test
+$e^v<d^u$; its polynomial descriptor cost is already included.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/compact-control-movement.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/compact-control-movement.tex
new file mode 100644
index 0000000000..06b6a9ef24
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/compact-control-movement.tex
@@ -0,0 +1,167 @@
+\subsection{Compact dirty controls for selected-bit additions}
+\label{sec:compact-control-movement}
+The following replacement for the wide-slot packed operation moves only
+compact control fields. Temporary address fields have arbitrary contents;
+they are complete ranges of existing address bits, not newly allocated
+independent coordinates. Their availability in every recursive call is
+proved separately below.
+
+\begin{lemma}[Controlled rotations with record-paid offset work]
+\label{lem:record-paid-rotation}
+Consider $M$ records of $R$ bits on a complete rectangular address set, of
+volume $V=MR$. Its fixed number of field lengths and controls have at most
+$A=\lceil\log_2(2V)\rceil$ bits each. A binary target field follows all its
+controls. Suppose its rotation offset, independent of that target, is
+computable from the controls and descriptors in $O(A^C)$ tape steps for
+some fixed $C$. Then the rotation can be performed on fixed tapes in
+$O(V+MA^{C'})$ time for a fixed $C'$. In particular, this is $O(V)$ when
+$A=O(p)$ and $R$ exceeds every fixed power of $p$.
+\end{lemma}
+\begin{proof}
+Fix the prefix before the target. If its range is $Q$ and each target block
+has $B$ suffix bits, rotate by $a$ through the two-piece split at $Q-a$ and
+merge in the opposite piece order. This is the controlled-rotation
+construction from the ordered-affine streaming lemma. Each data bit is
+copied a bounded number of times. There are at most $M$ prefix fibers, since
+every fiber contains at least one complete record. At each fiber, compute
+the offset, initialize its two piece lengths, and reset the finite collection
+of counters; recompute the offset at the merge. Ordinary binary arithmetic
+and descriptor copies cost a fixed polynomial in $A$ per fiber. The controls
+can be wider than the target: their lengths are bounded by $A$, not by the
+target width. Local suffix-length copies and ripple counters are charged as
+in the original streaming proof, so no growing descriptor is scanned per
+payload bit. Two piece tapes, output and fixed arithmetic work tapes suffice;
+rewinds and clearing are over the regions just written. This gives the stated
+bound. Finally $MA^{C'}/V=A^{C'}/R=o(1)$ in the specified record regime.
+\end{proof}
+
+Let $x,y$ be disjoint slots of $fK$ bits, with corresponding selected
+positions $j_i=\rho+iK$, $0\le i<f$, $0\le\rho<K$. Put $n=f-1$.
+For $f=1$ use the elementary two-bit XOR. Otherwise fix a positive integer
+$G$, put $B=2^G$, and assume two disjoint complete $nG$-bit fields $u,t$
+precede both slots and a third such field $b$ follows both slots. Arbitrary
+spectator fields may intervene. Each compact field has $n$ radix-$B$ digits.
+The selected-bit operation will preserve these three entire fields.
+
+\paragraph{Earlier source.}
+Suppose $x$ precedes $y$. The unused field $u$ is a spectator. For an integer
+target segment $v$, a bit $z$, and an arbitrary integer temporary $w$, perform
+\[
+ v\gets v+2zw,\qquad w\gets w+(v\bmod2),\qquad
+ v\gets v+z(1-2w),\qquad w\gets w-((v\bmod2)\mathbin\oplus z).
+\]
+Writing the original parity as $a$, the first update leaves it unchanged.
+The final values are $v+z(1-2a)$ and the original $w$. Thus this toggles
+only the parity of $v$ when $z=1$, and restores the dirty temporary.
+
+Apply these four updates simultaneously, with $z_i=x_{j_i}$, to the low
+$n$ selected segments of $y$ and the digits $t_i$ of $t$. A target-slot
+update is one modular rotation of $y$, whose offsets are respectively
+\[
+ \sum_{i<n}2x_{j_i}t_i2^{j_i},\qquad
+ \sum_{i<n}x_{j_i}(1-2t_i)2^{j_i} \pmod{2^{fK}}.
+\]
+Both control fields precede $y$. For a temporary update, swap $t$ with $b$,
+rotate the back field by the packed selected bits of the current $y$, and
+swap back. For unloading, use minus the packed bits
+$y_{j_i}\mathbin\oplus x_{j_i}$. These controls precede the back field.
+There are four width-$nG$ swaps and four rotations. The arbitrary original
+contents of $b$ return after each pair of swaps.
+
+\paragraph{Later source.}
+If $x$ follows $y$, first execute the earlier-source construction with control
+bits $u_i\bmod2$. Load the selected bits of $x$ into $u$ by swapping $u,b$,
+rotating the back field by their packed radix-$B$ representation, and swapping
+back. Repeat the earlier-source construction with the new parities of $u$,
+then unload the selected bits of $x$ from $u$ by the inverse load.
+When the digit loads do not overflow, the two control parities differ by
+exactly $x_{j_i}$. The resulting target update is the required XOR, with
+$u,t,b$ restored. This version uses twelve compact swaps and ten rotations.
+Every offset depends on a fixed number of fields preceding its target.
+
+\paragraph{Guards and deterministic repair.}
+Temporarily omit the highest selected position. The low $n$ segments
+$[j_i,j_i+K)$ are disjoint and fit inside $y$, including when $\rho=K-1$.
+Write each initial segment as $2g_i+a_i$, $a_i\in\{0,1\}$.
+Declare an address bad if a $t$ digit is $B-1$, or a target guard fails
+\[
+ 2B\le g_i<2^{K-1}-2B.
+\]
+For a later source also declare it bad if any $u$ digit is $B-1$.
+On a good address each temporary load stays within its digit, and the target
+displacement is at most $2B$ in either execution of the four-step identity.
+The conservative guard interval therefore prevents every carry or borrow
+between the wide segments. After each completed identity the guard is
+unchanged. Induction through the later-source sequence proves the desired
+map on the good set, including restoration of every temporary and every
+unselected address bit.
+
+Uniform complete ranges give the common bound
+\[
+ \delta=\min\{1,n(2\cdot2^{-G}+8\cdot2^{G-K})\}
+\]
+on the bad fraction; for an earlier source the first factor 2 can be omitted.
+The ideal map $T$ changes only the selected target parities, so it preserves
+the bad set. The actual sequence $S$ is a bijection on the entire rectangle:
+each rotation is independent of its target and all swaps are bijections.
+Since $S=T$ off the bad set, $S$ preserves that set too. Thus $TS^{-1}$ is
+supported there, exactly as in the original exceptional-stream repair.
+
+Extract the bad records, retaining marked holes in the full stream. For each
+extracted address $q$, reverse the swaps and modular rotations to compute
+$S^{-1}q$, then compute $T(S^{-1}q)$. All fields and descriptors have $O(A)$
+bits. A constant number of offset calculations each scan at most $n\le A$
+digits and combine shifted integers of $O(A)$ bits. Integer arithmetic,
+mixed-radix decoding, inverse offsets and the destination key can consequently
+be computed in $O(A^3)$ per record. Sort only the extracted records by their
+$O(A)$-bit destination keys, using stable binary radix passes, then reinsert
+them in their marked holes. Keys are distinct and fill precisely those holes
+because $TS^{-1}$ permutes the bad set. This uses fixed tapes and costs
+\[
+ O(V+MA^3+\delta MA(R+A)).
+\]
+Every inverse offset is evaluated on the current inverse controls; modular
+overflow on bad addresses is handled exactly, rather than treated as an
+integer identity. Finally, supply the omitted highest selected position
+through the elementary two-bit XOR in $O(V)$ time.
+
+\begin{proposition}[Compact-control selected-bit addition]
+\label{prop:compact-selected-addition}
+Under the stated complete-field hypotheses, take
+\[
+ G=4\lceil\log_2 p\rceil+6,\quad f\le p,\quad A=O(p),
+ \quad K/\log p\longrightarrow\infty,
+\]
+and let $R$ exceed every fixed power of $p$. The exact selected-bit row
+addition, with all temporary fields restored, costs
+\[
+ O\bigl(V((f\log p)^\tau+1)\bigr)
+\]
+on a fixed number of tapes, for either order of the two slots. Constants and
+cutoffs are uniform within each fixed parameter family of the layer theorem.
+\end{proposition}
+\begin{proof}
+Use the retained arbitrary-width chunk-swap primitive for the at most twelve
+swaps, each of width $nG$. Its padding, cleanup and all spectator intervals
+are covered by that interface. For every rotation, apply
+Lemma~\ref{lem:record-paid-rotation}; its offset arithmetic is polynomial
+in $A$. No new record volume is introduced by describing the compact fields.
+For $\ell_p=\lceil\log_2 p\rceil$, eventually
+$K\ge G+4\ell_p+10$. Then
+\[
+ \delta\le \frac{5}{128p^3},\qquad
+ \frac{A^3}{R}=o(1),\qquad
+ \delta A(1+A/R)=O(p^{-2}).
+\]
+The repair is therefore $O(V)$ per call, including predicate scans and key
+arithmetic. The elementary highest-bit operation costs $O(V)$. All calls
+reuse their fixed work tapes and finish in the declared physical field order.
+\end{proof}
+
+\paragraph{Application to a fixed binary change of basis.}
+The original phase-frame construction expresses each binary basis change
+as a fixed number of row additions on $m$ slots of $f=e/m$ axes. Use the
+two slots of each addition as $x,y$ and the reserved front/back compact
+fields as controls. The complete basis change and its inverse cost
+$O(V((e\log p)^\tau+1))$. The reservations below guarantee their complete
+ranges, independently of which slots are involved, at every recursive node.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/copied-centers-assembly.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/copied-centers-assembly.tex
new file mode 100644
index 0000000000..b0c69166c3
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/copied-centers-assembly.tex
@@ -0,0 +1,118 @@
+\subsection{Selected semantic guard and product rows}
+For each local producer retain
+\[
+ g_h=4(c_h+v_h)+10v_h+4hv_h+4h^2+8h+8.
+\]
+The two-stage literal scalar count includes two additional groups per
+copied center and one endpoint-addition group per data pair:
+\[
+ G=N_c+2v(g_{28}+2\cdot28)=4793351472.
+\]
+These are local scalar charges; the recursive copied transformations
+are already included in $s_c$. Set
+\[
+\begin{aligned}
+ E&=64(W_c+m_c+G+1)^3=9696565176891520488192506033216,\\
+ \mathcal E&=2GW_c^2+8s_c+4W_c+4+32m_c\\
+           &=2771683137698171397039558468<E,\\
+ B_{
m guard}&=s_c+E,\qquad C_0=32m_cB_{
m guard}^2.
+\end{aligned}
+\]
+A completed $u$-axis child has coefficients in $2^{-u}\mathbb Z[i]$
+and absolute row sum at most $2^u$. Its internal excess stays local;
+other streams, including originals of active copies, are parked.
+No return rounding or encoding change is performed. A copied input
+has the same incoming magnitude/grid bound as its original, and its
+completed output obeys the same semantic bound. Consequently, with
+$f=\lfloor e/m_c\rfloor$,
+\[
+ A(e)\le A(756f)+s_cf+E\le2B_{
m guard}e,
+\]
+using $2B_{
m guard}(m_c-756)\ge s_c+E$ and the direct-leaf bound
+$A(e)\le8e$. Prefix kernels, phases and normalization add the retained
+$18e$, which is less than $C_0e-2B_{
m guard}e$. Thus $C_1=1$,
+with the fixed fine-grid precision proof of RaD/PR23 unchanged.
+
+The actual least halving degrees and wire bitlengths are
+\[
+ (t_b,w_b)=(9,28),\qquad(t_c,w_c)=(20,30),
+\]
+where $m_j^{t_j}>2r_j^{t_j}$ for largest children $r_b=529,r_c=756$.
+At width $e$ reserve the product
+$Q=W_c^{D_c(e)}W_b^{D_b(e)}$, with
+$D_j(e)=t_j\lceil\log_2e\rceil$. Its coefficient is
+$9\cdot28+20\cdot30=852$, and
+\[
+ 2000>\frac{51}{25}\,852.
+\]
+The sufficient stock is therefore $p^{2000}$, supplied by the retained
+physically preceding transformed prefix and a single complete-row
+padding. Nested bit stock is restored before another complex child.
+Sequential copies introduce no independent row field. The supplementary
+suffix condition $b_{\rm in}^{1-\epsilon}>8000(\log_2b_{\rm in}+8)$
+is eventual for fixed $\epsilon<1$.
+
+\subsection{Exact conditional assembly}
+Use the analytic proof map in
+\path{notes/structured-bulk-assembly.tex}: arbitrary-source routing
+with active masking and paid repair scans; one rounded phase-cell
+matrix with preserved period cuts and downward-weight error bounds;
+persistent target halos, sequential overlap tapes and factor pages;
+Baker--Harman--Pintz prime packing; and the retained exact-recovery
+interface. Their full costs are unchanged. In particular the bulk
+bound retains the terms
+\[
+ O\!\left(Tp\left[p^\tau\operatorname{polylog}p+
+ d\operatorname{polylog}p+dp^\delta+w^2p^\delta+
+ dw^2p^\delta/L\right]\right)+n^{o(1)},
+\]
+with $L=2^{\lceil8\log_2p\rceil}$,
+$w^2=O(p^{1-r})$, and normalization exponent requiring
+$\epsilon+r<1$. These arguments, not a change of arithmetic model,
+justify the seven margins below.
+
+\begin{theorem}[Conditional fixed-tape multiplication bound]
+Under the retained analytic and fixed-tape interfaces of PR23/PR29
+and the preceding proof map, the selected copied-center networks give
+\[
+ T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad
+ \boxed{\kappa=\frac{384569}{10000000000}=3.84569\times10^{-5}}.
+\]
+\end{theorem}
+\begin{proof}
+Take the strict finite savings $a=a_b=384599/10^{10}$ and
+$b=a_c=717/10^7$, with $\tau=1-a$, $\sigma=1-b$, and put
+\[
+\begin{gathered}
+ \eta=10^{-8},\quad\beta=\tfrac14,\quad q=a(1-2\eta),\quad
+ c=q(1+\eta),\quad\epsilon=\frac{1-\eta}{1+c+q},\\
+ \lambda'=1-q,\quad\lambda=(\tau+\lambda')/2,\quad
+ g=\epsilon q,\quad r=(g+1-\epsilon)/2,\quad\delta=\eta/8.
+\end{gathered}
+\]
+The stopped complex leaf saving $(1-\beta)b=53.775\times10^{-6}$
+is strictly above $a$, so paid internal adapters use exponent $\tau$
+and both layer exponents lie below $\lambda'$. The exact certificate
+checks all 47 strict constraints of the retained semantic/bulk
+composition, using the new literal scalar charge and product-row gap.
+These include compact reservations, geometry, the linear guard,
+$\epsilon+r<1$, phase-cell/band separation, prime packing, short-record
+fallback and artificial-boundary allowances.
+
+The seven final savings are
+\[
+ 1-\epsilon(1+c),\quad a,\quad g,\quad a,\quad
+ \min(1-\epsilon-\delta,r-\delta),\quad
+ 1-\epsilon-\delta,\quad\epsilon.
+\]
+Their minimum is exactly $g$ and the prefix margin equals $g+\eta$.
+Exact rational comparison gives
+\[
+ g-\frac{384569}{10^{10}}>4.0746056580\times10^{-11}>0.
+\]
+These positive gaps absorb fixed logarithms. The all-size conclusion
+retains constructive finite setup, descriptor and catalogue domination,
+prime existence and analytic recovery as eventual thresholds. The
+strict bit and complex moments, copied-stream recurrence contracts and
+these assembly inequalities prove the claimed conditional bound.
+\end{proof}
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/copied-centers-lemma.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/copied-centers-lemma.tex
new file mode 100644
index 0000000000..8933aaf508
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/copied-centers-lemma.tex
@@ -0,0 +1,103 @@
+\subsection{Scalar, frame and temporary-stream contracts}
+The retained source-copy, reversible mixer and scatter maps satisfy
+$JLV=I$. Over $\mathbb F_2$ the chronological word
+\[
+ L,\ J,\ L^{-1},\ V,\ L,\ J,\ L^{-1},\ V
+\]
+adds the input to the target and restores every arbitrary auxiliary.
+Over Gaussian dyadics use its corresponding old-value subtraction and
+new-value addition. A designated retained output has a distinct terminal
+output-use carrier: a matching may feed that carrier, but cannot merge
+two designated terminals or append a later middle-producer consumer.
+Its remaining uses before cleanup are its scatter reads, all of which
+leave its scalar value unchanged.
+
+Within one tensor invocation suppress the fixed future line and put
+\[
+ D_0=B\otimes F_h,\quad D_1=A\otimes F_h,\quad
+ A=B\mathbin{\perp}P,\quad D_U=D_0\mathbin{\perp}(P\otimes U),
+\]
+where $P$ and the suppressed future factor are one-dimensional and
+$U$ is a nondegenerate retained-center space of dimension $r$.
+Thus a local change of rank $d$ has ambient rank $d$.
+Write $\mathcal F_Q$ for the address frame: it is the rational partial
+swap $D_Q$ in the bit construction, and the binary phase $C_Q$ in the
+complex construction. Changing a copy from frame $Q_1$ to $Q_2$ means
+applying $\mathcal F_{Q_2}\mathcal F_{Q_1}^{-1}$ to its physical stream.
+Orthogonal backgrounds cancel in this quotient.
+
+Copies use Paureel's retained copy/transform/read/discard interface
+\cite{paureel,pr29}. A copy has precisely the original complete role
+stream, including all control and spectator ranges, and volume $V/W$.
+It is processed while inactive original streams are parked on the fixed
+depth-first stack tapes. Copying, pointwise reads and erasure are linear
+in that stream's volume. Sequential processing needs one additional
+fixed work stream, not an independently varying row coordinate.
+
+\begin{lemma}[Copied retained-center schedule]
+In either invocation orientation a designated retained center's
+physical rank profile can be changed from $z^r+z^h$ to
+$z^r+z^{h-r}$, with the same scalar action, original role endpoints,
+and arbitrary-scratch restoration. The rank-$r$ transform on the copy
+is included in the recursive call list.
+\end{lemma}
+\begin{proof}
+In the forward orientation the original center has scalar value $w$
+at frame $D_U$ after the middle mixer. Its old sequence was
+$D_U\to D_0\to D_1$: scatter at $D_0$, then cleanup at $D_1$,
+with ranks $r,h$.
+Keep the original at $D_U$, copy its physical stream, and transform
+only the copy to $D_0$, paying rank $r$. Supply every scatter read
+from that transformed copy while its data targets remain at their
+unchanged common frame $D_0$, then erase the temporary. The reads
+are exactly those of $w$ in the old schedule. Since they do not change
+$w$, move the original directly from $D_U$ to $D_1$ before its first
+cleanup incidence; this costs $h-r$. Every subsequent original gate
+therefore receives the same scalar value at its required frame.
+
+In the reverse complementary orientation the old sequence was
+$D_0\to D_1\to D_{U^\perp}$, with ranks $h,r$ and scatter at $D_1$.
+After the preceding all-$D_0$ operations, advance the original directly
+to $D_{U^\perp}=D_0\mathbin{\perp}(P\otimes U^\perp)$, paying
+$h-r$. Copy it and transform the copy to $D_1$, paying $r$.
+Use that copy for all early scatter reads, then erase it. The original
+already has the exact frame and unchanged scalar value required by the
+following inverse mixer. Terminal output-use separation ensures no
+intervening producer consumer has been bypassed.
+
+For partial swaps either direction of the rank-$r$ change is the same
+involution. For complex phases the forward copy uses $C_U^{-1}$,
+the direct original growth uses $C_{U^\perp}$, and the reverse copy
+uses $C_FC_{U^\perp}^{-1}=C_U$. These are the same charged ranks,
+implemented by the retained forward/inverse residual interface.
+All tensor backgrounds cancel as stated. Every original scalar
+incidence, final source-copy cancellation and auxiliary source/sink
+operator is unchanged. Thus the scalar identity and all endpoints
+remain exact on arbitrary initial auxiliary values.
+\end{proof}
+
+For the selected centers $r=h-1$, and there are $h$ distinct retained
+output uses per invocation. Their old histogram has rank mass
+$hR_h+2\ell_h$, where $\ell_h=h(h-1)$. The new histogram is exactly
+\[
+ H'_{h,1}=H_{h,1}+h,\qquad H'_{h,h}=H_{h,h}-h,
+ \qquad H'_{h,r}=H_{h,r}\quad(r\ne1,h),
+\]
+and hence $\sum_r rH'_{h,r}=hR_h+\ell_h$.
+Every old rank-$(h-1)$ residual remains as a paid transform of a copy;
+its projector and ordinary bit pivot profile are unchanged. Only the
+full-rank original transition becomes the rank-one complement.
+The physical role count $R_h$ is unchanged.
+
+For two factors, put $N=v_av_b$, $B_a=v_bR_a$, $B_b=v_aR_b$,
+$W=2N+B_a+B_b$ and $L=v_b\ell_a+v_a\ell_b$.
+All exterior, data-front and endpoint-correction calls remain in place.
+The resulting complete rank mass is
+\[
+ s=Wm-N+L,\qquad Wm-s=N-L.
+\]
+This follows by subtracting exactly $L$ from the retained two-stage
+physical mass $Wm-N+2L$. The $N$ rank-one endpoint-copy calls are
+separate and remain fully charged. Because center copies retain the
+same complete role-volume fraction $1/W$, the existing complete-row,
+integer-width remainder and fixed-tape recurrence proofs apply.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/endpoint-gauge-complex.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/endpoint-gauge-complex.tex
new file mode 100644
index 0000000000..907a0ceda8
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/endpoint-gauge-complex.tex
@@ -0,0 +1,225 @@
+\subsection{A normal form for every nondegenerate binary residual}
+Let $E$ have binary basis matrix $V$ and nonsingular Gram matrix
+$G=V^tV$. In dual Fourier coordinates put
+$q(z)=\operatorname{wt}(VG^{-1}z)\pmod4$.
+Its polarization is $2z^tG^{-1}w$. The same argument applies to mixed
+signs on orthogonal summands, since reversing a sign preserves this
+polarization. Write $S_q=\sum_z i^{q(z)}$. Completing the square gives
+\[
+\begin{aligned}
+K(x,y)&=2^{-r}\sum_z i^{q(z)}(-1)^{z^t(x+y)}\\
+ &=2^{-r}S_q\,i^{-q(Gx)}(-1)^{x^tGy}i^{-q(Gy)}.
+\end{aligned}
+\]
+The scaled Walsh kernel in the middle is a binary permutation of
+$H_0^{\otimes r}$, where
+\[
+ H_0=\tfrac12\begin{pmatrix}1&1\\1&-1\end{pmatrix}
+     =bSCS,\qquad b=(1-i)/2,\quad S=\operatorname{diag}(1,i).
+\]
+The remaining scalar $S_qb^r$ is a fourth root of unity. To verify
+this, decompose the nondegenerate quadratic module into odd
+one-dimensional and alternating two-dimensional blocks. Their Gauss
+sums are $1\pm i$ and $\pm2$, respectively; multiplying by $b$ and
+$b^2$ gives a fourth root in each case. This is a proof device, not
+an orthonormal-basis assumption on $E$.
+
+Consequently one rank-$r$ child suffices, with binary address changes,
+diagonal fourth-root phases, and one scalar fourth-root phase.
+On $f$ parallel columns it is one $C^{\otimes rf}$ child, the scalar
+raised to power $f$, and columnwise quadratic phases modulo four.
+The retained packed address operations evaluate these fixed formulas.
+These wrappers have modulus one and introduce no denominator loss.
+
+\subsection{The selected Gaussian-dyadic producer}
+Use paired triple exclusion with base threshold two, complete unsplit
+disjoint and pair-star sums, and sharing by actual ordinary support.
+For an ordinary support with at least two common points use the span
+of its triple indicators; these form an orthonormal common-pair star.
+Otherwise use the coordinate space of its union. Support inclusion
+preserves these labels: losing the common pair enters a containing
+coordinate space. Source lines use ordinary triple containment.
+
+Retain every full pair-star $P_{uv}=\sum_{w\ne u,v}X_{uvw}$ and form
+$B_u=\sum_{v\ne u}P_{uv}=2\sum_{T\ni u}X_T$.
+For even $h$ label these central additions by the nondegenerate
+hyperplane $E_u=\{x:\sum_{j\ne u}x_j=0\}$; every contributing star
+lies in it. Retain the global total $T$ with full-space label.
+The central correction at target $S$ is
+\[
+ \frac14\sum_{u\in S}B_u-\frac12T
+       =\sum_U\frac{|S\cap U|-1}{2}X_U.
+\]
+Adding half the disjoint sum and subtracting half the intersection-two
+sum gives exactly $X_S$. All coefficients are Gaussian dyadic.
+The transparent retained-output wrapper and oriented carrier compiler
+apply to these nested nondegenerate labels. The $h$ hyperplane centers
+lose $h(h-1)$ and the global center loses $h$, so loss is $h^2$.
+The selected counts, including all point centers, are
+\[
+\begin{array}{c|rrrrrr}
+h&v_h&c_h&q_h&|\mathcal M_h|&R_h&\text{loss}\\\hline
+32&4960&122512&19873&19241&123144&1024\\
+30&4060&99153&16271&15873&99551&900\\
+40&9880&252023&39561&37642&253942&1600
+\end{array}
+\]
+Their internal histograms satisfy $\sum_r rH_{h,r}=hR_h+2h^2$.
+They are distinct from the bit histograms.
+
+\subsection{Endpoint normalization and the complex characteristic}
+For nondegenerate $U$, Fourier phases give
+\[
+ C_U^2=X_{P_U\mathbf1},\qquad
+ C_{U^\perp}C_U^{-1}=C_FX_{P_U\mathbf1}.
+\]
+Put $v=P_U\mathbf1$. On coordinates in $v$, this endpoint has
+$C^{-1}$ instead of $C$. The identity $C^{-1}=-iZCZ$ shows that
+conjugating by $Z_v$ and multiplying by $i^{\operatorname{wt}(v)}$
+normalizes it to $C_F$; for $f$ columns the exponent is
+$f\operatorname{wt}(v)$. These are diagonal wrappers without a child.
+
+Choose stage-two source $C_{D_0}$ and sink $C_{D_0^\perp}$, where
+$D_1=D_0\mathbin{\perp} A$ and $\dim A=b$. The same refined copy
+schedule removes the entrance on every auxiliary role. With
+$R=D_1^\perp$, the exit is $C_RC_{D_0}^{-1}$ on
+$E=R\mathbin{\perp}D_0=A^\perp$. Its rank is $m-b$ and its
+nondegenerate polar form is unchanged by the mixed signs. The normal
+form above executes it as one child. Arbitrary auxiliary restoration
+justifies the endpoint normalization on the entire $B_2$ bank.
+
+Use the complex counts to define $B_i=NR_{h_i}/v_{h_i}$, and now
+\[
+\begin{aligned}
+W&=2N+B_2+B_3=10390178240000,\\
+L&=\sum_i(N/v_{h_i})h_i^2=117399987200,\\
+s&=Wm-2N+2L=398982681296998400.
+\end{aligned}
+\]
+The whole-residual macro list is
+\[
+\begin{array}{c|rrrrr}
+t&38328&38360&38370&37401&899\\\hline
+n_t&B_1&B_3-B_1&B_2&2N&2N.
+\end{array}
+\]
+Add $(N/v_h)H_{h,r}$ rank-$r$ children for each positive internal rank.
+Leave the remaining physical-data rank, 39393978624000, as singleton
+calls. The resulting list has weighted rank exactly $s$.
+For $a_c=3/125000$ and $\sigma=1-a_c$, the rational logarithm bounds
+above and $e^u\le(1-u)^{-1}$, $0\le u<1$, give
+\[
+ \Psi_c(\sigma)\le\sum_t\frac{n_tt}{Wm(1-a_c\ell_t)}
+ <1-\frac{792981575160764}{10^{23}}.
+\]
+
+\subsection{The dependency-path guard}
+Before gauging, nested producer labels telescope along every arithmetic
+path, including wire switches at common-frame scalar gates. Retained
+center drops occur on one return frontier per stage, crossed at most
+once by a path, and each costs at most that axis dimension. Carrier
+reuse adds only increasing continuations. This gives
+$q_0=m+2(a+b+k)$. Gauging removes an early edge and adds $ab-b$ at
+a late stage-two edge. A path meets at most one such edge, since it
+terminates that stage-two role, which is not shared across stages.
+Thus the conservative total rank budget is
+\[
+ q=m+2(a+b+k)+ab=39564.
+\]
+Every child except the four large macros is at most 899; two large
+macros cannot fit within $q$. Set $\rho=19/10$, $\gamma=9997/10000$.
+The integer comparisons $m^{19}>500000000^{10}$ and
+$899^9<460^{10}$ give $m^\rho>500000000$ and
+$899^{\rho-1}<460$.
+If a path has one large child $t$, its moment is at most
+\[
+ (t/m)^\rho+(q-t)899^{\rho-1}/m^\rho.
+\]
+This expression increases over the large-child range, since its
+numerator derivative is $\rho t^{\rho-1}-899^{\rho-1}>0$.
+Use $t=m-b$ and the concavity bound
+$(1-x)^{19/10}\le1-19x/10+9x^2/10$ to obtain
+\[
+ \sum_{\rm path}(r/m)^\rho
+ <1-\frac{19}{12800}+\frac9{10\cdot1280^2}
+       +\frac{1194\cdot460}{500000000}
+ =\frac{51180270301}{51200000000}<\gamma.
+\]
+Without a large macro the bound is $227493/6250000<\gamma$.
+
+For coefficient-depth accounting take $E_0=128(W+m+1)^3$.
+There are at most $s$ positive-rank residual calls and $W$ endpoint
+normalizations. Combining the quadratic phases with the $S$ factors,
+each uses at most two diagonal phase passes and one scalar phase.
+The inherited gate and remainder count is therefore bounded conservatively by
+\[
+ 36W^3+16s+16W+8m+4<E_0.
+\]
+Binary address changes only permute coefficients; descriptor evaluation
+is paid by the retained packed record work and does not increase
+coefficient depth.
+Stop below width $d^\beta$, where $\beta=1/1000$.
+For $e=mf+r$, $0\le r<m$, recurse on $tf$ and treat the remainder
+individually. For sufficiently large $d$, a leaf descending from an
+internal node has width at least $d^\beta/(2m)$. Choose
+$C_{\rm dep}\ge16m$ and
+$(1-\gamma)C_{\rm dep}\ge E_0+16m+1$.
+The retained elementary-kernel bound $A(e)\le8e$ and strong induction
+using the path moment imply
+\[
+ A(e)\le C_{\rm dep}d^{-\beta(\rho-1)}e^\rho.
+\]
+At a leaf the lower width bound proves this inequality, while at an
+internal node the unused $1-\gamma$ fraction covers local work.
+Small roots are handled directly. With $\zeta=1/10000$ take
+\[
+ C_1=\rho-(\rho-1)\beta+\zeta=\frac{1187}{625},\quad
+ C_0=\left\lceil128m(1+1/\zeta)C_{\rm dep}\right\rceil,
+ \quad\Delta=\lceil C_0d^{C_1}\rceil.
+\]
+The retained exact denominator/magnitude-depth induction gives
+$p+\Delta$ fractional bits and $\Delta+3$ integer/sign bits.
+All selected scalar coefficients are Gaussian dyadic and the new
+wrappers have modulus one, so that induction still applies.
+For $\epsilon C_1<1$ their total width is $O(p)$.
+\subsection{Rows, stopping, and transfer to the layer interface}
+Let $t_*<m$ be the largest child and compute
+$D(e)=0$ for $e<m$ and $D(e)=1+D(t_*\lfloor e/m\rfloor)$ otherwise.
+It is $O(\log e)$ and bounds every descendant depth.
+With the retained compact-control parameters, reserve
+\[
+ q_0=\lceil\log_2W\rceil D(d),\qquad Q_0=q_0+q_F+q_B.
+\]
+Process the first $q_0+q_F$ and last $q_B$ selected axes individually;
+if at most $Q_0$ axes exist, process them all individually. Otherwise
+the middle active interval is consecutive. Only the $q_0$ row chunks
+supply row indices, separate from the two compact fields. Pad their
+count once to a multiple of $W^{D(d)}$, by a factor below two.
+Every child retains complete compact and spectator ranges and has
+exactly $1/W$ of its parent's volume. No internal padding is needed.
+The reserved-axis bound remains
+\[
+ Q_0=O(\log(2d)+d^{\max\{1-c,0\}}\log p+1).
+\]
+Remainders commute with the completed tensor map and cost $O(V)$ per
+node. The fixed-tape depth-first scheduler and complete-row argument
+of the bit construction apply with the retained compact descriptors.
+
+Since $\Psi_c(\sigma)<1$, the total leaf $\sigma$-weighted width,
+including the volume factor $W^{-j}$ at depth $j$, is at most
+$d^\sigma$. Thus leaf work is
+$O(d^{\sigma+\beta(1-\sigma)})$. Internal compact operations cost
+$O(G^\tau e^\tau+1)$ per current volume. Summing the strict moments
+gives the retained complete normalized layer bound
+\[
+ O\!\left((\log p)^3\left[
+ d^\chi+d^{\sigma+\beta(1-\sigma)}+d^{\max\{1-c,0\}}+1
+ \right]\right),\qquad
+ \chi=\tau+(1-\beta)\max\{\sigma-\tau,0\}.
+\]
+For $\sigma\le\tau$, use $\Psi_c(\tau)\le\Psi_c(\sigma)$;
+otherwise use $e^\tau\le d^{\beta(\tau-\sigma)}e^\sigma$ at each
+internal node. These arguments do not assume equal leaf depth.
+The usual strict conditions on $\lambda,\lambda'$ therefore give
+the retained $O(Vd^{\lambda'})$ layer interface, now with the new
+moment and the new $C_{\rm dep}$.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/general-clifford-frames.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/general-clifford-frames.tex
new file mode 100644
index 0000000000..0367eeb005
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/general-clifford-frames.tex
@@ -0,0 +1,102 @@
+\subsection{Preimage frames for arbitrary binary subspaces}
+This frame construction is due to icekylinx with OpenAI GPT-6 Astra assistance;
+the present exposition and integration use Codex.
+Let $H=\mathbb F_2^h$ with the standard dot product. In the binary
+symplectic space $H\oplus H$ put
+\[
+ L_0=\{(0,z)\},\qquad
+ F=\begin{pmatrix}I&I\\0&I\end{pmatrix},\qquad
+ L_F=FL_0=\{(z,z)\}.
+\]
+We also write $F$ for the exact Gaussian-dyadic operator $C^{\otimes h}$.
+Its exact square is a Pauli translation; only its binary symplectic square
+is the identity. For an exact Clifford operator $T$ the frame label is
+$L(T)=T^{-1}L_0$. The physical transition from $T$ to $S$ is $ST^{-1}$,
+and its Fourier rank is
+$d(L(S),L(T))$, where $d(L,L')=h-\dim(L\cap L')$.
+This follows by transporting the intersection by $S$: the intersection
+with $L_0$ computes the kernel dimension of the $B$ block of $ST^{-1}$.
+
+\begin{lemma}
+For every subspace $U\subseteq H$, including degenerate subspaces,
+\[
+ L_U=\{(u,u+v):u\in U,\ v\in U^\perp\}
+\]
+is Lagrangian, and
+\[
+ d(L_U,L_V)=\dim U+\dim V-2\dim(U\cap V),\qquad
+ FL_U=L_{U^\perp}.
+\]
+\end{lemma}
+\begin{proof}
+The displayed parametrization is injective and has dimension $h$.
+Its symplectic pairing is $u\cdot v'+v\cdot u'=0$.
+In an intersection, $u$ belongs to $U\cap V$ and $v$ to
+$(U+V)^\perp$, giving the asserted dimension and distance.
+Finally $F(u,u+v)=(v,u+v)$ proves the complement identity.
+\end{proof}
+
+\subsection{Exact representatives and nested children}
+Choose a deterministic invertible binary matrix $G$ carrying the first
+$r=\dim U$ coordinate space $E_r$ to $U$, and set
+\[
+ K_G=\begin{pmatrix}G&0\\G+G^{-T}&G^{-T}\end{pmatrix},\qquad
+ T_U=K_G T_{E_r}K_G^{-1}.
+\]
+Here $T_{E_r}$ is the exact coordinate $C$ operator, and the $K_G$ are
+exact Gaussian-dyadic Clifford lifts. The matrix $K_G$ is symplectic
+because $G^TG+I$ is symmetric. It fixes both $L_0,L_F$ and maps $L_V$
+to $L_{GV}$. Thus both $K_G$ and $FK_GF^{-1}$ have Fourier rank zero;
+their lifts are fixed binary address permutations with unit quadratic
+phases. In particular,
+\[
+ L(T_U)=L_U,\quad \operatorname{rank}B(T_U)=r,\quad
+ \operatorname{rank}B(FT_UF^{-1})=r,\quad T_U^2\text{ is Pauli}.
+\]
+Set $V_U=GE_r^\perp$, a direct complement of $U$. The binary action gives
+$T_U^{-1}L_F=L_{V_U}$ and hence
+$\operatorname{rank}B(FT_U^{-1})=h-r$.
+No assertion $V_U=U^\perp$ is needed.
+For the norm-one source lines and their orthogonal target hyperplanes,
+retain the inherited exact representatives; set $T_0=I,T_H=F$.
+At every common scalar gate use one identical exact representative on all
+incident registers. If separately transported representatives have the
+same preimage, their physical ratio has rank zero and is implemented as
+an actual left adapter before the gate.
+
+For $U\subseteq V$, the exact transition $T_VT_U^{-1}$ has rank
+$\dim V-\dim U$. Clifford elimination expresses it as two rank-zero
+adapters surrounding that many coordinate Fourier factors. These factors
+are a single $C^{\otimes r}$ child: the scaled Hadamard satisfies
+\[
+ \frac{1+i}{2}\begin{pmatrix}1&1\\1&-1\end{pmatrix}
+   =SCS,\qquad S=\operatorname{diag}(1,i).
+\]
+Thus no new irrational field is introduced. All adapters are charged
+finite movement and scalar operations. Exact transitions telescope;
+commutativity between distinct $T_U$ is unnecessary.
+
+\subsection{Dirty tails and reverse/complement words}
+A dirty role entering with gauge $T_\sigma$ and whose last active frame
+is $T_U$, with $\sigma\subseteq U$, is assigned terminal gauge
+$FT_\sigma$. Its logical value is restored by the complete transparent
+scalar word, so its physical action is exactly $F$. The tail is
+$FT_\sigma T_U^{-1}$. Its rank is
+\[
+ d(L_U,L_{V_\sigma})=h-\dim U+\dim\sigma.
+\]
+Indeed $H=\sigma\oplus V_\sigma$ and $U\supseteq\sigma$ imply
+$\dim(U\cap V_\sigma)=\dim U-\dim\sigma$.
+An inactive exterior adds $m-h$, giving $m-\dim U+\dim\sigma$.
+
+For the complete time-reversed word use
+\[
+ D_U=T_UF^{-1},\qquad L(D_U)=L_{U^\perp},\qquad
+ D_UD_V^{-1}=T_UT_V^{-1}.
+\]
+The last equality is exact, so reversal preserves every inverse transition
+rank. Reverse the scalar signs and the whole transparent word, including
+old-value corrections and final cleanup. The endpoints $D_0=F^{-1}$
+and $F$ differ by a Pauli, and the inherited norm-one endpoints are
+reconciled by actual rank-zero adapters. Neither equality of binary
+matrices nor equality of frame cosets substitutes for these operators.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/stopped-product-complex.tex b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/stopped-product-complex.tex
new file mode 100644
index 0000000000..4a9037137c
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/retained/stopped-product-complex.tex
@@ -0,0 +1,137 @@
+\subsection{All-disjoint retained centers}
+Use two factors $h=24$. For triple inputs write $G=\sum_TX_T$,
+$T_i=\sum_{T\ni i}X_T$, and retain all $A_i=G-T_i$.
+Each input triple avoids exactly 21 points, so
+\[
+ \sum_{i=1}^{24}A_i=21G,\qquad G=\frac1{21}\sum_i A_i.
+\]
+For a target triple $S$ the central correction is
+\[
+ G-\frac12\sum_{i\in S}A_i
+       =\frac{\sum_{i\in S}T_i-G}{2}.
+\]
+An input triple meeting $S$ in $j$ points has central coefficient
+$(j-1)/2$. Adding half the disjoint sum and subtracting half the
+intersection-two sum leaves coefficient one exactly when $j=3$.
+The scalar source-to-scatter transfer is therefore the identity.
+The transparent old-value subtraction and new-value addition use this
+identity only on fresh contributions and restore arbitrary old values.
+
+The base-two paired exclusion and aligned pair-star producer retains
+nested binary labels: common-pair supports have their orthonormal triple
+span, other ordinary sums have their coordinate cover. Each retained
+$A_i$ has the nondegenerate coordinate hyperplane excluding $i$,
+of dimension 23. Hence all copied-center arguments and general
+nondegenerate binary residuals of the preceding proof apply. The
+selected local counts are
+\[
+ v=2024,\quad c_h=45764,\quad q_h=8120,\quad
+ |\mathcal M|=8966,\quad R=44918,\quad\ell=552.
+\]
+The old internal histogram, starting at rank zero, is
+\begin{small}\begin{align*}
+[&8930,49042,30844,15972,11883,8272,6399,4356,6682,2263,\\
+ &5109,1808,5317,1733,5391,1757,4908,3290,6233,4363,\\
+ &4056,264,564,24,24].
+\end{align*}\end{small}
+It has rank mass $24R+2\ell$. Replace 24 rank-24 original transitions
+by 24 rank-one transitions; all rank-23 copied transforms remain.
+The new mass is $24R+\ell$.
+
+\subsection{Physical endpoints and strict complex moment}
+The copied-center two-stage complex contract in
+\path{notes/copied-centers-complex.tex} is unchanged by the scalar
+center decoding. For the tensor triple line $U$, let
+$T=C_U$, $F=C_I$, $E=C_{U^\perp}=FT^{-1}$.
+The two data outputs are $A=-Fy$ and $B=FT^{-2}x+Ey$.
+Add $T^{-1}$ applied to a copy of $A$ into $B$, paying one rank-one
+child per data pair. The inherited input/output $Z$ phases and
+$i^{9f}$ scalar normalize $FT^{-2}$ to $F$; sign and bank corrections
+complete the exact tensor $C$. Auxiliary source/sink operators remain
+$C_{D_0}$ and $FC_{D_0}$ in the second stage. Every original role
+therefore returns the exact selected-axis tensor operation on arbitrary
+inputs. This algebraic statement holds over $\mathbb Q(i)$ as well as
+over Gaussian dyadics.
+
+With $m_c=576$, $N_c=v^2=4096576$, $B_c=vR=90914032$, put
+\[
+ W_c=2N_c+2B_c=190021216,\quad L_c=2v\ell=2234496,
+\]
+\[
+ s_c=W_cm_c-N_c+L_c=109450358336,\qquad N_c-L_c=1862080.
+\]
+The complete list is $2B_c$ width-552 auxiliary exteriors,
+$2N_c$ width-529 data macros, $2vH'_r$ width-$r$ internal children,
+$4N_c$ width-23 data fronts, and $N_c$ width-one endpoint copies.
+These disjoint classes include both kinds of paid copies and sum to
+$s_c$. All binary residuals, including alternating forms, use the retained
+one-child Gauss normal form with paid bit adapters and unit phases.
+At $a_c=1949/25000000$ the exact rational enclosure gives
+\[
+ \sum_r\frac{n_r}{W_c}(r/m_c)^{1-a_c}
+ <1-1.3338373969\times10^{-10}.
+\]
+
+\subsection{One exact odd-denominator grid}
+The only new odd divisor is 21. Let $d$ bound the root axis count,
+$D$ bound its maximum complex recursion depth, and $G_0$ bound the
+number of grouped scalar operations per node. Choose
+\[
+ K=G_0(D+1),\qquad \text{common grid }2^{-P}21^{-K}.
+\]
+Root inputs and arbitrary dirty auxiliaries start Gaussian dyadic.
+Multiply their integer numerators by $21^K$ once at the outer boundary.
+Every local coefficient contains at most one factor 21 in its denominator,
+so a local finite program adds at most $G_0$ to the odd-denominator
+exponent. A completed $u$-axis child has Gaussian-dyadic coefficients
+and therefore preserves its input's existing odd-denominator exponent;
+it adds no new odd factor. Only the active chain of unfinished calls
+can accumulate new factors. Its length is at most $D+1$, proving that
+all intermediates lie on the common grid and every local division by
+21 is an exact integer division of its encoded numerator.
+
+This divisibility claim uses the root dyadic-input invariant, not an
+assumption about arbitrary numerators on the finest grid. Internal values
+may have odd denominators. They are neither rounded nor re-encoded when
+a child returns. At the completed outer return the operator is the exact
+Gaussian-dyadic tensor on root dyadic inputs, so the final numerators
+are divisible by $21^K$; exact unscaling restores dyadic encoding.
+
+Since the largest child is $552<576$, $D=O(\log d)$ and
+$K=O(\log d)$ with fixed constants. Constant-divisor long division
+is linear in numerator length. Initial and final scaling by $K$
+successive constant multiplications/divisions cost $O(V\log d)$ and
+occur only at the outer boundary. The extra numerator length is
+$O(\log d)$, preserving the retained $O(p)$ word bound. This overhead
+is subordinate to the positive-power complex layer bound.
+
+For explicit semantic constants use
+\[
+ g_h=4(c_h+v)+10v+4hv+4h^2+8h+8=408200,
+\]
+\[
+ G_0=N_c+2v(g_h+2h)=1656684480,
+\]
+where endpoint additions and copied-center scalar work are included.
+The complete child contributes at most $u$ binary denominator bits
+and row-norm factor $2^u$, with no additional odd exponent. A local
+21-division contributes fewer than five denominator-height bits,
+covered by the fixed scalar charge. Set
+\[
+\begin{aligned}
+ E_0&=64(W_c+m_c+G_0+1)^3=403063477262941121443761178688,\\
+ \mathcal E&=2G_0W_c^2+8s_c+4W_c+4+32m_c\\
+           &=119639333593035096270287748<E_0,\\
+ B_0&=s_c+E_0,\qquad C_0=32m_cB_0^2.
+\end{aligned}
+\]
+With $f=\lfloor e/m_c\rfloor$, the completed-child induction is
+\[
+ A(e)\le A(552f)+s_cf+E_0\le2B_0e,
+\]
+since $2B_0(m_c-552)\ge s_c+E_0$. It counts total denominator height
+and magnitude, including the local odd factor. The retained prefix and
+normalization allowance $18e$ fits inside $C_0e$. Together with the
+$O(\log d)$ common-grid encoding overhead this gives $C_1=1$ and
+$O(p)$ records for $d=\lfloor b_{\rm in}^{\epsilon}\rfloor$,
+$p=6b_{\rm in}$, fixed $\epsilon<1$.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/source-pins.json b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/source-pins.json
new file mode 100644
index 0000000000..5cb04b0c72
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/source-pins.json
@@ -0,0 +1,215 @@
+{
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+  "certificate": {
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+    "uncompressed_sha256": "c64d2a95431c3cf24452de7391cce780bd71521da44ce23923ebb235f6c7962c",
+    "path": "inputs/complex/gcert1-p11-pr193.json.gz"
+  },
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+      "sha256": "dfee33b0281e5551bb6927f757ff0240abade60ae1800f715afd88853ae0191e",
+      "upstream": "notes/endpoint-gauge-complex.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/copied-centers-lemma.tex": {
+      "sha256": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe",
+      "upstream": "notes/copied-centers-lemma.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/copied-centers-assembly.tex": {
+      "sha256": "00117892971ae766188ace0af03030c44164fda105e42b70d84f52c3339a7dcb",
+      "upstream": "notes/copied-centers-assembly.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/stopped-product-complex.tex": {
+      "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a",
+      "upstream": "notes/stopped-product-complex.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/compact-control-layout.tex": {
+      "sha256": "2bc28e50f3eb092195294cafa81213e520f6d42e7935e9905ad8a6199e2a7c87",
+      "upstream": "notes/compact-control-layout.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/compact-control-movement.tex": {
+      "sha256": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+      "upstream": "notes/compact-control-movement.tex",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    },
+    "inputs/complex/retained/FINITE_BRIDGE.txt": {
+      "sha256": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46",
+      "upstream": "research/source-assisted/global/FINITE_BRIDGE.txt",
+      "source_pin": "187e1010ac8b259af8e9b5166f68b64bc27b4b47"
+    }
+  }
+}
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Bridge__Cert.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Bridge__Cert.lean
new file mode 100644
index 0000000000..f7bdc3d903
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Bridge__Cert.lean
@@ -0,0 +1,241 @@
+import Work.Bridge.Net
+
+/-!
+# (key: bridge-net) The certificate of the BRIDGED five-stage network B_2
+
+The three layers of free gates between twins, the signed exchange, and
+
+    theorem bridge2_certificate (N : Bridge2 H T Sl C α Γ) :
+        BCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) (fun φ => card Γ * N.unit φ)
+
+Scalar chain of one class (`x1 y1 x2 y2` on `X1 Y1 X2 Y2`), as in `bridged-word.md`:
+
+    stage 0  F on pair 1     Y1 = y1 + x1
+    stage 1  B on pair 1     X1 = -y1
+    gates A  X1 += X2,  Y2 -= Y1
+    stage 2  F on pair 1     Y1 = x1 + x2
+    gates B  Y2 += Y1,  X1 -= X2          (X1 = -y1, Y2 = y2 - y1 + x2)
+    stage 3  B on pair 2     X2 = y1 - y2
+    stage 4  F on pair 2     Y2 = x2
+    gates C  Y1 -= Y2,  X2 += X1          (X1 = -y1, X2 = -y2, Y1 = x1, Y2 = x2)
+    exchange X_i := Y_i, Y_i := -X_i
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace BR
+open Binary Matrix Finset RAM SS CB RF
+noncomputable section
+
+section Gates
+variable {Γ T Sl C : Type}
+
+/-- source of the gates of the layers A and B: `X1 ← X2`, `Y2 ← Y1`. -/
+def pAB : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kX2 (g,t)) (fun g t => kY1 (g,t)) (fun g t => kX2 (g,t))
+    (fun g t => kY1 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+/-- layer A: `X1 += X2`, `Y2 -= Y1`. -/
+def kA : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => -1) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- layer B: `X1 -= X2`, `Y2 += Y1`. -/
+def kB : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => -1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- source of the gates of the layer C: `Y1 ← Y2`, `X2 ← X1`. -/
+def pC : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kX1 (g,t)) (fun g t => kY2 (g,t)) (fun g t => kX1 (g,t))
+    (fun g t => kY2 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+/-- layer C: `Y1 -= Y2`, `X2 += X1`. -/
+def kCc : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 0) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => 0) (fun _ _ => 0) (fun _ _ => 0)
+
+/-- scalar map of a gate layer. -/
+def gsc (p : BRole Γ T Sl C → BRole Γ T Sl C) (k : BRole Γ T Sl C → ℚ)
+    (x : BRole Γ T Sl C → ℂ) : BRole Γ T Sl C → ℂ := fun i => x i + (k i : ℂ) * x (p i)
+
+/-- the signed exchange `X_i := Y_i`, `Y_i := -X_i` on both pairs. -/
+def bpull : BRole Γ T Sl C → BRole Γ T Sl C :=
+  mkB (fun g t => kY1 (g,t)) (fun g t => kX1 (g,t)) (fun g t => kY2 (g,t))
+    (fun g t => kX2 (g,t)) (fun g q => kS (g,q)) (fun g c => kC (g,c))
+
+def bsgn : BRole Γ T Sl C → ℚ :=
+  mkB (fun _ _ => 1) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => -1) (fun _ _ => 1) (fun _ _ => 1)
+
+variable [Fintype Γ] [DecidableEq Γ] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+def brecM : Matrix (BRole Γ T Sl C) (BRole Γ T Sl C) ℚ :=
+  fun i j => if j = bpull i then bsgn i else 0
+
+lemma actPoint_brecM (x : BRole Γ T Sl C → ℂ) (i : BRole Γ T Sl C) :
+    actPoint brecM x i = (bsgn i : ℂ) * x (bpull i) := by
+  unfold actPoint
+  rw [sum_eq_single (bpull i)]
+  · simp [brecM]
+  · intro j _ hj; simp [brecM, hj]
+  · simp
+
+/-- the scalar map of the whole network before the exchange, on one class. -/
+def chain (x : BRole Γ T Sl C → ℂ) : BRole Γ T Sl C → ℂ :=
+  gsc pC kCc (lift2 GF (lift2 GB (gsc pAB kB (lift1 GF (gsc pAB kA (lift1 GB (lift1 GF x)))))))
+
+/-- **The scalar identity of the bridged chain**: `X_i = -y_i`, `Y_i = x_i` on both pairs,
+helper slots unchanged. -/
+lemma chain_eq (x : BRole Γ T Sl C → ℂ) (l : BLive Γ T Sl) :
+    chain x (Sum.inl l) = mkB (fun g t => -x (kY1 (g,t))) (fun g t => x (kX1 (g,t)))
+      (fun g t => -x (kY2 (g,t))) (fun g t => x (kX2 (g,t)))
+      (fun g q => x (kS (g,q))) (fun g c => x (kC (g,c))) (Sum.inl l) := by
+  rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+  all_goals
+    simp only [chain, gsc, lift1, lift2, GF, GB, mkB, mkS, pAB, pC, kA, kB, kCc, pos1, pos2,
+      kX1, kY1, kX2, kY2, kS, kC, jX, jY, jS, jC, Function.comp_apply]
+    first
+      | (push_cast; ring)
+      | (push_cast; done)
+      | ring
+
+end Gates
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : Bridge2 H T Sl C α Γ)
+
+/-- gate layer A, after stage 1 and the first idle climb of pair 2: twins have equal frames. -/
+lemma Bridge2.gateA : XRoute N.S3 N.S3 (gsc pAB kA) (fun _ => 0) := by
+  refine gateP pAB kA N.S3 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer B, after stage 2 and the second idle climb of pair 2. -/
+lemma Bridge2.gateB : XRoute N.S5 N.S5 (gsc pAB kB) (fun _ => 0) := by
+  refine gateP pAB kB N.S5 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact N.x23 g t
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (N.y23 g t).symm
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer C, after the final climbs. -/
+lemma Bridge2.gateC : XRoute N.S8 N.S8 (gsc pC kCc) (fun _ => 0) := by
+  refine gateP pC kCc N.S8 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact (hk rfl).elim
+  · rfl
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- the free shifts at the end. -/
+def Bridge2.corr : BRole Γ T Sl C → Space α :=
+  mkB (fun _ _ => 0) (fun g t => N.u g t) (fun _ _ => 0) (fun g t => N.u g t)
+    (fun _ _ => 0) (fun _ _ => 0)
+
+def Bridge2.S9 : BRole Γ T Sl C → CMat α := fun r => shift (N.corr r) * N.S8 r
+
+/-- the whole word before the exchange: five stages, three idle-climb layers, three gate
+layers. -/
+lemma Bridge2.route :
+    XRoute N.S0 N.S8 chain (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R := ((((((((((N.stage0.trans N.stage1).trans N.climbA).trans N.gateA).trans
+    N.stage2).trans N.climbB).trans N.gateB).trans N.stage3).trans N.stage4).trans
+    N.fin).trans N.gateC)
+  refine (R.castg ?_).cast (fun φ => ?_)
+  · rfl
+  · simp only [Bridge2.unit]
+    ring
+
+/-- **The scratch certificate of the bridged five-stage network with shared helper sets**,
+in whole blocks, with its exact price for every price list. -/
+theorem bridge2_certificate :
+    BCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C)
+      (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R2 : XRoute N.S8 N.S9 id (fun _ => 0) := XRoute.shifts N.hm N.S8 N.corr
+  have R3 : XRoute N.S9 (fun r => N.S9 (bpull r)) (actPoint brecM) (fun _ => 0) :=
+    XRoute.gate brecM N.S9 _ (fun i j h => by
+      have hj : j = bpull i := by
+        by_contra hne
+        exact h (by simp [brecM, hne])
+      rw [hj])
+  have Rt := ((N.route.trans R2).trans R3).cast (c' := fun φ => (Fintype.card Γ : ℝ) * N.unit φ)
+    (fun φ => by first | ring | simp)
+  have hSinv : ∀ r, ∃ M, N.S0 r * M = 1 := by
+    rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.M0 g).Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.M0 g).Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact ⟨1, Matrix.mul_one _⟩
+    · exact ⟨1, Matrix.mul_one _⟩
+  choose S' hS' using hSinv
+  have hT : ∀ l : BLive Γ T Sl, N.S9 (bpull (Sum.inl l)) = kernel α * N.S0 (Sum.inl l) := by
+    rintro (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.M0 g).Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.M0 g).Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.M0 g).Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.M0 g).Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (0 : Space α) * kernel α = kernel α * 1
+      rw [shift_zero, Matrix.one_mul, Matrix.mul_one]
+  have hg : ∀ x : BRole Γ T Sl C → ℂ,
+      (∀ s, (∀ l : BLive Γ T Sl, (Sum.inl l : BRole Γ T Sl C) ≠ s) → x s = 0) →
+      ∀ l : BLive Γ T Sl,
+        (actPoint brecM ∘ (id ∘ chain)) x (Sum.inl l) = x (Sum.inl l) := by
+    intro x _ l
+    change actPoint brecM (chain x) (Sum.inl l) = _
+    rw [actPoint_brecM]
+    rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX1 (g,t)) = x (kX1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY1 (g,t))) = x (kY1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX2 (g,t)) = x (kX2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY2 (g,t))) = x (kY2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inr (g,q))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kS (g,q)) = x (kS (g,q))
+      first | (push_cast; ring) | simp
+  exact XRoute.liveKernel (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) N.S0 S'
+    (fun r => N.S9 (bpull r)) hS' _ _ Rt hg hT
+
+end Net
+end
+end BR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BR.chain_eq
+#print axioms OAI.PowerSaving.BR.Bridge2.route
+#print axioms OAI.PowerSaving.BR.bridge2_certificate
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Bridge__Net.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Bridge__Net.lean
new file mode 100644
index 0000000000..204f6d9cf9
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Bridge__Net.lean
@@ -0,0 +1,345 @@
+import Work.Bridge.Inv
+
+/-!
+# (key: bridge-net) The BRIDGED five-stage network B_2 with shared helper sets, abstract form
+
+Generalises `RF.Fold3S` / `RF.fold3s_certificate` (`Work.Reframe.SCert`) to the bridged word
+of PLAN2.md B1: every class `(g,t)` has TWO bank pairs `(X1,Y1)`, `(X2,Y2)` with the same
+line; five stages of invocations
+
+    stage 0  forward   on pair 1      invocation of the class (g,t):  g
+    stage 1  backward  on pair 1                                      r1 t g
+    stage 2  forward   on pair 1                                      r2 t g
+    stage 3  backward  on pair 2                                      r3 t g
+    stage 4  forward   on pair 2                                      r4 t g
+
+and three layers of FREE gates between twins at equal frames:
+
+    after stage 1 (pair 2 has climbed to the frames of pair 1):   X1 += X2,  Y2 -= Y1
+    after stage 2 (pair 2 has climbed one more window):           Y2 += Y1,  X1 -= X2
+    after the final climbs (all four roles at their end frames):  Y1 -= Y2,  X2 += X1
+
+Result on both pairs: `X_i = -y_i`, `Y_i = x_i`; then the usual signed exchange.
+
+The idle pair does not move during a stage.  Its climbs are ONE block per role:
+`aX2`, `aY2` (pair 2 before the first gate layer, prices `caX`, `caY`; in B_2 ONE block of
+rank `2h-2` each),
+the window of stage 2 (pair 2 before the second gate layer, rank `card H - 1`, from the
+package: `Inv.climbX`, `Inv.climbY`), `fX1`, `fY1` (pair 1 at the end, prices `cX1`, `cY1`;
+in B_2 ONE block of rank `2h+2` each), `fX2`, `fY2` (pair 2 at the end, prices `cX2`, `cY2`;
+in B_2 one block of rank `4` each).  The prices are arbitrary functions of the price list, so
+a geometry that makes an idle climb in several blocks can be plugged in as well.
+
+`Bridge2 H T Sl C α Γ` is everything the wiring needs to know about the geometry;
+`bridge2_certificate`: a `BCert` on the live roles `BLive Γ T Sl`
+(`card Γ * (4 card T + card Sl)` of them, `BR.card_BLive`) whose price, for EVERY price
+list, is `card Γ * N.unit φ`,
+
+    N.unit φ = 5 * N.I.cost φ + card T * ((caX φ + caY φ) + 2 * bcost φ (card H - 1)
+                 + (cX1 φ + cY1 φ) + (cX2 φ + cY2 φ)).
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace BR
+open Binary Matrix Finset RAM SS CB RF
+noncomputable section
+
+/-- See the file header.  Fields in the style of `RF.Fold3S`; stages are numbered 0 to 4. -/
+structure Bridge2 (H T Sl C α Γ : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α] where
+  /-- the invocation (for a block circuit `X`: `X.inv`). -/
+  I : Inv H T Sl C
+  /-- frame maps of the invocations of the five stages. -/
+  M0 : Γ → XMap H α
+  M1 : Γ → XMap H α
+  M2 : Γ → XMap H α
+  M3 : Γ → XMap H α
+  M4 : Γ → XMap H α
+  /-- the class `(g,t)` is served by the invocation `g` in stage 0 and `r_l t g` in stage `l`. -/
+  r1 : T → Γ ≃ Γ
+  r2 : T → Γ ≃ Γ
+  r3 : T → Γ ≃ Γ
+  r4 : T → Γ ≃ Γ
+  /-- the invocation `d` of stage `l` uses the helper set (and the copies) `s_l d`. -/
+  s1 : Γ ≃ Γ
+  s2 : Γ ≃ Γ
+  s3 : Γ ≃ Γ
+  s4 : Γ ≃ Γ
+  /-- inverse of the frame of the base, and frame of the window, of every invocation. -/
+  N1 : Γ → CMat α
+  W1 : Γ → CMat α
+  N2 : Γ → CMat α
+  W2 : Γ → CMat α
+  N3 : Γ → CMat α
+  W3 : Γ → CMat α
+  N4 : Γ → CMat α
+  W4 : Γ → CMat α
+  u : Γ → T → Space α
+  YF : Γ → T → CMat α
+  hm : 2 ≤ Fintype.card α
+  /-- prices of the idle climbs, for every price list.  B_2 with merged climbs:
+  `caX = caY = fun φ => bcost φ (2h-2)`, `cX1 = cY1 = fun φ => bcost φ (2h+2)`,
+  `cX2 = cY2 = fun φ => bcost φ 4`. -/
+  caX : (ℕ → ℝ) → ℝ
+  caY : (ℕ → ℝ) → ℝ
+  cX1 : (ℕ → ℝ) → ℝ
+  cY1 : (ℕ → ℝ) → ℝ
+  cX2 : (ℕ → ℝ) → ℝ
+  cY2 : (ℕ → ℝ) → ℝ
+  inv0 : ∀ g t, ∃ N : CMat α, (M0 g).Φ (tt (I.tv t)) * N = 1
+  z0 : ∀ g, (M0 g).Φ 0 = 1
+  hN1 : ∀ d, (M1 d).Φ 0 * N1 d = 1
+  hW1 : ∀ d, (M1 d).Φ 1 = W1 d * (M1 d).Φ 0
+  hN2 : ∀ d, (M2 d).Φ 0 * N2 d = 1
+  hW2 : ∀ d, (M2 d).Φ 1 = W2 d * (M2 d).Φ 0
+  hN3 : ∀ d, (M3 d).Φ 0 * N3 d = 1
+  hW3 : ∀ d, (M3 d).Φ 1 = W3 d * (M3 d).Φ 0
+  hN4 : ∀ d, (M4 d).Φ 0 * N4 d = 1
+  hW4 : ∀ d, (M4 d).Φ 1 = W4 d * (M4 d).Φ 0
+  /-- the bank frames a stage leaves are the bank frames the next stage starts from. -/
+  x01 : ∀ g t, (M0 g).Φ 1 = (M1 (r1 t g)).Φ (tt (I.tv t))
+  y01 : ∀ g t, (M0 g).Φ (1 + tt (I.tv t)) = (M1 (r1 t g)).Φ 0
+  x12 : ∀ g t, (M1 (r1 t g)).Φ 1 = (M2 (r2 t g)).Φ (tt (I.tv t))
+  y12 : ∀ g t, (M1 (r1 t g)).Φ (1 + tt (I.tv t)) = (M2 (r2 t g)).Φ 0
+  x23 : ∀ g t, (M2 (r2 t g)).Φ 1 = (M3 (r3 t g)).Φ (tt (I.tv t))
+  y23 : ∀ g t, (M2 (r2 t g)).Φ (1 + tt (I.tv t)) = (M3 (r3 t g)).Φ 0
+  x34 : ∀ g t, (M3 (r3 t g)).Φ 1 = (M4 (r4 t g)).Φ (tt (I.tv t))
+  y34 : ∀ g t, (M3 (r3 t g)).Φ (1 + tt (I.tv t)) = (M4 (r4 t g)).Φ 0
+  /-- the five windows of a helper set make up the kernel. -/
+  sfin : ∀ g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) *
+    (W1 (s1.symm g) * (M0 g).Φ 1))) = kernel α
+  /-- pair 2, idle in stages 0 and 1: ONE block from its start frame to the frame of its
+  twin after stage 1. -/
+  aX2 : ∀ g t, XReach ((M0 g).Φ (tt (I.tv t))) ((M1 (r1 t g)).Φ 1) caX
+  aY2 : ∀ g t, XReach ((M0 g).Φ 0) ((M1 (r1 t g)).Φ (1 + tt (I.tv t))) caY
+  /-- pair 1, idle in stages 3 and 4: ONE block from its frame after stage 2 to the end. -/
+  fX1 : ∀ g t, XReach ((M2 (r2 t g)).Φ 1) (kernel α) cX1
+  fY1 : ∀ g t, XReach ((M2 (r2 t g)).Φ (1 + tt (I.tv t))) (YF g t) cY1
+  /-- pair 2 after stage 4: ONE final block. -/
+  fX2 : ∀ g t, XReach ((M4 (r4 t g)).Φ 1) (kernel α) cX2
+  fY2 : ∀ g t, XReach ((M4 (r4 t g)).Φ (1 + tt (I.tv t))) (YF g t) cY2
+  term : ∀ g t, kernel α * (M0 g).Φ (tt (I.tv t)) = shift (u g t) * YF g t
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : Bridge2 H T Sl C α Γ)
+
+/-- price of the blocks of one unit (one element of `Γ`): five invocations and the idle
+climbs of the four bank roles of every class. -/
+def Bridge2.unit (φ : ℕ → ℝ) : ℝ :=
+  5 * N.I.cost φ + (Fintype.card T : ℝ) * ((N.caX φ + N.caY φ)
+    + 2 * bcost φ (Fintype.card H - 1)
+    + (N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ))
+
+/-- scratch copies always enter and leave with the matrix `1` (also: the helper slots at the
+start, with `C := Sl`). -/
+def cOne (Γ C α : Type) [Fintype α] [DecidableEq α] : Γ → C → CMat α := fun _ _ => 1
+
+/-- the bank index of stage 0: the class `(g,t)` belongs to the invocation `g`. -/
+abbrev bid (Γ T : Type) : T → Γ ≃ Γ := fun _ => Equiv.refl Γ
+
+/-! bank frames of the class `(g,t)`: `xi l`, `yi l` at the START of stage `l`; `xo l`,
+`yo l` at the END of stage `l` (only where no next stage follows on that pair). -/
+def Bridge2.xi0 (g : Γ) (t : T) : CMat α := (N.M0 g).Φ (tt (N.I.tv t))
+def Bridge2.yi0 (g : Γ) (t : T) : CMat α := (N.M0 g).Φ 0
+def Bridge2.xi1 (g : Γ) (t : T) : CMat α := (N.M1 (N.r1 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi1 (g : Γ) (t : T) : CMat α := (N.M1 (N.r1 t g)).Φ 0
+def Bridge2.xi2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ 0
+def Bridge2.xo2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ 1
+def Bridge2.yo2 (g : Γ) (t : T) : CMat α := (N.M2 (N.r2 t g)).Φ (1 + tt (N.I.tv t))
+def Bridge2.xi3 (g : Γ) (t : T) : CMat α := (N.M3 (N.r3 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi3 (g : Γ) (t : T) : CMat α := (N.M3 (N.r3 t g)).Φ 0
+def Bridge2.xi4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ (tt (N.I.tv t))
+def Bridge2.yi4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ 0
+def Bridge2.xo4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ 1
+def Bridge2.yo4 (g : Γ) (t : T) : CMat α := (N.M4 (N.r4 t g)).Φ (1 + tt (N.I.tv t))
+
+/-- helper slots after the stages 0, 1, 2, 3, 4 (at the start: `cOne Γ Sl α`). -/
+def Bridge2.Z1 : Γ → Sl → CMat α := fun g _ => (N.M0 g).Φ 1
+def Bridge2.Z2 : Γ → Sl → CMat α := fun g q => N.W1 (N.s1.symm g) * N.Z1 g q
+def Bridge2.Z3 : Γ → Sl → CMat α := fun g q => N.W2 (N.s2.symm g) * N.Z2 g q
+def Bridge2.Z4 : Γ → Sl → CMat α := fun g q => N.W3 (N.s3.symm g) * N.Z3 g q
+def Bridge2.Z5 : Γ → Sl → CMat α := fun g q => N.W4 (N.s4.symm g) * N.Z4 g q
+
+/-- frames: at the start; after stage 0; after stage 1; after the first idle climb of pair 2
+(first gate layer here); after stage 2; after the second idle climb of pair 2 (second gate
+layer here); after stage 3; after stage 4; after the final climbs (third gate layer here). -/
+def Bridge2.S0 : BRole Γ T Sl C → CMat α := mkB N.xi0 N.yi0 N.xi0 N.yi0 (cOne Γ Sl α) (cOne Γ C α)
+def Bridge2.S1 : BRole Γ T Sl C → CMat α := mkB N.xi1 N.yi1 N.xi0 N.yi0 N.Z1 (cOne Γ C α)
+def Bridge2.S2 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi0 N.yi0 N.Z2 (cOne Γ C α)
+def Bridge2.S3 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi2 N.yi2 N.Z2 (cOne Γ C α)
+def Bridge2.S4 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi2 N.yi2 N.Z3 (cOne Γ C α)
+def Bridge2.S5 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi3 N.yi3 N.Z3 (cOne Γ C α)
+def Bridge2.S6 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi4 N.yi4 N.Z4 (cOne Γ C α)
+def Bridge2.S7 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xo4 N.yo4 N.Z5 (cOne Γ C α)
+def Bridge2.S8 : BRole Γ T Sl C → CMat α :=
+  mkB (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) (cOne Γ C α)
+
+/-- stage 0: forward on pair 1, every helper set starts at the matrix `1`. -/
+lemma Bridge2.stage0 :
+    XRoute N.S0 N.S1 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_fwd N.I (bid Γ T) (Equiv.refl Γ) N.M0 (fun _ => 1) (fun g => (N.M0 g).Φ 1)
+    (fun d => by rw [N.z0, Matrix.mul_one]) (fun d => by rw [N.z0, Matrix.mul_one])
+    (cOne Γ Sl α) (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv (bid Γ T) N.M0
+      (fun g (q : Sl) => (N.M0 ((Equiv.refl Γ).symm g)).Φ 1 * cOne Γ Sl α g q) (cOne Γ C α)
+      = mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x01 g t
+    · exact N.y01 g t
+    · show (N.M0 g).Φ 1 * 1 = (N.M0 g).Φ 1
+      rw [Matrix.mul_one]
+    · rfl
+  have h' : XRoute (bIn N.I.tv (bid Γ T) N.M0 (cOne Γ Sl α) (cOne Γ C α))
+      (mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α)) GF (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift1 N.xi0 N.yi0 h'
+
+/-- stage 1: backward on pair 1; the helper set `g` serves the invocation `s1⁻¹ g`. -/
+lemma Bridge2.stage1 :
+    XRoute N.S1 N.S2 (lift1 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_bwd N.I N.r1 N.s1 N.M1 N.N1 N.W1 N.hN1 N.hW1 N.Z1 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r1 N.M1 (fun g q => N.W1 (N.s1.symm g) * N.Z1 g q) (cOne Γ C α)
+      = mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x12 g t
+    · exact N.y12 g t
+    · rfl
+    · rfl
+  have h' : XRoute (bIn N.I.tv N.r1 N.M1 N.Z1 (cOne Γ C α))
+      (mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift1 N.xi0 N.yi0 h'
+
+/-- stage 2: forward on pair 1. -/
+lemma Bridge2.stage2 :
+    XRoute N.S3 N.S4 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  blift1 N.xi2 N.yi2
+    (istage_fwd N.I N.r2 N.s2 N.M2 N.N2 N.W2 N.hN2 N.hW2 N.Z2 (cOne Γ C α) (cOne Γ C α))
+
+/-- stage 3: backward on pair 2. -/
+lemma Bridge2.stage3 :
+    XRoute N.S5 N.S6 (lift2 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := istage_bwd N.I N.r3 N.s3 N.M3 N.N3 N.W3 N.hN3 N.hW3 N.Z3 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r3 N.M3 (fun g q => N.W3 (N.s3.symm g) * N.Z3 g q) (cOne Γ C α)
+      = mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x34 g t
+    · exact N.y34 g t
+    · rfl
+    · rfl
+  have h' : XRoute (bIn N.I.tv N.r3 N.M3 N.Z3 (cOne Γ C α))
+      (mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact blift2 N.xo2 N.yo2 h'
+
+/-- stage 4: forward on pair 2. -/
+lemma Bridge2.stage4 :
+    XRoute N.S6 N.S7 (lift2 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  blift2 N.xo2 N.yo2
+    (istage_fwd N.I N.r4 N.s4 N.M4 N.N4 N.W4 N.hN4 N.hW4 N.Z4 (cOne Γ C α) (cOne Γ C α))
+
+/-- first idle climb of pair 2 (stages 0 and 1 in ONE block per role), to the frames of
+pair 1 after stage 1. -/
+lemma Bridge2.climbA :
+    XRoute N.S2 N.S3 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (N.caX φ + N.caY φ))) := by
+  have H1 := XRoute.reach_all N.S2 N.S3
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ => N.caX)
+      (fun _ _ => N.caY) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.M0 g).Φ (tt (N.I.tv t))) ((N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))) N.caX
+        rw [← N.x12 g t]
+        exact N.aX2 g t
+      · show XReach ((N.M0 g).Φ 0) ((N.M2 (N.r2 t g)).Φ 0) N.caY
+        rw [← N.y12 g t]
+        exact N.aY2 g t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- second idle climb of pair 2: the window of stage 2, ONE block of rank `card H - 1` per
+role, to the frames of pair 1 after stage 2. -/
+lemma Bridge2.climbB :
+    XRoute N.S4 N.S5 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (2 * bcost φ (Fintype.card H - 1)))) := by
+  have H1 := XRoute.reach_all N.S4 N.S5
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ φ => bcost φ (Fintype.card H - 1))
+      (fun _ _ φ => bcost φ (Fintype.card H - 1)) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.M2 (N.r2 t g)).Φ (tt (N.I.tv t))) ((N.M3 (N.r3 t g)).Φ (tt (N.I.tv t)))
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.x23 g t]
+        exact N.I.climbX (N.M2 (N.r2 t g)) t
+      · show XReach ((N.M2 (N.r2 t g)).Φ 0) ((N.M3 (N.r3 t g)).Φ 0)
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.y23 g t]
+        exact N.I.climbY (N.M2 (N.r2 t g)) t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- the final climbs: pair 1 from its frames after stage 2 (ONE block per role for the
+stages 3, 4 and the rest), pair 2 from its frames after stage 4; the helper slots are
+already at the kernel. -/
+lemma Bridge2.fin :
+    XRoute N.S7 N.S8 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * ((N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ)))) := by
+  have H1 := XRoute.reach_all N.S7 N.S8
+    (mkB (fun _ _ => N.cX1) (fun _ _ => N.cY1) (fun _ _ => N.cX2) (fun _ _ => N.cY2)
+      (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact N.fX1 g t
+      · exact N.fY1 g t
+      · exact N.fX2 g t
+      · exact N.fY2 g t
+      · show XReach (N.W4 (N.s4.symm g) * (N.W3 (N.s3.symm g) * (N.W2 (N.s2.symm g) *
+          (N.W1 (N.s1.symm g) * (N.M0 g).Φ 1)))) (kernel α) (fun _ => 0)
+        rw [N.sfin g]
+        exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+end Net
+end
+end BR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BR.Bridge2.stage0
+#print axioms OAI.PowerSaving.BR.Bridge2.stage1
+#print axioms OAI.PowerSaving.BR.Bridge2.stage2
+#print axioms OAI.PowerSaving.BR.Bridge2.stage3
+#print axioms OAI.PowerSaving.BR.Bridge2.stage4
+#print axioms OAI.PowerSaving.BR.Bridge2.climbA
+#print axioms OAI.PowerSaving.BR.Bridge2.climbB
+#print axioms OAI.PowerSaving.BR.Bridge2.fin
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Carrier__Live.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Carrier__Live.lean
new file mode 100644
index 0000000000..b8306527d6
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Carrier__Live.lean
@@ -0,0 +1,232 @@
+import Work.Carrier.Pack
+import Work.Carrier.Ring
+
+/-!
+# (key: carrier-thm) The live roles of an invocation, and the four dirt gates as matrices
+
+`L3 T Sl = (T ⊕ T) ⊕ Sl`: the bank roles `x` (`lX`), `y` (`lY`) and the helper slots (`lS`), all
+on the same footing (no scratch copies).  `PX`, `PY`: the coordinate projectors.
+
+For the matrix `M` of all gates of the main phase and its inverse `Mi`:
+
+    g1 M  = 1 - PY * M * PS      `y -= K s`            g1i M = 1 + PY * M * PS   (its inverse)
+    g8 Mi = PX + PY + PS * Mi    slot rows of `M⁻¹`    h8 M  = PX + PY + PS * M  (its inverse)
+
+(`PS = 1 - PX - PY`).  This file: unit rows / columns of these gates (hence between which roles
+their entries can be nonzero), the scatter with the copies eliminated (`scatM`), and the scalar
+maps of `1 + PY * M * PX` and of the transpose of `1 - PY * M * PX`.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace CR
+open Binary Matrix Finset RAM SS CB BR
+noncomputable section
+
+section Diag
+variable {ρ : Type*} [Fintype ρ] [DecidableEq ρ]
+
+lemma col_zero_of {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : G * Matrix.diagonal d = Matrix.diagonal d) {i j : ρ} (hj : d j = 1) (hij : i ≠ j) :
+    G i j = 0 := by
+  have e := congrFun (congrFun h i) j
+  rw [Matrix.mul_diagonal, Matrix.diagonal_apply_ne _ hij, hj, mul_one] at e
+  exact e
+
+lemma row_zero_of {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : Matrix.diagonal d * G = Matrix.diagonal d) {i j : ρ} (hi : d i = 1) (hij : i ≠ j) :
+    G i j = 0 := by
+  have e := congrFun (congrFun h i) j
+  rw [Matrix.diagonal_mul, Matrix.diagonal_apply_ne _ hij, hi, one_mul] at e
+  exact e
+
+lemma diag_mul_of_rows {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : ∀ i j, d i ≠ 0 → G i j = if i = j then 1 else 0) :
+    Matrix.diagonal d * G = Matrix.diagonal d := by
+  ext i j
+  rw [Matrix.diagonal_mul]
+  by_cases hd : d i = 0
+  · rw [hd, zero_mul]
+    by_cases hij : i = j
+    · subst hij; rw [Matrix.diagonal_apply_eq, hd]
+    · rw [Matrix.diagonal_apply_ne _ hij]
+  · rw [h i j hd]
+    by_cases hij : i = j
+    · subst hij; rw [if_pos rfl, mul_one, Matrix.diagonal_apply_eq]
+    · rw [if_neg hij, mul_zero, Matrix.diagonal_apply_ne _ hij]
+
+lemma mul_diag_of_cols {d : ρ → ℚ} {G : Matrix ρ ρ ℚ}
+    (h : ∀ i j, d j ≠ 0 → G i j = if i = j then 1 else 0) :
+    G * Matrix.diagonal d = Matrix.diagonal d := by
+  ext i j
+  rw [Matrix.mul_diagonal]
+  by_cases hd : d j = 0
+  · rw [hd, mul_zero]
+    by_cases hij : i = j
+    · subst hij; rw [Matrix.diagonal_apply_eq, hd]
+    · rw [Matrix.diagonal_apply_ne _ hij]
+  · rw [h i j hd]
+    by_cases hij : i = j
+    · subst hij; rw [if_pos rfl, one_mul, Matrix.diagonal_apply_eq]
+    · rw [if_neg hij, zero_mul, Matrix.diagonal_apply_ne _ hij]
+
+/-- scalar map of a diagonal gate matrix. -/
+lemma act_diag (d : ρ → ℚ) (u : ρ → ℂ) :
+    actPoint (Matrix.diagonal d) u = fun i => ((d i : ℚ) : ℂ) * u i := by
+  funext i
+  show ∑ j, ((Matrix.diagonal d i j : ℚ) : ℂ) * u j = ((d i : ℚ) : ℂ) * u i
+  rw [Finset.sum_eq_single i]
+  · rw [Matrix.diagonal_apply_eq]
+  · intro j _ hj
+    rw [Matrix.diagonal_apply_ne _ (Ne.symm hj), Rat.cast_zero, zero_mul]
+  · intro h
+    exact absurd (Finset.mem_univ i) h
+
+lemma actPoint_mul (A B : Matrix ρ ρ ℚ) (u : ρ → ℂ) :
+    actPoint (A * B) u = actPoint A (actPoint B u) :=
+  ap_mul A B u
+
+end Diag
+
+section Live
+variable {T Sl : Type} [Fintype T] [DecidableEq T] [Fintype Sl] [DecidableEq Sl]
+
+/-- live roles of one invocation: `x`, `y`, helper slots. -/
+abbrev L3 (T Sl : Type) := (T ⊕ T) ⊕ Sl
+abbrev lX (t : T) : L3 T Sl := Sum.inl (Sum.inl t)
+abbrev lY (t : T) : L3 T Sl := Sum.inl (Sum.inr t)
+abbrev lS (q : Sl) : L3 T Sl := Sum.inr q
+
+/-- indicator of the x roles. -/
+def iX : L3 T Sl → ℚ := Sum.elim (Sum.elim (fun _ => 1) (fun _ => 0)) (fun _ => 0)
+/-- indicator of the y roles. -/
+def iY : L3 T Sl → ℚ := Sum.elim (Sum.elim (fun _ => 0) (fun _ => 1)) (fun _ => 0)
+
+def PX : Matrix (L3 T Sl) (L3 T Sl) ℚ := Matrix.diagonal iX
+def PY : Matrix (L3 T Sl) (L3 T Sl) ℚ := Matrix.diagonal iY
+
+lemma iX_cases (i : L3 T Sl) : iX i = 0 ∨ iX i = 1 := by
+  rcases i with ((t|t)|q)
+  · exact Or.inr rfl
+  · exact Or.inl rfl
+  · exact Or.inl rfl
+
+lemma iY_cases (i : L3 T Sl) : iY i = 0 ∨ iY i = 1 := by
+  rcases i with ((t|t)|q)
+  · exact Or.inl rfl
+  · exact Or.inr rfl
+  · exact Or.inl rfl
+
+lemma PX_sq : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PX = PX := by
+  unfold PX
+  have e : (fun i : L3 T Sl => iX i * iX i) = iX := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX]
+  rw [Matrix.diagonal_mul_diagonal, e]
+
+lemma PY_sq : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PY = PY := by
+  unfold PY
+  have e : (fun i : L3 T Sl => iY i * iY i) = iY := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iY]
+  rw [Matrix.diagonal_mul_diagonal, e]
+
+lemma PX_PY : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PY = 0 := by
+  unfold PX PY
+  rw [Matrix.diagonal_mul_diagonal]
+  have e : (fun i : L3 T Sl => iX i * iY i) = fun _ => 0 := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX, iY]
+  rw [e]
+  exact Matrix.diagonal_zero
+
+lemma PY_PX : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ) * PX = 0 := by
+  unfold PX PY
+  rw [Matrix.diagonal_mul_diagonal]
+  have e : (fun i : L3 T Sl => iY i * iX i) = fun _ => 0 := by
+    funext i
+    rcases i with ((t|t)|q) <;> simp [iX, iY]
+  rw [e]
+  exact Matrix.diagonal_zero
+
+lemma PX_T : (PX : Matrix (L3 T Sl) (L3 T Sl) ℚ)ᵀ = PX := Matrix.diagonal_transpose _
+lemma PY_T : (PY : Matrix (L3 T Sl) (L3 T Sl) ℚ)ᵀ = PY := Matrix.diagonal_transpose _
+
+/-- "no gate into an x role": the x rows are unit rows. -/
+lemma PX_mul_of {M : Matrix (L3 T Sl) (L3 T Sl) ℚ}
+    (hx : ∀ t j, M (lX t) j = if lX t = j then 1 else 0) : PX * M = PX := by
+  unfold PX
+  apply diag_mul_of_rows
+  intro i j hi
+  rcases i with ((t|t)|q)
+  · exact hx t j
+  · exact absurd rfl hi
+  · exact absurd rfl hi
+
+/-- "no gate reads a y role": the y columns are unit columns. -/
+lemma mul_PY_of {M : Matrix (L3 T Sl) (L3 T Sl) ℚ}
+    (hy : ∀ i t, M i (lY t) = if i = lY t then 1 else 0) : M * PY = PY := by
+  unfold PY
+  apply mul_diag_of_cols
+  intro i j hj
+  rcases j with ((t|t)|q)
+  · exact absurd rfl hj
+  · exact hy i t
+  · exact absurd rfl hj
+
+/-! ### the four dirt gates -/
+
+def g1 (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  1 - PY * M * (1 - PX - PY)
+def g1i (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  1 + PY * M * (1 - PX - PY)
+def g8 (Mi : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  PX + PY + (1 - PX - PY) * Mi
+def h8 (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : Matrix (L3 T Sl) (L3 T Sl) ℚ :=
+  PX + PY + (1 - PX - PY) * M
+
+/-- a gate with unit x rows and unit x columns joins two different roles only if neither is an
+x role. -/
+lemma offdiag_x {G : Matrix (L3 T Sl) (L3 T Sl) ℚ} (h1 : G * PX = PX) (h2 : PX * G = PX)
+    {i j : L3 T Sl} (hij : G i j ≠ 0) (e : i ≠ j) : iX i = 0 ∧ iX j = 0 := by
+  constructor
+  · by_contra h
+    exact hij (row_zero_of h2 ((iX_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (col_zero_of h1 ((iX_cases j).resolve_left h) e)
+
+/-- a gate with unit x rows, unit y rows and unit y columns: a nonzero entry off the diagonal
+is in a slot row and not in a y column. -/
+lemma offdiag_s {G : Matrix (L3 T Sl) (L3 T Sl) ℚ} (hx : PX * G = PX) (hy : PY * G = PY)
+    (hyc : G * PY = PY) {i j : L3 T Sl} (hij : G i j ≠ 0) (e : i ≠ j) :
+    iX i = 0 ∧ iY i = 0 ∧ iY j = 0 := by
+  refine ⟨?_, ?_, ?_⟩
+  · by_contra h
+    exact hij (row_zero_of hx ((iX_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (row_zero_of hy ((iY_cases i).resolve_left h) e)
+  · by_contra h
+    exact hij (col_zero_of hyc ((iY_cases j).resolve_left h) e)
+
+lemma g1_x (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : g1 M * PX = PX ∧ PX * g1 M = PX := by
+  unfold g1
+  constructor
+  · rw [sub_mul, one_mul, side_n_right (PX_sq (T := T) (Sl := Sl)) PY_PX, sub_zero]
+  · rw [mul_sub, mul_one, side_n_left (PX_PY (T := T) (Sl := Sl)), sub_zero]
+
+lemma g1i_x (M : Matrix (L3 T Sl) (L3 T Sl) ℚ) : g1i M * PX = PX ∧ PX * g1i M = PX := by
+  unfold g1i
+  constructor
+  · rw [add_mul, one_mul, side_n_right (PX_sq (T := T) (Sl := Sl)) PY_PX, add_zero]
+  · rw [mul_add, mul_one, side_n_left (PX_PY (T := T) (Sl := Sl)), add_zero]
+
+end Live
+end
+end CR
+end PowerSaving
+end OAI
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean
new file mode 100644
index 0000000000..305da15b5d
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Carrier__Phases.lean
@@ -0,0 +1,192 @@
+import Work.Carrier.Glue
+
+/-!
+# (key: carrier-thm) A carrier circuit given by its phases: hypotheses and scalar identities
+
+`Phased H T Sl C` is the hypothesis structure of the carrier invocation theorem in the general
+scope (any ordered mix of gates `(x, slot)`, `(slot, slot)`, `(x, y)`, `(slot, y)`):
+
+* phase A (before the scatter), phase B (after it) and the final climbs F are exact block routes
+  on the LIVE roles `L3 T Sl` (`x`, `y`, slots: all on the same footing), for every block frame
+  map, with the gate products `MA`, `MB` (and the transposed inverses for the backward word);
+* the scatter goes through the scratch copies: `c += Cc s` at the labels `cen`, the copies come
+  down, `y += Jr c` at 0;
+* `hx`: no gate INTO an x role, `hy`: no gate READS a y role, `hid`: the y roles receive exactly
+  the x roles — three facts about the ONE matrix `Mt = MB * scatM (Jr * Cc) * MA`.
+
+This file: `Mt`, its inverse `Mti`, and the scalar identities of the forward and of the backward
+word (`fwd_scalar`, `bwd_scalar`): with the two dirt gates `g1`, `g8` (resp. the transposes of
+`g1i`, `h8`) the word does `y += x` (resp. `x -= y`) for ARBITRARY slot contents.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace CR
+open Binary Matrix Finset RAM SS CB BR
+noncomputable section
+
+/-- labels of the live roles at the START of an invocation. -/
+def lab3 {H T Sl : Type} (tv : T → Space H) : L3 T Sl → Lbl H :=
+  Sum.elim (Sum.elim (fun t => lineL (tv t)) (fun _ => zeroL)) (fun _ => zeroL)
+
+/-- **The hypotheses of the carrier invocation theorem, by phases.**  See the file header. -/
+structure Phased (H T Sl C : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] where
+  tv : T → Space H
+  kx : ∀ t, Climb (lineL (tv t)) fullL
+  ky : ∀ t, Climb zeroL (perpL (tv t))
+  cen : C → Lbl H
+  kc : ∀ k, Climb zeroL (cen k)
+  Cc : Matrix C Sl ℚ
+  Jr : Matrix T C ℚ
+  labA : L3 T Sl → Lbl H
+  labB : L3 T Sl → Lbl H
+  labF : L3 T Sl → Lbl H
+  hAy : ∀ t, (labA (lY t)).P = 0
+  hAc : ∀ k q, Cc k q ≠ 0 → (cen k).P = (labA (lS q)).P
+  hFx : ∀ t, (labF (lX t)).P = 1
+  hFy : ∀ t, (labF (lY t)).P = 1 + tt (tv t)
+  hFs : ∀ q, (labF (lS q)).P = 1
+  MA : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MAi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MB : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MBi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  hAi : MAi * MA = 1
+  hBi : MBi * MB = 1
+  hx : ∀ t j, (MB * scatM (Jr * Cc) * MA) (lX t) j = if lX t = j then 1 else 0
+  hy : ∀ i t, (MB * scatM (Jr * Cc) * MA) i (lY t) = if i = lY t then 1 else 0
+  hid : ∀ S t, (MB * scatM (Jr * Cc) * MA) (lY S) (lX t) = if S = t then 1 else 0
+  rA : List ℕ
+  rB : List ℕ
+  rF : List ℕ
+  pA : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (lab3 tv r).P) (fun r => Xm.Φ (labA r).P) (actPoint MA)
+        (fun φ => rcost φ rA) ∧
+    XRoute (fun r => Xm.Φ (lab3 tv r).P) (fun r => Xm.Φ (labA r).P) (actPoint MAiᵀ)
+        (fun φ => rcost φ rA)
+  pB : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (labA r).P) (fun r => Xm.Φ (labB r).P) (actPoint MB)
+        (fun φ => rcost φ rB) ∧
+    XRoute (fun r => Xm.Φ (labA r).P) (fun r => Xm.Φ (labB r).P) (actPoint MBiᵀ)
+        (fun φ => rcost φ rB)
+  pF : ∀ {α : Type} [Fintype α] [DecidableEq α] (Xm : XMap H α),
+    XRoute (fun r => Xm.Φ (labB r).P) (fun r => Xm.Φ (labF r).P) id (fun φ => rcost φ rF)
+
+section Alg
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+namespace Phased
+variable (K : Phased H T Sl C)
+
+/-- the product of ALL gates of the main phase (scatter with the copies eliminated). -/
+def Mt : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MB * scatM (K.Jr * K.Cc) * K.MA
+/-- its inverse. -/
+def Mti : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MAi * scatMi (K.Jr * K.Cc) * K.MBi
+
+/-- price of one invocation: the blocks of the three phases and one block per copy. -/
+def cost (φ : ℕ → ℝ) : ℝ :=
+  rcost φ K.rA + (∑ k, bcost φ (K.cen k).d) + rcost φ K.rB + rcost φ K.rF
+
+lemma im : K.Mti * K.Mt = 1 := by
+  unfold Mti Mt
+  have hB : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ, K.MBi * (K.MB * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, K.hBi, Matrix.one_mul]
+  have hS : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ,
+      scatMi (K.Jr * K.Cc) * (scatM (K.Jr * K.Cc) * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, scat_inv, Matrix.one_mul]
+  rw [Matrix.mul_assoc, Matrix.mul_assoc, Matrix.mul_assoc, hB, hS, K.hAi]
+
+lemma mi : K.Mt * K.Mti = 1 := mul_eq_one_comm.mp K.im
+
+lemma hxm : PX * K.Mt = PX := PX_mul_of (M := K.Mt) K.hx
+lemma hmy : K.Mt * PY = PY := mul_PY_of (M := K.Mt) K.hy
+lemma hiy : K.Mti * PY = PY := dirt_iy K.hmy K.im
+
+/-- **the dirt rule, forward**, for the matrices of the circuit. -/
+lemma hF : g8 K.Mti * K.Mt * g1 K.Mt = 1 + PY * K.Mt * PX := by
+  unfold g8 g1
+  exact dirt_fwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- **the dirt rule, backward.** -/
+lemma hB : g1i K.Mt * K.Mti * h8 K.Mt = 1 - PY * K.Mt * PX := by
+  unfold g1i h8
+  exact dirt_bwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- live part of the forward word before the scatter: `y -= K s`, then phase A. -/
+def f1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MA (actPoint (g1 K.Mt) u)
+/-- after the scatter: phase B, then the slot rows of the inverse. -/
+def f2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (g8 K.Mti) (actPoint K.MB u)
+/-- the same for the backward word (transposed inverses). -/
+def b1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u)
+def b2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ u)
+
+lemma fwd_live (u : L3 T Sl → ℂ) :
+    K.f2 (actPoint (scatM (K.Jr * K.Cc)) (K.f1 u)) = actPoint (1 + PY * K.Mt * PX) u := by
+  rw [← K.hF]
+  show actPoint (g8 K.Mti) (actPoint K.MB (actPoint (scatM (K.Jr * K.Cc))
+      (actPoint K.MA (actPoint (g1 K.Mt) u))))
+    = actPoint (g8 K.Mti * (K.MB * scatM (K.Jr * K.Cc) * K.MA) * g1 K.Mt) u
+  rw [actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma bwd_live (u : L3 T Sl → ℂ) :
+    K.b2 (actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 u))
+      = actPoint ((1 - PY * K.Mt * PX)ᵀ) u := by
+  rw [← K.hB]
+  show actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ (actPoint (scatMi (K.Jr * K.Cc))ᵀ
+      (actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u))))
+    = actPoint ((g1i K.Mt * (K.MAi * scatMi (K.Jr * K.Cc) * K.MBi) * h8 K.Mt)ᵀ) u
+  rw [Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul,
+    actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma liveAct_glue (φ : (L3 T Sl → ℂ) → (L3 T Sl → ℂ)) (u : L3 T Sl → ℂ) (c : C → ℂ) :
+    liveAct φ (glue u c) = glue (φ u) c :=
+  congrArg (fun v => glue (φ v) c) (glue_up u c)
+
+/-- **Scalar identity of the forward word**: `y += x`, slots restored, for ARBITRARY slot
+contents (the copies are erased before and after). -/
+theorem fwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.f2 (gateS bY bC K.Jr (gateS bC bS K.Cc (liveAct K.f1 (eraseC z)))))
+      = shearF z := by
+  have h1 : liveAct K.f1 (eraseC z) = glue (K.f1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bY bC K.Jr (gateS bC bS K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint (scatM (K.Jr * K.Cc)) (K.f1 (z ∘ upE)) := by
+    have h := scat_glue K.Jr K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.fwd_live, act_shear K.Mt K.hid]
+  exact glue_shearF z
+
+/-- **Scalar identity of the backward word**: `x -= y`, slots restored. -/
+theorem bwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.b2 (gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (liveAct K.b1 (eraseC z)))))
+      = shearB z := by
+  have h1 : liveAct K.b1 (eraseC z) = glue (K.b1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (glue (K.b1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 (z ∘ upE)) := by
+    have h := scat_glueT K.Jr K.Cc (glue (K.b1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.bwd_live, act_shearT K.Mt K.hid]
+  exact glue_shearB z
+
+end Phased
+end Alg
+end
+end CR
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.CR.Phased.fwd_scalar
+#print axioms OAI.PowerSaving.CR.Phased.bwd_scalar
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean
new file mode 100644
index 0000000000..9aa06b5bf2
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__Fourier__Main.lean
@@ -0,0 +1,176 @@
+import Work.Fourier.Asymptotics
+import OAI.Computability.FourierTransform.RegisterBounds
+import Work.Fourier.Goal
+
+/-
+Modified copy of lean/OAI/Computability/FourierTransform/Main.lean of github.com/openai/math
+(commit fd4aeeb, Apache-2.0), generated by `tools/fourier/mkchain.py`. OpenAI's file itself is
+unmodified in this repository and still imported. Changed for this repository, all mechanically:
+  * every declaration of this file (and of the other 10 copied files) has the suffix `Z`
+    on its name, so that it does not collide with OpenAI's original;
+  * OpenAI's exponent `alpha = 1 - 2/10^11` and envelope `hills` are replaced by
+    `alphaZ = 1 - 7474547/10^10` and `hillsZ` (Work/Fourier/Seam.lean), and the single use of
+    OpenAI's `hills_program` by `hillsZ_program`;
+  * `decimalExponent`, `decimalTime`, `TimeBounds`, `DFTGoal`, `ConvGoal` are replaced by their
+    `Z` versions from Work/Fourier/Goal.lean (exponent `1 - 7474546/10^10`);
+  * imports point to the copies.
+  * literal `let d : ℝ := 2/(10:ℝ)^11` -> `let d : ℝ := 7474547/(10:ℝ)^10` (alpha_thetaZ: the local constant d must equal 1 - alphaZ)
+  * `theorem transform_mainZ : DFTGoalZ :=`: docstring added
+  * `theorem convolution_mainZ : ConvGoalZ :=`: docstring added
+Comments and docstrings below are OpenAI's and describe OpenAI's network, not ours.
+-/
+
+namespace OAI
+
+/-!
+Exact uniform Fourier transforms and convolution.
+
+The construction formalizes the exact arithmetic algorithms of
+*An explicit power saving for the exact discrete Fourier transform* (OpenAI).
+The finite phase network originates in the complex construction of
+*Integer multiplication below n log n*.
+
+`transform_mainZ` and `convolution_mainZ` give fixed finite RAM programs, including
+preparation and index work, polynomial storage bounds, and a canonical root whose
+order is computed from the input length. Each includes the paper exponent, decimal
+power saving, and little-o bound. The `_order` variants also specify the root order.
+
+The implementation uses a smaller concrete tensor network (32 binary coordinates
+per factor, 4060 triples, and a `2^50` role envelope) with a stronger saving that
+implies the stated paper constants. The general rational-algebra extraction,
+symbolic certificate search, circuit printer, and bounded-printer uniformization
+from the synthesis appendix are outside this formalization.
+-/
+namespace PowerSaving
+open RAM Bench Selection Filter Asymptotics Real
+noncomputable section
+namespace Skies
+
+lemma multiplier_rangeZ : 1 < paperMultiplier ∧ paperMultiplier < paperM := by
+  norm_num [paperMultiplier,paperM,paperDelta,paperW]
+
+lemma theta_ltZ : theta < 1 := by
+  have h := multiplier_rangeZ
+  have hg : 0<log paperM := Real.log_pos (lt_trans h.1 h.2)
+  rw [theta,div_lt_iff₀ hg,one_mul]
+  exact Real.log_lt_log (by linarith) h.2
+
+lemma alpha_thetaZ : alphaZ < theta := by
+  let d : ℝ := 7474547/(10:ℝ)^10
+  have hp : 0<d := by dsimp [d]; norm_num
+  have hm : 2 ≤ paperM := by norm_num [paperM]
+  have hx : 0<paperMultiplier := lt_trans zero_lt_one multiplier_rangeZ.1
+  have hu : 0<paperM := by linarith
+  have h2 := (Real.log_le_log (by norm_num : 0 < (2:ℝ)) hm)
+  have he := log2_minZ
+  have hh : 0<log paperM := by linarith
+  have hk := Real.log_le_sub_one_of_pos (show 0<paperM/paperMultiplier by positivity)
+  rw [log_div hu.ne' hx.ne'] at hk
+  have H : paperM/paperMultiplier-1 < d*(2/3) := by
+    norm_num [d,paperM,paperMultiplier,paperW,paperDelta]
+  rw [theta,lt_div_iff₀ hh]
+  change (1-d)*log paperM < log paperMultiplier
+  have H' := mul_le_mul_of_nonneg_left (he.trans h2) hp.le
+  have hy := hk.trans_lt (lt_of_lt_of_le H H')
+  rw [sub_mul,one_mul]
+  linarith only [hy]
+
+lemma decimal_rangeZ : alphaZ < decimalExponentZ ∧ decimalExponentZ < 1 := by
+  norm_num [decimalExponentZ,alphaZ]
+
+def speedZ (v : ℝ) (n : ℕ) := (n:ℝ)*(TmZ n)^v
+
+lemma flight_littleZ {v : ℝ} (h : alphaZ < v) :
+    flightZ =o[atTop] speedZ v := by
+  rw [isLittleO_iff]
+  intro c hc
+  filter_upwards [TtopZ.eventually_ge_atTop 1,dwarfZ TtopZ 2
+    (p:=v-alphaZ) (sub_pos.mpr h) hc] with n hn hh
+  have he : 0<TmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^alphaZ*QmZ n^2‖ ≤ c*‖(n:ℝ)*TmZ n^v‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity)]
+  calc
+    _ ≤ ((n:ℝ)*TmZ n^alphaZ)*(c*TmZ n^(v-alphaZ)) :=
+      mul_le_mul_of_nonneg_left hh (by positivity)
+    _ = c*((n:ℝ)*(TmZ n^alphaZ*TmZ n^(v-alphaZ))) := by ring
+    _ = _ := by rw [← rpow_add he, show alphaZ + (v-alphaZ)=v by ring] -- a+(v-a)
+
+lemma speed_littleZ {u v : ℝ} (h : u < v) :
+    speedZ u =o[atTop] speedZ v := by
+  rw [isLittleO_iff]
+  intro c hc
+  filter_upwards [TtopZ.eventually_ge_atTop 1,dwarfZ TtopZ 0
+    (p:=v-u) (sub_pos.mpr h) hc] with n hn hh
+  have he : 0<TmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^u‖ ≤ c*‖(n:ℝ)*TmZ n^v‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity)]
+  have hh' : 1 ≤ c * TmZ n^(v-u) := by simpa only [pow_zero] using hh
+  calc
+    _ = ((n:ℝ)*TmZ n^u)*1 := by ring
+    _ ≤ ((n:ℝ)*TmZ n^u)*(c*TmZ n^(v-u)) := mul_le_mul_of_nonneg_left hh' (by positivity)
+    _ = c*((n:ℝ)*(TmZ n^u*TmZ n^(v-u))) := by ring
+    _ = _ := by rw [← rpow_add he, show u+(v-u)=v by ring]
+
+theorem decimal_littleZ : decimalTimeZ =o[atTop] nlogn := by
+  have H := speed_littleZ decimal_rangeZ.2
+  have h : speedZ 1 = nlogn := funext fun n => by rw [speedZ,Real.rpow_one]; rfl
+  rw [h] at H; exact H
+
+lemma speed_paperZ : speedZ theta =O[atTop] paperTime := by
+  rw [isBigO_iff]
+  refine ⟨1,?_⟩
+  filter_upwards [TtopZ.eventually_ge_atTop 1,QtopZ.eventually_ge_atTop 1] with n hn hh
+  have he : 0<TmZ n := by linarith
+  have he' : 0<QmZ n := by linarith
+  change ‖(n:ℝ)*TmZ n^theta‖ ≤ 1*‖(n:ℝ)*TmZ n^theta*QmZ n^(4-theta)‖
+  rw [Real.norm_of_nonneg (by positivity),Real.norm_of_nonneg (by positivity),one_mul]
+  have hb := Real.one_le_rpow hh (show 0 ≤ 4-theta by linarith [theta_ltZ])
+  exact le_mul_of_one_le_right (by positivity) hb
+
+lemma time_boundZ {N} (h : ∀ n:ℕ,n ≤ N n ∧ N n ≤ 2*n) (a b : RationZ) :
+    TimeBoundsZ (lunchZ a b N) := by
+  have H := lunch_bigZ a b h
+  have hp := H.trans_isLittleO (flight_littleZ alpha_thetaZ)
+  have hd := H.trans_isLittleO (flight_littleZ decimal_rangeZ.1)
+  have ht : (fun n => (lunchZ a b N n:ℝ)) =O[atTop] decimalTimeZ := hd.isBigO
+  exact ⟨hp.isBigO.trans speed_paperZ,ht,ht.trans_isLittleO decimal_littleZ⟩
+
+end Skies
+
+/-! Main results. Provide formula for the order besides the existential specification. -/
+theorem transform_main_orderZ : ∃ order solve W,
+    DFTProgram order solve W ∧ TimeBoundsZ W ∧
+    ∀ n, 0<n → (run order n).val = receipt n ∧ (run order n).val < 8*n^3 := by
+  obtain ⟨o,s,a,b,hp,ho⟩ := flagshipOneZ
+  exact ⟨o,s,lunchZ a b id,hp,Skies.time_boundZ (N:=id) (fun n => ⟨le_rfl,by dsimp; omega⟩)
+    a b,fun n hn => ⟨ho n hn,(ho n hn).symm ▸ (receipt_bound n hn).2⟩⟩
+
+theorem convolution_main_orderZ : ∃ order solve W,
+    ConvProgram order solve W ∧ TimeBoundsZ W ∧
+    ∀ n, 0<n → (run order n).val = receipt (2*n-1) ∧ (run order n).val < 8*(2*n-1)^3 := by
+  obtain ⟨o,s,a,b,hp,ho⟩ := flagshipBothZ
+  have h (n : ℕ) : n ≤ stretchZ n ∧ stretchZ n ≤ 2*n := by unfold stretchZ; omega
+  exact ⟨o,s,lunchZ a b stretchZ,hp,Skies.time_boundZ h a b,fun n hn =>
+    ⟨ho n hn,(ho n hn).symm ▸ (receipt_bound _ (stretch_posZ hn)).2⟩⟩
+
+/-- **The discrete Fourier transform of every length in `O(n (log n)^(1 - 7474546/10^10))`.**
+OpenAI's `transform_main` (one fixed program, OpenAI's own `DFTProgram`, `paperTime` and `nlogn`)
+with the decimal exponent `1 - 1/10^13` replaced by `decimalExponentZ = 1 - 7474546/10^10`
+(Work/Fourier/Goal.lean). Sibling of the Walsh-Hadamard theorem `wht_main_block_B2Gp193x`: both
+follow from one kernel program, `RAM.hillsZ_program` (Work/Fourier/Seam.lean). -/
+theorem transform_mainZ : DFTGoalZ :=
+  let ⟨o,s,W,h,g,_⟩ := transform_main_orderZ
+  ⟨o,s,W,h,g⟩
+
+/-- **Convolution of every length with the same bounds** (OpenAI's `convolution_main`, same change). -/
+theorem convolution_mainZ : ConvGoalZ :=
+  let ⟨o,s,W,h,g,_⟩ := convolution_main_orderZ
+  ⟨o,s,W,h,g⟩
+
+lemma matrix_definitionZ (n : ℕ) (x : Vec n) : dft n x = Matrix.mulVec (dftMatrix n) x :=
+  rfl
+
+end
+end PowerSaving
+
+end OAI
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean
new file mode 100644
index 0000000000..eb4490af8b
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Geom.lean
@@ -0,0 +1,210 @@
+import Work.GCert.Chain.NetCert
+import Work.GCert.Chain.WinB
+import Work.BridgeGeom.B2
+
+/-!
+# (key: gx-chain) THE NETWORK LEMMA (spec statement 6): the bridged word B_2 delivers a `GCert`
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/BridgeGeom/Net.lean (section Net):
+the geometry of `BG.geomBridge2`, word for word, with the windows `gwinB` (`.Xm = BG.fmapB`).
+
+`bridge2_gcert I hH`: for every generalised invocation package, a `GCert` on
+`card Γ * (4 card T + card Sl)` live roles, label dimension `5h`, unit price
+`5 * I.cost φ + card T * BG.bankPrice h φ` (unchanged).  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF BG
+noncomputable section
+
+section Net
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+variable (I : GInv H T Sl C) (base : T → OBase H) (l : H)
+  (hbase : ∀ t, I.tv t = (base t).v l) (hH : 1 ≤ Fintype.card H)
+include hbase
+
+lemma ggeom_x01 (g : Orth (L5 H)) (t : T) :
+    PhiB g ∅ 1 = PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) (tt (I.tv t)) := by
+  rw [hbase t]
+  exact bankT_x0 (base t) l (0 : Fin 4) g
+
+lemma ggeom_y01 (g : Orth (L5 H)) (t : T) :
+    PhiB g ∅ (1 + tt (I.tv t)) = PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) 0 := by
+  rw [hbase t]
+  exact bankT_y0 (base t) l (0 : Fin 4) g
+
+/-- consecutive stages `c ∈ bs`, `c' ∉ bs`: `X` leaves where it enters. -/
+lemma ggeom_xx (bs : Finset (Fin 4)) (c c' : Fin 4) (hc : c ∈ bs) (hc' : c' ∉ bs)
+    (g : Orth (L5 H)) (t : T) :
+    PhiB (RrB (base t) l c g) (qS bs l) 1
+      = PhiB (RrB (base t) l c' g) (qS (insert c' bs) l) (tt (I.tv t)) := by
+  rw [hbase t]
+  exact bankT_xx (base t) l bs c c' hc hc' g
+
+/-- consecutive stages: `Y` leaves where it enters. -/
+lemma ggeom_yy (bs : Finset (Fin 4)) (c c' : Fin 4) (hc : c ∈ bs) (hc' : c' ∉ bs)
+    (g : Orth (L5 H)) (t : T) :
+    PhiB (RrB (base t) l c g) (qS bs l) (1 + tt (I.tv t))
+      = PhiB (RrB (base t) l c' g) (qS (insert c' bs) l) 0 := by
+  rw [hbase t]
+  exact bankT_yy (base t) l bs c c' hc hc' g
+
+/-- terminal identity of the bank pairs of the class `(g,t)`. -/
+lemma ggeom_term5 (g : Orth (L5 H)) (t : T) :
+    kernel (L5 H) * PhiB g ∅ (tt (I.tv t))
+      = shift ((BBB (base t) g).v (Sum.inl l))
+          * frame (BBB (base t) g) (univ \ {Sum.inl l}) := by
+  rw [hbase t]
+  exact class_term (base t) l g
+
+include hH
+
+/-- pair 2 before the first gate layer, `X`: ONE block of rank `2h-2`. -/
+lemma ggeom_aX2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB g ∅ (tt (I.tv t))) (PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) 1)
+      (fun φ => bcost φ (2 * Fintype.card H - 2)) := by
+  rw [hbase t]
+  exact idle_X0 (base t) l hB4 hH (0 : Fin 4) g _ (by omega)
+
+/-- pair 2 before the first gate layer, `Y`: ONE block of rank `2h-2`. -/
+lemma ggeom_aY2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB g ∅ 0) (PhiB (RrB (base t) l (0 : Fin 4) g) (qS bs1 l) (1 + tt (I.tv t)))
+      (fun φ => bcost φ (2 * Fintype.card H - 2)) := by
+  rw [hbase t]
+  exact idle_Y0 (base t) l hB4 hH (0 : Fin 4) g _ (by omega)
+
+/-- pair 1 at the end (idle in stages 3, 4, then the last four moves), `X`: ONE block `2h+2`. -/
+lemma ggeom_fX1 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (1 : Fin 4) g) (qS bs2 l) 1) (kernel (L5 H))
+      (fun φ => bcost φ (2 * Fintype.card H + 2)) :=
+  idle_Xend (base t) l hB4 hH bs2 (1 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs2, Fintype.card_fin]; omega)
+
+/-- pair 1 at the end, `Y`: ONE block of rank `2h+2`. -/
+lemma ggeom_fY1 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (1 : Fin 4) g) (qS bs2 l) (1 + tt (I.tv t)))
+      (frame (BBB (base t) g) (univ \ {Sum.inl l}))
+      (fun φ => bcost φ (2 * Fintype.card H + 2)) := by
+  rw [hbase t]
+  exact idle_Yend (base t) l hB4 hH bs2 (1 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs2, Fintype.card_fin]; omega)
+
+/-- pair 2 after stage 4, `X`: ONE block of rank `4`. -/
+lemma ggeom_fX2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (3 : Fin 4) g) (qS bs4 l) 1) (kernel (L5 H))
+      (fun φ => bcost φ 4) :=
+  idle_Xend (base t) l hB4 hH bs4 (3 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs4, Fintype.card_fin]; omega)
+
+/-- pair 2 after stage 4, `Y`: ONE block of rank `4`. -/
+lemma ggeom_fY2 (g : Orth (L5 H)) (t : T) :
+    XReach (PhiB (RrB (base t) l (3 : Fin 4) g) (qS bs4 l) (1 + tt (I.tv t)))
+      (frame (BBB (base t) g) (univ \ {Sum.inl l})) (fun φ => bcost φ 4) := by
+  rw [hbase t]
+  exact idle_Yend (base t) l hB4 hH bs4 (3 : Fin 4) (Finset.mem_insert_self _ _) g _
+    (by rw [card_bs4, Fintype.card_fin]; omega)
+
+/-- **The bridged word B_2 as a term of `BR.Bridge2`**: five stages on the label space
+`H ⊕ (Fin 4 × H)`, for any invocation package whose lines are the vectors of index `l` of
+orthonormal bases. -/
+def ggeomBridge2 : GBridge2 H T Sl C (L5 H) (Orth (L5 H)) where
+  I := I
+  G0 := fun g => gwinB hB4 hH g ∅
+  G1 := fun d => gwinB hB4 hH d (qS bs1 l)
+  G2 := fun d => gwinB hB4 hH d (qS bs2 l)
+  G3 := fun d => gwinB hB4 hH d (qS bs3 l)
+  G4 := fun d => gwinB hB4 hH d (qS bs4 l)
+  r1 := fun t => RrB (base t) l (0 : Fin 4)
+  r2 := fun t => RrB (base t) l (1 : Fin 4)
+  r3 := fun t => RrB (base t) l (2 : Fin 4)
+  r4 := fun t => RrB (base t) l (3 : Fin 4)
+  s1 := (Orth.colPerm (tauB (0 : Fin 4))).symm
+  s2 := (Orth.colPerm (tauB (1 : Fin 4))).symm
+  s3 := (Orth.colPerm (tauB (2 : Fin 4))).symm
+  s4 := (Orth.colPerm (tauB (3 : Fin 4))).symm
+  N1 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs1 l)) * d.1ᵀ)
+  W1 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N2 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs2 l)) * d.1ᵀ)
+  W2 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N3 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs3 l)) * d.1ᵀ)
+  W3 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  N4 := fun d => unframeM (d.1 * Matrix.fromBlocks 0 0 0 (diagI (qS bs4 l)) * d.1ᵀ)
+  W4 := fun d => frameM (d.1 * diagI (JB univ ∅) * d.1ᵀ)
+  u := fun g t => (BBB (base t) g).v (Sum.inl l)
+  YF := fun g t => frame (BBB (base t) g) (univ \ {Sum.inl l})
+  hm := two_le_card_LB hB4 hH
+  caX := fun φ => bcost φ (2 * Fintype.card H - 2)
+  caY := fun φ => bcost φ (2 * Fintype.card H - 2)
+  cX1 := fun φ => bcost φ (2 * Fintype.card H + 2)
+  cY1 := fun φ => bcost φ (2 * Fintype.card H + 2)
+  cX2 := fun φ => bcost φ 4
+  cY2 := fun φ => bcost φ 4
+  inv0 := fun g t => ⟨unframeM (g.1 * Matrix.fromBlocks (tt (I.tv t)) 0 0 (diagI ∅) * g.1ᵀ),
+    frameM_unframeM _⟩
+  z0 := fun g => PhiB_zero_empty g
+  hN1 := fun d => frameM_unframeM _
+  hW1 := fun d => PhiB_one d (qS bs1 l)
+  hN2 := fun d => frameM_unframeM _
+  hW2 := fun d => PhiB_one d (qS bs2 l)
+  hN3 := fun d => frameM_unframeM _
+  hW3 := fun d => PhiB_one d (qS bs3 l)
+  hN4 := fun d => frameM_unframeM _
+  hW4 := fun d => PhiB_one d (qS bs4 l)
+  x01 := fun g t => ggeom_x01 I base l hbase g t
+  y01 := fun g t => ggeom_y01 I base l hbase g t
+  x12 := fun g t => ggeom_xx I base l hbase bs1 0 1 (Finset.mem_singleton_self _) mem1 g t
+  y12 := fun g t => ggeom_yy I base l hbase bs1 0 1 (Finset.mem_singleton_self _) mem1 g t
+  x23 := fun g t => ggeom_xx I base l hbase bs2 1 2 (Finset.mem_insert_self _ _) mem2 g t
+  y23 := fun g t => ggeom_yy I base l hbase bs2 1 2 (Finset.mem_insert_self _ _) mem2 g t
+  x34 := fun g t => ggeom_xx I base l hbase bs3 2 3 (Finset.mem_insert_self _ _) mem3 g t
+  y34 := fun g t => ggeom_yy I base l hbase bs3 2 3 (Finset.mem_insert_self _ _) mem3 g t
+  sfin := fun g => helper_fin5 g
+  aX2 := fun g t => ggeom_aX2 I base l hbase hH g t
+  aY2 := fun g t => ggeom_aY2 I base l hbase hH g t
+  fX1 := fun g t => ggeom_fX1 I base l hbase hH g t
+  fY1 := fun g t => ggeom_fY1 I base l hbase hH g t
+  fX2 := fun g t => ggeom_fX2 I base l hbase hH g t
+  fY2 := fun g t => ggeom_fY2 I base l hbase hH g t
+  term := fun g t => ggeom_term5 I base l hbase g t
+
+end Net
+
+section End
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+/-- an orthonormal basis through a unit vector with a zero coordinate, at any index. -/
+theorem base_ex (z : Space H) (hz : dot z z = 1) (hg : ∃ p, z p = 0) (l : H) :
+    ∃ A : OBase H, z = A.v l := by
+  obtain ⟨p, hp⟩ := hg
+  obtain ⟨A, k, hA⟩ := exists_base_one z hz p hp
+  refine ⟨reindex A (Equiv.swap k l), ?_⟩
+  rw [← hA]
+  show A.v k = A.v (Equiv.swap k l l)
+  rw [Equiv.swap_apply_right]
+
+/-- **Generalised certificate of the bridged word B_2** for a generalised invocation package. -/
+theorem bridge2_gcert (I : GInv H T Sl C) (hH : 1 ≤ Fintype.card H) :
+    GCert (L5 H) (Sum.inl : BLive (Orth (L5 H)) T Sl → BRole (Orth (L5 H)) T Sl C)
+      (fun φ => (Fintype.card (Orth (L5 H)) : ℝ)
+        * (5 * I.cost φ + (Fintype.card T : ℝ) * bankPrice (Fintype.card H) φ)) := by
+  obtain ⟨l⟩ : Nonempty H := Fintype.card_pos_iff.mp (by omega)
+  have hb : ∀ t, ∃ A : OBase H, I.tv t = A.v l :=
+    fun t => base_ex (I.tv t) (I.hunit t) (I.hgap t) l
+  choose base hbase using hb
+  exact gbridge2_certificate (ggeomBridge2 I base l hbase hH)
+
+end End
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.ggeomBridge2
+#print axioms OAI.PowerSaving.GX.bridge2_gcert
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean
new file mode 100644
index 0000000000..d69fcb4992
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__InvThm.lean
@@ -0,0 +1,164 @@
+import Work.GCert.Chain.Inv
+
+/-!
+# (key: gx-chain) THE CARRIER INVOCATION THEOREM on the generalised engine: `Lab.inv`
+
+`CR.Phased.inv` (`Work/Carrier/PhasedInv.lean`) with subspace labels and `GRoute`.  Forward word:
+
+    erase | y -= K s (old frame 0) | free adapters to the labels of the certificate | phase A |
+    c += Cc s | copies down | y += Jr c | phase B | final climbs | free adapters to the old
+    frames | slots := slot rows of the inverse (old frame 1) | erase
+
+The backward word is the transposed inverse, gate by gate, on the same labels.  The scalar
+identities are `Scal.fwd_scalar` / `Scal.bwd_scalar` (those of `CR.Phased`).
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB BR CR GF RF
+noncomputable section
+
+section Thm
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+variable {α : Type} [Fintype α] [DecidableEq α]
+variable {S : Scal T Sl C} (L : Lab H S) (W : GWin H α)
+
+/-- **Forward word on clean frames.** -/
+theorem Lab.fwd_erased (c0 c1 : C → CMat α) :
+    GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) shearF L.cost := by
+  have a1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (actPoint (g1 S.Mt)) (fun _ => 0) :=
+    GRoute.gate (g1 S.Mt) _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · obtain ⟨h1, h2⟩ := offdiag_x (g1_x S.Mt).1 (g1_x S.Mt).2 hij e
+        exact start_frames W.Xm L.tv i j h1 h2)
+  have b3 : GRoute (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (actPoint (g8 S.Mti)) (fun _ => 0) :=
+    GRoute.gate (g8 S.Mti) _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have f := g8_facts S.hiy
+        obtain ⟨h1, h2, h3⟩ := offdiag_s f.1 f.2.1 f.2.2 hij e
+        exact end_old W.Xm L.tv i j h1 h2 h3)
+  have seg1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun r => W.X.Φ (L.labA r))
+      S.f1 (fun φ => rcost φ L.rA) :=
+    ((a1.trans (L.ad0 W)).trans (L.pA W.X W.big).1).cast (fun φ => by simp)
+  have seg2 : GRoute (fun r => W.X.Φ (L.labA r)) (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      S.f2 (fun φ => rcost φ L.rB + rcost φ L.rF) :=
+    ((((L.pB W.X W.big).1.trans (L.pF W.X W.big)).trans (L.adF W)).trans b3).cast
+      (fun φ => by simp)
+  have e0 : GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (glue (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun k => W.X.Φ (L.cen k)))
+      eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have L1 := glift_live (fun k => W.X.Φ (L.cen k)) seg1
+  have m1 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (fun z => addBlk bC (ap S.Cc (z ∘ bS)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bC bS bS_inj S.Cc (fun k q h => congrArg W.X.Φ (L.hAc k q h)))
+  have m2 := L.cdown W (fun r => W.X.Φ (L.labA r))
+  have m3 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (fun z => addBlk bY (ap S.Jr (z ∘ bC)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bY bC bC_inj S.Jr (fun t k _ => congrArg W.X.Φ (L.hAy t)))
+  have L2 := glift_live (fun _ : C => W.X.Φ L.z0) seg2
+  have e1 : GRoute (glue (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r)) (fun _ : C => W.X.Φ L.z0))
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have tot := (((((e0.trans L1).trans m1).trans m2).trans m3).trans L2).trans e1
+  refine (tot.castg (g' := shearF) (funext fun z => S.fwd_scalar z)).cast (fun φ => ?_)
+  simp only [Lab.cost, zero_add, add_zero]
+  ring
+
+/-- **Backward word on clean frames**: the transposed inverse gates, same labels; the copies
+start at the zero frame and climb. -/
+theorem Lab.bwd_erased (c0 c1 : C → CMat α) :
+    GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) shearB L.cost := by
+  have a1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P)
+      (actPoint (g1i S.Mt)ᵀ) (fun _ => 0) :=
+    GRoute.gate (g1i S.Mt)ᵀ _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have hij' : g1i S.Mt j i ≠ 0 := hij
+        obtain ⟨h1, h2⟩ := offdiag_x (g1i_x S.Mt).1 (g1i_x S.Mt).2 hij' (Ne.symm e)
+        exact start_frames W.Xm L.tv i j h2 h1)
+  have b3 : GRoute (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      (actPoint (h8 S.Mt)ᵀ) (fun _ => 0) :=
+    GRoute.gate (h8 S.Mt)ᵀ _ _ (fun i j hij => by
+      by_cases e : i = j
+      · subst e; rfl
+      · have hij' : h8 S.Mt j i ≠ 0 := hij
+        have f := h8_facts S.hmy
+        obtain ⟨h1, h2, h3⟩ := offdiag_s f.1 f.2.1 f.2.2 hij' (Ne.symm e)
+        exact (end_old W.Xm L.tv j i h1 h2 h3).symm)
+  have seg1 : GRoute (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun r => W.X.Φ (L.labA r))
+      S.b1 (fun φ => rcost φ L.rA) :=
+    ((a1.trans (L.ad0 W)).trans (L.pA W.X W.big).2).cast (fun φ => by simp)
+  have seg2 : GRoute (fun r => W.X.Φ (L.labA r)) (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r))
+      S.b2 (fun φ => rcost φ L.rB + rcost φ L.rF) :=
+    ((((L.pB W.X W.big).2.trans (L.pF W.X W.big)).trans (L.adF W)).trans b3).cast
+      (fun φ => by simp)
+  have e0 : GRoute (iin W.Xm L.tv (fun _ : Sl => W.Xm.Φ 0) c0)
+      (glue (fun r : L3 T Sl => W.Xm.Φ (lab3 L.tv r).P) (fun _ : C => W.X.Φ L.z0))
+      eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have L1 := glift_live (fun _ : C => W.X.Φ L.z0) seg1
+  have m1 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun _ : C => W.X.Φ L.z0))
+      (fun z => addBlk bC (ap S.Jrᵀ (z ∘ bY)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bC bY bY_inj S.Jrᵀ (fun k t _ => (congrArg W.X.Φ (L.hAy t)).symm))
+  have m2 := L.cup W (fun r => W.X.Φ (L.labA r))
+  have m3 : GRoute (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (glue (fun r => W.X.Φ (L.labA r)) (fun k => W.X.Φ (L.cen k)))
+      (fun z => addBlk bS (ap (-S.Ccᵀ) (z ∘ bC)) z) (fun _ => 0) :=
+    GRoute.ofX (xgate_shear bS bC bC_inj (-S.Ccᵀ)
+      (fun q k h => (congrArg W.X.Φ (L.hAc k q (ne_of_negT S.Cc h))).symm))
+  have L2 := glift_live (fun k => W.X.Φ (L.cen k)) seg2
+  have e1 : GRoute (glue (fun r : L3 T Sl => W.Xm.Φ (labE L.tv r)) (fun k => W.X.Φ (L.cen k)))
+      (iout W.Xm L.tv (fun _ : Sl => W.Xm.Φ 1) c1) eraseC (fun _ => 0) :=
+    GRoute.ofX (xerase (fun t => rfl) (fun t => rfl) (fun q => rfl))
+  have tot := (((((e0.trans L1).trans m1).trans m2).trans m3).trans L2).trans e1
+  refine (tot.castg (g' := shearB) (funext fun z => S.bwd_scalar z)).cast (fun φ => ?_)
+  simp only [Lab.cost, zero_add, add_zero]
+  ring
+
+/-- **THE CARRIER INVOCATION THEOREM on the generalised engine.**  The two halves of a
+certificate are an invocation package for the bridged network, with the price `L.cost`. -/
+def Lab.inv : GInv H T Sl C where
+  tv := L.tv
+  hunit := L.hunit
+  hgap := L.hgap
+  cost := L.cost
+  fwd := fun W N0 Wn hN hW Z c0 c1 =>
+    gdirty_of_erased W.Xm L.tv N0 Wn hN hW Z c0 c1 (L.fwd_erased W c0 c1)
+      (shearF_comm (fun _ => 1) (fun q => N0 * Z q) (fun _ => 1))
+  bwd := fun W N0 Wn hN hW Z c0 c1 =>
+    gdirty_of_erased W.Xm L.tv N0 Wn hN hW Z c0 c1 (L.bwd_erased W c0 c1)
+      (shearB_comm (fun _ => 1) (fun q => N0 * Z q) (fun _ => 1))
+
+@[simp] lemma Lab.inv_cost (φ : ℕ → ℝ) : L.inv.cost φ = L.cost φ := rfl
+@[simp] lemma Lab.inv_tv : L.inv.tv = L.tv := rfl
+
+end Thm
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.Lab.fwd_erased
+#print axioms OAI.PowerSaving.GX.Lab.bwd_erased
+#print axioms OAI.PowerSaving.GX.Lab.inv
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean
new file mode 100644
index 0000000000..6336ba0766
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetCert.lean
@@ -0,0 +1,157 @@
+import Work.GCert.Chain.NetStage
+import Work.GFrame.Top.Assemble
+
+/-!
+# (key: gx-chain) The bridged word B_2 on the generalised engine: the certificate `GCert`
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Cert.lean (section Net).
+`gbridge2_certificate`: a `GCert` on the live roles `BLive Γ T Sl` with price `card Γ * N.unit φ`.
+The gate layers, the idle climbs and the exchange are the old routes (`GRoute.ofX`).  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- gate layer A, after stage 1 and the first idle climb of pair 2: twins have equal frames. -/
+lemma GBridge2.gateA : XRoute N.S3 N.S3 (gsc pAB kA) (fun _ => 0) := by
+  refine gateP pAB kA N.S3 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer B, after stage 2 and the second idle climb of pair 2. -/
+lemma GBridge2.gateB : XRoute N.S5 N.S5 (gsc pAB kB) (fun _ => 0) := by
+  refine gateP pAB kB N.S5 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact N.x23 g t
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (N.y23 g t).symm
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- gate layer C, after the final climbs. -/
+lemma GBridge2.gateC : XRoute N.S8 N.S8 (gsc pC kCc) (fun _ => 0) := by
+  refine gateP pC kCc N.S8 ?_
+  rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩) hk
+  · exact (hk rfl).elim
+  · rfl
+  · rfl
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+  · exact (hk rfl).elim
+
+/-- the free shifts at the end. -/
+def GBridge2.corr : BRole Γ T Sl C → Space α :=
+  mkB (fun _ _ => 0) (fun g t => N.u g t) (fun _ _ => 0) (fun g t => N.u g t)
+    (fun _ _ => 0) (fun _ _ => 0)
+
+def GBridge2.S9 : BRole Γ T Sl C → CMat α := fun r => shift (N.corr r) * N.S8 r
+
+/-- the whole word before the exchange: five stages, three idle-climb layers, three gate
+layers. -/
+lemma GBridge2.route :
+    GRoute N.S0 N.S8 chain (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R := ((((((((((N.stage0.trans N.stage1).trans (GRoute.ofX N.climbA)).trans
+    (GRoute.ofX N.gateA)).trans N.stage2).trans (GRoute.ofX N.climbB)).trans
+    (GRoute.ofX N.gateB)).trans N.stage3).trans N.stage4).trans
+    (GRoute.ofX N.fin)).trans (GRoute.ofX N.gateC))
+  refine (R.castg ?_).cast (fun φ => ?_)
+  · rfl
+  · simp only [GBridge2.unit]
+    ring
+
+/-- **The scratch certificate of the bridged five-stage network with shared helper sets**,
+in whole blocks, with its exact price for every price list. -/
+theorem gbridge2_certificate :
+    GCert α (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C)
+      (fun φ => (Fintype.card Γ : ℝ) * N.unit φ) := by
+  have R2 : GRoute N.S8 N.S9 id (fun _ => 0) := GRoute.shifts N.hm N.S8 N.corr
+  have R3 : GRoute N.S9 (fun r => N.S9 (bpull r)) (actPoint brecM) (fun _ => 0) :=
+    GRoute.gate brecM N.S9 _ (fun i j h => by
+      have hj : j = bpull i := by
+        by_contra hne
+        exact h (by simp [brecM, hne])
+      rw [hj])
+  have Rt := ((N.route.trans R2).trans R3).cast (c' := fun φ => (Fintype.card Γ : ℝ) * N.unit φ)
+    (fun φ => by first | ring | simp)
+  have hSinv : ∀ r, ∃ M, N.S0 r * M = 1 := by
+    rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.G0 g).Xm.Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact N.inv0 g t
+    · refine ⟨1, ?_⟩
+      show (N.G0 g).Xm.Φ 0 * 1 = 1
+      rw [N.z0, Matrix.mul_one]
+    · exact ⟨1, Matrix.mul_one _⟩
+    · exact ⟨1, Matrix.mul_one _⟩
+  have hT : ∀ l : BLive Γ T Sl, N.S9 (bpull (Sum.inl l)) = kernel α * N.S0 (Sum.inl l) := by
+    rintro (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.G0 g).Xm.Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.G0 g).Xm.Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (N.u g t) * N.YF g t = kernel α * (N.G0 g).Xm.Φ (tt (N.I.tv t))
+      exact (N.term g t).symm
+    · show shift (0 : Space α) * kernel α = kernel α * (N.G0 g).Xm.Φ 0
+      rw [shift_zero, Matrix.one_mul, N.z0, Matrix.mul_one]
+    · show shift (0 : Space α) * kernel α = kernel α * 1
+      rw [shift_zero, Matrix.one_mul, Matrix.mul_one]
+  have hg : ∀ x : BRole Γ T Sl C → ℂ,
+      (∀ s, (∀ l : BLive Γ T Sl, (Sum.inl l : BRole Γ T Sl C) ≠ s) → x s = 0) →
+      ∀ l : BLive Γ T Sl,
+        (actPoint brecM ∘ (id ∘ chain)) x (Sum.inl l) = x (Sum.inl l) := by
+    intro x _ l
+    change actPoint brecM (chain x) (Sum.inl l) = _
+    rw [actPoint_brecM]
+    rcases l with (((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX1 (g,t)) = x (kX1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inl (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY1 (g,t))) = x (kY1 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inr (g,t))))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kX2 (g,t)) = x (kX2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((-1:ℚ):ℂ) * chain x (Sum.inl (Sum.inl (Sum.inr (Sum.inl (g,t))))) = _
+      rw [chain_eq]
+      show ((-1:ℚ):ℂ) * (-x (kY2 (g,t))) = x (kY2 (g,t))
+      first | (push_cast; ring) | simp
+    · show ((1:ℚ):ℂ) * chain x (Sum.inl (Sum.inr (g,q))) = _
+      rw [chain_eq]
+      show ((1:ℚ):ℂ) * x (kS (g,q)) = x (kS (g,q))
+      first | (push_cast; ring) | simp
+  exact gcert_of_groute (Sum.inl : BLive Γ T Sl → BRole Γ T Sl C) N.S0
+    (fun r => N.S9 (bpull r)) _ _ Rt hSinv hg hT
+
+end Net
+
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.route
+#print axioms OAI.PowerSaving.GX.gbridge2_certificate
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean
new file mode 100644
index 0000000000..c13042eb43
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetDef.lean
@@ -0,0 +1,157 @@
+import Work.GCert.Chain.Stage
+
+/-!
+# (key: gx-chain) The bridged five-stage word B_2 on the generalised engine: data and frames
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Net.lean (`BR.Bridge2`): the
+invocation is a `GInv`, the frame maps of the stages are windows `GWin` (`G0 .. G4`; the old
+frame map of a window is `.Xm`).  Everything else word for word.  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+/-- See the file header.  Fields in the style of `RF.Fold3S`; stages are numbered 0 to 4. -/
+structure GBridge2 (H T Sl C α Γ : Type) [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α] where
+  /-- the invocation (for a block circuit `X`: `X.inv`). -/
+  I : GInv H T Sl C
+  /-- frame maps of the invocations of the five stages. -/
+  G0 : Γ → GWin H α
+  G1 : Γ → GWin H α
+  G2 : Γ → GWin H α
+  G3 : Γ → GWin H α
+  G4 : Γ → GWin H α
+  /-- the class `(g,t)` is served by the invocation `g` in stage 0 and `r_l t g` in stage `l`. -/
+  r1 : T → Γ ≃ Γ
+  r2 : T → Γ ≃ Γ
+  r3 : T → Γ ≃ Γ
+  r4 : T → Γ ≃ Γ
+  /-- the invocation `d` of stage `l` uses the helper set (and the copies) `s_l d`. -/
+  s1 : Γ ≃ Γ
+  s2 : Γ ≃ Γ
+  s3 : Γ ≃ Γ
+  s4 : Γ ≃ Γ
+  /-- inverse of the frame of the base, and frame of the window, of every invocation. -/
+  N1 : Γ → CMat α
+  W1 : Γ → CMat α
+  N2 : Γ → CMat α
+  W2 : Γ → CMat α
+  N3 : Γ → CMat α
+  W3 : Γ → CMat α
+  N4 : Γ → CMat α
+  W4 : Γ → CMat α
+  u : Γ → T → Space α
+  YF : Γ → T → CMat α
+  hm : 2 ≤ Fintype.card α
+  /-- prices of the idle climbs, for every price list.  B_2 with merged climbs:
+  `caX = caY = fun φ => bcost φ (2h-2)`, `cX1 = cY1 = fun φ => bcost φ (2h+2)`,
+  `cX2 = cY2 = fun φ => bcost φ 4`. -/
+  caX : (ℕ → ℝ) → ℝ
+  caY : (ℕ → ℝ) → ℝ
+  cX1 : (ℕ → ℝ) → ℝ
+  cY1 : (ℕ → ℝ) → ℝ
+  cX2 : (ℕ → ℝ) → ℝ
+  cY2 : (ℕ → ℝ) → ℝ
+  inv0 : ∀ g t, ∃ N : CMat α, (G0 g).Xm.Φ (tt (I.tv t)) * N = 1
+  z0 : ∀ g, (G0 g).Xm.Φ 0 = 1
+  hN1 : ∀ d, (G1 d).Xm.Φ 0 * N1 d = 1
+  hW1 : ∀ d, (G1 d).Xm.Φ 1 = W1 d * (G1 d).Xm.Φ 0
+  hN2 : ∀ d, (G2 d).Xm.Φ 0 * N2 d = 1
+  hW2 : ∀ d, (G2 d).Xm.Φ 1 = W2 d * (G2 d).Xm.Φ 0
+  hN3 : ∀ d, (G3 d).Xm.Φ 0 * N3 d = 1
+  hW3 : ∀ d, (G3 d).Xm.Φ 1 = W3 d * (G3 d).Xm.Φ 0
+  hN4 : ∀ d, (G4 d).Xm.Φ 0 * N4 d = 1
+  hW4 : ∀ d, (G4 d).Xm.Φ 1 = W4 d * (G4 d).Xm.Φ 0
+  /-- the bank frames a stage leaves are the bank frames the next stage starts from. -/
+  x01 : ∀ g t, (G0 g).Xm.Φ 1 = (G1 (r1 t g)).Xm.Φ (tt (I.tv t))
+  y01 : ∀ g t, (G0 g).Xm.Φ (1 + tt (I.tv t)) = (G1 (r1 t g)).Xm.Φ 0
+  x12 : ∀ g t, (G1 (r1 t g)).Xm.Φ 1 = (G2 (r2 t g)).Xm.Φ (tt (I.tv t))
+  y12 : ∀ g t, (G1 (r1 t g)).Xm.Φ (1 + tt (I.tv t)) = (G2 (r2 t g)).Xm.Φ 0
+  x23 : ∀ g t, (G2 (r2 t g)).Xm.Φ 1 = (G3 (r3 t g)).Xm.Φ (tt (I.tv t))
+  y23 : ∀ g t, (G2 (r2 t g)).Xm.Φ (1 + tt (I.tv t)) = (G3 (r3 t g)).Xm.Φ 0
+  x34 : ∀ g t, (G3 (r3 t g)).Xm.Φ 1 = (G4 (r4 t g)).Xm.Φ (tt (I.tv t))
+  y34 : ∀ g t, (G3 (r3 t g)).Xm.Φ (1 + tt (I.tv t)) = (G4 (r4 t g)).Xm.Φ 0
+  /-- the five windows of a helper set make up the kernel. -/
+  sfin : ∀ g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) *
+    (W1 (s1.symm g) * (G0 g).Xm.Φ 1))) = kernel α
+  /-- pair 2, idle in stages 0 and 1: ONE block from its start frame to the frame of its
+  twin after stage 1. -/
+  aX2 : ∀ g t, XReach ((G0 g).Xm.Φ (tt (I.tv t))) ((G1 (r1 t g)).Xm.Φ 1) caX
+  aY2 : ∀ g t, XReach ((G0 g).Xm.Φ 0) ((G1 (r1 t g)).Xm.Φ (1 + tt (I.tv t))) caY
+  /-- pair 1, idle in stages 3 and 4: ONE block from its frame after stage 2 to the end. -/
+  fX1 : ∀ g t, XReach ((G2 (r2 t g)).Xm.Φ 1) (kernel α) cX1
+  fY1 : ∀ g t, XReach ((G2 (r2 t g)).Xm.Φ (1 + tt (I.tv t))) (YF g t) cY1
+  /-- pair 2 after stage 4: ONE final block. -/
+  fX2 : ∀ g t, XReach ((G4 (r4 t g)).Xm.Φ 1) (kernel α) cX2
+  fY2 : ∀ g t, XReach ((G4 (r4 t g)).Xm.Φ (1 + tt (I.tv t))) (YF g t) cY2
+  term : ∀ g t, kernel α * (G0 g).Xm.Φ (tt (I.tv t)) = shift (u g t) * YF g t
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- price of the blocks of one unit (one element of `Γ`): five invocations and the idle
+climbs of the four bank roles of every class. -/
+def GBridge2.unit (φ : ℕ → ℝ) : ℝ :=
+  5 * N.I.cost φ + (Fintype.card T : ℝ) * ((N.caX φ + N.caY φ)
+    + 2 * bcost φ (Fintype.card H - 1)
+    + (N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ))
+
+/-- the bank index of stage 0: the class `(g,t)` belongs to the invocation `g`. -/
+abbrev bid (Γ T : Type) : T → Γ ≃ Γ := fun _ => Equiv.refl Γ
+
+/-! bank frames of the class `(g,t)`: `xi l`, `yi l` at the START of stage `l`; `xo l`,
+`yo l` at the END of stage `l` (only where no next stage follows on that pair). -/
+def GBridge2.xi0 (g : Γ) (t : T) : CMat α := (N.G0 g).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi0 (g : Γ) (t : T) : CMat α := (N.G0 g).Xm.Φ 0
+def GBridge2.xi1 (g : Γ) (t : T) : CMat α := (N.G1 (N.r1 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi1 (g : Γ) (t : T) : CMat α := (N.G1 (N.r1 t g)).Xm.Φ 0
+def GBridge2.xi2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ 0
+def GBridge2.xo2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ 1
+def GBridge2.yo2 (g : Γ) (t : T) : CMat α := (N.G2 (N.r2 t g)).Xm.Φ (1 + tt (N.I.tv t))
+def GBridge2.xi3 (g : Γ) (t : T) : CMat α := (N.G3 (N.r3 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi3 (g : Γ) (t : T) : CMat α := (N.G3 (N.r3 t g)).Xm.Φ 0
+def GBridge2.xi4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ (tt (N.I.tv t))
+def GBridge2.yi4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ 0
+def GBridge2.xo4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ 1
+def GBridge2.yo4 (g : Γ) (t : T) : CMat α := (N.G4 (N.r4 t g)).Xm.Φ (1 + tt (N.I.tv t))
+
+/-- helper slots after the stages 0, 1, 2, 3, 4 (at the start: `cOne Γ Sl α`). -/
+def GBridge2.Z1 : Γ → Sl → CMat α := fun g _ => (N.G0 g).Xm.Φ 1
+def GBridge2.Z2 : Γ → Sl → CMat α := fun g q => N.W1 (N.s1.symm g) * N.Z1 g q
+def GBridge2.Z3 : Γ → Sl → CMat α := fun g q => N.W2 (N.s2.symm g) * N.Z2 g q
+def GBridge2.Z4 : Γ → Sl → CMat α := fun g q => N.W3 (N.s3.symm g) * N.Z3 g q
+def GBridge2.Z5 : Γ → Sl → CMat α := fun g q => N.W4 (N.s4.symm g) * N.Z4 g q
+
+/-- frames: at the start; after stage 0; after stage 1; after the first idle climb of pair 2
+(first gate layer here); after stage 2; after the second idle climb of pair 2 (second gate
+layer here); after stage 3; after stage 4; after the final climbs (third gate layer here). -/
+def GBridge2.S0 : BRole Γ T Sl C → CMat α := mkB N.xi0 N.yi0 N.xi0 N.yi0 (cOne Γ Sl α) (cOne Γ C α)
+def GBridge2.S1 : BRole Γ T Sl C → CMat α := mkB N.xi1 N.yi1 N.xi0 N.yi0 N.Z1 (cOne Γ C α)
+def GBridge2.S2 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi0 N.yi0 N.Z2 (cOne Γ C α)
+def GBridge2.S3 : BRole Γ T Sl C → CMat α := mkB N.xi2 N.yi2 N.xi2 N.yi2 N.Z2 (cOne Γ C α)
+def GBridge2.S4 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi2 N.yi2 N.Z3 (cOne Γ C α)
+def GBridge2.S5 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi3 N.yi3 N.Z3 (cOne Γ C α)
+def GBridge2.S6 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xi4 N.yi4 N.Z4 (cOne Γ C α)
+def GBridge2.S7 : BRole Γ T Sl C → CMat α := mkB N.xo2 N.yo2 N.xo4 N.yo4 N.Z5 (cOne Γ C α)
+def GBridge2.S8 : BRole Γ T Sl C → CMat α :=
+  mkB (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) N.YF (fun _ _ => kernel α) (cOne Γ C α)
+
+
+end Net
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.unit
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean
new file mode 100644
index 0000000000..670f4c6a84
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__NetStage.lean
@@ -0,0 +1,186 @@
+import Work.GCert.Chain.NetDef
+
+/-!
+# (key: gx-chain) The bridged word B_2 on the generalised engine: the five stages and the idle climbs
+
+GENERATED by checks/wht26/gx-chain/py/netgen.py from Work/Bridge/Net.lean.  The stages are
+`GRoute`s (`gistage_fwd` / `gistage_bwd`, `gblift1` / `gblift2`); the idle climbs of the bank
+roles are the OLD block routes, unchanged.  No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR GF
+noncomputable section
+
+section Net
+variable {H T Sl C α Γ : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] [Fintype α] [DecidableEq α]
+  [Fintype Γ] [DecidableEq Γ]
+variable (N : GBridge2 H T Sl C α Γ)
+
+/-- stage 0: forward on pair 1, every helper set starts at the matrix `1`. -/
+lemma GBridge2.stage0 :
+    GRoute N.S0 N.S1 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_fwd N.I (bid Γ T) (Equiv.refl Γ) N.G0 (fun _ => 1) (fun g => (N.G0 g).Xm.Φ 1)
+    (fun d => by rw [N.z0, Matrix.mul_one]) (fun d => by rw [N.z0, Matrix.mul_one])
+    (cOne Γ Sl α) (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv (bid Γ T) (fun d => (N.G0 d).Xm)
+      (fun g (q : Sl) => (N.G0 ((Equiv.refl Γ).symm g)).Xm.Φ 1 * cOne Γ Sl α g q) (cOne Γ C α)
+      = mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x01 g t
+    · exact N.y01 g t
+    · show (N.G0 g).Xm.Φ 1 * 1 = (N.G0 g).Xm.Φ 1
+      rw [Matrix.mul_one]
+    · rfl
+  have h' : GRoute (bIn N.I.tv (bid Γ T) (fun d => (N.G0 d).Xm) (cOne Γ Sl α) (cOne Γ C α))
+      (mkS N.xi1 N.yi1 N.Z1 (cOne Γ C α)) GF (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift1 N.xi0 N.yi0 h'
+
+/-- stage 1: backward on pair 1; the helper set `g` serves the invocation `s1⁻¹ g`. -/
+lemma GBridge2.stage1 :
+    GRoute N.S1 N.S2 (lift1 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_bwd N.I N.r1 N.s1 N.G1 N.N1 N.W1 N.hN1 N.hW1 N.Z1 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r1 (fun d => (N.G1 d).Xm) (fun g q => N.W1 (N.s1.symm g) * N.Z1 g q) (cOne Γ C α)
+      = mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x12 g t
+    · exact N.y12 g t
+    · rfl
+    · rfl
+  have h' : GRoute (bIn N.I.tv N.r1 (fun d => (N.G1 d).Xm) N.Z1 (cOne Γ C α))
+      (mkS N.xi2 N.yi2 N.Z2 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift1 N.xi0 N.yi0 h'
+
+/-- stage 2: forward on pair 1. -/
+lemma GBridge2.stage2 :
+    GRoute N.S3 N.S4 (lift1 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  gblift1 N.xi2 N.yi2
+    (gistage_fwd N.I N.r2 N.s2 N.G2 N.N2 N.W2 N.hN2 N.hW2 N.Z2 (cOne Γ C α) (cOne Γ C α))
+
+/-- stage 3: backward on pair 2. -/
+lemma GBridge2.stage3 :
+    GRoute N.S5 N.S6 (lift2 GB) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+  have h := gistage_bwd N.I N.r3 N.s3 N.G3 N.N3 N.W3 N.hN3 N.hW3 N.Z3 (cOne Γ C α) (cOne Γ C α)
+  have e : bOut N.I.tv N.r3 (fun d => (N.G3 d).Xm) (fun g q => N.W3 (N.s3.symm g) * N.Z3 g q) (cOne Γ C α)
+      = mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α) := by
+    funext r
+    rcases r with (((⟨g,t⟩|⟨g,t⟩)|⟨g,q⟩)|⟨g,c⟩)
+    · exact N.x34 g t
+    · exact N.y34 g t
+    · rfl
+    · rfl
+  have h' : GRoute (bIn N.I.tv N.r3 (fun d => (N.G3 d).Xm) N.Z3 (cOne Γ C α))
+      (mkS N.xi4 N.yi4 N.Z4 (cOne Γ C α)) GB (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) := by
+    rw [← e]
+    exact h
+  exact gblift2 N.xo2 N.yo2 h'
+
+/-- stage 4: forward on pair 2. -/
+lemma GBridge2.stage4 :
+    GRoute N.S6 N.S7 (lift2 GF) (fun φ => (Fintype.card Γ : ℝ) * N.I.cost φ) :=
+  gblift2 N.xo2 N.yo2
+    (gistage_fwd N.I N.r4 N.s4 N.G4 N.N4 N.W4 N.hN4 N.hW4 N.Z4 (cOne Γ C α) (cOne Γ C α))
+
+/-- first idle climb of pair 2 (stages 0 and 1 in ONE block per role), to the frames of
+pair 1 after stage 1. -/
+lemma GBridge2.climbA :
+    XRoute N.S2 N.S3 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (N.caX φ + N.caY φ))) := by
+  have H1 := XRoute.reach_all N.S2 N.S3
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ => N.caX)
+      (fun _ _ => N.caY) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.G0 g).Xm.Φ (tt (N.I.tv t))) ((N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))) N.caX
+        rw [← N.x12 g t]
+        exact N.aX2 g t
+      · show XReach ((N.G0 g).Xm.Φ 0) ((N.G2 (N.r2 t g)).Xm.Φ 0) N.caY
+        rw [← N.y12 g t]
+        exact N.aY2 g t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- second idle climb of pair 2: the window of stage 2, ONE block of rank `card H - 1` per
+role, to the frames of pair 1 after stage 2. -/
+lemma GBridge2.climbB :
+    XRoute N.S4 N.S5 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * (2 * bcost φ (Fintype.card H - 1)))) := by
+  have H1 := XRoute.reach_all N.S4 N.S5
+    (mkB (fun _ _ _ => 0) (fun _ _ _ => 0) (fun _ _ φ => bcost φ (Fintype.card H - 1))
+      (fun _ _ φ => bcost φ (Fintype.card H - 1)) (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact XReach.refl _
+      · exact XReach.refl _
+      · show XReach ((N.G2 (N.r2 t g)).Xm.Φ (tt (N.I.tv t))) ((N.G3 (N.r3 t g)).Xm.Φ (tt (N.I.tv t)))
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.x23 g t]
+        exact N.I.climbX (N.G2 (N.r2 t g)).Xm t
+      · show XReach ((N.G2 (N.r2 t g)).Xm.Φ 0) ((N.G3 (N.r3 t g)).Xm.Φ 0)
+          (fun φ => bcost φ (Fintype.card H - 1))
+        rw [← N.y23 g t]
+        exact N.I.climbY (N.G2 (N.r2 t g)).Xm t
+      · exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+/-- the final climbs: pair 1 from its frames after stage 2 (ONE block per role for the
+stages 3, 4 and the rest), pair 2 from its frames after stage 4; the helper slots are
+already at the kernel. -/
+lemma GBridge2.fin :
+    XRoute N.S7 N.S8 id (fun φ => (Fintype.card Γ : ℝ) *
+      ((Fintype.card T : ℝ) * ((N.cX1 φ + N.cY1 φ) + (N.cX2 φ + N.cY2 φ)))) := by
+  have H1 := XRoute.reach_all N.S7 N.S8
+    (mkB (fun _ _ => N.cX1) (fun _ _ => N.cY1) (fun _ _ => N.cX2) (fun _ _ => N.cY2)
+      (fun _ _ _ => 0) (fun _ _ _ => 0)) (by
+      rintro ((((⟨g,t⟩|⟨g,t⟩)|(⟨g,t⟩|⟨g,t⟩))|⟨g,q⟩)|⟨g,c⟩)
+      · exact N.fX1 g t
+      · exact N.fY1 g t
+      · exact N.fX2 g t
+      · exact N.fY2 g t
+      · show XReach (N.W4 (N.s4.symm g) * (N.W3 (N.s3.symm g) * (N.W2 (N.s2.symm g) *
+          (N.W1 (N.s1.symm g) * (N.G0 g).Xm.Φ 1)))) (kernel α) (fun _ => 0)
+        rw [N.sfin g]
+        exact XReach.refl _
+      · exact XReach.refl _)
+  refine H1.cast (fun φ => ?_)
+  simp_rw [mkB_map (fun c : (ℕ → ℝ) → ℝ => c φ)]
+  rw [sum_mkB]
+  simp only [sum_const, card_univ, nsmul_eq_mul, mul_zero, add_zero, zero_add]
+  ring
+
+end Net
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.GBridge2.stage0
+#print axioms OAI.PowerSaving.GX.GBridge2.stage1
+#print axioms OAI.PowerSaving.GX.GBridge2.stage2
+#print axioms OAI.PowerSaving.GX.GBridge2.stage3
+#print axioms OAI.PowerSaving.GX.GBridge2.stage4
+#print axioms OAI.PowerSaving.GX.GBridge2.climbA
+#print axioms OAI.PowerSaving.GX.GBridge2.climbB
+#print axioms OAI.PowerSaving.GX.GBridge2.fin
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean
new file mode 100644
index 0000000000..e68c42377f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__Phased.lean
@@ -0,0 +1,199 @@
+import Work.Carrier.Phases
+import Work.GFrame.Labels.All
+
+/-!
+# (key: gx-chain) The certificate as two halves: `Scal` (scalar half) and `Lab` (label half)
+
+`Scal T Sl C`: the scalar fields of `CR.Phased` (three facts about ONE matrix
+`Mt = MB * scatM (Jr * Cc) * MA`).  The scalar identities of the forward and of the backward
+word (`fwd_scalar`, `bwd_scalar`) are those of `Work/Carrier/Phases.lean`, word for word.
+
+`Lab H S`: subspace labels (`GF.SLbl H`), routes of the three phases on the generalised engine
+(`GF.GRoute`) through every stage-B frame map (`GF.BXMap H α`), and facts about dimensions at
+the two ends.  No projector, no `Climb`.
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB BR CR GF
+noncomputable section
+
+/-- **The scalar half.** -/
+structure Scal (T Sl C : Type) [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] where
+  Cc : Matrix C Sl ℚ
+  Jr : Matrix T C ℚ
+  MA : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MAi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MB : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  MBi : Matrix (L3 T Sl) (L3 T Sl) ℚ
+  hAi : MAi * MA = 1
+  hBi : MBi * MB = 1
+  hx : ∀ t j, (MB * scatM (Jr * Cc) * MA) (lX t) j = if lX t = j then 1 else 0
+  hy : ∀ i t, (MB * scatM (Jr * Cc) * MA) i (lY t) = if i = lY t then 1 else 0
+  hid : ∀ S t, (MB * scatM (Jr * Cc) * MA) (lY S) (lX t) = if S = t then 1 else 0
+
+/-- **The label half.**  See `checks/wht26/shared/gcert-interface.md`, section CHAIN. -/
+structure Lab (H : Type) [Fintype H] [DecidableEq H] {T Sl C : Type} [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] (S : Scal T Sl C) where
+  tv : T → Space H
+  hunit : ∀ t, dot (tv t) (tv t) = 1
+  hgap : ∀ t, ∃ p, tv t p = 0
+  lab0 : L3 T Sl → SLbl H
+  labA : L3 T Sl → SLbl H
+  labB : L3 T Sl → SLbl H
+  labF : L3 T Sl → SLbl H
+  cen : C → SLbl H
+  z0 : SLbl H
+  hz0 : z0.dim = 0
+  h0x : ∀ t, (lab0 (lX t)).dim = 1 ∧ (lab0 (lX t)).Mem (tv t)
+  h0y : ∀ t, (lab0 (lY t)).dim = 0
+  h0s : ∀ q, (lab0 (lS q)).dim = 0
+  hAy : ∀ t, labA (lY t) = z0
+  hAc : ∀ k q, S.Cc k q ≠ 0 → cen k = labA (lS q)
+  hcen : ∀ k, 0 < (cen k).dim
+  hFx : ∀ t, (labF (lX t)).dim = Fintype.card H
+  hFs : ∀ q, (labF (lS q)).dim = Fintype.card H
+  hFy : ∀ t, (labF (lY t)).dim + 1 = Fintype.card H ∧
+    ∀ x, (labF (lY t)).Mem x → dot (tv t) x = 0
+  rA : List ℕ
+  rB : List ℕ
+  rF : List ℕ
+  pA : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (lab0 r)) (fun r => X.Φ (labA r)) (actPoint S.MA)
+        (fun φ => rcost φ rA) ∧
+    GRoute (fun r => X.Φ (lab0 r)) (fun r => X.Φ (labA r)) (actPoint S.MAiᵀ)
+        (fun φ => rcost φ rA)
+  pB : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (labA r)) (fun r => X.Φ (labB r)) (actPoint S.MB)
+        (fun φ => rcost φ rB) ∧
+    GRoute (fun r => X.Φ (labA r)) (fun r => X.Φ (labB r)) (actPoint S.MBiᵀ)
+        (fun φ => rcost φ rB)
+  pF : ∀ {α : Type} [Fintype α] [DecidableEq α] (X : BXMap H α),
+    Fintype.card H < Fintype.card α →
+    GRoute (fun r => X.Φ (labB r)) (fun r => X.Φ (labF r)) id (fun φ => rcost φ rF)
+
+/-- price of one invocation: the blocks of the three phases and one block per copy. -/
+def Lab.cost {H : Type} [Fintype H] [DecidableEq H] {T Sl C : Type} [Fintype T] [DecidableEq T]
+    [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C] {S : Scal T Sl C} (L : Lab H S)
+    (φ : ℕ → ℝ) : ℝ :=
+  rcost φ L.rA + (∑ k, bcost φ (L.cen k).dim) + rcost φ L.rB + rcost φ L.rF
+
+section Alg
+variable {H T Sl C : Type} [Fintype H] [DecidableEq H] [Fintype T] [DecidableEq T]
+  [Fintype Sl] [DecidableEq Sl] [Fintype C] [DecidableEq C]
+
+namespace Scal
+variable (K : Scal T Sl C)
+
+/-- the product of ALL gates of the main phase (scatter with the copies eliminated). -/
+def Mt : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MB * scatM (K.Jr * K.Cc) * K.MA
+/-- its inverse. -/
+def Mti : Matrix (L3 T Sl) (L3 T Sl) ℚ := K.MAi * scatMi (K.Jr * K.Cc) * K.MBi
+
+
+lemma im : K.Mti * K.Mt = 1 := by
+  unfold Mti Mt
+  have hB : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ, K.MBi * (K.MB * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, K.hBi, Matrix.one_mul]
+  have hS : ∀ X : Matrix (L3 T Sl) (L3 T Sl) ℚ,
+      scatMi (K.Jr * K.Cc) * (scatM (K.Jr * K.Cc) * X) = X := fun X => by
+    rw [← Matrix.mul_assoc, scat_inv, Matrix.one_mul]
+  rw [Matrix.mul_assoc, Matrix.mul_assoc, Matrix.mul_assoc, hB, hS, K.hAi]
+
+lemma mi : K.Mt * K.Mti = 1 := mul_eq_one_comm.mp K.im
+
+lemma hxm : PX * K.Mt = PX := PX_mul_of (M := K.Mt) K.hx
+lemma hmy : K.Mt * PY = PY := mul_PY_of (M := K.Mt) K.hy
+lemma hiy : K.Mti * PY = PY := dirt_iy K.hmy K.im
+
+/-- **the dirt rule, forward**, for the matrices of the circuit. -/
+lemma hF : g8 K.Mti * K.Mt * g1 K.Mt = 1 + PY * K.Mt * PX := by
+  unfold g8 g1
+  exact dirt_fwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- **the dirt rule, backward.** -/
+lemma hB : g1i K.Mt * K.Mti * h8 K.Mt = 1 - PY * K.Mt * PX := by
+  unfold g1i h8
+  exact dirt_bwd PX_sq PY_sq PX_PY PY_PX K.hxm K.hmy K.im K.mi
+
+/-- live part of the forward word before the scatter: `y -= K s`, then phase A. -/
+def f1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MA (actPoint (g1 K.Mt) u)
+/-- after the scatter: phase B, then the slot rows of the inverse. -/
+def f2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (g8 K.Mti) (actPoint K.MB u)
+/-- the same for the backward word (transposed inverses). -/
+def b1 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u)
+def b2 (u : L3 T Sl → ℂ) : L3 T Sl → ℂ := actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ u)
+
+lemma fwd_live (u : L3 T Sl → ℂ) :
+    K.f2 (actPoint (scatM (K.Jr * K.Cc)) (K.f1 u)) = actPoint (1 + PY * K.Mt * PX) u := by
+  rw [← K.hF]
+  show actPoint (g8 K.Mti) (actPoint K.MB (actPoint (scatM (K.Jr * K.Cc))
+      (actPoint K.MA (actPoint (g1 K.Mt) u))))
+    = actPoint (g8 K.Mti * (K.MB * scatM (K.Jr * K.Cc) * K.MA) * g1 K.Mt) u
+  rw [actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma bwd_live (u : L3 T Sl → ℂ) :
+    K.b2 (actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 u))
+      = actPoint ((1 - PY * K.Mt * PX)ᵀ) u := by
+  rw [← K.hB]
+  show actPoint (h8 K.Mt)ᵀ (actPoint K.MBiᵀ (actPoint (scatMi (K.Jr * K.Cc))ᵀ
+      (actPoint K.MAiᵀ (actPoint (g1i K.Mt)ᵀ u))))
+    = actPoint ((g1i K.Mt * (K.MAi * scatMi (K.Jr * K.Cc) * K.MBi) * h8 K.Mt)ᵀ) u
+  rw [Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul, Matrix.transpose_mul,
+    actPoint_mul, actPoint_mul, actPoint_mul, actPoint_mul]
+
+lemma liveAct_glue (φ : (L3 T Sl → ℂ) → (L3 T Sl → ℂ)) (u : L3 T Sl → ℂ) (c : C → ℂ) :
+    liveAct φ (glue u c) = glue (φ u) c :=
+  congrArg (fun v => glue (φ v) c) (glue_up u c)
+
+/-- **Scalar identity of the forward word**: `y += x`, slots restored, for ARBITRARY slot
+contents (the copies are erased before and after). -/
+theorem fwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.f2 (gateS bY bC K.Jr (gateS bC bS K.Cc (liveAct K.f1 (eraseC z)))))
+      = shearF z := by
+  have h1 : liveAct K.f1 (eraseC z) = glue (K.f1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bY bC K.Jr (gateS bC bS K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint (scatM (K.Jr * K.Cc)) (K.f1 (z ∘ upE)) := by
+    have h := scat_glue K.Jr K.Cc (glue (K.f1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.fwd_live, act_shear K.Mt K.hid]
+  exact glue_shearF z
+
+/-- **Scalar identity of the backward word**: `x -= y`, slots restored. -/
+theorem bwd_scalar (z : Box T Sl C → ℂ) :
+    eraseC (liveAct K.b2 (gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (liveAct K.b1 (eraseC z)))))
+      = shearB z := by
+  have h1 : liveAct K.b1 (eraseC z) = glue (K.b1 (z ∘ upE)) (fun _ => 0) := by
+    rw [erase_glue z, liveAct_glue]
+  have hs : gateS bS bC (-K.Ccᵀ) (gateS bC bY K.Jrᵀ (glue (K.b1 (z ∘ upE)) (fun _ => 0))) ∘ upE
+      = actPoint ((scatMi (K.Jr * K.Cc))ᵀ) (K.b1 (z ∘ upE)) := by
+    have h := scat_glueT K.Jr K.Cc (glue (K.b1 (z ∘ upE)) (fun _ => 0)) rfl
+    rw [glue_up] at h
+    exact h
+  rw [h1]
+  unfold liveAct
+  rw [erase_of_glue, hs, K.bwd_live, act_shearT K.Mt K.hid]
+  exact glue_shearB z
+
+end Scal
+end Alg
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.Scal.fwd_scalar
+#print axioms OAI.PowerSaving.GX.Scal.bwd_scalar
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean
new file mode 100644
index 0000000000..951edde5cf
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Chain__WinB.lean
@@ -0,0 +1,132 @@
+import Work.GCert.Chain.Win
+import Work.BridgeGeom.Stage
+
+/-!
+# (key: gx-chain) THE WINDOW LIFT (spec statement 3): the windows of the bridged geometry
+
+For the block frame map `BG.fmapB hB hH d q` of a stage of the bridged word (label space
+`LB B H = H ⊕ (B × H)`, old frame of the projector `P`: `PhiB d q P`) the stage-B frame map is
+`BXMap.ofConj d q` (`U ↦ d (U ⊕ span q)`, arbitrary subspaces `U` of `H`).  At a coordinate
+subspace of an orthonormal basis `A` of `H` the two name the SAME subspace of the address space
+(`insub_old_new`), so the old frame and the representative of any label of that subspace
+differ by a free factor (`frame_core_free`, `rep_change`): `old_to_new`, `new_to_old`.
+
+`gwinB hB hH d q : GWin H (LB B H)` with `(gwinB hB hH d q).Xm = fmapB hB hH d q` (`rfl`).
+
+No `sorry`.
+-/
+
+set_option linter.unusedSectionVars false
+set_option linter.unusedVariables false
+
+namespace OAI
+namespace PowerSaving
+namespace GX
+open Binary Matrix Finset RAM SS CB RF BR BG GF
+noncomputable section
+
+section
+variable {B H : Type} [Fintype B] [DecidableEq B] [Fintype H] [DecidableEq H]
+
+lemma blkT_mulVec (A : OBase H) (z : Space (LB B H)) (k : LB B H) :
+    ((blkB B A)ᵀ *ᵥ z) k = Sum.elim (fun i => dot (A.v i) (fun j => z (Sum.inl j)))
+      (fun b => z (Sum.inr b)) k := by
+  cases k with
+  | inl i =>
+    simp [blkB, Matrix.fromBlocks_transpose, Matrix.mulVec, dotProduct, Fintype.sum_sum_type,
+      cmat, dot]
+  | inr b =>
+    simp [blkB, Matrix.fromBlocks_transpose, Matrix.mulVec, dotProduct, Fintype.sum_sum_type,
+      Matrix.one_apply]
+
+/-- coordinates of `y` in the basis `d (A ⊕ std)`. -/
+lemma dot_cols (d : Orth (LB B H)) (A : OBase H) (y : Space (LB B H)) (k : LB B H) :
+    dot ((ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))).v k) y
+      = Sum.elim (fun i => dot (A.v i) (fun j => (d.1ᵀ *ᵥ y) (Sum.inl j)))
+          (fun b => (d.1ᵀ *ᵥ y) (Sum.inr b)) k := by
+  rw [← blkT_mulVec A (d.1ᵀ *ᵥ y) k, Matrix.mulVec_mulVec, ← Matrix.transpose_mul]
+  rfl
+
+/-- **the old frame and the lifted label name the same subspace of the address space.** -/
+theorem insub_old_new (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) (y : Space (LB B H)) :
+    InSub (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q) y ↔
+      InSub (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q) y := by
+  rw [insub_conj, insub_coordPerm]
+  have hU := h (fun i => (d.1ᵀ *ᵥ y) (Sum.inl i))
+  constructor
+  · intro hk
+    refine ⟨hU.mpr ((insub_coordPerm A s _).mpr (fun i hi => ?_)), fun b hb => ?_⟩
+    · have h1 := hk (Sum.inl i) (fun hm => hi (Finset.inl_mem_disjSum.mp hm))
+      rw [dot_cols] at h1
+      exact h1
+    · have h1 := hk (Sum.inr b) (fun hm => hb (Finset.inr_mem_disjSum.mp hm))
+      rw [dot_cols] at h1
+      exact h1
+  · rintro ⟨h1, h2⟩ k hk
+    rw [dot_cols]
+    cases k with
+    | inl i =>
+      exact (insub_coordPerm A s _).mp (hU.mp h1) i
+        (fun hm => hk (Finset.inl_mem_disjSum.mpr hm))
+    | inr b => exact h2 b (fun hm => hk (Finset.inr_mem_disjSum.mpr hm))
+
+/-- old frame of a coordinate subspace → representative of any label naming it: FREE. -/
+theorem old_to_new (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) :
+    GReach (PhiB d q (A.mat s)) ((BXMap.ofConj d.1 d.2 (Orth.orth' d) q).Φ U) (fun _ => 0) := by
+  rw [PhiB_eq]
+  obtain ⟨N, hN, e⟩ := repChange (LB B H) _ _ _ _ (insub_old_new d q A s U h)
+  have a : GReach (frame (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))) (JB s q))
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_old_to_core _ _).reach
+  have b : GReach
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (core (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q)) (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_of_free hN e).reach
+  exact (a.trans b).cast (fun φ => by simp [rcost])
+
+/-- the same, backwards. -/
+theorem new_to_old (d : Orth (LB B H)) (q : Finset (B × H)) (A : OBase H) (s : Finset H)
+    (U : SLbl H) (h : ∀ x, U.Mem x ↔ InSub (coordPerm A) s x) :
+    GReach ((BXMap.ofConj d.1 d.2 (Orth.orth' d) q).Φ U) (PhiB d q (A.mat s)) (fun _ => 0) := by
+  rw [PhiB_eq]
+  obtain ⟨N, hN, e⟩ := repChange (LB B H) _ _ _ _
+    (fun y => (insub_old_new d q A s U h y).symm)
+  have a : GReach (core (conjPerm d.1 d.2 (Orth.orth' d) U.G) (U.s.disjSum q))
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_of_free hN e).reach
+  have b : GReach
+      (core (coordPerm (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A)))) (JB s q))
+      (frame (ofCols (d.1 * blkB B A) (mul_orth d.2 (blkB_orth A))) (JB s q))
+      (fun φ => rcost φ []) :=
+    GReach.ofReach (fmv_core_to_old _ _).reach
+  exact (a.trans b).cast (fun φ => by simp [rcost])
+
+/-- **The window of a stage of the bridged geometry.** -/
+def gwinB (hB : 1 ≤ Fintype.card B) (hH : 1 ≤ Fintype.card H) (d : Orth (LB B H))
+    (q : Finset (B × H)) : GWin H (LB B H) where
+  Xm := fmapB hB hH d q
+  X := BXMap.ofConj d.1 d.2 (Orth.orth' d) q
+  big := by
+    rw [card_LB]
+    have := Nat.mul_le_mul_right (Fintype.card H) (show 2 ≤ Fintype.card B + 1 by omega)
+    omega
+  toNew := fun A s U h => old_to_new d q A s U h
+  toOld := fun A s U h => new_to_old d q A s U h
+
+@[simp] lemma gwinB_Xm (hB : 1 ≤ Fintype.card B) (hH : 1 ≤ Fintype.card H) (d : Orth (LB B H))
+    (q : Finset (B × H)) : (gwinB hB hH d q).Xm = fmapB hB hH d q := rfl
+
+end
+end
+end GX
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.GX.insub_old_new
+#print axioms OAI.PowerSaving.GX.old_to_new
+#print axioms OAI.PowerSaving.GX.new_to_old
+#print axioms OAI.PowerSaving.GX.gwinB
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean
new file mode 100644
index 0000000000..d7ecfebcea
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__B2Gp193Main.lean
@@ -0,0 +1,33 @@
+import Work.GCert.Scalar.Main
+import Work.GCert.Data.P193ScalOK
+import Work.GCert.Data.B2Gp193
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `P193`: THE CLOSED THEOREMS
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`wht_B2Gp193_of_ids` (label half, price, unit list, rate fact, gx-chain's end theorem) applied to the scalar half
+`GXD.P193.scalOK : GS.ScalOK GXD.P193.raw` (kernel checks `scal<i>_ok`, `ychk_ok`; soundness: gx-scalar).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - 74745/10^8))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `P193`.** -/
+theorem wht_main_B2Gp193 :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 74745/(10:ℝ)^8) W :=
+  wht_B2Gp193_of_ids GXD.P193.scalOK.hv GXD.P193.scalOK.hAi GXD.P193.scalOK.hBi GXD.P193.scalOK.hx GXD.P193.scalOK.hy GXD.P193.scalOK.hid
+
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - 7474547/10^10))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `P193`.** -/
+theorem wht_main_B2Gp193x :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W :=
+  wht_B2Gp193x_of_ids GXD.P193.scalOK.hv GXD.P193.scalOK.hAi GXD.P193.scalOK.hBi GXD.P193.scalOK.hx GXD.P193.scalOK.hy GXD.P193.scalOK.hid
+
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_main_B2Gp193
+#print axioms OAI.PowerSaving.WHT.wht_main_B2Gp193x
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean
new file mode 100644
index 0000000000..c6cbac38e3
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Glue.lean
@@ -0,0 +1,97 @@
+import Work.GCert.Scalar.Roles
+import Work.GCert.Labels.Main
+
+/-!
+# (key: gx-data) Glue between the scalar half (gx-scalar) and the label half (gx-labels)
+
+For ANY `c : GXD.Raw` (nothing is evaluated here):
+
+* `roles`   gx-scalar's numbering `GS.emb` / `GS.unemb` is gx-labels' `GLab.Roles`;
+* `scalOf`  gx-chain's record `GX.Scal (Fin v) (Fin R) (Fin ret.length)` from the FIVE scalar
+            identities of the matrices `GS.MA`, `GS.MAi`, `GS.MB`, `GS.MBi`, `GS.Jrm`, `GS.Ccm`;
+* `scalOf_MA .. scalOf_MBi`  its gate matrices are the ordered products of the adds of `c`, in
+            the form asked by `GLab.Valid.lab` (`GLab.mic GS.toCoef`);
+* `reg`, `reg_slot`, `reg_mem`  copy `k` reads the retained register `(c.ret.getD k (0,0)).1`.
+
+So a generated instance needs from the scalar side exactly `hAi hBi hx hy hid` (see
+`wht_<Inst>_of_ids` in `Work/GCert/Data/<Inst>.lean`).  No `sorry`.
+-/
+
+namespace GXD
+open SSC OAI.PowerSaving OAI.PowerSaving.CR Matrix
+
+/-- the numbering of the roles: `x_t = t`, `y_t = v + t`, slot `q = 2 v + q` -/
+theorem roles (c : Raw) (hv : 0 < c.v) : GLab.Roles c.v c.R (GS.emb c) (GS.unemb c hv) where
+  hun := GS.unemb_emb hv
+  hin := GS.emb_unemb hv
+  hlt := fun q => by
+    rcases q with (t | S) | q
+    · have := t.isLt; show t.val < 2 * c.v + c.R; omega
+    · have := S.isLt; show c.v + S.val < 2 * c.v + c.R; omega
+    · have := q.isLt; show 2 * c.v + q.val < 2 * c.v + c.R; omega
+  eX := fun _ => rfl
+  eY := fun _ => rfl
+  eS := fun _ => rfl
+
+/-- **the scalar half as gx-chain's record**, from the five scalar identities -/
+noncomputable def scalOf (c : Raw) (hv : 0 < c.v)
+    (hAi : GS.MAi c hv * GS.MA c hv = 1) (hBi : GS.MBi c hv * GS.MB c hv = 1)
+    (hx : ∀ (t : Fin c.v) (j : GS.Rl c), (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      (lX t) j = if lX t = j then 1 else 0)
+    (hy : ∀ (i : GS.Rl c) (t : Fin c.v), (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      i (lY t) = if i = lY t then 1 else 0)
+    (hid : ∀ S t : Fin c.v, (GS.MB c hv * scatM (GS.Jrm c * GS.Ccm c) * GS.MA c hv)
+      (lY S) (lX t) = if S = t then 1 else 0) :
+    GX.Scal (Fin c.v) (Fin c.R) (Fin c.ret.length) where
+  Cc := GS.Ccm c
+  Jr := GS.Jrm c
+  MA := GS.MA c hv
+  MAi := GS.MAi c hv
+  MB := GS.MB c hv
+  MBi := GS.MBi c hv
+  hAi := hAi
+  hBi := hBi
+  hx := hx
+  hy := hy
+  hid := hid
+
+section
+variable (c : Raw) (hv : 0 < c.v) (hAi) (hBi) (hx) (hy) (hid)
+
+theorem scalOf_MA : (scalOf c hv hAi hBi hx hy hid).MA
+    = matP (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesA.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MAi : (scalOf c hv hAi hBi hx hy hid).MAi
+    = matPinv (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesA.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MB : (scalOf c hv hAi hBi hx hy hid).MB
+    = matP (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesB.flatMap Gate.adds)) := rfl
+
+theorem scalOf_MBi : (scalOf c hv hAi hBi hx hy hid).MBi
+    = matPinv (GS.unemb c hv) (GLab.mic GS.toCoef (c.gatesB.flatMap Gate.adds)) := rfl
+
+end
+
+/-- the register read by copy `k` (the slot of the retained total `k`) -/
+def reg (c : Raw) (k : Fin c.ret.length) : Nat := (c.ret.getD k.val (0, 0)).1
+
+theorem reg_slot (c : Raw) (hv : 0 < c.v) (hAi) (hBi) (hx) (hy) (hid) (k : Fin c.ret.length)
+    (q : Fin c.R) (h : (scalOf c hv hAi hBi hx hy hid).Cc k q ≠ 0) :
+    reg c k = 2 * c.v + q.val := by
+  have h' : (if 2 * c.v + q.val = (c.ret.getD k.val (0, 0)).1 then (1:ℚ) else 0) ≠ 0 := h
+  by_cases e : 2 * c.v + q.val = (c.ret.getD k.val (0, 0)).1
+  · exact e.symm
+  · rw [if_neg e] at h'; exact absurd rfl h'
+
+theorem reg_mem (c : Raw) (k : Fin c.ret.length) : reg c k ∈ c.ret.map Prod.fst := by
+  unfold reg
+  rw [List.getD_eq_getElem _ _ k.isLt]
+  exact List.mem_map.mpr ⟨_, List.getElem_mem k.isLt, rfl⟩
+
+end GXD
+
+#print axioms GXD.roles
+#print axioms GXD.scalOf
+#print axioms GXD.scalOf_MA
+#print axioms GXD.reg_slot
+#print axioms GXD.reg_mem
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean
new file mode 100644
index 0000000000..9b9925ce26
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__InstB2Gp193.lean
@@ -0,0 +1,55 @@
+import Work.BridgeGeom.B2
+import Work.FoldRate.Group
+import Work.GCert.Data.RateB2Gp193
+import Work.GCert.Data.RateB2Gp193x
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `P193`, h = 22: the unit price is the price of the block list
+
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.  Arithmetic only (no certificate is imported).
+
+One unit: `W = 14692` live roles (`4 v + R`, `v = 1320`, `R = 9412`), label dimension `m = 110`, deficit `D = 3080`.
+`invPrice φ` = the price of the blocks of ONE invocation (the kernel-counted list `GXD.P193.hist`, by rank);
+`unitPrice φ = 5 * invPrice φ + v * BG.bankPrice h φ = listCost φ BlockAccounting.blocksB2Gp193` (`unit_cost`).
+Whole-block `1 - 74745/10^8` (fails at 74746), ten decimals `1 - 7474547/10^10` (fails at 7474550).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace BridgeRate
+namespace B2Gp193
+open Finset Binary Matrix RAM CB FoldRate
+noncomputable section
+
+/-- price of the blocks of ONE invocation of `P193` (all roles and scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+
+/-- price of ONE unit of the bridged word B_2 -/
+def unitPrice (φ : ℕ → ℝ) : ℝ := 5 * invPrice φ + ((1320:ℕ):ℝ) * BG.bankPrice 22 φ
+
+/-- **The unit price is the price of the unit block list.** -/
+theorem unit_cost (φ : ℕ → ℝ) : unitPrice φ = listCost φ BlockAccounting.blocksB2Gp193 := by
+  unfold unitPrice invPrice
+  simp only [BG.bankPrice, listCost, BlockAccounting.blocksB2Gp193, List.map_cons, List.map_nil,
+    List.sum_cons, List.sum_nil]
+  norm_num [bcost]
+  try ring
+
+theorem blocks_x : BlockAccounting.blocksB2Gp193 = BlockAccounting.blocksB2Gp193x := rfl
+
+theorem unit_cost_x (φ : ℕ → ℝ) : unitPrice φ = listCost φ BlockAccounting.blocksB2Gp193x := by
+  rw [unit_cost, blocks_x]
+
+/-- one unit stands for `W * m - D` unit moves -/
+theorem unit_tally : unitPrice (fun r => (r:ℝ)) = ((14692:ℕ):ℝ) * ((110:ℕ):ℝ) - ((3080:ℕ):ℝ) := by
+  rw [unit_cost]
+  exact BlockAccounting.blocksB2Gp193_tally
+
+end
+end B2Gp193
+end BridgeRate
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.BridgeRate.B2Gp193.unit_cost
+#print axioms OAI.PowerSaving.BridgeRate.B2Gp193.unit_tally
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean
new file mode 100644
index 0000000000..3c3250279e
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Cert.lean
@@ -0,0 +1,81 @@
+import Work.GCert.Labels.Main
+import Work.GCert.Data.P193Price
+import Work.GCert.Data.Gen.P193Tab0
+import Work.GCert.Data.Gen.P193Tab1
+import Work.GCert.Data.Gen.P193Tab2
+import Work.GCert.Data.Gen.P193Tab3
+import Work.GCert.Data.Gen.P193Seg0
+import Work.GCert.Data.Gen.P193Seg1
+import Work.GCert.Data.Gen.P193Seg2
+import Work.GCert.Data.Gen.P193Seg3
+import Work.GCert.Data.Gen.P193Seg4
+import Work.GCert.Data.Gen.P193SegF
+import Work.GCert.Data.Gen.P193End
+/-! # (key: gx-data) gcert/1 certificate `P193` (h = 22): THE LABEL HALF and its price
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+`v = 1320` ports, `R = 9412` slots, 22 scratch copies of rank 20, copy cost `cst = 440`, `N = 262944` unit moves.
+* `aux : GLab.Aux`, `valid : GLab.Valid raw aux`: frame table (`tab<i>_ok` composed by `tabK_node`), the replays of phase A
+  and phase B (`seg<i>_ok` composed by `Run.append`), the final climbs (`segF_ok`, `fin_ok`), the ends (`end_ok`);
+* `lab_cost`, `lab_price`: for ANY scalar half `S` the label half `valid.lab S ..` costs
+  `rcost rA + card C * bcost 20 + rcost rB + rcost rF` = `invPrice φ` = 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+  (`Gen.P193Hist`, `P193Price`) when there are 22 copies. -/
+set_option maxRecDepth 100000
+namespace GXD.P193
+open GXD OAI.PowerSaving OAI.PowerSaving.CB
+theorem raw_h : raw.h = 22 := rfl
+theorem raw_v : raw.v = 1320 := rfl
+theorem raw_R : raw.R = 9412 := rfl
+/-- what the label checks read next to `raw` -/
+noncomputable def aux : GLab.Aux := ⟨par, st0, st2, st5, st6, fins, rA, rB, rF⟩
+theorem fin_ok : GLab.noAdds fins = true := by decide +kernel
+theorem cen_ok : (raw.ret.map Prod.fst).all (fun r => Nat.beq (GLab.cdim (par.tab.get (st2.get r))) 20) = true := by
+  decide +kernel
+theorem tab_ok : GLab.tabK par.h par.tab = true := (GLab.tabK_node _ _ _ (GLab.tabK_node _ _ _ tab0_ok tab1_ok) (GLab.tabK_node _ _ _ tab2_ok tab3_ok))
+theorem gatesA_eq : raw.gatesA = seg0 ++ (seg1) := by
+  show List.flatten [seg0, seg1] = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase A, composed from its kernel-checked segments -/
+theorem runA : GLab.Run par st0 raw.gatesA st2 rA := by
+  rw [gatesA_eq]
+  exact GLab.Run.append (GLab.Run.of_seg seg0_ok) (GLab.Run.of_seg seg1_ok)
+theorem gatesB_eq : raw.gatesB = seg2 ++ (seg3 ++ (seg4)) := by
+  show List.flatten [seg2, seg3, seg4] = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase B, composed from its kernel-checked segments -/
+theorem runB : GLab.Run par st2 raw.gatesB st5 rB := by
+  rw [gatesB_eq]
+  exact GLab.Run.append (GLab.Run.of_seg seg2_ok) (GLab.Run.append (GLab.Run.of_seg seg3_ok) (GLab.Run.of_seg seg4_ok))
+/-- **the kernel-checked label facts** of the certificate -/
+theorem valid : GLab.Valid raw aux where
+  hn := rfl
+  tab := tab_ok
+  runA := runA
+  runB := runB
+  runF := GLab.Run.of_seg segF_ok
+  fin := fin_ok
+  ends := end_ok
+theorem cen_dim (r : Nat) (hr : r ∈ raw.ret.map Prod.fst) : GLab.cdim (par.tab.get (st2.get r)) = 20 :=
+  Nat.eq_of_beq_eq_true (List.all_eq_true.mp cen_ok r hr)
+/-- price of the label half over ANY scalar half -/
+theorem lab_cost {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (φ : ℕ → ℝ) :
+    (valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cost φ
+      = rcost φ rA + (Fintype.card C : ℝ) * bcost φ 20 + rcost φ rB + rcost φ rF := by
+  obtain ⟨h1, h2, h3, h4⟩ := valid.lab_ranks S Ro cf hMA hMAi hMB hMBi reg hCc hreg
+  have h5 : ∀ k, bcost φ (((valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cen k).dim) = bcost φ 20 :=
+    fun k => by rw [h4 k]; exact congrArg (bcost φ) (cen_dim _ (hreg k))
+  rw [GX.Lab.cost, h1, h2, h3, Finset.sum_congr rfl (fun k _ => h5 k), Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
+  rfl
+/-- **the label half costs one invocation price** (`invPrice`, by rank, from the kernel counts) -/
+theorem lab_price {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (hC : Fintype.card C = 22) (φ : ℕ → ℝ) :
+    (valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg).cost φ = invPrice φ := by
+  rw [lab_cost S Ro cf hMA hMAi hMB hMBi reg hCc hreg φ, hC, ← inv_cost φ]
+  norm_num [bcost]
+end GXD.P193
+#print axioms GXD.P193.valid
+#print axioms GXD.P193.lab_price
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean
new file mode 100644
index 0000000000..eeed011d64
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193Price.lean
@@ -0,0 +1,54 @@
+import Work.GCert.Data.Price
+import Work.GCert.Data.Gen.P193Hist
+
+/-!
+# (key: gx-data) gcert/1 certificate `P193` (h = 22): the price of one invocation
+
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+`rA_cost`, `rB_cost`, `rF_cost`: the price of the block rank lists of phase A, phase B and the final climbs
+(lists `GXD.P193.rA / rB / rF`, counted by the kernel in `Gen.P193Hist`);
+`inv_cost`: with the 22 scratch copies (22 * φ 20) the blocks of ONE invocation cost
+`invPrice φ` = 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20;  `inv_moves`: they stand for `R h + 2 v (h - 1) + cst = 262944` unit moves.
+-/
+
+namespace GXD.P193
+open GXD OAI.PowerSaving.CB
+
+/-- price of the blocks of phase A, from the kernel counts -/
+theorem rA_cost (φ : ℕ → ℝ) : rcost φ rA = 9900 * φ 1 + 500 * φ 2 + 2402 * φ 3 + 82 * φ 4 + 242 * φ 5 + 175 * φ 6 + 88 * φ 7 + 68 * φ 8 + 110 * φ 9 + 132 * φ 10 + 10 * φ 11 + 67 * φ 12 + 3 * φ 13 + 19 * φ 15 := by
+  rw [GXD.rcost_wsumK φ rA 19 rankBoundA]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankA0_ok, rankA1_ok, rankA2_ok, rankA3_ok, rankA4_ok, rankA5_ok, rankA6_ok, rankA7_ok, rankA8_ok, rankA9_ok, rankA10_ok, rankA11_ok, rankA12_ok, rankA13_ok, rankA14_ok, rankA15_ok, rankA16_ok, rankA17_ok, rankA18_ok, rankA19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of phase B, from the kernel counts -/
+theorem rB_cost (φ : ℕ → ℝ) : rcost φ rB = 16638 * φ 1 + 10380 * φ 2 + 4111 * φ 3 + 3476 * φ 4 + 1531 * φ 5 + 1137 * φ 6 + 531 * φ 7 + 1346 * φ 8 + 293 * φ 9 + 629 * φ 10 + 343 * φ 11 + 1067 * φ 12 + 123 * φ 13 + 712 * φ 14 + 1860 * φ 15 + 81 * φ 16 + 39 * φ 17 + 2640 * φ 18 := by
+  rw [GXD.rcost_wsumK φ rB 19 rankBoundB]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankB0_ok, rankB1_ok, rankB2_ok, rankB3_ok, rankB4_ok, rankB5_ok, rankB6_ok, rankB7_ok, rankB8_ok, rankB9_ok, rankB10_ok, rankB11_ok, rankB12_ok, rankB13_ok, rankB14_ok, rankB15_ok, rankB16_ok, rankB17_ok, rankB18_ok, rankB19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of the final climbs, from the kernel counts -/
+theorem rF_cost (φ : ℕ → ℝ) : rcost φ rF = 2640 * φ 1 + 1518 * φ 2 + 3410 * φ 3 + 651 * φ 4 + 177 * φ 5 + 293 * φ 6 + 87 * φ 7 + 117 * φ 8 + 26 * φ 9 + 169 * φ 10 + 1 * φ 11 + 63 * φ 12 + 1 * φ 13 + 30 * φ 14 + 7 * φ 16 + 42 * φ 17 + 13 * φ 18 + 167 * φ 19 := by
+  rw [GXD.rcost_wsumK φ rF 19 rankBoundF]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, rankF0_ok, rankF1_ok, rankF2_ok, rankF3_ok, rankF4_ok, rankF5_ok, rankF6_ok, rankF7_ok, rankF8_ok, rankF9_ok, rankF10_ok, rankF11_ok, rankF12_ok, rankF13_ok, rankF14_ok, rankF15_ok, rankF16_ok, rankF17_ok, rankF18_ok, rankF19_ok]
+  norm_num [bcost]
+
+/-- price of the blocks of ONE invocation (x roles, y roles, slots, scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := 29178 * φ 1 + 12398 * φ 2 + 9923 * φ 3 + 4209 * φ 4 + 1950 * φ 5 + 1605 * φ 6 + 706 * φ 7 + 1531 * φ 8 + 429 * φ 9 + 930 * φ 10 + 354 * φ 11 + 1197 * φ 12 + 127 * φ 13 + 742 * φ 14 + 1879 * φ 15 + 88 * φ 16 + 81 * φ 17 + 2653 * φ 18 + 167 * φ 19 + 22 * φ 20
+
+/-- **Price of ONE invocation** in the shape of `GX.Lab.cost`: phase A, the scratch copies, phase B, final climbs. -/
+theorem inv_cost (φ : ℕ → ℝ) : rcost φ rA + (22 * φ 20) + rcost φ rB + rcost φ rF = invPrice φ := by
+  rw [rA_cost, rB_cost, rF_cost]
+  unfold invPrice
+  ring
+
+theorem inv_moves : invPrice (fun r => (r:ℝ)) = 9412 * 22 + 2 * 1320 * (22 - 1) + 440 := by
+  unfold invPrice
+  norm_num
+
+theorem inv_count : invPrice (fun _ => (1:ℝ)) = 70169 := by
+  unfold invPrice
+  norm_num
+
+end GXD.P193
+#print axioms GXD.P193.inv_cost
+#print axioms GXD.P193.inv_moves
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean
new file mode 100644
index 0000000000..3539192ac1
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__P193ScalOK.lean
@@ -0,0 +1,17 @@
+import Work.GCert.Scalar.Main
+import Work.GCert.Data.Gen.P193Scal0
+import Work.GCert.Data.Gen.P193Scal1
+import Work.GCert.Data.Gen.P193YChk
+/-! # (key: gx-data) gcert/1 certificate `P193` (h = 22): THE SCALAR HALF `scalOK : GS.ScalOK raw`
+GENERATED by checks/wht26/gx-data/py/gxgen.py from gcert1-p11-pr193.json.gz.  No `sorry`.
+Kernel checks `scal<i>_ok` (2 source batches) and `ychk_ok`. -/
+namespace GXD.P193
+open GXD
+theorem scalOK : GS.ScalOK raw where
+  hv := by decide
+  hs := fun t ht =>
+    if h0 : t < 660 then ⟨0, 660, Nat.zero_le t, h0, GS.XRun.of_check scal0_ok⟩ else
+    ⟨660, 660, Nat.le_of_not_lt h0, Nat.lt_of_lt_of_le ht (by decide), GS.XRun.of_check scal1_ok⟩
+  hyc := fun t ht => ⟨0, 1320, Nat.zero_le t, Nat.lt_of_lt_of_le ht (by decide), GS.YRun.of_check ychk_ok⟩
+end GXD.P193
+#print axioms GXD.P193.scalOK
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean
new file mode 100644
index 0000000000..df563cde73
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__RateB2Gp193x.lean
@@ -0,0 +1,327 @@
+import Work.BlockAccounting.Moment
+import Work.BlockAccounting.Sharp
+import Work.FoldRate.RankTools
+
+/-!
+# (key: gx-data) Rate lemmas for one unit of the bridged word B_2 with the gcert/1 circuit `P193` (h = 22)
+
+GENERATED by checks/wht26/gx-data/py/gxrate.py with the text generators of checks/wht9/bridge-rate/py
+(used read-only).  No `sorry`.  Arithmetic only.
+
+One unit: `W = 14692` live roles, label dimension `m = 110`, deficit `D = 3080`.
+
+* `blocksB2Gp193x`            the block list (rank, count) of ONE unit;
+* `fold_B2Gp193x`             whole-block fact at `1 - 7474547/10^10`, fill parameter `s = 40` (slack 2.37e-12);
+* `fold_B2Gp193x_sharp`       `W ≤ moment` at `1 - 7474550/10^10`: fails for every table (excess 1.40e-10);
+* `foldRank_B2Gp193x`         per-rank fact at `1 - 4058344/10^10`, `s = 40` (slack 1.10e-07);
+* `foldRank_B2Gp193x_sharp`   per-rank: fails for every table at `1 - 4058349/10^10`.
+
+That a Lean word has `G` times this list as its block histogram is NOT proved here.
+-/
+
+set_option maxRecDepth 4000
+
+namespace OAI.PowerSaving.BlockAccounting
+open Finset
+
+/-- Block list `(rank, count)` of ONE unit of the bridged five-stage word B_2 with the gcert/1 circuit `P193` (h = 22, m = 110): five invocations (ALL blocks of one invocation: x roles, y roles, slots, scratch copies; the kernel-counted list `GXD.P193.hist`), and for each of the v = 1320 ports the idle climbs of its two twins (2 blocks each of rank h-1, 2h-2, 2h+2, 4); R = 9412 slots shared by the five stages. -/
+def blocksB2Gp193x : List (ℕ × ℕ) := [(1, 145890), (2, 61990), (3, 49615), (4, 23685), (5, 9750), (6, 8025), (7, 3530), (8, 7655), (9, 2145), (10, 4650), (11, 1770), (12, 5985), (13, 635), (14, 3710), (15, 9395), (16, 440), (17, 405), (18, 13265), (19, 835), (20, 110), (21, 2640), (42, 2640), (46, 2640)]
+
+/-- total rank of one unit (= number of unit moves it stands for): `W * m - D` -/
+theorem blocksB2Gp193x_rank : (blocksB2Gp193x.map fun b => b.1 * b.2).sum = 14692 * 110 - 3080 := by
+  norm_num [blocksB2Gp193x]
+
+/-- the same as a price: the unit list at the price list `r ↦ r` (shape of `hPid` in `RAM.engine_program_group_perRank`) -/
+theorem blocksB2Gp193x_tally : (blocksB2Gp193x.map fun b => (b.2:ℝ) * ((b.1:ℕ):ℝ)).sum = ((14692:ℕ):ℝ) * ((110:ℕ):ℝ) - ((3080:ℕ):ℝ) := by
+  norm_num [blocksB2Gp193x]
+
+theorem blocksB2Gp193x_count : (blocksB2Gp193x.map fun b => b.2).sum = 361405 := by
+  norm_num [blocksB2Gp193x]
+
+theorem blocksB2Gp193x_proper : ∀ b ∈ blocksB2Gp193x, 1 ≤ b.1 ∧ b.1 < 110 := by
+  decide
+
+/-- **whole-block fact** of `blocksB2Gp193x` at exponent `1 - 7474547/10^10`, fill parameter `s = 40`: the hypothesis `hnum` of `RAM.engine_program_group_list` (u = 110, W = 14692).  Relative slack of the rational certificate: 2.37e-12. -/
+theorem fold_B2Gp193x :
+    ((2:ℝ)^40 - 1) * moment 110 (1 - 7474547/(10:ℝ)^10) blocksB2Gp193x
+      + ((14692:ℕ):ℝ) * (T 110 (1 - 7474547/(10:ℝ)^10) (110 - 1) 1 + T 110 (1 - 7474547/(10:ℝ)^10) 1 1)
+      < (2:ℝ)^40 * ((14692:ℕ):ℝ) := by
+  have hsum : moment 110 (1 - 7474547/(10:ℝ)^10) blocksB2Gp193x
+      = T 110 (1 - 7474547/(10:ℝ)^10) 1 145890 + (T 110 (1 - 7474547/(10:ℝ)^10) 2 61990 + (T 110 (1 - 7474547/(10:ℝ)^10) 3 49615 + (T 110 (1 - 7474547/(10:ℝ)^10) 4 23685 + (T 110 (1 - 7474547/(10:ℝ)^10) 5 9750 + (T 110 (1 - 7474547/(10:ℝ)^10) 6 8025 + (T 110 (1 - 7474547/(10:ℝ)^10) 7 3530 + (T 110 (1 - 7474547/(10:ℝ)^10) 8 7655 + (T 110 (1 - 7474547/(10:ℝ)^10) 9 2145 + (T 110 (1 - 7474547/(10:ℝ)^10) 10 4650 + (T 110 (1 - 7474547/(10:ℝ)^10) 11 1770 + (T 110 (1 - 7474547/(10:ℝ)^10) 12 5985 + (T 110 (1 - 7474547/(10:ℝ)^10) 13 635 + (T 110 (1 - 7474547/(10:ℝ)^10) 14 3710 + (T 110 (1 - 7474547/(10:ℝ)^10) 15 9395 + (T 110 (1 - 7474547/(10:ℝ)^10) 16 440 + (T 110 (1 - 7474547/(10:ℝ)^10) 17 405 + (T 110 (1 - 7474547/(10:ℝ)^10) 18 13265 + (T 110 (1 - 7474547/(10:ℝ)^10) 19 835 + (T 110 (1 - 7474547/(10:ℝ)^10) 20 110 + (T 110 (1 - 7474547/(10:ℝ)^10) 21 2640 + (T 110 (1 - 7474547/(10:ℝ)^10) 42 2640 + (T 110 (1 - 7474547/(10:ℝ)^10) 46 2640 + 0)))))))))))))))))))))) := rfl
+  have b0 : T 110 (1 - 7474547/(10:ℝ)^10) 1 145890 ≤ ((16636758090767:ℝ)/12500000000) :=
+    term_le 110 1 145890 (7474547/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b1 : T 110 (1 - 7474547/(10:ℝ)^10) 2 61990 ≤ ((22609438945563:ℝ)/20000000000) :=
+    term_le 110 2 61990 (7474547/(10:ℝ)^10) ((2003666592617:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 26 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b2 : T 110 (1 - 7474547/(10:ℝ)^10) 3 49615 ≤ ((135678423202471:ℝ)/100000000000) :=
+    term_le 110 3 49615 (7474547/(10:ℝ)^10) ((1800934038563:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 24 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b3 : T 110 (1 - 7474547/(10:ℝ)^10) 4 23685 ≤ ((43170446048157:ℝ)/50000000000) :=
+    term_le 110 4 23685 (7474547/(10:ℝ)^10) ((1657093002337:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 24 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b4 : T 110 (1 - 7474547/(10:ℝ)^10) 5 9750 ≤ ((44420693582197:ℝ)/100000000000) :=
+    term_le 110 5 9750 (7474547/(10:ℝ)^10) ((38638030667:ℝ)/12500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 23 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b5 : T 110 (1 - 7474547/(10:ℝ)^10) 6 8025 ≤ ((43867998737293:ℝ)/100000000000) :=
+    term_le 110 6 8025 (7474547/(10:ℝ)^10) ((1454360448283:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 22 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b6 : T 110 (1 - 7474547/(10:ℝ)^10) 7 3530 ≤ ((2250993477097:ℝ)/10000000000) :=
+    term_le 110 7 3530 (7474547/(10:ℝ)^10) ((2754570216739:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 22 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b7 : T 110 (1 - 7474547/(10:ℝ)^10) 8 7655 ≤ ((55781903078171:ℝ)/100000000000) :=
+    term_le 110 8 7655 (7474547/(10:ℝ)^10) ((1310519412057:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b8 : T 110 (1 - 7474547/(10:ℝ)^10) 9 2145 ≤ ((17582868029823:ℝ)/100000000000) :=
+    term_le 110 9 2145 (7474547/(10:ℝ)^10) ((1251627894229:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b9 : T 110 (1 - 7474547/(10:ℝ)^10) 10 4650 ≤ ((10587140349809:ℝ)/25000000000) :=
+    term_le 110 10 4650 (7474547/(10:ℝ)^10) ((2997369091:ℝ)/1250000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 21 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b10 : T 110 (1 - 7474547/(10:ℝ)^10) 11 1770 ≤ ((17730489316207:ℝ)/100000000000) :=
+    term_le 110 11 1770 (7474547/(10:ℝ)^10) ((575646273249:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b11 : T 110 (1 - 7474547/(10:ℝ)^10) 12 5985 ≤ ((65399123107589:ℝ)/100000000000) :=
+    term_le 110 12 5985 (7474547/(10:ℝ)^10) ((1107786858003:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b12 : T 110 (1 - 7474547/(10:ℝ)^10) 13 635 ≤ ((3758266936203:ℝ)/50000000000) :=
+    term_le 110 13 635 (7474547/(10:ℝ)^10) ((533882752083:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 20 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b13 : T 110 (1 - 7474547/(10:ℝ)^10) 14 3710 ≤ ((47290992642379:ℝ)/100000000000) :=
+    term_le 110 14 3710 (7474547/(10:ℝ)^10) ((2061423036179:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b14 : T 110 (1 - 7474547/(10:ℝ)^10) 15 9395 ≤ ((128304571925681:ℝ)/100000000000) :=
+    term_le 110 15 9395 (7474547/(10:ℝ)^10) ((498107541173:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b15 : T 110 (1 - 7474547/(10:ℝ)^10) 16 440 ≤ ((6409229123791:ℝ)/100000000000) :=
+    term_le 110 16 440 (7474547/(10:ℝ)^10) ((963945821777:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b16 : T 110 (1 - 7474547/(10:ℝ)^10) 17 405 ≤ ((1253566561349:ℝ)/20000000000) :=
+    term_le 110 17 405 (7474547/(10:ℝ)^10) ((933633510869:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 19 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b17 : T 110 (1 - 7474547/(10:ℝ)^10) 18 13265 ≤ ((217357516651669:ℝ)/100000000000) :=
+    term_le 110 18 13265 (7474547/(10:ℝ)^10) ((905054303949:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b18 : T 110 (1 - 7474547/(10:ℝ)^10) 19 835 ≤ ((14441670418763:ℝ)/100000000000) :=
+    term_le 110 19 835 (7474547/(10:ℝ)^10) ((1756041386627:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b19 : T 110 (1 - 7474547/(10:ℝ)^10) 20 110 ≤ ((2002550068509:ℝ)/100000000000) :=
+    term_le 110 20 110 (7474547/(10:ℝ)^10) ((21309351153:ℝ)/12500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b20 : T 110 (1 - 7474547/(10:ℝ)^10) 21 2640 ≤ ((25231210703361:ℝ)/50000000000) :=
+    term_le 110 21 2640 (7474547/(10:ℝ)^10) ((165595792807:ℝ)/100000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 18 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b21 : T 110 (1 - 7474547/(10:ℝ)^10) 42 2640 ≤ ((100872567578631:ℝ)/100000000000) :=
+    term_le 110 42 2640 (7474547/(10:ℝ)^10) ((962810747511:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 15 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b22 : T 110 (1 - 7474547/(10:ℝ)^10) 46 2640 ≤ ((22094393345401:ℝ)/20000000000) :=
+    term_le 110 46 2640 (7474547/(10:ℝ)^10) ((174367793861:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 14 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b23 : T 110 (1 - 7474547/(10:ℝ)^10) 109 1 ≤ ((198183171:ℝ)/200000000) :=
+    term_le 110 109 1 (7474547/(10:ℝ)^10) ((1826496713:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 5 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have b24 : T 110 (1 - 7474547/(10:ℝ)^10) 1 1 ≤ ((456145263:ℝ)/50000000000) :=
+    term_le 110 1 1 (7474547/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num) (by norm_num)
+  have e1 : ((2:ℝ)^40 - 1) = 1099511627775 := by norm_num
+  have e2 : (2:ℝ)^40 = 1099511627776 := by norm_num
+  have e3 : ((14692:ℕ):ℝ) = 14692 := by norm_num
+  have e4 : T 110 (1 - 7474547/(10:ℝ)^10) (110 - 1) 1 = T 110 (1 - 7474547/(10:ℝ)^10) 109 1 := rfl
+  rw [e1, e2, e3, e4, hsum]
+  linarith
+
+/-- **sharpness**: at exponent `1 - 7474550/10^10` the moment of one unit is at least its number of live roles `14692`, so the moment criterion fails for EVERY table made of copies of the unit and idle roles (`FoldRate.block_fails`).  Relative excess of the rational certificate: 1.40e-10. -/
+theorem fold_B2Gp193x_sharp : ((14692:ℕ):ℝ) ≤ moment 110 (1 - 7474550/(10:ℝ)^10) blocksB2Gp193x := by
+  have hsum : moment 110 (1 - 7474550/(10:ℝ)^10) blocksB2Gp193x
+      = T 110 (1 - 7474550/(10:ℝ)^10) 1 145890 + (T 110 (1 - 7474550/(10:ℝ)^10) 2 61990 + (T 110 (1 - 7474550/(10:ℝ)^10) 3 49615 + (T 110 (1 - 7474550/(10:ℝ)^10) 4 23685 + (T 110 (1 - 7474550/(10:ℝ)^10) 5 9750 + (T 110 (1 - 7474550/(10:ℝ)^10) 6 8025 + (T 110 (1 - 7474550/(10:ℝ)^10) 7 3530 + (T 110 (1 - 7474550/(10:ℝ)^10) 8 7655 + (T 110 (1 - 7474550/(10:ℝ)^10) 9 2145 + (T 110 (1 - 7474550/(10:ℝ)^10) 10 4650 + (T 110 (1 - 7474550/(10:ℝ)^10) 11 1770 + (T 110 (1 - 7474550/(10:ℝ)^10) 12 5985 + (T 110 (1 - 7474550/(10:ℝ)^10) 13 635 + (T 110 (1 - 7474550/(10:ℝ)^10) 14 3710 + (T 110 (1 - 7474550/(10:ℝ)^10) 15 9395 + (T 110 (1 - 7474550/(10:ℝ)^10) 16 440 + (T 110 (1 - 7474550/(10:ℝ)^10) 17 405 + (T 110 (1 - 7474550/(10:ℝ)^10) 18 13265 + (T 110 (1 - 7474550/(10:ℝ)^10) 19 835 + (T 110 (1 - 7474550/(10:ℝ)^10) 20 110 + (T 110 (1 - 7474550/(10:ℝ)^10) 21 2640 + (T 110 (1 - 7474550/(10:ℝ)^10) 42 2640 + (T 110 (1 - 7474550/(10:ℝ)^10) 46 2640 + 0)))))))))))))))))))))) := rfl
+  have c0 : ((665470322971:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 1 145890 :=
+    term_ge 110 1 145890 (7474550/(10:ℝ)^10) ((4700480365791:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c1 : ((565235973477:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 2 61990 :=
+    term_ge 110 2 61990 (7474550/(10:ℝ)^10) ((4007333185231:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c2 : ((1356784232023:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 3 49615 :=
+    term_ge 110 3 49615 (7474550/(10:ℝ)^10) ((3601868077123:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c3 : ((431704460547:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 4 23685 :=
+    term_ge 110 4 23685 (7474550/(10:ℝ)^10) ((3314186004671:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c4 : ((44420693593:ℝ)/100000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 5 9750 :=
+    term_ge 110 5 9750 (7474550/(10:ℝ)^10) ((3091042453357:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c5 : ((87735997501:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 6 8025 :=
+    term_ge 110 6 8025 (7474550/(10:ℝ)^10) ((2908720896563:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c6 : ((112549673893:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 7 3530 :=
+    term_ge 110 7 3530 (7474550/(10:ℝ)^10) ((86080319273:ℝ)/31250000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c7 : ((557819030987:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 8 7655 :=
+    term_ge 110 8 7655 (7474550/(10:ℝ)^10) ((2621038824111:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c8 : ((87914340183:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 9 2145 :=
+    term_ge 110 9 2145 (7474550/(10:ℝ)^10) ((500651157691:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c9 : ((423485614161:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 10 4650 :=
+    term_ge 110 10 4650 (7474550/(10:ℝ)^10) ((2397895272797:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c10 : ((88652446617:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 11 1770 :=
+    term_ge 110 11 1770 (7474550/(10:ℝ)^10) ((2302585092993:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c11 : ((130798246269:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 12 5985 :=
+    term_ge 110 12 5985 (7474550/(10:ℝ)^10) ((2215573716003:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c12 : ((15033067751:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 13 635 :=
+    term_ge 110 13 635 (7474550/(10:ℝ)^10) ((2135531008329:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c13 : ((23645496331:ℝ)/50000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 14 3710 :=
+    term_ge 110 14 3710 (7474550/(10:ℝ)^10) ((128838939761:ℝ)/62500000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 3 10 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c14 : ((320761429947:ℝ)/250000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 15 9395 :=
+    term_ge 110 15 9395 (7474550/(10:ℝ)^10) ((1992430164689:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 12 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c15 : ((1001442051:ℝ)/15625000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 16 440 :=
+    term_ge 110 16 440 (7474550/(10:ℝ)^10) ((1927891643551:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c16 : ((62678328093:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 17 405 :=
+    term_ge 110 17 405 (7474550/(10:ℝ)^10) ((373453404347:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c17 : ((1086787583699:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 18 13265 :=
+    term_ge 110 18 13265 (7474550/(10:ℝ)^10) ((362021721579:ℝ)/200000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c18 : ((28883340849:ℝ)/200000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 19 835 :=
+    term_ge 110 19 835 (7474550/(10:ℝ)^10) ((13719073333:ℝ)/7812500000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c19 : ((20025500693:ℝ)/1000000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 20 110 :=
+    term_ge 110 20 110 (7474550/(10:ℝ)^10) ((1704748092237:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c20 : ((63078026783:ℝ)/125000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 21 2640 :=
+    term_ge 110 21 2640 (7474550/(10:ℝ)^10) ((1655957928067:ℝ)/1000000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 2 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c21 : ((126090709507:ℝ)/125000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 42 2640 :=
+    term_ge 110 42 2640 (7474550/(10:ℝ)^10) ((240702686877:ℝ)/250000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 1 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have c22 : ((552359833771:ℝ)/500000000) ≤ T 110 (1 - 7474550/(10:ℝ)^10) 46 2640 :=
+    term_ge 110 46 2640 (7474550/(10:ℝ)^10) ((435919484651:ℝ)/500000000000) _ (by norm_num) (by norm_num) (by norm_num) (by norm_num)
+      (le_log_of_expbound _ _ 1 11 (by norm_num) (by norm_num) (by norm_num)
+        (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+      (by norm_num)
+  have e3 : ((14692:ℕ):ℝ) = 14692 := by norm_num
+  rw [e3, hsum]
+  linarith
+
+/-- **per-rank fact** at exponent `1 - 4058344/10^10`, fill parameter `s = 40`: the hypothesis `hnum` of `RAM.engine_program_group_perRank` (u = 110, W = 14692, D = 3080).  Relative slack: 1.10e-07. -/
+theorem foldRank_B2Gp193x :
+    (2:ℝ)^40 * ((14692:ℕ):ℝ) * (((110:ℕ):ℝ) - ((110:ℕ):ℝ)^(1 - 4058344/(10:ℝ)^10)) < ((2:ℝ)^40 - 1) * ((3080:ℕ):ℝ) :=
+  FoldRate.rank_fact3 110 14692 3080 40 (4058344/(10:ℝ)^10) ((2350240182897:ℝ)/500000000000) (by norm_num) (by norm_num) (by norm_num)
+    (log_le_of_le_expsum _ _ 27 (by norm_num) (by norm_num)
+      (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+    (by norm_num) (by norm_num)
+
+/-- **per-rank sharpness**: at exponent `1 - 4058349/10^10` the deficit of one unit is at most `W (m - m^z)`, so the per-rank inequality fails for EVERY table made of copies of the unit and idle roles (`FoldRate.rank_fails`). -/
+theorem foldRank_B2Gp193x_sharp :
+    ((3080:ℕ):ℝ) ≤ ((14692:ℕ):ℝ) * (((110:ℕ):ℝ) - ((110:ℕ):ℝ)^(1 - 4058349/(10:ℝ)^10)) :=
+  FoldRate.rank_fact_sharp 110 14692 3080 (4058349/(10:ℝ)^10) ((4700480365791:ℝ)/1000000000000) (by norm_num) (by norm_num) (by norm_num)
+    (le_log_of_expbound _ _ 4 10 (by norm_num) (by norm_num) (by norm_num)
+      (by norm_num [Finset.sum_range_succ, Nat.factorial]))
+    (by norm_num) (by norm_num)
+
+end OAI.PowerSaving.BlockAccounting
+
+#print axioms OAI.PowerSaving.BlockAccounting.fold_B2Gp193x
+#print axioms OAI.PowerSaving.BlockAccounting.fold_B2Gp193x_sharp
+#print axioms OAI.PowerSaving.BlockAccounting.foldRank_B2Gp193x
+#print axioms OAI.PowerSaving.BlockAccounting.foldRank_B2Gp193x_sharp
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean
new file mode 100644
index 0000000000..499fa67e88
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__Raw.lean
@@ -0,0 +1,93 @@
+/-!
+# (key: gx-data) Raw Lean form of a `gcert/1` file (EXTENDED-CERT-SPEC section 1)
+
+Core Lean only (no Mathlib): the generated data modules import nothing else, so they elaborate
+cheaply.  Field order and meaning are those of the JSON; `pairs` and `cuts` are DERIVED by the
+generator (`checks/wht26/gx-data/py/gxgen.py`) and must be tested by the label check.
+
+Registers: `x_t = t`, `y_t = v + t`, slot `k = 2 v + k`.  Vectors are bit masks.
+-/
+
+namespace GXD
+
+/-- the rational `(-1)^neg * num / den` (`den > 0`) -/
+structure Co where
+  neg : Bool
+  num : Nat
+  den : Nat
+  deriving DecidableEq, Repr
+
+/-- a gate: every register named (extras too) first moves to `frame`; then the adds happen in order -/
+inductive Gate where
+  /-- `tgt += co * src` for each `(tgt, co)` -/
+  | out (frame src : Nat) (tgts : List (Nat × Co)) (extra : List Nat)
+  /-- `tgt += co * src` for each `(src, co)` -/
+  | inn (frame tgt : Nat) (srcs : List (Nat × Co))
+  deriving Repr
+
+/-- the scatter `y_t += sum over k of coef(t, k) * total k` -/
+inductive Scat where
+  /-- star rule: `inside` if coordinate `k` is in port `t`, else `outside` -/
+  | star (inside outside : Co)
+  /-- explicit rows: row `t` = `[(total k, coef)]` -/
+  | table (rows : List (List (Nat × Co)))
+  deriving Repr
+
+/-- a `gcert/1` file -/
+structure Raw where
+  h : Nat
+  v : Nat
+  R : Nat
+  N : Nat
+  cst : Nat
+  /-- `v` masks: the unit vectors of the ports -/
+  ports : List Nat
+  /-- CHUNKED frame table (`flatten` = the table); an entry is a reduced echelon basis, leading bits descending -/
+  frames : List (List (List Nat))
+  /-- frame id per register at the start -/
+  start : List Nat
+  /-- frame id per register at the end -/
+  final : List Nat
+  /-- position `k` = retained total `k`: (slot REGISTER, frame id) -/
+  ret : List (Nat × Nat)
+  scat : Scat
+  /-- CHUNKED gates before the scatter -/
+  A : List (List Gate)
+  /-- CHUNKED gates after the scatter -/
+  B : List (List Gate)
+  /-- CHUNKED, derived: the distinct climbs `(a, b)`, `a ≠ b`, in order of first use -/
+  pairs : List (List (Nat × Nat))
+  /-- derived: replay cut points `(gates of A ++ B before the cut, frame id per register there)` -/
+  cuts : List (Nat × List Nat)
+  /-- slots that start off the zero frame `(slot REGISTER, frame id)` (rule 2); EMPTY on the path -/
+  ext : List (Nat × Nat)
+  /-- derived (questions.md Q1): per port `h` masks, the first is the port, pairwise dots = delta
+  (an orthonormal basis of `F_2^h` through the port) -/
+  obase : List (List Nat)
+
+/-- registers of a gate, in the order they are moved -/
+def Gate.regs : Gate → List Nat
+  | .out _ s ts ex => s :: (ts.map Prod.fst ++ ex)
+  | .inn _ t ss => t :: ss.map Prod.fst
+
+/-- frame of a gate -/
+def Gate.frame : Gate → Nat
+  | .out f _ _ _ => f
+  | .inn f _ _ => f
+
+/-- single adds `(tgt, src, co)` of a gate, in order -/
+def Gate.adds : Gate → List (Nat × Nat × Co)
+  | .out _ s ts _ => ts.map fun p => (p.1, s, p.2)
+  | .inn _ t ss => ss.map fun p => (t, p.1, p.2)
+
+/-- the frame table -/
+def Raw.frameTab (c : Raw) : List (List Nat) := c.frames.flatten
+
+/-- all gates of phase A / phase B -/
+def Raw.gatesA (c : Raw) : List Gate := c.A.flatten
+def Raw.gatesB (c : Raw) : List Gate := c.B.flatten
+
+/-- number of registers -/
+def Raw.nreg (c : Raw) : Nat := 2 * c.v + c.R
+
+end GXD
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean
new file mode 100644
index 0000000000..0392e1f05b
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GCert__Data__SolutionB2Gp193x.lean
@@ -0,0 +1,38 @@
+import Work.GCert.Data.B2Gp193Main
+
+/-!
+Comparator solution `Work.GCert.Data.SolutionB2Gp193x` (not part of github.com/openai/math).
+
+The whole proof is in `Work.GCert.Data.B2Gp193Main` (and its imports), which ends with
+
+    theorem wht_main_B2Gp193x :
+        ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W
+
+This module adds nothing mathematical: it defines `WHT.WHTTimeBoundsAt` with the text of the
+challenge (the same definition as `BlockWHT.WHTTimeBoundsAt` of `Work.Block.WHT`) and restates
+the theorem under the name the challenge uses.  Its proof is that single term.
+`WHTProgram`, `wht`, `whtInKind`, `whtOutKind` come from `WHTCheck.Solution`.
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open Filter Asymptotics
+
+/-- `W = O(2^k (k+1)^β)` and `W = o(2^k k)` (`WHTTimeBounds` is the case `β = 1 - 2/10^11`). -/
+def WHTTimeBoundsAt (β : ℝ) (W : ℕ → ℕ) : Prop :=
+  let W' := fun k : ℕ => (W k : ℝ)
+  W' =O[atTop] (fun k : ℕ => (2:ℝ)^k * ((k:ℝ)+1)^β) ∧
+  W' =o[atTop] (fun k : ℕ => (2:ℝ)^k * (k:ℝ))
+
+/-- **Walsh-Hadamard transform with the improved exponent**: the statement `WHTGoal` of
+`WHTCheck/Challenge.lean` with `1 - 2/10^11` replaced by `1 - 7474547/10^10`. -/
+theorem wht_main_block_B2Gp193x :
+    ∃ solve W, WHTProgram solve W ∧ WHTTimeBoundsAt (1 - 7474547/(10:ℝ)^10) W :=
+  wht_main_B2Gp193x
+
+end WHT
+end PowerSaving
+end OAI
+
+#print axioms OAI.PowerSaving.WHT.wht_main_block_B2Gp193x
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean
new file mode 100644
index 0000000000..24e261ad08
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Adapt.lean
@@ -0,0 +1,183 @@
+import Work.GFrame.Engine.Letters
+
+/-!
+# GFrame engine, part 2: the free adapter letters in the RAM (agent key: eng-ram)
+
+One free adapter on the array of one role is ONE linear pass, no recursive call:
+
+* `Gear.permuted`     the address of `x ↦ G.π x` (columnwise), O(1) per entry with the XOR table
+                      (as `Gear.shifted`, through `Gear.body_additive` of `Work/Block/Address.lean`);
+* `Gear.phase_row`    the `f`-bit row `(z·x_j + c)_j` of an entry, O(1);
+* `GRig`              a rig together with the table of `lum` over `Bits f` (`i^popcount`);
+* `Rig.perm_cost`, `GRig.phase_cost`   the two letters, work = length of the role table.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.GF
+open Binary Matrix Finset
+noncomputable section
+section
+variable {α : Type*} [Fintype α] [DecidableEq α]
+
+/-- An address permutation acts on an array with `f` columns by moving the address. -/
+lemma act_perm (G : APerm α) (f : ℕ) (x : Sky α f → ℂ) (j : Sky α f) :
+    matAct f (permMat G) x j = x (fun k => G.π (j k)) := by
+  change ∑ i, digitProd (fun _ : Fin f => permMat G) j i * x i = _
+  have h (i : Sky α f) : digitProd (fun _ : Fin f => permMat G) j i =
+      if (fun k => G.π (j k)) = i then 1 else 0 :=
+    prod_delta (κ:=fun _ : Fin f => Space α) _ _
+  simp_rw [h]
+  simp [ite_mul]
+
+/-- A diagonal phase acts by the scalar `lum` of the row of phase bits. -/
+lemma act_phase (z : Space α) (c : F) (f : ℕ) (x : Sky α f → ℂ) (j : Sky α f) :
+    matAct f (phaseMat z c) x j = lum (fun k : Fin f => dot z (j k) + c) * x j := by
+  unfold matAct phaseMat
+  rw [digitProd_diagonal, Matrix.mulVec_diagonal]
+  rfl
+
+end
+end
+end PowerSaving.GF
+
+namespace PowerSaving.RAM
+open Binary Ty Finset GF
+noncomputable section
+universe U V
+variable {ι : Type U}
+
+namespace Gear
+variable {m : Bool} {B f : ι → ℕ} {s t : Ty} {x : ι → T s}
+variable (g : Gear m B f s x)
+include g
+variable {α : Type*} [Fintype α] [DecidableEq α] (X : Layout α) (r : ℕ)
+
+/-- Address moved by an additive bijection (across the `f` columns). -/
+lemma permuted (G : APerm α) (v : ∀ i, Grid α r (f i))
+    (h : Knows m B s x (fun i => (book X r (f i)).loc (v i))) :
+    Knows m B s x (fun i => (book X r (f i)).loc ((v i).1,
+      fun j => G.π ((v i).2 j))) := by
+  obtain ⟨hg, hh⟩ := g.grid_fetch X r (v:=v) h
+  let K (i : ι) : Grid α r (f i) := ((v i).1, fun j => G.π ((v i).2 j))
+  apply g.grid_combine X r (v:=K) hg (g.body_set X (fun i => (K i).2) _)
+  intro a
+  exact g.body_additive X (fun y => G.π y a) (fun p q => by rw [G.add]; rfl)
+    (fun i => (v i).2) hh
+
+/-- The row of phase bits `(z·x_j + c)_j` of an address. -/
+lemma phase_row (z : Space α) (c : F) (v : ∀ i, Grid α r (f i))
+    (h : Knows m B s x (fun i => (book X r (f i)).loc (v i))) :
+    Knows m B s x (fun i => (bits (f i)).loc (fun l : Fin (f i) => dot z ((v i).2 l) + c)) := by
+  obtain ⟨_, hh⟩ := g.grid_fetch X r (v:=v) h
+  have hv := g.body_additive X (fun y => dot z y) (fun p q => dot_add_right z p q)
+    (fun i => (v i).2) hh
+  rcases bit_cases c with hc|hc
+  · refine hv.cong (fun _ => rfl) (fun i => ?_)
+    simp [hc]
+  · let q i : Bits (f i) × Bits (f i) := (fun l => dot z ((v i).2 l), fun _ => 1)
+    have hf : Knows m B s x (fun i => (bits (f i)).loc (q i).2) :=
+      (g.power.minus (Can.wc 1) g.bound).cong (fun _ => rfl) (fun i => by
+        change 2^f i-1=(bits _).loc (fun _ => 1)
+        rw [← bits_lit]
+        simp)
+    refine (g.addr_xor q hv hf).cong (fun _ => rfl) (fun i => ?_)
+    apply congr_arg (bits (f i)).loc
+    ext k; simp [q,hc]
+
+end Gear
+
+/-- A rig together with the table of `lum` over `Bits f` (the fourth roots `i^popcount`). -/
+structure GRig {α ρ : Type*} (m : Bool) (B f : ι → ℕ) (s : Ty) (x : ι → T s)
+    (cl : Paint) (X : Layout α) (R : Layout ρ) (r : ℕ) (v : ∀ i, Grain α ρ r (f i)) : Prop where
+  rig : Rig m B f s x cl X R r v
+  lumT : Has m B s (a sc) x fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)
+
+section
+variable {α ρ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+variable {m : Bool} {B f : ι → ℕ} {s t : Ty} {x : ι → T s}
+    {cl : Paint} {X : Layout α} {R : Layout ρ} {r : ℕ} {v : ∀ i, Grain α ρ r (f i)}
+
+omit [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ] in
+lemma GRig.gather (h : GRig m B f s x cl X R r v) {κ : Type V} (j : κ → ι) (y : κ → T t)
+    (g : Has m (fun k => B (j k)) t s y (fun k => x (j k))) :
+    GRig m (fun k => B (j k)) (fun k => f (j k)) t y cl X R r (fun k => v (j k)) :=
+  ⟨h.rig.gather j y g, g.then_do (h.lumT.reindex j)⟩
+
+lemma Rig.ferry_perm (h : Rig m B f s x cl X R r v) (l : ρ) (G : APerm α)
+    (q : ∀ i, Beach α ρ r (f i))
+    (g : Knows m B s x fun i => (fleet X R r (f i)).loc (q i)) :
+    Has m B s (c cl) x fun i => ferryM r (f i) l (permMat G) (v i) (q i) := by
+  obtain ⟨hl,hk⟩ := h.addrs q g
+  have hb := h.read q hl hk
+  let t i : Beach α ρ r (f i) := ((q i).1,(q i).2.1,fun j => G.π ((q i).2.2 j))
+  have hh := h.read t hl (h.gear.permuted X r G _ hk)
+  apply Can.cases_code (q:=fun i => (q i).1) R hl
+  intro p
+  by_cases he : p=l
+  · refine (hh.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have hql : (q i.val).1 = l := i.property.trans he
+    change v i.val ((q i.val).1,(q i.val).2.1,fun j => G.π ((q i.val).2.2 j)) = _
+    simp only [ferryM, roleAct, hql, if_true, act_perm]
+  · refine (hb.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have H : (q i.val).1≠l := fun hh => he (i.property.symm.trans hh)
+    simp only [ferryM, roleAct, H, ite_false, Prod.mk.eta]
+
+/-- **Free address permutation**: one pass over the role table. -/
+lemma Rig.perm_cost (h : Rig m B f s x cl X R r v) (l : ρ) (G : APerm α) :
+    Can m B s (a (c cl)) x
+      (fun i => (fleet X R r (f i)).tape (ferryM r (f i) l (permMat G) (v i)))
+      (fun i => (fleet X R r (f i)).n) := by
+  refine h.chart _ ?_
+  let S := Σ i, Beach α ρ r (f i)
+  have hg := h.gather (fun d : S => d.1)
+    (fun d => ((x d.1, (fleet X R r (f d.1)).loc d.2):T (p s w))) (t:=p s w) Can.first
+  exact hg.ferry_perm l G (fun d => d.2) Can.second
+
+lemma GRig.ferry_phase (h : GRig m B f s x cl X R r v) (l : ρ) (z : Space α) (c' : F)
+    (q : ∀ i, Beach α ρ r (f i))
+    (g : Knows m B s x fun i => (fleet X R r (f i)).loc (q i)) :
+    Has m B s (c cl) x fun i => ferryM r (f i) l (phaseMat z c') (v i) (q i) := by
+  obtain ⟨hl,hk⟩ := h.rig.addrs q g
+  have hb := h.rig.read q hl hk
+  have hrow := h.rig.gear.phase_row X r z c' (fun i => (q i).2) hk
+  have hs : Has m B s sc x
+      (fun i => lum (fun k : Fin (f i) => dot z ((q i).2.2 k) + c')) :=
+    Can.fetch (t:=sc) (L:=fun i => bits (f i)) (v:=fun i (y : Bits (f i)) => lum y)
+      (i:=fun i => (fun k : Fin (f i) => dot z ((q i).2.2 k) + c')) h.lumT hrow
+  have hh := hs.mul hb
+  apply Can.cases_code (q:=fun i => (q i).1) R hl
+  intro p
+  by_cases he : p=l
+  · refine (hh.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have hql : (q i.val).1 = l := i.property.trans he
+    change lum (fun k : Fin (f i.val) => dot z ((q i.val).2.2 k) + c') *
+      v i.val ((q i.val).1,(q i.val).2.1,(q i.val).2.2) = _
+    simp only [ferryM, roleAct, hql, if_true, act_phase]
+  · refine (hb.reindex (fun i : {i // (q i).1=p} => i.1)).cong (fun _ => rfl)
+      (fun i => ?_)
+    have H : (q i.val).1≠l := fun hh => he (i.property.symm.trans hh)
+    simp only [ferryM, roleAct, H, ite_false, Prod.mk.eta]
+
+/-- **Free diagonal phase**: one pass over the role table (one table look-up per entry). -/
+lemma GRig.phase_cost (h : GRig m B f s x cl X R r v) (l : ρ) (z : Space α) (c' : F) :
+    Can m B s (a (c cl)) x
+      (fun i => (fleet X R r (f i)).tape (ferryM r (f i) l (phaseMat z c') (v i)))
+      (fun i => (fleet X R r (f i)).n) := by
+  refine h.rig.chart _ ?_
+  let S := Σ i, Beach α ρ r (f i)
+  have hg := h.gather (fun d : S => d.1)
+    (fun d => ((x d.1, (fleet X R r (f d.1)).loc d.2):T (p s w))) (t:=p s w) Can.first
+  exact hg.ferry_phase l z c' (fun d => d.2) Can.second
+
+end
+end
+end PowerSaving.RAM
+end OAI
+
+#print axioms OAI.PowerSaving.RAM.Rig.perm_cost
+#print axioms OAI.PowerSaving.RAM.GRig.phase_cost
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean
new file mode 100644
index 0000000000..2eca6e713b
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Letters.lean
@@ -0,0 +1,199 @@
+import Work.Block.Bridge
+
+/-!
+# GFrame engine, part 1: the generalised word language (agent key: eng-ram)
+
+Letters = the letters of `BWord` (`localM`, `shift`, `block`) plus TWO FREE ADAPTER letters on
+one role:
+
+* `perm l G`      address permutation by an additive bijection `G` of the label space
+                  (matrix `permMat G`, `(permMat G) x y = 1` iff `G.π x = y`);
+* `phase l z c`   the diagonal phase `i^[z·x + c]` IN THE STANDARD BASIS
+                  (matrix `phaseMat z c = diagonal (fun x => tint (dot z x + c))`).
+
+Products of `phaseMat` are exactly the diagonal matrices `i^Q(x)`, `Q` a `ℤ/4`-valued quadratic
+form plus a constant; with the old free letter `shift` the free letters generate every affine
+address permutation times such a phase.  A "twisted block" is NOT a primitive letter: it is the
+word `free adapters ++ [block] ++ free adapters` (see `Free.lean`, `gstep_of_factor`).
+
+The semantics is `gwalk` (no unit-move word behind it: the new letters are not Walsh-diagonal).
+Old words embed by `GWord.ofB`, and `gwalk f (ofB w) = walk f w.flat`.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.GF
+open Binary Matrix Finset
+noncomputable section
+
+/-- An additive bijection of the label space. -/
+structure APerm (α : Type*) where
+  π : Space α ≃ Space α
+  add : ∀ x y, π (x + y) = π x + π y
+
+section Mats
+variable {α : Type*} [Fintype α] [DecidableEq α]
+
+/-- Permutation matrix of an additive bijection: `(permMat G *ᵥ v) x = v (G.π x)`. -/
+def permMat (G : APerm α) : CMat α := fun x y => if G.π x = y then 1 else 0
+
+/-- Elementary diagonal phase in the standard basis: `i^[z·x + c]`. -/
+def phaseMat (z : Space α) (c : F) : CMat α := Matrix.diagonal fun x => tint (dot z x + c)
+
+end Mats
+
+/-- Letters of the generalised word language. -/
+inductive GMove (α ρ : Type*)
+  | old (mv : BMove α ρ)
+  | perm (l : ρ) (G : APerm α)
+  | phase (l : ρ) (z : Space α) (c : F)
+
+abbrev GWord (α ρ : Type*) := List (GMove α ρ)
+
+namespace GMove
+variable {α ρ : Type*}
+
+/-- The letter of `BWord` with the same price (free adapters ↦ a free letter). -/
+def shadow : GMove α ρ → BMove α ρ
+  | .old mv => mv
+  | .perm _ _ => .localM 0
+  | .phase _ _ _ => .localM 0
+
+/-- Rank paid by a letter (`none` = free). -/
+def rk? (mv : GMove α ρ) : Option ℕ := mv.shadow.rk?
+def costR (φ : ℕ → ℝ) (mv : GMove α ρ) : ℝ := mv.shadow.costR φ
+def Proper (u : ℕ) (mv : GMove α ρ) : Prop := mv.shadow.Proper u
+
+@[simp] lemma costR_perm (φ : ℕ → ℝ) (l : ρ) (G : APerm α) :
+    (GMove.perm l G : GMove α ρ).costR φ = 0 := rfl
+@[simp] lemma costR_phase (φ : ℕ → ℝ) (l : ρ) (z : Space α) (c : F) :
+    (GMove.phase l z c : GMove α ρ).costR φ = 0 := rfl
+@[simp] lemma costR_old (φ : ℕ → ℝ) (mv : BMove α ρ) : (GMove.old mv).costR φ = mv.costR φ := rfl
+lemma proper_perm (u : ℕ) (l : ρ) (G : APerm α) : (GMove.perm l G : GMove α ρ).Proper u :=
+  trivial
+lemma proper_phase (u : ℕ) (l : ρ) (z : Space α) (c : F) :
+    (GMove.phase l z c : GMove α ρ).Proper u := trivial
+@[simp] lemma proper_old (u : ℕ) (mv : BMove α ρ) : (GMove.old mv).Proper u ↔ mv.Proper u :=
+  Iff.rfl
+
+end GMove
+
+namespace GWord
+variable {α ρ : Type*}
+
+def shadow (w : GWord α ρ) : BWord α ρ := w.map GMove.shadow
+def costR (φ : ℕ → ℝ) (w : GWord α ρ) : ℝ := (w.map (GMove.costR φ)).sum
+def Proper (u : ℕ) (w : GWord α ρ) : Prop := ∀ mv ∈ w, mv.Proper u
+def hist (w : GWord α ρ) (r : ℕ) : ℕ := w.shadow.hist r
+/-- Natural-number cost when a block of rank `rk` costs `g rk`. -/
+def cost (g : ℕ → ℕ) (w : GWord α ρ) : ℕ := w.shadow.cost g
+/-- An old block word as a generalised word. -/
+def ofB (w : BWord α ρ) : GWord α ρ := w.map GMove.old
+
+@[simp] lemma shadow_nil : shadow ([] : GWord α ρ) = [] := rfl
+@[simp] lemma shadow_cons (mv : GMove α ρ) (w : GWord α ρ) :
+    shadow (mv :: w) = mv.shadow :: shadow w := rfl
+@[simp] lemma shadow_ofB (w : BWord α ρ) : shadow (ofB w) = w := by
+  simp [shadow, ofB, List.map_map, Function.comp_def, GMove.shadow]
+
+lemma costR_shadow (φ : ℕ → ℝ) (w : GWord α ρ) : costR φ w = BWord.costR φ w.shadow := by
+  unfold costR BWord.costR shadow
+  rw [List.map_map]
+  rfl
+@[simp] lemma costR_nil (φ : ℕ → ℝ) : costR φ ([] : GWord α ρ) = 0 := rfl
+lemma costR_cons (φ : ℕ → ℝ) (mv : GMove α ρ) (w : GWord α ρ) :
+    costR φ (mv :: w) = mv.costR φ + costR φ w := by simp [costR]
+lemma costR_append (φ : ℕ → ℝ) (w w' : GWord α ρ) :
+    costR φ (w ++ w') = costR φ w + costR φ w' := by simp [costR]
+lemma costR_ofB (φ : ℕ → ℝ) (w : BWord α ρ) : costR φ (ofB w) = BWord.costR φ w := by
+  rw [costR_shadow, shadow_ofB]
+@[simp] lemma cost_nil (g : ℕ → ℕ) : cost g ([] : GWord α ρ) = 0 := rfl
+lemma cost_cons (g : ℕ → ℕ) (mv : GMove α ρ) (w : GWord α ρ) :
+    cost g (mv :: w) = mv.shadow.cost g + cost g w := BWord.cost_cons g _ _
+
+lemma Proper.shadow {u : ℕ} {w : GWord α ρ} (h : Proper u w) : BWord.Proper u w.shadow := by
+  intro mv hmv
+  obtain ⟨g, hg, rfl⟩ := List.mem_map.mp hmv
+  exact h g hg
+lemma Proper.tail {u : ℕ} {mv : GMove α ρ} {w : GWord α ρ} (h : Proper u (mv :: w)) :
+    Proper u w := fun x hx => h x (List.mem_cons_of_mem _ hx)
+lemma Proper.head {u : ℕ} {mv : GMove α ρ} {w : GWord α ρ} (h : Proper u (mv :: w)) :
+    mv.Proper u := h mv List.mem_cons_self
+lemma Proper.append {u : ℕ} {w w' : GWord α ρ} (h : Proper u w) (h' : Proper u w') :
+    Proper u (w ++ w') := by
+  intro mv hmv
+  rcases List.mem_append.mp hmv with h1|h1
+  · exact h mv h1
+  · exact h' mv h1
+lemma proper_nil (u : ℕ) : Proper u ([] : GWord α ρ) := fun _ h => by simp at h
+lemma proper_ofB {u : ℕ} {w : BWord α ρ} (h : w.Proper u) : Proper u (ofB w) := by
+  intro mv hmv
+  obtain ⟨g, hg, rfl⟩ := List.mem_map.mp hmv
+  exact h g hg
+
+lemma costR_eq_sum (u : ℕ) (φ : ℕ → ℝ) (w : GWord α ρ) (hw : Proper u w) :
+    costR φ w = ∑ r : Fin u, (w.hist r:ℝ) * φ r := by
+  rw [costR_shadow]; exact BWord.costR_eq_sum u φ _ hw.shadow
+lemma cost_eq_sum (u : ℕ) (g : ℕ → ℕ) (w : GWord α ρ) (hw : Proper u w) :
+    cost g w = ∑ r : Fin u, hist w r * g r := BWord.cost_eq_sum u g _ hw.shadow
+lemma hist_zero (u : ℕ) (w : GWord α ρ) (hw : Proper u w) : hist w 0 = 0 :=
+  BWord.hist_zero u _ hw.shadow
+lemma hist_large (u : ℕ) (w : GWord α ρ) (hw : Proper u w) (r : ℕ) (hr : u ≤ r) :
+    hist w r = 0 := BWord.hist_large u _ hw.shadow r hr
+
+end GWord
+
+section Sem
+variable {α ρ σ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+
+/-- The action of one letter. -/
+def GMove.act (f : ℕ) : GMove α ρ → Data α ρ f → Data α ρ f
+  | .old mv => mv.act f
+  | .perm l G => roleAct f l (permMat G)
+  | .phase l z c => roleAct f l (phaseMat z c)
+
+/-- **Semantics of a generalised word.** -/
+def gwalk (f : ℕ) (w : GWord α ρ) (x : Data α ρ f) : Data α ρ f :=
+  w.foldl (fun y mv => mv.act f y) x
+
+@[simp] lemma gwalk_nil (f : ℕ) (x : Data α ρ f) : gwalk f ([] : GWord α ρ) x = x := rfl
+lemma gwalk_cons (f : ℕ) (mv : GMove α ρ) (w : GWord α ρ) (x : Data α ρ f) :
+    gwalk f (mv :: w) x = gwalk f w (mv.act f x) := rfl
+lemma gwalk_append (f : ℕ) (p q : GWord α ρ) (x : Data α ρ f) :
+    gwalk f (p ++ q) x = gwalk f q (gwalk f p x) := by simp [gwalk]
+
+/-- Old words keep their meaning. -/
+lemma gwalk_ofB (f : ℕ) (w : BWord α ρ) (x : Data α ρ f) :
+    gwalk f (GWord.ofB w) x = walk f w.flat x := by
+  induction w generalizing x with
+  | nil => rfl
+  | cons mv w ih =>
+    rw [walk_flat_cons, ← ih]
+    rfl
+
+/-- The scratch certificate for the generalised language (cf. `RAM.LiveKernel`). -/
+def GLiveKernel (e : σ → ρ) (w : GWord α ρ) : Prop :=
+  ∀ (f : ℕ) (v : Data α ρ f), (∀ s, (∀ l, e l ≠ s) → v s = 0) →
+    ∀ l, gwalk f w v (e l) = matAct f (kernel α) (v (e l))
+
+/-- Every old certificate is a generalised certificate. -/
+theorem GLiveKernel.ofB {e : σ → ρ} {w : BWord α ρ} (h : RAM.LiveKernel e w.flat) :
+    GLiveKernel e (GWord.ofB w) := by
+  intro f v hv l
+  rw [gwalk_ofB]
+  exact h f v hv l
+
+/-- One role goes from matrix `M` to `N` by a generalised word (cf. `XStep`). -/
+def GStep (l : ρ) (M N : CMat α) (c : (ℕ → ℝ) → ℝ) : Prop :=
+  ∃ (w : GWord α ρ) (U : CMat α), w.Proper (Fintype.card α) ∧ (∀ φ, w.costR φ = c φ) ∧
+    U * M = N ∧ ∀ (f : ℕ) (x : Data α ρ f), gwalk f w x = roleAct f l U x
+
+end Sem
+end
+end PowerSaving.GF
+end OAI
+
+#print axioms OAI.PowerSaving.GF.gwalk_ofB
+#print axioms OAI.PowerSaving.GF.GLiveKernel.ofB
+#print axioms OAI.PowerSaving.GF.GWord.costR_eq_sum
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean
new file mode 100644
index 0000000000..6bd7cfa0c3
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/Work__GFrame__Engine__Level.lean
@@ -0,0 +1,163 @@
+import Work.GFrame.Engine.Sweep
+import WHTCheck.Solution
+
+/-!
+# GFrame engine, part 4: one level of the recursion for generalised words (agent key: eng-ram)
+
+Copy of `amplifyB` (`Work/Block/Recursion.lean`) with two changes:
+
+* the word is a `GWord` with certificate `GLiveKernel e w` (semantics `gwalk`);
+* after the XOR table the level also builds the table of `lum` over `Bits f`
+  (`WHT.lum_tables`, doubling construction, `O(2^f)` work), which the free diagonal phases
+  read; it is part of the environment of the sweep (`GRig`).
+
+Cost: the same `2^k` linear term and the same recursive calls as `amplifyB`.
+-/
+
+set_option linter.unusedSectionVars false
+
+namespace OAI
+namespace PowerSaving.RAM
+open Binary Matrix Ty Finset GF
+noncomputable section
+
+section
+universe U
+variable {α ρ σ : Type*} [Fintype α] [DecidableEq α] [Fintype ρ] [DecidableEq ρ]
+  [Fintype σ] [DecidableEq σ]
+variable {ι : Type U} {m : Bool}
+    {k f : ι → ℕ} {cl : Paint} {b : Bank (hatch cl) ι}
+    {v : ∀ i, Sim σ (k i)→ℂ}
+
+/-- **One level of the recursion for a generalised word** (replaces `amplifyB`). -/
+lemma gamplify (m : Bool) (b : Bank (hatch cl) ι) (v : ∀ i, Sim σ (k i) → ℂ)
+    (X : Layout α) (R : Layout ρ) (Q : Layout σ) (e : σ → ρ) (he : Function.Injective e)
+    (r : ℕ) (hr : 3 ≤ X.n) (hq : ∀ i, X.n*f i+r=k i) (hd : r < X.n) (hQ : 0<Q.n)
+    (n τ : ℕ → ι → ℕ)
+    (hc : ∀ rk, 1 ≤ rk → rk < X.n → ∀ i, n rk i*(sim Q (rk * f i)).n=2^k i)
+    (hk : ∀ rk, 1 ≤ rk → rk < X.n → Contract cl b (fun i => rk * f i) (τ rk) Q)
+    (hB : Small b.B (fun i => 2^k i))
+    (w : GWord α ρ) (hw : GLiveKernel e w) (hP : w.Proper X.n) :
+    Able m b (simIn cl) (bundle cl) (fun i => loaded cl Q (k i) (v i))
+      (fun i => (sim Q (k i)).tape (whole (k i) (v i)))
+      (fun i => 2^k i) (fun i => w.cost (fun rk => n rk i * τ rk i)) := by
+  let W i := 2^k i
+  let s := simIn cl
+  let eQ (i : ι) := ebb X r (f i) (k i) (hq i) (v i)
+  let zQ (i : ι) : Grain α σ r (f i) :=
+    fun j => chords r (f i) (fun l => eQ i (j.1,l)) j.2
+  let Z (i : ι) : Grain α ρ r (f i) := crossAct r (f i) (embM e) (zQ i)
+  let O (i : ι) : Grain α σ r (f i) :=
+    crossAct r (f i) (extM e) (gcoast r (f i) w (Z i))
+  let szQ i := (fleet X Q r (f i)).n
+  let szR i := (fleet X R r (f i)).n
+  have hszQ : Dom W szQ := by
+    refine ⟨Q.n+1, fun i => ?_⟩
+    unfold W szQ fleet
+    rw [Layout.pair_len, book_len,hq]
+    simp only [mul_add,add_mul,mul_one,one_mul]
+    gcongr <;> simp
+  have hszR : Dom W szR := by
+    refine ⟨R.n+1, fun i => ?_⟩
+    unfold W szR fleet
+    rw [Layout.pair_len, book_len,hq]
+    simp only [mul_add,add_mul,mul_one,one_mul]
+    gcongr <;> simp
+  have hn (i : ι) : 0 < W i := pow_pos (by decide) _
+  have hf (i) : f i ≤ k i := by
+    have g := hq i
+    have h := Nat.le_mul_of_pos_left (f i) (show 0 < X.n by omega)
+    omega
+  have hy (i) : k i ≤ W i := Nat.lt_two_pow_self.le
+  have sd := hB.mono hy
+  have sq := sd.mono hf
+  let p2 i := 2^f i
+  have hm : Small b.B p2 :=
+    hB.mono (fun i => Nat.pow_le_pow_right (by omega) (hf i))
+  have hcube (i) : p2 i ^ 3 ≤ W i := by
+    unfold p2 W
+    rw [← pow_mul]
+    apply Nat.pow_le_pow_right (by omega)
+    have hh : 3*f i ≤ X.n*f i := Nat.mul_le_mul_right _ hr
+    have hg := hq i
+    rw [mul_comm]
+    omega
+  let env (i : ι) := loaded cl Q (k i) (v i)
+  -- construct fields (f,p2)
+  have hmf : Can m b.B s Ty.w env f W := by
+    have ht : Can m b.B s Ty.w env k W := Can.first
+    refine (ht.dvdW (Can.wc X.n) sd).cong (fun _ => rfl) ?_
+    intro i
+    rw [← hq,mul_comm X.n]
+    exact Layout.div_join hd
+  have hmp : Can m b.B s (Ty.p Ty.w Ty.w) env (fun i => (f i,p2 i)) W :=
+    hmf.pair (hmf.wTwo sq hm (Dom.of_le (fun i => (hf i).trans (hy i))))
+  let T1 := Ty.p s (Ty.p Ty.w Ty.w)
+  let Y (i : ι) : T T1 := (env i,f i,p2 i)
+  have hmx : Can m b.B T1 (Ty.a Ty.w) Y (fun i => xorTab (f i)) W :=
+    (Can.xor_prepare (m:=m) (f:=f) (B:=b.B) (s:=T1) (x:=Y)
+      (Can.fst Can.second) (Can.snd Can.second) sq hm).mono hcube
+  let T2 := Ty.p T1 (Ty.a Ty.w)
+  let Y' (i : ι) : T T2 := (Y i,xorTab (f i))
+  -- NEW: the table of `lum` over `Bits f`
+  have hE2 : Has m b.B T2 s Y' env := Can.fst Can.first
+  have hml : Can m b.B T2 (Ty.a sc) Y'
+      (fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)) W :=
+    (WHT.lum_tables (k:=f) (Can.fst (Can.snd Can.first)) sq hm hE2.snd.fst).1.mono
+      (fun i => Nat.pow_le_pow_right (by omega) (hf i))
+  let T2' := Ty.p T2 (Ty.a sc)
+  let Y'' (i : ι) : T T2' := (Y' i,(bits (f i)).tape (fun y : Bits (f i) => lum y))
+  -- the input, read as a table on the slots
+  have hG0 : Rig m b.B f T2 Y' cl X Q r eQ := by
+    refine ⟨⟨?_,?_,Can.second,hm⟩,?_,?_⟩
+    · exact Can.snd (Can.snd Can.first)
+    · exact Can.fst (Can.snd Can.first)
+    · exact hE2.snd.fst
+    · exact hE2.snd.snd.cong (fun _ => rfl) (fun i => (ebb_eq ..).symm)
+  have hG : Rig m b.B f T2' Y'' cl X Q r eQ := hG0.gather id Y'' (t:=T2') Can.first
+  -- leftover bits, still on the slots
+  have HH : Can m b.B T2' (bundle cl) Y'' (fun i => (fleet X Q r (f i)).tape (zQ i)) W :=
+    hG.dots_cost.weaken hszQ
+  let T3 := Ty.p T2' (bundle cl)
+  let A (i) : T T3 := (Y'' i,(fleet X Q r (f i)).tape (zQ i))
+  have Hg := hG.gather id A (t:=T3) Can.first
+  have G : Rig m b.B f T3 A cl X Q r zQ := ⟨Hg.gear,Hg.imag,Can.second⟩
+  -- embed the slots into the table of roles; scratch roles are created as zero
+  have HE : Can m b.B T3 (bundle cl) A (fun i => (fleet X R r (f i)).tape (Z i)) W :=
+    (G.cross_point R (embM e)).weaken hszR
+  let T4 := Ty.p T3 (bundle cl)
+  let A4 (i) : T T4 := (A i,(fleet X R r (f i)).tape (Z i))
+  have Hg4 := G.gather id A4 (t:=T4) Can.first
+  have hL4 : Has m b.B T4 (Ty.a sc) A4
+      (fun i => (bits (f i)).tape (fun y : Bits (f i) => lum y)) :=
+    Can.snd (Can.fst Can.first)
+  have G4 : GRig m b.B f T4 A4 cl X R r Z := ⟨⟨Hg4.gear,Hg4.imag,Can.second⟩,hL4⟩
+  -- the GENERALISED word on the table of roles
+  have Hy := G4.gsweep n τ Q hQ hk
+    (fun rk h1 h2 i => by rw [book_len,hq]; exact hc rk h1 h2 i) w hP
+  -- extract the slots; scratch roles are dropped
+  let T5 := Ty.p T4 (bundle cl)
+  let A5 (i) : T T5 := (A4 i,(fleet X R r (f i)).tape (gcoast r (f i) w (Z i)))
+  have Hg5 := G4.rig.gather id A5 (t:=T5) Can.first
+  have G5 : Rig m b.B f T5 A5 cl X R r (fun i => gcoast r (f i) w (Z i)) :=
+    ⟨Hg5.gear,Hg5.imag,Can.second⟩
+  have HX : Can m b.B T5 (bundle cl) A5 (fun i => (fleet X Q r (f i)).tape (O i)) W :=
+    (G5.cross_point Q (extM e)).weaken hszQ
+  have heq (i) : O i = ebb X r (f i) (k i) (hq i) (whole (k i) (v i)) :=
+    gamplifies X r (f i) (k i) (hq i) e he w hw (v i)
+  have ha (i) : (fleet X Q r (f i)).tape (O i) =
+      (sim Q (k i)).tape (whole (k i) (v i)) := by
+    rw [heq]; exact ebb_eq ..
+  have Ho := ((Hy.weaken hszR (fun _ => le_rfl)).save_keep
+    (Able.of_can (b:=b) HX)).cong (fun _ => rfl) ha
+  have Hx := (Able.of_can (b:=b) hmp).save_keep
+    ((Able.of_can (b:=b) hmx).save_keep ((Able.of_can (b:=b) hml).save_keep
+      ((Able.of_can (b:=b) HH).save_keep ((Able.of_can (b:=b) HE).save_keep Ho))))
+  simpa only [Nat.zero_add,Nat.add_zero] using Hx
+
+end
+end
+end PowerSaving.RAM
+end OAI
+
+#print axioms OAI.PowerSaving.RAM.gamplify
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md
new file mode 100644
index 0000000000..e28b355d0a
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__ORIGIN.md
@@ -0,0 +1,64 @@
+# tools/gx/ and tools/certificate/gcert1-p11-pr193.json.gz: where they come from
+
+Everything in this directory is Python 3 (standard library only). No Lean is run by these scripts.
+"The outside repository" means github.com/CrocSwap/integer-mult-bounds (Apache-2.0, `LICENSE` and `NOTICE`
+of that repository; `NOTICE`: "A sharper exponent for integer multiplication, Copyright 2026 Douglas Colkitt").
+
+## The scripts (this project)
+
+| file | what it is |
+|---|---|
+| `gxcore.py` | loads a certificate of format gcert/1, brings it to normal form, and is a Python mirror of both Lean checks (labels and scalars); cut points and label data for the generator |
+| `gxunit.py` | split plan of the kernel evaluations, the unit of the word, expected exponents |
+| `gxbind.py` | the texts of the generated Lean modules (check, histogram, price, certificate and final modules) |
+| `gxgen.py` | certificate -> Lean data modules and one module per kernel evaluation |
+| `gxrate.py` | rate lemmas, unit price list, final theorem modules, comparator challenge / solution / configuration |
+| `gxdry.py`, `gxmut.py` | dry run (mirror, sizes, plan, exponents); mutants that the mirror must reject |
+| `gxconv.py` | converts the earlier format gcert/0 to gcert/1 when a step scales its target (the in-place pair step of #193) |
+| `gsmirror.py` | a second, separately written Python mirror of the scalar check `GS.scalCheck` / `GS.yCheck`; `gxbind.py` calls it for the check parameters |
+| `gx.py`, `gxrun.py` | the reference checker of the format (`gx.check1`: labels and exact scalar identity) and its command line |
+| `gxpaths.py`, `regen_check.py`, `refcheck.py` | written for this repository: relative paths; regenerate and compare; `gx.check1` on a gcert/1 file |
+
+The scripts are the working copies with path edits only (absolute paths of the author's machine replaced through
+`gxpaths.py`; templates read from `tools/gen/templates/`; `foldlib.py` / `foldgen.py` taken from `tools/gen/`).
+The sentences "Generated by checks/..." that the generators print into Lean files name the scripts by their
+working paths; they are kept so that the generated modules come out byte for byte.
+No script of the outside repository is included, imported or executed.
+
+## The certificate `tools/certificate/gcert1-p11-pr193.json.gz`
+
+sha256 of the file: `15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633`
+(gzip stores a time stamp; sha256 of the uncompressed JSON: `c64d2a95431c3cf24452de7391cce780bd71521da44ce23923ebb235f6c7962c`).
+
+It is ONE explicit program (numbered registers, every addition, every frame) for the helper circuit at
+h = 22: 1,320 ports, 9,412 slots, 262,944 unit moves. **The design of that circuit is not this project's.** It is the
+"paired-cube" circuit of the outside repository as of pull request #193 (which builds on #191, #184, #168 and #144).
+The outside repository publishes the design as generator scripts, frozen data files and a ledger; it has no file
+of this kind. This file was produced by this project's own code, which
+
+1. loaded the following files of the outside repository **as data** (JSON; nothing was executed):
+   - at pull request #168, commit `4a3c769e5c5430e7114c4d3e099ff34664677f17`:
+     `references/paired-cube/sources/local_L1.json`,
+     `references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json`,
+     `references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json`,
+     `references/paired-cube/sources/qmod_climb3u_best.json` (the local modules),
+     `references/paired-cube/selected-module/matching-arcs.json` (carrier arcs),
+     `references/paired-cube/physical/frames.json` (moved frames);
+   - at pull request #193, commit `187e1010ac8b259af8e9b5166f68b64bc27b4b47`:
+     `research/source-assisted-v4/data/physical-pairs.json` (the hand-over pairs);
+2. rebuilt the circuit from them step by step, following the algorithms of the outside scripts (read as text),
+   and checked the result exactly (every published count reproduced; the scalar identity as an identity of
+   linear maps with arbitrary contents of the helper registers);
+3. converted it to gcert/1 with `gxconv.py` (tested by `gx.check1`).
+
+Step 1 and step 2 (the rebuild scripts and the outside inputs they read) are NOT part of this repository;
+the inputs can be fetched from the outside repository at the two commits above.
+What this repository proves about the file does not depend on how it was made: the Lean kernel checks the
+generated modules (labels, scalar identity, price), and `regen_check.py` shows that those modules are exactly
+what `gxgen.py` / `gxrate.py` produce from this file.
+
+## Check it yourself
+
+    python3 tools/gx/regen_check.py                       # regenerates the Lean modules and compares
+    python3 tools/gx/gxdry.py tools/certificate/gcert1-p11-pr193.json.gz      # Python mirror of both checks
+    python3 tools/gx/refcheck.py                          # the reference checker gx.check1 on the certificate
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py
new file mode 100644
index 0000000000..fcb625619c
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxbind.py
@@ -0,0 +1,438 @@
+"""gxbind.py: THE BINDING of the generator to the Lean terms of gx-scalar / gx-labels /
+gx-chain.  Everything that names somebody else's definition is in this file (tables SCAL, LAB, CHAIN)."""
+import os, re, subprocess
+import gxpaths
+ROOT = gxpaths.OUT
+GSM = gxpaths.HERE + '/gsmirror.py'
+
+# gx-scalar (gcert-interface.md, SCALAR v1): GS.scalCheck c p lo n, GS.yCheck c p lo n, p : GS.SPar = <d, sw, ux, us, uy>
+SCAL = dict(imports=['Work.GCert.Scalar.Seg'], scal='GS.scalCheck raw ⟨%(d)d, %(sw)d, %(ux)d, %(us)d, %(uy)d⟩ %(lo)d %(n)d',
+            ychk='GS.yCheck raw ⟨%(d)d, %(sw)d, %(ux)d, %(us)d, %(uy)d⟩ 0 %(v)d')
+# gx-labels (gcert-interface.md LABELS v1 + questions.md N1): namespace GLab; frame = code, table and states = SSC.Trie,
+# GLab.Par = <h, n, d, K, tab>.  `end` = GLab.endK of Labels/EndDef.lean (questions.md N2; no obaseK: Q1 closed).
+LAB = dict(imports=['Work.GCert.Labels.Def'], end_imports=['Work.GCert.Labels.EndDef'], par='⟨%(h)d, %(n)d, %(d)d, %(K)d, tab⟩', ns='GLab',
+           tab='GLab.tabK %(h)d %(sub)s', seg='GLab.segK par %(gs)s st%(i)d st%(j)d %(rs)s',
+           end='GLab.endK par %(v)d ports (raw.ret.map Prod.fst) st0 st%(a)d st%(f)d', noadds='GLab.noAdds fins')
+# gx-chain (CHAIN v1): GX.wht_of_halves; the terms below are PLACEHOLDERS until Labels/Main and Scalar/Main compile
+CHAIN = dict(imports=['Work.GCert.Chain.End', 'Work.GCert.Labels.Main'], scal='(GS.ScalOK.scal GXD.%(c)s.scalOK)',
+             lab='(GXD.%(c)s.valid.lab GXD.%(c)s.scalOK)', lab_cost='GXD.%(c)s.lab_cost')
+
+
+def code(h, basis):
+    """gx-labels' code of a reduced echelon basis: dim + 2^8 M + 2^(8+h) P (M = pivot mask, vector of pivot p at digit p)"""
+    M = P = 0
+    for b in basis:
+        p = b.bit_length() - 1
+        M |= 1 << p
+        P |= b << (h * p)
+    return len(basis) + (M << 8) + (P << (8 + h))
+
+
+MOD = '''import %(imports)s
+/-! Kernel check (%(doc)s) of the gcert/1 certificate `GXD.%(name)s.raw`.  Source: %(src)s.
+Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/
+set_option maxRecDepth 100000
+namespace GXD.%(name)s
+open GXD
+theorem %(thm)s : %(stmt)s := by decide +kernel
+end GXD.%(name)s
+#print axioms GXD.%(name)s.%(thm)s
+'''
+
+
+def spar(D, path):
+    """scalar parameters: from gx-scalar's mirror when it exists, else from my own replay (sw is then a GUESS)"""
+    import gxcore as gc
+    n, d = 2 * D['v'] + D['R'], 0
+    while (1 << d) < n:
+        d += 1
+    dg = gc.digits(D)
+    S = dict(d=d, sw=16, ux=dg['x'][0], us=dg['s'][0], uy=dg['y'][0], source='gx-data replay; sw = 16 is a GUESS', digits=dg)
+    if os.path.exists(GSM):
+        try:
+            o = subprocess.run(['python3', '-B', GSM, path], capture_output=True, text=True, timeout=1800).stdout
+            m = re.search(r'SPar[^\d]*(\d+)[, ]+(\d+)[, ]+(\d+)[, ]+(\d+)[, ]+(\d+)', o)
+            if m:
+                S.update(zip(('d', 'sw', 'ux', 'us', 'uy'), map(int, m.groups())), source='gsmirror.py')
+        except Exception as e:
+            S['source'] += ' (gsmirror.py failed: %r)' % (e,)
+    return S
+
+
+def write_checks(D, M, name, src, out, L, S, plan):
+    base = out[len(ROOT):].replace('/', '.')
+    raw = '%s.Gen.%s' % (base, name)
+    h, v, n = D['h'], D['v'], 2 * D['v'] + D['R']
+    res = []
+
+    def mod(suffix, imports, thm, stmt, doc):
+        m = '%s.Gen.%s%s' % (base, name, suffix)
+        open('%s/Gen/%s%s.lean' % (out, name, suffix), 'w').write(MOD % dict(
+            imports='\nimport '.join(imports), doc=doc, name=name, src=src, thm=thm, stmt=stmt))
+        res.append((m, thm, stmt))
+    for i, (lo, hi) in enumerate(M['scal']['batches']):
+        mod('Scal%d' % i, SCAL['imports'] + [raw], 'scal%d_ok' % i, SCAL['scal'] % dict(S, lo=lo, n=hi - lo) + ' = true',
+            'scalar identity E3 E5 for the sources %d .. %d' % (lo, hi - 1))
+    mod('YChk', SCAL['imports'] + [raw], 'ychk_ok', SCAL['ychk'] % dict(S, v=v) + ' = true', 'the y -> y adds, E4')
+    par = '%s.Gen.%sPar' % (base, name)
+    open('%s/Gen/%sPar.lean' % (out, name), 'w').write(
+        'import %s\nimport %s\n/-! Parameters `GLab.Par` of the label check of `GXD.%s.raw` (h, registers, trie depth, K, frame table).\n'
+        'Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/\nnamespace GXD.%s\nopen GXD\n'
+        'noncomputable def par : GLab.Par := %s\nend GXD.%s\n'
+        % (LAB['imports'][0], raw, name, name, LAB['par'] % dict(h=h, n=n, d=L['d'], K=L['K']), name))
+    paths = [format(i, '0%db' % L['ts']) for i in range(1 << L['ts'])] if L['ts'] else ['']
+    for i, pth in enumerate(paths):
+        mod('Tab%d' % i, LAB['imports'] + [raw], 'tab%d_ok' % i,
+            LAB['tab'] % dict(h=h, sub='tab_n' + pth if pth else 'tab') + ' = true',
+            'E0: subtrie %d of %d of the frame table (codes of reduced echelon bases)' % (i, len(paths)))
+    for i in range(L['nseg']):
+        mod('Seg%d' % i, [par], 'seg%d_ok' % i,
+            LAB['seg'] % dict(gs='seg%d' % i, i=i, j=i + 1, rs='rs%d' % i) + ' = true',
+            'E1: replay of the gates %d .. %d (phase %s) and their block ranks' % (
+                M['cuts'][i], M['cuts'][i + 1] - 1, 'A' if i < L['nsegA'] else 'B'))
+    mod('SegF', [par], 'segF_ok', LAB['seg'] % dict(gs='fins', i=L['nseg'], j=L['nseg'] + 1, rs='rF') + ' = true',
+        'E1: the final climbs and their block ranks')
+    if LAB['end']:
+        mod('End', LAB['end_imports'] + [par], 'end_ok', LAB['end'] % dict(v=v, a=L['nsegA'], f=L['nseg'] + 1) + ' = true',
+            'E1 E2: frames at the start, at the scatter, at the end')
+    return res
+
+
+def nest(xs):
+    return ' ++ ('.join(xs) + ')' * (len(xs) - 1) if xs else '[]'
+
+
+def write_hist(D, M, name, src, out, L):
+    """kernel counts of the block ranks on the EXPLICIT rank lists rA, rB, rF (no replay)"""
+    base = out[len(ROOT):].replace('/', '.')
+    h, rs = D['h'], M['lab']['rs']
+    ph = {'A': sum(rs[:L['nsegA']], []), 'B': sum(rs[L['nsegA']:], []), 'F': M['lab']['rF']}
+    top = max(max(x) if x else 0 for x in ph.values())
+    cop = [M['dim'][f] for _, f in D['ret']]
+    tot = {r: sum(x.count(r) for x in ph.values()) + cop.count(r) for r in range(1, max(top, max(cop)) + 1)}
+    assert {r: c for r, c in tot.items() if c} == M['hist'], 'histogram of the rank lists differs from the mirror'
+    lines = ['/-- block ranks of phase A / phase B, in order (the lists of the replay segments) -/',
+             'noncomputable def rA : List Nat := ' + nest(['rs%d' % i for i in range(L['nsegA'])]),
+             'noncomputable def rB : List Nat := ' + nest(['rs%d' % i for i in range(L['nsegA'], L['nseg'])])]
+    names = []
+    for X, lst in sorted(ph.items()):
+        l = 'r' + X
+        lines.append('theorem rankBound%s : wsumK (SSC.wGt %d) %s 0 = 0 := by decide +kernel' % (X, top, l))
+        lines += ['theorem rank%s%d_ok : wsumK (SSC.wEq %d) %s 0 = %d := by decide +kernel' % (X, r, r, l, lst.count(r))
+                  for r in range(top + 1)]
+        names += ['rankBound' + X] + ['rank%s%d_ok' % (X, r) for r in range(top + 1)]
+    txt = ('import Work.GCert.Data.Count\nimport %s.Gen.%s\n' % (base, name) +
+           '/-! Kernel count of the BLOCK RANKS of the gcert/1 certificate `GXD.%s.raw` (h = %d) on the explicit rank lists\n'
+           '`rA`, `rB`, `rF` (phase A, phase B, final climbs): `wsumK (SSC.wEq r) l 0` blocks of rank `r`, none above %d\n'
+           '(`GXD.sum_of_wsumK` turns a count into `(l.map wt).sum` = `SSC.wsum wt l`).\n'
+           'The %d scratch copies (ranks %s) are not in these lists.  Whole invocation, by rank: %s.\n'
+           'Source: %s.  Generated by checks/wht26/gx-data/py/gxgen.py (do not edit). -/\n'
+           'set_option maxRecDepth 100000\nnamespace GXD.%s\nopen GXD\n' % (
+               name, h, top, len(cop), sorted(set(cop)), M['hist'], src, name) + '\n'.join(lines) +
+           '\nend GXD.%s\n' % name + '\n'.join('#print axioms GXD.%s.%s' % (name, x) for x in names[:2]) + '\n')
+    open('%s/Gen/%sHist.lean' % (out, name), 'w').write(txt)
+    return '%s.Gen.%sHist' % (base, name)
+
+
+def write_price(D, M, name, src, out, L):
+    """Mathlib module: the price of the rank lists rA, rB, rF from the kernel counts, and of one whole invocation"""
+    base = out[len(ROOT):].replace('/', '.')
+    rs = M['lab']['rs']
+    ph = {'A': sum(rs[:L['nsegA']], []), 'B': sum(rs[L['nsegA']:], []), 'F': M['lab']['rF']}
+    top = max(max(x) if x else 0 for x in ph.values())
+    cop = [M['dim'][f] for _, f in D['ret']]
+    tm = lambda cnt: ' + '.join('%d * φ %d' % (n, r) for r, n in sorted(cnt.items()) if n) or '0'
+    thms = ''
+    for X in 'ABF':
+        cnt = {r: ph[X].count(r) for r in range(1, top + 1)}
+        thms += '''
+/-- price of the blocks of %s, from the kernel counts -/
+theorem r%s_cost (φ : ℕ → ℝ) : rcost φ r%s = %s := by
+  rw [GXD.rcost_wsumK φ r%s %d rankBound%s]
+  simp only [Finset.sum_range_succ, Finset.sum_range_zero, %s]
+  norm_num [bcost]
+''' % ({'A': 'phase A', 'B': 'phase B', 'F': 'the final climbs'}[X], X, X, tm(cnt), X, top, X,
+       ', '.join('rank%s%d_ok' % (X, r) for r in range(top + 1)))
+    copies = tm({r: cop.count(r) for r in set(cop)})
+    txt = '''import Work.GCert.Data.Price
+import %(base)s.Gen.%(name)sHist
+
+/-!
+# (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): the price of one invocation
+
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+`rA_cost`, `rB_cost`, `rF_cost`: the price of the block rank lists of phase A, phase B and the final climbs
+(lists `GXD.%(name)s.rA / rB / rF`, counted by the kernel in `Gen.%(name)sHist`);
+`inv_cost`: with the %(nc)d scratch copies (%(copies)s) the blocks of ONE invocation cost
+`invPrice φ` = %(terms)s;  `inv_moves`: they stand for `R h + 2 v (h - 1) + cst = %(N)d` unit moves.
+-/
+
+namespace GXD.%(name)s
+open GXD OAI.PowerSaving.CB
+%(thms)s
+/-- price of the blocks of ONE invocation (x roles, y roles, slots, scratch copies), by rank -/
+def invPrice (φ : ℕ → ℝ) : ℝ := %(terms)s
+
+/-- **Price of ONE invocation** in the shape of `GX.Lab.cost`: phase A, the scratch copies, phase B, final climbs. -/
+theorem inv_cost (φ : ℕ → ℝ) : rcost φ rA + (%(copies)s) + rcost φ rB + rcost φ rF = invPrice φ := by
+  rw [rA_cost, rB_cost, rF_cost]
+  unfold invPrice
+  ring
+
+theorem inv_moves : invPrice (fun r => (r:ℝ)) = %(R)d * %(h)d + 2 * %(v)d * (%(h)d - 1) + %(cst)d := by
+  unfold invPrice
+  norm_num
+
+theorem inv_count : invPrice (fun _ => (1:ℝ)) = %(count)d := by
+  unfold invPrice
+  norm_num
+
+end GXD.%(name)s
+#print axioms GXD.%(name)s.inv_cost
+#print axioms GXD.%(name)s.inv_moves
+''' % dict(base=base, name=name, h=D['h'], src=src, nc=len(cop), copies=copies, terms=tm(M['hist']), N=D['N'], thms=thms,
+           R=D['R'], v=D['v'], cst=D['cst'], count=sum(M['hist'].values()))
+    open('%s/%sPrice.lean' % (out, name), 'w').write(txt)
+    return '%s.%sPrice' % (base, name)
+
+
+def write_cert(D, M, name, src, out, chk, L):
+    """<Name>Cert: THE LABEL HALF (aux, valid : GLab.Valid raw aux, lab_cost, lab_price) -- compiles without the scalar half;
+    <Name>ScalOK: the scalar half `scalOK : GS.ScalOK raw` (needs Work/GCert/Scalar/Main)."""
+    base = out[len(ROOT):].replace('/', '.')
+    bs = M['scal']['batches']
+    hs = ''
+    for i, (lo, hi) in enumerate(bs):
+        lo_pf = 'Nat.zero_le t' if i == 0 else 'Nat.le_of_not_lt h%d' % (i - 1)
+        if i + 1 < len(bs):
+            hs += '    if h%d : t < %d then ⟨%d, %d, %s, h%d, GS.XRun.of_check scal%d_ok⟩ else\n' % (i, hi, lo, hi - lo, lo_pf, i, i)
+        else:
+            hs += '    ⟨%d, %d, %s, Nat.lt_of_lt_of_le ht (by decide), GS.XRun.of_check scal%d_ok⟩' % (lo, hi - lo, lo_pf, i)
+    terms = ' + '.join('%d * φ %d' % (n, r) for r, n in M['hist'].items())
+    info = dict(base=base, name=name, h=D['h'], src=src, v=D['v'], R=D['R'], nc=len(D['ret']), cst=D['cst'], N=D['N'],
+                nb=len(bs), terms=terms, hs=hs)
+    txt = '''import Work.GCert.Scalar.Main
+import %(imps)s
+/-! # (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): THE SCALAR HALF `scalOK : GS.ScalOK raw`
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+Kernel checks `scal<i>_ok` (%(nb)d source batches) and `ychk_ok`. -/
+namespace GXD.%(name)s
+open GXD
+theorem scalOK : GS.ScalOK raw where
+  hv := by decide
+  hs := fun t ht =>
+%(hs)s
+  hyc := fun t ht => ⟨0, %(v)d, Nat.zero_le t, Nat.lt_of_lt_of_le ht (by decide), GS.YRun.of_check ychk_ok⟩
+end GXD.%(name)s
+#print axioms GXD.%(name)s.scalOK
+''' % dict(info, imps='\nimport '.join(c[0] for c in chk if 'Scal' in c[0] or 'YChk' in c[0]))
+    open('%s/%sScalOK.lean' % (out, name), 'w').write(txt)
+    # ---- the label half
+    nA, ns, ts = L['nsegA'], L['nseg'], L['ts']
+    cop = sorted(set(M['dim'][f] for _, f in D['ret']))
+    assert len(cop) == 1, 'scratch copies of several ranks %s: lab_cost of gxbind.py assumes one' % cop
+
+    def tabpf(path):
+        if len(path) == ts:
+            return 'tab%d_ok' % (int(path, 2) if path else 0)
+        return '(GLab.tabK_node _ _ _ %s %s)' % (tabpf(path + '0'), tabpf(path + '1'))
+
+    def runpf(a, b):
+        return 'GLab.Run.of_seg seg%d_ok' % a if a + 1 == b else 'GLab.Run.append (GLab.Run.of_seg seg%d_ok) (%s)' % (a, runpf(a + 1, b))
+
+    def run(X, a, b):
+        segs = ['seg%d' % i for i in range(a, b)]
+        return '''theorem gates%(X)s_eq : raw.gates%(X)s = %(cat)s := by
+  show List.flatten %(lst)s = _
+  simp only [List.flatten_cons, List.flatten_nil, List.append_nil]
+/-- the replay of phase %(X)s, composed from its kernel-checked segments -/
+theorem run%(X)s : GLab.Run par st%(a)d raw.gates%(X)s st%(b)d r%(X)s := by
+  rw [gates%(X)s_eq]
+  exact %(pf)s
+''' % dict(X=X, cat=nest(segs), lst=ll_(segs), a=a, b=b, pf=runpf(a, b))
+    lab = 'valid.lab S Ro cf hMA hMAi hMB hMBi reg hCc hreg'
+    txt = '''import Work.GCert.Labels.Main
+import %(base)s.%(name)sPrice
+import %(imps)s
+/-! # (key: gx-data) gcert/1 certificate `%(name)s` (h = %(h)d): THE LABEL HALF and its price
+GENERATED by checks/wht26/gx-data/py/gxgen.py from %(src)s.  No `sorry`.
+`v = %(v)d` ports, `R = %(R)d` slots, %(nc)d scratch copies of rank %(c)d, copy cost `cst = %(cst)d`, `N = %(N)d` unit moves.
+* `aux : GLab.Aux`, `valid : GLab.Valid raw aux`: frame table (`tab<i>_ok` composed by `tabK_node`), the replays of phase A
+  and phase B (`seg<i>_ok` composed by `Run.append`), the final climbs (`segF_ok`, `fin_ok`), the ends (`end_ok`);
+* `lab_cost`, `lab_price`: for ANY scalar half `S` the label half `valid.lab S ..` costs
+  `rcost rA + card C * bcost %(c)d + rcost rB + rcost rF` = `invPrice φ` = %(terms)s
+  (`Gen.%(name)sHist`, `%(name)sPrice`) when there are %(nc)d copies. -/
+set_option maxRecDepth 100000
+namespace GXD.%(name)s
+open GXD OAI.PowerSaving OAI.PowerSaving.CB
+theorem raw_h : raw.h = %(h)d := rfl
+theorem raw_v : raw.v = %(v)d := rfl
+theorem raw_R : raw.R = %(R)d := rfl
+/-- what the label checks read next to `raw` -/
+noncomputable def aux : GLab.Aux := ⟨par, st0, st%(a)d, st%(n)d, st%(f)d, fins, rA, rB, rF⟩
+theorem fin_ok : GLab.noAdds fins = true := by decide +kernel
+theorem cen_ok : (raw.ret.map Prod.fst).all (fun r => Nat.beq (GLab.cdim (par.tab.get (st%(a)d.get r))) %(c)d) = true := by
+  decide +kernel
+theorem tab_ok : GLab.tabK par.h par.tab = true := %(tabpf)s
+%(runA)s%(runB)s/-- **the kernel-checked label facts** of the certificate -/
+theorem valid : GLab.Valid raw aux where
+  hn := rfl
+  tab := tab_ok
+  runA := runA
+  runB := runB
+  runF := GLab.Run.of_seg segF_ok
+  fin := fin_ok
+  ends := end_ok
+theorem cen_dim (r : Nat) (hr : r ∈ raw.ret.map Prod.fst) : GLab.cdim (par.tab.get (st%(a)d.get r)) = %(c)d :=
+  Nat.eq_of_beq_eq_true (List.all_eq_true.mp cen_ok r hr)
+/-- price of the label half over ANY scalar half -/
+theorem lab_cost {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (φ : ℕ → ℝ) :
+    (%(lab)s).cost φ
+      = rcost φ rA + (Fintype.card C : ℝ) * bcost φ %(c)d + rcost φ rB + rcost φ rF := by
+  obtain ⟨h1, h2, h3, h4⟩ := valid.lab_ranks S Ro cf hMA hMAi hMB hMBi reg hCc hreg
+  have h5 : ∀ k, bcost φ (((%(lab)s).cen k).dim) = bcost φ %(c)d :=
+    fun k => by rw [h4 k]; exact congrArg (bcost φ) (cen_dim _ (hreg k))
+  rw [GX.Lab.cost, h1, h2, h3, Finset.sum_congr rfl (fun k _ => h5 k), Finset.sum_const, Finset.card_univ, nsmul_eq_mul]
+  rfl
+/-- **the label half costs one invocation price** (`invPrice`, by rank, from the kernel counts) -/
+theorem lab_price {C : Type} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin raw.v) (Fin raw.R) C)
+    {emb : CR.L3 (Fin raw.v) (Fin raw.R) → Nat} {un : Nat → CR.L3 (Fin raw.v) (Fin raw.R)}
+    (Ro : GLab.Roles raw.v raw.R emb un) (cf : Co → SSC.Coef) (hMA) (hMAi) (hMB) (hMBi)
+    (reg : C → Nat) (hCc) (hreg) (hC : Fintype.card C = %(nc)d) (φ : ℕ → ℝ) :
+    (%(lab)s).cost φ = invPrice φ := by
+  rw [lab_cost S Ro cf hMA hMAi hMB hMBi reg hCc hreg φ, hC, ← inv_cost φ]
+  norm_num [bcost]
+end GXD.%(name)s
+#print axioms GXD.%(name)s.valid
+#print axioms GXD.%(name)s.lab_price
+''' % dict(info, imps='\nimport '.join(c[0] for c in chk if 'Scal' not in c[0] and 'YChk' not in c[0]), c=cop[0], a=nA, n=ns,
+           f=ns + 1, tabpf=tabpf(''), runA=run('A', 0, nA), runB=run('B', nA, ns), lab=lab)
+    open('%s/%sCert.lean' % (out, name), 'w').write(txt)
+    return ['%s.%sCert' % (base, name), '%s.%sScalOK' % (base, name)]
+
+
+def ll_(xs):
+    return '[' + ', '.join(xs) + ']'
+
+
+def final_module(name, cname, d, dx, g, out):
+    """<Inst>.lean: the final theorems OVER ANY SCALAR HALF (compiles as soon as <C>Cert does): label half, price,
+    unit list, rate fact and gx-chain's `GX.wht_of_halves` are all closed; what is left is `S : GX.Scal` with its
+    gate matrices = the ordered products of the adds of `raw` (gx-scalar)."""
+    h, v, R, W, m, nc = g['h'], g['v'], g['R'], d['W'], d['m'], g['nc']
+    X = 'GXD.%s' % cname
+    args = 'S Ro cf hMA hMAi hMB hMBi reg hCc hreg'
+
+    def thm(nm, rate, A, B, s, ux):
+        return f'''
+/-- **Walsh-Hadamard transform, whole-block recursion on the bridged word B_2 with the gcert/1 circuit `{cname}`**,
+over any scalar half of `{X}.raw`: the statement `WHTGoal` of `WHTCheck/Challenge.lean` with `1 - 2/10^11`
+replaced by `1 - {A}/10^{B}`. -/
+theorem {nm} (Ro : GLab.Roles {X}.raw.v {X}.raw.R emb un)
+    (hMA : S.MA = SSC.matP un (GLab.mic cf ({X}.raw.gatesA.flatMap GXD.Gate.adds)))
+    (hMAi : S.MAi = SSC.matPinv un (GLab.mic cf ({X}.raw.gatesA.flatMap GXD.Gate.adds)))
+    (hMB : S.MB = SSC.matP un (GLab.mic cf ({X}.raw.gatesB.flatMap GXD.Gate.adds)))
+    (hMBi : S.MBi = SSC.matPinv un (GLab.mic cf ({X}.raw.gatesB.flatMap GXD.Gate.adds)))
+    (reg : C → Nat) (hCc : ∀ k (q : Fin {X}.raw.R), S.Cc k q ≠ 0 → reg k = 2 * {X}.raw.v + q.val)
+    (hreg : ∀ k, reg k ∈ {X}.raw.ret.map Prod.fst) (hC : Fintype.card C = {nc}) :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  GX.wht_of_halves S ({X}.valid.lab {args})
+    (by rw [Fintype.card_fin]; decide) {m} {W} (by rw [Fintype.card_fin]; rfl)
+    (by rw [Fintype.card_fin, Fintype.card_fin]; rfl) (by norm_num) BlockAccounting.blocks{rate}
+    (fun φ => by
+      rw [{X}.lab_price {args} hC φ, Fintype.card_fin, Fintype.card_fin]
+      exact BridgeRate.{name}.unit_cost{ux} φ)
+    {s} (1 - {A}/(10:ℝ)^{B}) (by norm_num) (by norm_num) BlockAccounting.fold_{rate}
+
+/-- the same from the FIVE scalar identities of gx-scalar's matrices of `{X}.raw` (`Work/GCert/Data/Glue.lean`) -/
+theorem {nm.replace('_of_scal', '_of_ids')} (hv : 0 < {X}.raw.v)
+    (hAi : GS.MAi {X}.raw hv * GS.MA {X}.raw hv = 1) (hBi : GS.MBi {X}.raw hv * GS.MB {X}.raw hv = 1)
+    (hx : ∀ (t : Fin {X}.raw.v) (j : GS.Rl {X}.raw), (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) (CR.lX t) j = if CR.lX t = j then 1 else 0)
+    (hy : ∀ (i : GS.Rl {X}.raw) (t : Fin {X}.raw.v), (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) i (CR.lY t) = if i = CR.lY t then 1 else 0)
+    (hid : ∀ S t : Fin {X}.raw.v, (GS.MB {X}.raw hv * CR.scatM (GS.Jrm {X}.raw * GS.Ccm {X}.raw)
+      * GS.MA {X}.raw hv) (CR.lY S) (CR.lX t) = if S = t then 1 else 0) :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  {nm} (GXD.scalOf {X}.raw hv hAi hBi hx hy hid) GS.toCoef (GXD.roles {X}.raw hv)
+    (GXD.scalOf_MA _ hv hAi hBi hx hy hid) (GXD.scalOf_MAi _ hv hAi hBi hx hy hid)
+    (GXD.scalOf_MB _ hv hAi hBi hx hy hid) (GXD.scalOf_MBi _ hv hAi hBi hx hy hid)
+    (GXD.reg {X}.raw) (GXD.reg_slot {X}.raw hv hAi hBi hx hy hid) (GXD.reg_mem {X}.raw)
+    (by rw [Fintype.card_fin]; decide)
+'''
+    txt = f'''import Work.GCert.Chain.End
+import Work.GCert.Data.Glue
+import Work.GCert.Data.{cname}Cert
+import Work.GCert.Data.Inst{name}
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `{cname}` (h = {h}, m = {m}): final theorems over a scalar half
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`GX.wht_of_halves` (gx-chain) on the label half `{X}.valid` (kernel checks of `Work/GCert/Data/Gen/{cname}*`), its
+price `{X}.lab_price`, the unit list `BlockAccounting.blocks{name}` (`W = {W}` live roles) and the rate facts
+`fold_{name}` (`1 - {d['A']}/10^{d['B']}`), `fold_{name}x` (`1 - {dx['A']}/10^{dx['B']}`).
+The ONLY hypothesis left is the scalar half: `S : GX.Scal (Fin {v}) (Fin {R}) C` whose gate matrices are the ordered
+products of the adds of `raw` (`hMA .. hMBi`), with `{nc}` copies read from the retained registers (`reg`, `hCc`, `hreg`, `hC`);
+`wht_{name}_of_ids`, `wht_{name}x_of_ids`: the same from the five identities `hAi hBi hx hy hid` of gx-scalar's matrices
+`GS.MA GS.MAi GS.MB GS.MBi GS.Jrm GS.Ccm` of `raw` (the fields of the planned `GS.ScalOK`).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+
+variable {{C : Type}} [Fintype C] [DecidableEq C] (S : GX.Scal (Fin {X}.raw.v) (Fin {X}.raw.R) C)
+  {{emb : CR.L3 (Fin {X}.raw.v) (Fin {X}.raw.R) → Nat}} {{un : Nat → CR.L3 (Fin {X}.raw.v) (Fin {X}.raw.R)}}
+  (cf : GXD.Co → SSC.Coef)
+''' + thm('wht_' + name + '_of_scal', name, d['A'], d['B'], d['s'], '') + thm('wht_' + name + 'x_of_scal', name + 'x', dx['A'], dx['B'], dx['s'], '_x') + f'''
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_{name}_of_scal
+#print axioms OAI.PowerSaving.WHT.wht_{name}x_of_scal
+#print axioms OAI.PowerSaving.WHT.wht_{name}_of_ids
+#print axioms OAI.PowerSaving.WHT.wht_{name}x_of_ids
+'''
+    open(out + '%s.lean' % name, 'w').write(txt)
+
+
+def main_module(name, cname, d, dx, out):
+    """<Inst>Main.lean: the CLOSED theorems (what the comparator solution cites).  WRITTEN against gx-scalar's planned
+    `GS.ScalOK` (fields / theorems hv hAi hBi hx hy hid, SCALAR v2); compiles when Work/GCert/Scalar/Main.lean exists."""
+    K = 'GXD.%s.scalOK' % cname
+
+    def thm(sfx, A, B):
+        return f'''
+/-- **Walsh-Hadamard transform in `O(n (log n)^(1 - {A}/10^{B}))`-type time bounds: whole-block recursion on the bridged
+word B_2 with the kernel-checked gcert/1 circuit `{cname}`.** -/
+theorem wht_main_{name}{sfx} :
+    ∃ solve W, WHTProgram solve W ∧ BlockWHT.WHTTimeBoundsAt (1 - {A}/(10:ℝ)^{B}) W :=
+  wht_{name}{sfx}_of_ids {K}.hv {K}.hAi {K}.hBi {K}.hx {K}.hy {K}.hid
+'''
+    txt = f'''import Work.GCert.Scalar.Main
+import Work.GCert.Data.{cname}ScalOK
+import Work.GCert.Data.{name}
+
+/-!
+# (key: gx-data) Bridged word B_2 with the gcert/1 circuit `{cname}`: THE CLOSED THEOREMS
+GENERATED by checks/wht26/gx-data/py/gxrate.py.  No `sorry`.
+`wht_{name}_of_ids` (label half, price, unit list, rate fact, gx-chain's end theorem) applied to the scalar half
+`{K} : GS.ScalOK GXD.{cname}.raw` (kernel checks `scal<i>_ok`, `ychk_ok`; soundness: gx-scalar).
+-/
+
+namespace OAI
+namespace PowerSaving
+namespace WHT
+open BlockWHT
+''' + thm('', d['A'], d['B']) + thm('x', dx['A'], dx['B']) + f'''
+end WHT
+end PowerSaving
+end OAI
+#print axioms OAI.PowerSaving.WHT.wht_main_{name}
+#print axioms OAI.PowerSaving.WHT.wht_main_{name}x
+'''
+    open(out + '%sMain.lean' % name, 'w').write(txt)
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py
new file mode 100644
index 0000000000..49ebb65973
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxconv.py
@@ -0,0 +1,131 @@
+"""gxconv.py: gcert/0 -> gcert/1 for files whose in-place pair op SCALES its target
+(`op dest ctrl ca cb`: dest := ca dest + cb ctrl with ca not in {1}; #193 has ca = -2), questions.md D2.
+COPY of `convert` of gx.py with ONE change: a scaling is not a gate, it changes the
+UNIT in which the register is stored.  wanted(r) = lam[r] * stored(r), lam = 1 at the start;
+    op dest ctrl ca cb :  lam[dest] *= ca ;  stored(dest) += (cb lam[ctrl] / lam[dest]) stored(ctrl)
+    any other add t += k s :  stored(t) += (k lam[s] / lam[t]) stored(s)
+    scatter y_t += coef(t, k) total_k :  coefficient coef(t, k) * lam[slot of total k]   (a TABLE if some lam != 1)
+Only slots may be scaled (tested: lam = 1 on every x and y register, always), so the x / y rows and columns of
+the product (E5: hx, hy, hid) are those of the unscaled circuit; frames, blocks and N are untouched.
+The result is tested by the reference checker `gx.check1` (labels and scalars) before it is written.
+
+usage: gxconv.py <gcert0.json[.gz]> out=<gcert1.json[.gz]> [noext]
+"""
+import sys, time
+from fractions import Fraction as Fr
+import gxpaths
+import gx
+import gxrun
+need = gx.need
+
+
+def convert(c0):
+    need(c0["format"] == "gcert/0", "input is not gcert/0")
+    v, h, R = c0["v"], c0["h"], c0["R"]
+    ev = c0["events"]
+    cen = [n for n, e in enumerate(ev) if e[0] == "centre"]
+    need(cen == list(range(cen[0], cen[0] + len(cen))), "centres are not contiguous: no single scatter cut")
+    A, B, ret = [], [], []
+    neg, openq, lam, nsc = set(), {}, {}, 0
+    L = lambda r: lam.get(r, Fr(1))
+
+    def co(t, s, a, b=1):                       # stored coefficient of the wanted add t += (a/b) s
+        w = Fr(a, b) * L(s) / L(t)
+        return [w.numerator, w.denominator]
+
+    def o(f, s, tg, ex=()):
+        return ["out", f, s, [[t] + co(t, s, a, b) for t, a, b in tg], list(ex)]
+
+    def i(f, t, sr):
+        return ["in", f, t, [[s] + co(t, s, a, b) for s, a, b in sr]]
+    scat_lam = None
+    for n, e in enumerate(ev):
+        k = e[0]
+        out = A if n < cen[0] else B
+        if k in ("read0", "undo", "uninj"):
+            continue
+        if k == "inj":
+            need(e[2] not in neg, "inj reads a negated x register")
+            out.append(o(e[3], e[2], [[e[1], 1, 1]]))
+        elif k == "op":
+            if e[3] != 1:
+                need(e[3] != 0 and e[1] >= 2 * v, "op scales a register that is not a slot (or by 0)")
+                lam[e[1]] = L(e[1]) * e[3]
+                nsc += 1
+            out.append(o(e[5], e[2], [[e[1], e[4], 1]]))
+        elif k == "centre":
+            ret.append([e[2], e[1], e[3]])
+            if scat_lam is None:
+                scat_lam = dict(lam)
+        elif k == "gread":
+            hit = set(t for t, _, _ in e[3])
+            out.append(o(e[2], e[1], [[v + t, a, b] for t, a, b in e[3]], [v + t for t in e[4] if t not in hit]))
+        elif k == "rread":
+            out.append(o(e[2], e[1], [[v + t, a, b] for t, a, b in e[3]]))
+        elif k == "ysh":
+            out.append(o(e[4], e[2], [[e[1], e[3], 1]]))
+        elif k == "yw":
+            out.append(o(e[4], e[2], [[e[1], e[3][0], e[3][1]]]))
+        elif k == "kd":
+            out.append(o(e[3], e[2], [[e[1], -1 if e[2] in neg else 1, 1]]))
+        elif k == "ktr":
+            q = tuple(e[1])
+            need(e[2] == gx.KJ, "ktr matrix is not 1 - J/2")
+            x1, rest = q[0], list(q[1:])
+            if q not in openq:
+                out.append(i(e[3], x1, [[r, 1, 1] for r in rest]))
+                out.append(o(e[3], x1, [[r, -1, 2] for r in rest]))
+                out.append(i(e[3], x1, [[r, 1, 1] for r in rest]))
+                openq[q] = n
+                neg.add(x1)
+            else:
+                out.append(i(e[3], x1, [[r, -1, 1] for r in rest]))
+                out.append(o(e[3], x1, [[r, 1, 2] for r in rest]))
+                out.append(i(e[3], x1, [[r, -1, 1] for r in rest]))
+                del openq[q]
+                neg.discard(x1)
+        else:
+            raise AssertionError("unknown event kind %r" % k)
+        need(all(r >= 2 * v for r, x in lam.items() if x != 1), "an x or y register is scaled")
+    need(not openq and not neg, "a K block is not closed")
+    ret = sorted(ret)
+    need([z[0] for z in ret] == list(range(len(ret))), "retained totals are not 0 .. n-1")
+    sin, sout = Fr(*c0["scat"]["inside"]), Fr(*c0["scat"]["outside"])
+    sl = [(scat_lam or {}).get(z[1], Fr(1)) for z in ret]
+    if all(x == 1 for x in sl):
+        scat = dict(inside=c0["scat"]["inside"], outside=c0["scat"]["outside"])
+    else:
+        need(len(ret) == h, "star rule with a number of totals other than h")
+        scat = dict(table=[[[kk, (w * sl[kk]).numerator, (w * sl[kk]).denominator]
+                            for kk in range(h) for w in [sin if c0["ports"][t] >> kk & 1 else sout]] for t in range(v)])
+    ext = sorted([z[3], z[1]] for z in c0["gauge"] if z[5])
+    c1 = dict(format="gcert/1", derived_from=c0["name"] + " (gcert/0; %d scalings as units, gxconv.py)" % nsc, p=c0["p"],
+              h=h, v=v, R=R, cst=c0["cst"], N=c0["N"], ports=c0["ports"], frames=c0["frames"], start=c0["start"],
+              final=c0["final"], ext=ext, ret=ret, scat=scat, A=A, B=B, blocks=c0["blocks"])
+    return c1, nsc, sorted(set(str(x) for x in lam.values())), sum(1 for x in sl if x != 1)
+
+
+if __name__ == "__main__":
+    t0 = time.time()
+    opt = dict(a.split("=", 1) for a in sys.argv[2:] if "=" in a)
+    c0 = gxrun.load(sys.argv[1])
+    c1, nsc, lams, nsl = convert(c0)
+    c1["two_hosts"] = sorted(2 * c0["v"] + i for i, hs in enumerate(c0["hosts"]) if len(hs) > 1)
+    if "noext" in sys.argv and c1["ext"]:        # as gxrun.py: exterior gauges become first blocks
+        for r, f in c1["ext"]:
+            d = str(len(c1["frames"][f]))
+            c1["start"][r] = 0
+            c1["blocks"]["s"][d] = c1["blocks"]["s"].get(d, 0) + 1
+            c1["N"] += int(d)
+        c1["blocks"]["s"] = {k: c1["blocks"]["s"][k] for k in sorted(c1["blocks"]["s"], key=int)}
+        c1["derived_from"] += ", exterior gauges turned into first blocks"
+        c1["ext"] = []
+    st = {}
+    gx.check1(c1, scalar=True, stats=st)
+    print("ACCEPTED by gx.check1: %s h=%d v=%d R=%d N=%d gates A=%d B=%d ext=%d; scalings %d, final units %s, scaled totals %d, "
+          "scatter %s, stats %s (%.1fs)" % (c0["name"], c1["h"], c1["v"], c1["R"], c1["N"], len(c1["A"]), len(c1["B"]),
+                                           len(c1["ext"]), nsc, lams, nsl, "table" if "table" in c1["scat"] else "star", st,
+                                           time.time() - t0))
+    if "out" in opt:
+        gxrun.dump(c1, opt["out"])
+        print("written", opt["out"])
diff --git a/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py
new file mode 100644
index 0000000000..3e3f0a3076
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/inputs/complex/sources/tools__gx__gxcore.py
@@ -0,0 +1,375 @@
+"""gxcore.py: gcert/1 JSON -> normal data D, PYTHON MIRROR of the two Lean checks
+(label side: E0 frames, E1 pairs, E1/E2/E6 replay in segments; scalar side: E3 kinds, E4 bracket, E5 replay
+in source batches, E7), derived data (distinct climbs, cut states, block histogram) and kernel sizes.
+Own code; the reference is gx.py (check1), not imported.  Python 3, standard library only."""
+import json, gzip
+from collections import Counter
+from math import gcd
+
+
+class Reject(Exception):
+    pass
+
+
+def need(c, msg):
+    if not c:
+        raise Reject(msg)
+
+
+def load(path):
+    c = json.load(gzip.open(path, "rt") if path.endswith(".gz") else open(path))
+    need(c.get("format") == "gcert/1", "E0: format is not gcert/1")
+    return c
+
+
+def co(num, den):
+    need(den > 0, "E0: denominator")
+    return (num < 0, abs(num), den)
+
+
+def normal(c):
+    """the Lean-facing data: gates as tuples, coefficients (neg, num, den), ret by total"""
+    def gate(g):
+        if g[0] == "out":
+            return ("out", g[1], g[2], [(t, co(a, b)) for t, a, b in g[3]], list(g[4]))
+        need(g[0] == "in", "E0: unknown gate kind %r" % (g[0],))
+        return ("in", g[1], g[2], [(s, co(a, b)) for s, a, b in g[3]])
+    ret = sorted(c["ret"])
+    need([k for k, _, _ in ret] == list(range(len(ret))), "E2: retained totals numbered 0..")
+    sc = c["scat"]
+    scat = ("table", [[(k, co(a, b)) for k, a, b in row] for row in sc["table"]]) if "table" in sc else \
+        ("star", co(*sc["inside"]), co(*sc["outside"]))
+    return dict(h=c["h"], v=c["v"], R=c["R"], N=c["N"], cst=c["cst"], ports=list(c["ports"]),
+                frames=[list(f) for f in c["frames"]], start=list(c["start"]), final=list(c["final"]),
+                ext=[tuple(e) for e in c.get("ext", [])], ret=[(s, f) for _, s, f in ret], scat=scat,
+                A=[gate(g) for g in c["A"]], B=[gate(g) for g in c["B"]],
+                blocks={k: {int(r): n for r, n in c["blocks"][k].items()} for k in "xysc"})
+
+
+def regs(g):
+    return [g[2]] + [t for t, _ in g[3]] + (g[4] if g[0] == "out" else [])
+
+
+def adds(g):
+    """single adds (tgt, src, coef) in order"""
+    return [(t, g[2], k) for t, k in g[3]] if g[0] == "out" else [(g[2], s, k) for s, k in g[3]]
+
+
+def reduce(u, basis):
+    for b in basis:
+        if u >> (b.bit_length() - 1) & 1:
+            u ^= b
+    return u
+
+
+def echelon_ok(f):
+    piv = [b.bit_length() - 1 for b in f]
+    if any(b == 0 for b in f) or any(piv[i] <= piv[i + 1] for i in range(len(piv) - 1)):
+        return False
+    return all(not (b >> p & 1) for i, b in enumerate(f) for j, p in enumerate(piv) if i != j)
+
+
+def par(x):
+    return bin(x).count("1") & 1
+
+
+def cls(D, r):
+    return "x" if r < D["v"] else "y" if r < 2 * D["v"] else "s"
+
+
+# ---- label side ------------------------------------------------------------------------------------------
+def chk_frames(D):
+    """E0: ports; frame table reduced echelon, no repeats, zero first, full second"""
+    h, v, fr = D["h"], D["v"], D["frames"]
+    p = D["ports"]
+    need(len(p) == v == len(set(p)) and all(par(q) and 0 < q < 1 << h for q in p), "E0: ports")
+    need(len(fr) >= 2 and fr[0] == [] and fr[1] == [1 << i for i in range(h - 1, -1, -1)], "E0: frames 0 and 1")
+    need(all(echelon_ok(f) and all(b < 1 << h for b in f) for f in fr), "E0: frame table not reduced echelon")
+    need(len(set(map(tuple, fr))) == len(fr), "E0: frame table has repeats")
+    return [len(f) for f in fr]
+
+
+def derive(D):
+    """distinct climbs in order of first use (NOT a check: plain replay of the frame ids)"""
+    cur, seen, pairs = list(D["start"]), set(), []
+
+    def go(r, f):
+        o = cur[r]
+        if o != f:
+            if (o, f) not in seen:
+                seen.add((o, f))
+                pairs.append((o, f))
+            cur[r] = f
+    for g in D["A"] + D["B"]:
+        for r in regs(g):
+            go(r, g[1])
+    for r, f in enumerate(D["final"]):
+        go(r, f)
+    return pairs
+
+
+def chk_pairs(D, dim, pairs):
+    """E1, level 2: every listed pair is a nested pair of the table; returns the mask-operation count"""
+    fr, n, work = D["frames"], len(D["frames"]), 0
+    for a, b in pairs:
+        need(a < n and b < n and dim[a] < dim[b], "E1: pair (%d, %d) does not climb" % (a, b))
+        need(all(reduce(u, fr[b]) == 0 for u in fr[a]), "E1: pair (%d, %d) is not nested" % (a, b))
+        work += dim[a] * dim[b]
+    return work
+
+
+def cut_points(D, gmax, wmax=210000):
+    """replay segments: each phase (A, B) is cut into k pieces of equal gate count, k = the least number with at
+    most `gmax` gates AND at most `wmax` work per piece on average (work = sum over gates of the dimension of the
+    gate's frame; measured at h = 22: about 1 ms of kernel time per unit, NOTES.md).
+    Cut points = gate counts in A ++ B (always 0, |A| and the end)."""
+    nA, nB = len(D["A"]), len(D["B"])
+    cuts = [0]
+    for off, gs in ((0, D["A"]), (nA, D["B"])):
+        n = len(gs)
+        k = max(1, -(-n // gmax), -(-sum(len(D["frames"][g[1]]) for g in gs) // wmax))
+        cuts += [off + (n * i) // k for i in range(1, k + 1)]
+    return sorted(set(cuts))
+
+
+def label_data(D, dim, cuts):
+    """for gx-labels (gcert-interface.md LABELS v1): ordered block ranks per replay segment, the final climbs as
+    gates without adds (same final frame, at most 32 registers, only registers that still climb), their ranks,
+    the largest number of registers named by one gate.  Plain replay (the mirror has accepted the file)."""
+    cur, G = list(D["start"]), D["A"] + D["B"]
+    rs, most = [], 0
+    for a, b in zip(cuts, cuts[1:]):
+        r = []
+        for g in G[a:b]:
+            most = max(most, len(regs(g)))
+            for x in regs(g):
+                if cur[x] != g[1]:
+                    r.append(dim[g[1]] - dim[cur[x]])
+                    cur[x] = g[1]
+        rs.append(r)
+    by = {}
+    for x, f in enumerate(D["final"]):
+        if cur[x] != f:
+            by.setdefault(f, []).append(x)
+    fins, rF = [], []
+    for f in sorted(by):
+        for i in range(0, len(by[f]), 32):
+            xs = by[f][i:i + 32]
+            fins.append(("out", f, xs[0], [], xs[1:]))
+            rF += [dim[f] - dim[cur[x]] for x in xs]
+    return dict(rs=rs, fins=fins, rF=rF, most=max(most, 32 if fins else 0))
+
+
+def chk_replay(D, dim, pairs, cuts):
+    """E1 (labels), E2 (scatter cut), E6 (price), in the segments given by `cuts`.
+    Returns (states at the cuts, histogram by class, visits per segment)."""
+    h, v, R, fr = D["h"], D["v"], D["R"], D["frames"]
+    n = 2 * v + R
+    start, final, ext = D["start"], D["final"], dict(D["ext"])
+    need(len(start) == len(final) == n, "E0: start / final")
+    for t in range(v):
+        need(fr[start[t]] == [D["ports"][t]] and final[t] == 1, "E1: x start / final")
+        f = fr[final[v + t]]
+        need(start[v + t] == 0 and len(f) == h - 1 and all(par(u & D["ports"][t]) == 0 for u in f), "E1: y start / final")
+    for r in range(2 * v, n):
+        need(start[r] == ext.get(r, 0) and final[r] == 1, "E1: slot start / final")
+    ok = set(pairs)
+    need(len(ok) == len(pairs), "E1: pair list has repeats")
+    cur = list(start)
+    H = {k: Counter() for k in "xysc"}
+
+    def climb(r, f, where):
+        o = cur[r]
+        if o != f:
+            need((o, f) in ok, "E1: climb (%d, %d) is not a tested pair (%s, register %d)" % (o, f, where, r))
+            H[cls(D, r)][dim[f] - dim[o]] += 1
+            seg[dim[f] - dim[o]] += 1
+            cur[r] = f
+    seg, segs = Counter(), []
+    G, nA = D["A"] + D["B"], len(D["A"])
+    states, visits = [], []
+    need(cuts[0] == 0 and cuts[-1] == len(G) and cuts == sorted(cuts), "cut points")
+    for a, b in zip(cuts, cuts[1:]):
+        states.append(list(cur))
+        vs = 0
+        for i in range(a, b):
+            if i == nA:
+                scatter_cut(D, cur, dim, H, seg)
+            g = G[i]
+            rs = regs(g)
+            need(all(0 <= r < n for r in rs) and len(set(rs)) == len(rs), "E3: registers of gate %d" % i)
+            need(i >= nA or all(r < v or r >= 2 * v for r in rs), "E2: y role named in phase A (gate %d)" % i)
+            vs += len(rs)
+            for r in rs:
+                climb(r, g[1], "gate %d" % i)
+        visits.append(vs)
+        if b < len(G):
+            segs.append(seg)
+            seg = Counter()
+    if nA == len(G):
+        scatter_cut(D, cur, dim, H, seg)
+    states.append(list(cur))
+    for r in range(n):
+        climb(r, final[r], "final")
+    segs.append(seg)
+    Hb = {k: dict(sorted(w.items())) for k, w in H.items()}
+    need(Hb == D["blocks"], "E6: block histogram differs from `blocks`")
+    N = sum(r * c for w in H.values() for r, c in w.items())
+    need(N == D["N"] and N + sum(dim[f] for f in ext.values()) == R * h + 2 * v * (h - 1) + D["cst"], "E6: N")
+    need(sum(r * c for r, c in H["c"].items()) == D["cst"], "E6: cst")
+    return states, Hb, visits, [[w[r] for r in range(h + 1)] for w in segs]
+
+
+def scatter_cut(D, cur, dim, H, seg):
+    v = D["v"]
+    if D["scat"][0] == "table":
+        need(len(D["scat"][1]) == v and all(k < len(D["ret"]) for row in D["scat"][1] for k, _ in row), "E2: scatter table")
+    else:
+        need(len(D["ret"]) == D["h"], "E2: one retained total per coordinate (star rule)")
+    for s, f in D["ret"]:
+        need(s >= 2 * v and cur[s] == f, "E2: retained slot %d is not at its frame" % s)
+        H["c"][dim[f]] += 1
+        seg[dim[f]] += 1
+    need(all(cur[v + t] == 0 for t in range(v)), "E2: a y role left frame 0 before the scatter")
+
+
+# ---- scalar side -----------------------------------------------------------------------------------------
+SC = 6            # all scalar entries are kept as integers in units of 1/6
+KINDS = {("x", "s"), ("s", "s"), ("s", "y"), ("x", "y"), ("x", "x"), ("y", "y")}
+
+
+def chk_shape(D):
+    """E3 kinds, E4 bracket"""
+    ysum, piv, ytg = Counter(), set(), set()
+    for ph in "AB":
+        for i, g in enumerate(D[ph]):
+            for t, s, (ng, a, b) in adds(g):
+                kd = (cls(D, s), cls(D, t))
+                need(kd in KINDS and t != s, "E3: gate kind %s -> %s (gate %s%d)" % (kd + (ph, i)))
+                need(ph == "B" or kd in {("x", "s"), ("s", "s")}, "E3: bank gate before the scatter (gate A%d)" % i)
+                if kd == ("y", "y"):
+                    need(SC % b == 0, "E4: denominator beyond sixths")
+                    ysum[s, t] += (-a if ng else a) * (SC // b)
+                    piv.add(s)
+                    ytg.add(t)
+    need(not (piv & ytg), "E4: a pivot is the target of a gate reading y")
+    need(all(x == 0 for x in ysum.values()), "E4: y-reads of a (pivot, target) pair do not cancel")
+    return len(ysum)
+
+
+def scat_row(D, t):
+    sc = D["scat"]
+    if sc[0] == "table":
+        return sc[1][t]
+    return [(k, sc[1] if D["ports"][t] >> k & 1 else sc[2]) for k in range(D["h"])]
+
+
+
+def replay(D, init, count=None):
+    """exact replay through A, scatter, B of sparse vectors with entries in sixths; `init` = register -> {key: 6}"""
+    v = D["v"]
+    reg = [dict(init.get(r, ())) for r in range(2 * v + D["R"])]
+
+    def axpy(t, src, k):
+        ng, a, b = k
+        d = reg[t]
+        for key, u in src.items():
+            w = u * a
+            need(w % b == 0, "E5: an entry needs a denominator beyond sixths (register %d)" % t)
+            w = w // b
+            w = d.get(key, 0) + (-w if ng else w)
+            if count is not None:
+                count[key] += 1
+            if w:
+                d[key] = w
+            else:
+                d.pop(key, None)
+
+    def run(gates):
+        for g in gates:
+            if g[0] == "out":
+                src = dict(reg[g[2]])
+                for t, k in g[3]:
+                    axpy(t, src, k)
+            else:
+                for s, k in g[3]:
+                    axpy(g[2], reg[s], k)
+    run(D["A"])
+    afterA = sum(len(d) for d in reg)
+    tot = [dict(reg[s]) for s, _ in D["ret"]]
+    for t in range(v):
+        for k, cf in scat_row(D, t):
+            if tot[k]:
+                axpy(v + t, tot[k], cf)
+    run(D["B"])
+    return reg, afterA
+
+
+def chk_scalar(D, batches=1):
+    """E5 (+ E7 when `ext` is non-empty).  Returns stats: denominators and largest numerators per class in the
+    units of the spec (x halves, y sixths, slots integers), updates per source batch, entries after A."""
+    v = D["v"]
+    count = Counter()
+    reg, afterA = replay(D, {t: {t: SC} for t in range(v)}, count)
+    need(all(reg[t] == {t: SC} for t in range(v)), "E5: an x role is not restored (X3)")
+    need(all(reg[v + t] == {t: SC} for t in range(v)), "E5: a target does not receive exactly its source (hid)")
+    if D["ext"]:
+        rg, _ = replay(D, {r: {r: SC} for r, _ in D["ext"]})
+        need(all(not rg[v + t] for t in range(v)), "E7: the dirt of an exterior-gauged slot reaches a y role")
+    step = -(-v // batches)
+    per = [sum(count[k] for k in range(lo, min(lo + step, v))) for lo in range(0, v, step)]
+    return dict(updates=sum(count.values()), per_batch=per, afterA=afterA,
+                batches=[(lo, min(lo + step, v)) for lo in range(0, v, step)])
+
+
+def digits(D):
+    """largest |entry| met and denominators per class, by a second replay that watches every write (slow path
+    kept separate from the check): returns {class: (lcm of denominators, largest |numerator| in units 1/den)}"""
+    v = D["v"]
+    den = {"x": 1, "y": 1, "s": 1}
+    mx = {"x": 0, "y": 0, "s": 0}
+    reg = [({r: SC} if r < v else {}) for r in range(2 * v + D["R"])]
+
+    def axpy(t, src, k):
+        ng, a, b = k
+        d, kk = reg[t], cls(D, t)
+        for key, u in src.items():
+            w = d.get(key, 0) + (-(u * a // b) if ng else u * a // b)
+            if w:
+                d[key] = w
+                q = SC // gcd(w, SC)
+                if den[kk] % q:
+                    den[kk] = den[kk] * q // gcd(den[kk], q)
+                if abs(w) > mx[kk]:
+                    mx[kk] = abs(w)
+            else:
+                d.pop(key, None)
+    for g in D["A"]:
+        for t, s, k in adds(g):
+            axpy(t, reg[s], k)
+    tot = [dict(reg[s]) for s, _ in D["ret"]]
+    for t in range(v):
+        for k, cf in scat_row(D, t):
+            axpy(v + t, tot[k], cf)
+    for g in D["B"]:
+        for t, s, k in adds(g):
+            axpy(t, reg[s], k)
+    return {k: (den[k], mx[k] * den[k] // SC if (mx[k] * den[k]) % SC == 0 else "%d/6" % mx[k]) for k in "xys"}
+
+
+def mirror(D, gmax=12000, batches=1, pairs=None, cuts=None):
+    """both checks; returns everything the generator and the dry run need"""
+    dim = chk_frames(D)
+    pairs = derive(D) if pairs is None else pairs
+    work = chk_pairs(D, dim, pairs)
+    cuts = cut_points(D, gmax) if cuts is None else cuts
+    states, H, visits, segH = chk_replay(D, dim, pairs, cuts)
+    ysh = chk_shape(D)
+    S = chk_scalar(D, batches)
+    hist = Counter()
+    for k in "xysc":
+        for r, n in H[k].items():
+            hist[r] += n
+    return dict(dim=dim, pairs=pairs, pair_work=work, cuts=cuts, states=states, H=H, visits=visits, ysh=ysh,
+                scal=S, hist=dict(sorted(hist.items())), segH=segH,
+                lab=label_data(D, dim, cuts))
diff --git a/research/gen4-retiming-entrances/vendor/pr276/math_check.py b/research/gen4-retiming-entrances/vendor/pr276/math_check.py
new file mode 100644
index 0000000000..e3453703bc
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/math_check.py
@@ -0,0 +1,57 @@
+"""Source-bound banked five-stage moments and all47outerconstraints.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+Uses PR234 five-stage architecture and complex baseline, the gen4 helper and
+PR197-derived actual five-stage entrance banks. Inputs must be live verifier outputs.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import importlib.util
+HERE=Path(__file__).resolve().parent
+
+def load(name):
+ p=HERE/(name+'.py');s=importlib.util.spec_from_file_location('banked527_'+name,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+
+def serial(x):
+ if isinstance(x,Q):return str(x)
+ if isinstance(x,dict):return {str(k):serial(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return list(map(serial,x))
+ return x
+
+def hist(x):return Counter({int(k):v for k,v in x.items()if v})
+
+def run(raw,complex_histogram,banks,global_result):
+ cost=load('moment');other=load('base_two_moment');outer=load('outer')
+ assert raw['source_aliases']==0 and raw['physical_R']==16410 and raw['h']==24 and raw['v']==1760
+ H=hist(raw['five_stage_profile']['histogram']);assert H==hist(global_result['paid_histogram'])
+ assert global_result['paid_rank_mass']==sum(k*n for k,n in H.items())==2809600
+ gauges=hist(raw['auxiliary_entrance_rank_histogram']);assert gauges=={20:2200,21:266}
+ assert banks['assignments']==4923000 and banks['gen4_roles']==16410 and banks['physical_replicas']==60
+ assert banks['literal_stock']==1283035 and banks['banks_total']==860635 and banks['charts']==370
+ for a,n in gauges.items():assert H.pop(5*a)==n
+ assert len(H)>0 and min(H.values())>0 and max(H)==50
+ literal={k:n*60 for k,n in H.items()};literal_mass=sum(k*n for k,n in literal.items());literal_W=banks['literal_stock']
+ assert 120*literal_W-literal_mass==60*4400
+ # Divide the literal profile by5 to an integer normalization. The executed
+ # realization is still60replicas, and finite accounting uses its literalstock.
+ assert literal_W%5==0 and all(n%5==0 for n in literal.values())
+ normalized={k:n//5 for k,n in literal.items()};W=literal_W//5;m=120;mass=sum(k*n for k,n in normalized.items())
+ bp=dict(m=m,W=W,histogram=normalized,calls=sum(normalized.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(normalized),normalization=12,physical_replicas=60,literal_stock=literal_W,literal_children=sum(literal.values()),literal_rank_mass=literal_mass)
+ root=cost.certify(normalized,m,W,True);c=Q(int(Q(root['lower'])*10**18),10**18);bm=cost.moment(normalized,m,W,c,True);nextbm=cost.moment(normalized,m,W,c+Q(1,10**18),True);assert bm[1]<1<nextbm[0]
+ fallback=32*m*m*sum(normalized.values())
+ _,upper=other.moment(m,W,list(normalized.items()),c);_,bad=other.moment(m,W,[(1,fallback)],c)
+ lower,_=other.moment(m,W,list(normalized.items()),c+Q(1,10**18));badlower,_=other.moment(m,W,[(1,fallback)],c+Q(1,10**18));assert upper+Q(1,10**16)*bad<1<lower+Q(1,10**16)*badlower
+ CH=hist(complex_histogram);assert sum(CH.values())==361405 and sum(k*n for k,n in CH.items())==1613040
+ cp=dict(m=110,W=14692,histogram=dict(CH),calls=sum(CH.values()),rank_mass=sum(k*n for k,n in CH.items()),deficit=3080,maxchild=max(CH));b=Q(747454944651775,10**18);cm=cost.moment(dict(CH),110,14692,b,False);assert cm[1]<1
+ chain=[Q(384599,10**10)]
+ for _ in range(3):
+  a=(1-c)*c+c*chain[-1];assert chain[-1]<a<c<1-a;chain.append(a)
+ bit=chain[-1];eta=Q(1,10**12);beta=Q(1,10**9);assert bit<(1-beta)*b
+ bridge=dict(proof='PROOF.md',representation='Exact powers with source-bound finite overcharges',semantic=dict(G=dict(base=2,exponent=30000),E=dict(base=2,exponent=100000),B_upper=dict(base=2,exponent=100001),C0=dict(base=2,exponent=210000),C1=1,strict_literal_gap=1,induction_gap_lower=1),rows=dict(coefficient=20161,degree=10**6,suffix_slope=4*10**6,degree_gap=Q(10**6)-Q(51*20161,25)))
+ assert bridge['rows']['degree_gap']>0
+ q=bit*(1-2*eta);minimum=(1-eta)*q/(1+q);ticks=minimum*10**18;k=Q((ticks.numerator-1)//ticks.denominator,10**18)
+ assembly=outer.assembly(bit,b,bridge,k,eta=eta,beta=beta);assert len(assembly['strict_constraints'])==47 and len(assembly['margins'])==7 and min(assembly['strict_constraints'].values())>0
+ try:outer.assembly(bit,b,bridge,k+Q(1,10**18),eta=eta,beta=beta)
+ except AssertionError:pass
+ else:raise AssertionError('Adjacentkappaadmitted')
+ return serial(dict(status='PASS_BANKED_FIVE_STAGE_GEN4_EXACT_MOMENTS_AND_OUTER47',mathematics=dict(bit_profile=bp,complex_profile=cp,bit_coarse=c,complex_coarse=b,bit_moment_interval=bm,complex_moment_interval=cm,next_bit_grid_excluded=nextbm,independent_base_two_pass=True,ordinary_bootstrap_chain=chain,finite_bridge=bridge,assembly=assembly,kappa=k,kappa_decimal=cost.decimal(k),kappa_scientific=format(float(k),'.15e'),binding='bit'),adjacent_grid_point_rejected=True))
diff --git a/research/gen4-retiming-entrances/vendor/pr276/moment.py b/research/gen4-retiming-entrances/vendor/pr276/moment.py
new file mode 100644
index 0000000000..1e43aaeaca
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/moment.py
@@ -0,0 +1,114 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v=1760,h=24):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell==4400
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=24,copy_rank=22,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m120 admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    result['source_owned_gauges_not_banked']={19:3,2:26,4:2}
+    print(json.dumps(result,indent=2))
diff --git a/research/gen4-retiming-entrances/vendor/pr276/notices/PR210-coordinated-crossover-NOTICE b/research/gen4-retiming-entrances/vendor/pr276/notices/PR210-coordinated-crossover-NOTICE
new file mode 100644
index 0000000000..d08cb66ac7
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/notices/PR210-coordinated-crossover-NOTICE
@@ -0,0 +1,431 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
+
+Fourth finite bootstrap refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+This arithmetic refinement builds on PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf
+level. The 302 frame overrides, completed banks, scalar words and upstream
+assistance disclosures are inherited, not newly attributed to this work.
+The Apache-2.0 license and all preceding notices remain applicable.
+
+PR211 plateau frame refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The additional seven equal-frame component moves build directly on Rohan
+Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347,
+prepared with Anthropic Claude assistance. Its original notice is preserved
+byte-for-byte in search/PR211-NOTICE. The offline certificate package and
+independent stage-private bank admission derive from Dugongue's PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices,
+licenses, source pins and all upstream AI disclosures remain applicable.
+
+The final refinement also includes seeded bidirectional cascade search after
+the seven initial component moves. Exact canonical subspace comparison
+records 274 changed operations beyond PR211. Search, integration and replay
+were prepared with substantial OpenAI Codex assistance.
+
+Shared rank-18 gauges and two donor substitutions (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The new actual gauge/read chronology, gauged-donor handoff, shared target
+transitions, rank6 residual banks and donor substitutions extend the same
+PR200/PR211 word and PR207/PR197 completed-bank framework. All original
+licenses, notices, authorship and upstream AI disclosures remain in force.
+
+Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/notices/PR230-NOTICE b/research/gen4-retiming-entrances/vendor/pr276/notices/PR230-NOTICE
new file mode 100644
index 0000000000..bc1cfc52a1
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/notices/PR230-NOTICE
@@ -0,0 +1,441 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
+
+Fourth finite bootstrap refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+This arithmetic refinement builds on PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc by adding one finite ordinary-leaf
+level. The 302 frame overrides, completed banks, scalar words and upstream
+assistance disclosures are inherited, not newly attributed to this work.
+The Apache-2.0 license and all preceding notices remain applicable.
+
+PR211 plateau frame refinement (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The additional seven equal-frame component moves build directly on Rohan
+Arun's PR211 cascade witness at c63e50a5dde96fe1459d6b29e55e47f42f104347,
+prepared with Anthropic Claude assistance. Its original notice is preserved
+byte-for-byte in search/PR211-NOTICE. The offline certificate package and
+independent stage-private bank admission derive from Dugongue's PR207 at
+cd14825023b75af4f5919a30e5e6d548b6ade5bc. Original contributor notices,
+licenses, source pins and all upstream AI disclosures remain applicable.
+
+The final refinement also includes seeded bidirectional cascade search after
+the seven initial component moves. Exact canonical subspace comparison
+records 274 changed operations beyond PR211. Search, integration and replay
+were prepared with substantial OpenAI Codex assistance.
+
+Shared rank-18 gauges and two donor substitutions (2026-10-09)
+Prepared by eumemic with substantial OpenAI Codex assistance.
+The new actual gauge/read chronology, gauged-donor handoff, shared target
+transitions, rank6 residual banks and donor substitutions extend the same
+PR200/PR211 word and PR207/PR197 completed-bank framework. All original
+licenses, notices, authorship and upstream AI disclosures remain in force.
+
+Nested-gauge extension: three rank-19 physical entrances compose with thirteen shared rank-18 entrances; all target transitions and mixed4/5/6/24 banks are explicit. Prepared by eumemic with substantial OpenAI Codex assistance. All retained authorship, licenses and AI disclosures remain applicable.
+
+Equal-frame plateau refinement on PR210's 471-source word (2026-10-10)
+Prepared by sennemmi with substantial OpenAI Codex assistance. The deterministic
+frame search, 19 operation retimings, exact price update and repository
+integration extend eumemic's PR210 head
+df95878d11190518e45ef9717c9ee05011f88ace. They do not claim the inherited
+source word, shared gauges, completed banks or upstream proof framework.
+All PR200, PR197, PR202/193, PR207, PR211, PR216 and PR210 attributions,
+licenses and AI disclosures remain in force; the repository's Apache-2.0
+license is unchanged.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/notices/PR230-PROVENANCE.json b/research/gen4-retiming-entrances/vendor/pr276/notices/PR230-PROVENANCE.json
new file mode 100644
index 0000000000..ff39579387
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/notices/PR230-PROVENANCE.json
@@ -0,0 +1,27 @@
+{
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/230",
+  "author": "sennemmi",
+  "assistance": "Substantial OpenAI Codex assistance, as disclosed by the original contributor.",
+  "imported_head": "fee4c05b91d4cdebc0b9d8cbb266a98069928a9a",
+  "scope": "Nineteen operation-frame changes inherited from the independently verified492-source composition and replayed with493sourcealiases,82equal-response groups,seven integer-response groups andfour signed echelon groups. Original search,result,framewitness andnotice remain byte-preserved.",
+  "original_files": {
+    "NOTICE": "7dfbad087ee49b74fd5075d517eaa263c5dd3d4fbd4c69bfba34ee1cb55e837f",
+    "joint-plateau-result-prdf958.json": "cd5731260af0daa62952c3b82debdb26cfb79e62a5c615688d8ccac6f7a95fcc",
+    "joint-plateau-search-prdf958.py": "80f3f9e8ba1972b911b701a4de4f811d6d25c9b4c0bc6282d640c2f44caafd0d",
+    "opframe-bases.json": "387ae1b5e69004426d094f4947b29c532d60fdf31f727f5e8830468278fe0f92"
+  },
+  "final_frame_sha256": "9a2bba5c72aebc9ee4f21e59b10ce810b2da98a1fa1748fbc44c50a080e584ff",
+  "raw_child_delta": {
+    "1": -27,
+    "2": -36,
+    "3": 51,
+    "4": -30,
+    "7": 30,
+    "8": -15,
+    "9": -15,
+    "10": 24,
+    "11": -24,
+    "12": 30,
+    "15": -15
+  }
+}
diff --git a/research/gen4-retiming-entrances/vendor/pr276/notices/README.md b/research/gen4-retiming-entrances/vendor/pr276/notices/README.md
new file mode 100644
index 0000000000..7af7caa733
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/notices/README.md
@@ -0,0 +1,15 @@
+# Retained upstream notices
+
+These notices are retained verbatim from eumemic's source527 package. They carry the contributor credits and
+AI-assistance disclosures for the package machinery reused here: the scalar program, emitters, parity fusion,
+census, banks, and the moment, prime and finite checks.
+
+| File | Origin |
+| --- | --- |
+| `source527-loader-NOTICE.md` | source527's source loader |
+| `PR230-NOTICE`, `PR230-PROVENANCE.json` | sennemmi's PR230 operation-frame witnesses, including the PR211 and PR216/207 lineage |
+| `base-bit-PR200-PR202-NOTICE` | Chafik Boukhalfa's PR200/PR202 base bit package |
+| `PR210-coordinated-crossover-NOTICE` | eumemic's PR210 coordinated-crossover package |
+
+The source471/source527 helper data they describe is not used by the gen4 word. The notices are kept for the
+inherited code and attribution.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/notices/base-bit-PR200-PR202-NOTICE b/research/gen4-retiming-entrances/vendor/pr276/notices/base-bit-PR200-PR202-NOTICE
new file mode 100644
index 0000000000..ba5ea80dd7
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/notices/base-bit-PR200-PR202-NOTICE
@@ -0,0 +1,399 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+Source-assisted common-frame extension (2026-10-09)
+Copyright 2026 icekylinx. Apache-2.0.
+Research construction and local certificates: OpenAI GPT-6 Astra assistance.
+Repository integration and independent complex scalar replay: Codex assistance.
+Substantial dependency: eumemic PR168, fd25adb7fbaa12ee761d02c733c54d1d2a7687ee;
+its byte-preserved sources, licenses and original Claude assistance disclosure
+are retained in research/source-assisted/public/pr168_fd25adb7.tar.gz.
+Additional inherited contributions are recorded in research/source-assisted/CREDITS.md.
+The new work concerns source-assisted invertible common-frame lifts, controlled
+affine cleanup and compatible zero-fresh reuse; no exclusive claim is made for
+broad register reuse, paired cubes, frame theory or ordinary linear elimination.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/notices/source527-loader-NOTICE.md b/research/gen4-retiming-entrances/vendor/pr276/notices/source527-loader-NOTICE.md
new file mode 100644
index 0000000000..47090d6e93
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/notices/source527-loader-NOTICE.md
@@ -0,0 +1,11 @@
+# Attribution
+
+This focused preparation adapter is distributed under Apache-2.0. It preserves the original source files, headers and notices in the supplied source roots.
+
+- eumemic: the current PR210 operation frames, joint gauges, donor assignments, source borrowing and retimed source471 schedule at df95878d11190518e45ef9717c9ee05011f88ace; original OpenAI Codex assistance disclosure retained.
+- Chafik Boukhalfa (chafreaky): the PR200 physical bit construction and terminal interfaces, carried by the consumed PR202 base at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d.
+- Rohan Arun, Dugongue, evmckinney9, icekylinx, James Chang, eumemic, Douglas Colkitt, OpenAI, and preceding contributors retain the attribution and assistance disclosures recorded in the supplied original notices.
+
+The new contribution here is the explicit public-root binding, source-derived terminal records, exact semantic comparison and independent raw-path recount. It does not claim authorship of the inherited helper, frames, compiler or theorem interfaces, nor review or endorsement by the named contributors.
+
+Assisted with ChatGPT.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/outer.py b/research/gen4-retiming-entrances/vendor/pr276/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/gen4-retiming-entrances/vendor/pr276/parity_transform.py b/research/gen4-retiming-entrances/vendor/pr276/parity_transform.py
new file mode 100644
index 0000000000..30528550be
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/parity_transform.py
@@ -0,0 +1,143 @@
+"""F2 payload identity elision and exact nested address-MOVE fusion.
+The inherited signed source decoder is retained as producer evidence.
+All odd-prime address projectors and routes remain unchanged.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+from array import array
+from collections import Counter
+from pathlib import Path
+import gzip,hashlib,json,time
+if not __debug__:raise SystemExit('assertions required')
+
+def transform(records):
+    out = array('i')
+    pending = {}
+    chains = []
+    removed = Counter()
+    hist = Counter()
+    merged = 0
+    maxchain = 0
+    uses = Counter()
+
+    def flush(a):
+        nonlocal merged, maxchain
+        if a in pending:
+            old, new, rank, count, first, last = pending.pop(a)
+            if rank:
+                hist[rank] += 1
+            out.extend((0, a, old, new, rank, 0))
+            merged += count - 1
+            maxchain = max(maxchain, count)
+            if count > 1:
+                chains.append(dict(stream=a, old=old, new=new, rank=rank, moves=count, first=first, last=last))
+    for index in range(0, len(records), 6):
+        op, a, b, c, f, z = records[index:index + 6]
+        if op == 1 and c % 2 == 0:
+            removed[c] += 1
+            continue
+        if op == 0:
+            assert z == 0
+            if a in pending:
+                old, prev, rank, count, first, last = pending[a]
+                assert prev == b, ('disconnected movechain', a, prev, b)
+                pending[a] = (old, c, rank + f, count + 1, first, index // 6)
+            else:
+                pending[a] = (b, c, f, 1, index // 6, index // 6)
+            continue
+        assert op in (1, 2, 3)
+        flush(a)
+        flush(b)
+        if op == 1:
+            uses[a] += 1
+            uses[b] += 1
+        elif op == 2:
+            hist[z] += 1
+            uses[a] += 1
+            uses[b] += 1
+        out.extend((op, a, b, c, f, z))
+    for a in sorted(pending):
+        flush(a)
+    return (out, dict(removed_even_adds=dict(removed), removed_even_add_count=sum(removed.values()), merged_move_count=merged, max_chain=maxchain, fused_chains=len(chains), paid_histogram=dict(sorted(hist.items())), paid_calls=sum(hist.values()), paid_rank_mass=sum((r * n for r, n in hist.items())), surviving_additions=sum((out[k] == 1 for k in range(0, len(out), 6))), output_records=len(out) // 6, unused_streams=[i for i in range(19930) if not uses[i]], stream_use_counts=dict(uses)), chains)
+
+def run(producer,output_dir=None):
+    begun=time.monotonic();W,C=producer['W'],producer['C'];v=W.v;n=19930;assert n==2*v+len(producer['context']['regs'])
+    old=producer['records'];out,stats,chains=transform(old);oldmeta=producer['physical']
+    assert stats['removed_even_add_count']==1510656 and stats['surviving_additions']==626360
+    assert stats['paid_rank_mass']==425742 and stats['merged_move_count']==0
+    initial=producer['initial_state'];ZERO,FULL=producer['ZERO'],producer['FULL']
+    # Independent required-frame census: ignore all original MOVE instructions.
+    # Use only surviving gate operands, copy sources and mathematical endpoints.
+    needs={i:[] for i in initial};copies=Counter();copy=None
+    for k in range(0,len(old),6):
+        op,a,b,c,f,z=old[k:k+6]
+        if op==1 and c%2:
+            needs[a].append(f)
+            if b!=n:needs[b].append(f)
+            else:assert copy is not None
+        elif op==2:
+            assert copy is None;copy=(a,b,c);needs[a].append(c);copies[z]+=1
+        elif op==3:assert copy==(a,b,c);copy=None
+    assert copy is None and copies=={22:24}
+    final={i:FULL for i in initial}
+    for t in range(v):final[v+t]=W.register(W.module.kernel([C.cov[t]],W.h)[0])
+    census=Counter(copies);per_role={};pairs=set()
+    for i,oldf in initial.items():
+        H=Counter()
+        for f in needs[i]+[final[i]]:
+            assert C.sub(oldf,f);rank=C.dimf[f]-C.dimf[oldf]
+            if rank:H[rank]+=1
+            pairs.add((oldf,f));oldf=f
+        per_role[i]=H;census.update(H)
+    assert census==Counter({int(r):c for r,c in stats['paid_histogram'].items()})
+    # Read back the actual annihilator rows as a separate reflected ledger.
+    # A(new) annihilating B(old) states new^perp <= old^perp exactly.
+    reflected_pairs=0;endpoint_frames={f for pair in pairs for f in pair};nondeg_bases=set()
+    for f in endpoint_frames:
+        assert len(C.B[f])==C.dimf[f] and len(C.A[f])+C.dimf[f]==24
+        key=tuple(map(tuple,C.B[f]))
+        if key not in nondeg_bases:
+            assert C.nondeg(f),'singular required endpoint frame'
+            nondeg_bases.add(key)
+    for oldf,newf in sorted(pairs):
+        assert len(C.A[newf])<=len(C.A[oldf])
+        assert all(W.module.dot(a,b)==0 for a in C.A[newf]for b in C.B[oldf])
+        reflected_pairs+=1
+    # Validate the actual transformed instruction stream against its own frames.
+    state=dict(initial);copy=None;used=set(initial.values());hist=Counter();cat=Counter();coeff=Counter();centers=[];count=0
+    scalar=hashlib.sha256();tagged=hashlib.sha256();category_names=oldmeta['category_names']
+    def event(d,row):d.update(json.dumps(row,separators=(',',':')).encode());d.update(b'\n')
+    for k in range(0,len(out),6):
+        op,a,b,c,f,z=out[k:k+6]
+        if op==0:
+            assert state[a]==b and C.sub(b,c) and C.dimf[c]-C.dimf[b]==f
+            # Complement reflection reverses containment and preserves the gap.
+            assert (24-C.dimf[b])-(24-C.dimf[c])==f
+            state[a]=c;used.update((b,c))
+            if f:hist[f]+=1
+        elif op==1:
+            assert c%2 and state[a]==state[b]==f and a!=b
+            kind=category_names[z];source=copy['source']if b==n else b
+            event(scalar,[a,source,c]);event(tagged,[a,b,c,f,kind]);count+=1;cat[kind]+=1;coeff[abs(c)]+=1;used.add(f)
+        elif op==2:
+            assert copy is None and b==n and state[a]==c and f==ZERO and z==22
+            state[b]=f;hist[z]+=1;copy=dict(source=a,frame=c,rank=z,temporary=b,first_event=count,copy_output_frame=f)
+        else:
+            assert op==3 and copy is not None and (a,b,c)==(copy['source'],copy['temporary'],copy['frame']) and state[b]==f==ZERO
+            copy.update(after_event=count,scatter_reads=count-copy['first_event']);assert copy['scatter_reads']==220
+            centers.append(copy);copy=None;del state[b]
+    assert copy is None and state==final and hist==census
+    assert count==626360 and coeff=={1:624600,3:1760} and len(centers)==24
+    delta=Counter(hist);delta.subtract(Counter({int(r):c for r,c in oldmeta['paid_histogram'].items()}));delta={r:c for r,c in delta.items()if c}
+    assert delta=={}
+    sourceH=Counter();targetH=Counter();internalH=Counter(copies)
+    for i,H in per_role.items():(sourceH if i<v else targetH if i<2*v else internalH).update(H)
+    receipt=dict(status='PASS_FRESH_PARITY_FUSION_AND_INDEPENDENT_REQUIRED_FRAME_CENSUS',removed_even_add_count=stats['removed_even_add_count'],remaining_payload_additions=count,merged_moves=stats['merged_move_count'],chains=chains,local_histogram_delta=delta,both_reflected_ledgers=True,unchanged_all_input_output_frames=True,unique_required_frame_pairs=len(pairs),explicit_reflected_annihilator_pairs=reflected_pairs,nondegenerate_endpoint_bases=len(nondeg_bases),source_histogram=dict(sourceH),target_histogram=dict(targetH),internal_histogram_including_copies=dict(internalH),copied_center_histogram=dict(copies),producer_scalar_sha256=oldmeta['scalar_projection_sha256'],producer_tagged_sha256=oldmeta['tagged_scalar_sha256'],transform_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest())
+    meta=dict(oldmeta);meta.update(status='PASS_PHYSICAL_GEN4_PARITY_FUSED_EXACT_FRAME_AND_SCALAR_PROJECTION',scalar_projection_sha256=scalar.hexdigest(),tagged_scalar_sha256=tagged.hexdigest(),weighted_scalar_events=count,coefficient_histogram=dict(coeff),categories=dict(cat),copied_center_blocks=centers,paid_histogram=dict(sorted(hist.items())),paid_rank_mass=sum(r*c for r,c in hist.items()),positive_rank_moves=sum(hist.values())-24,used_frames=[dict(frame_id=f,dimension=C.dimf[f],basis_sha256=hashlib.sha256(json.dumps(C.B[f],separators=(',',':')).encode()).hexdigest())for f in sorted(used)],parity_transform=receipt,producer_physical_emitter_sha256=oldmeta['physical_emitter_sha256'],physical_emitter_sha256=receipt['transform_sha256'])
+    result=dict(producer);result.update(records=out,physical=meta,result=meta,producer_physical=oldmeta,parity_census=receipt)
+    if output_dir is not None:
+        p=Path(output_dir);p.mkdir(parents=True,exist_ok=True)
+        (p/'records.bin.gz').write_bytes(gzip.compress(out.tobytes(),mtime=0))
+        (p/'physical.json').write_text(json.dumps(meta,indent=2)+'\n')
+        (p/'parity.json').write_text(json.dumps(receipt,indent=2)+'\n')
+    print('PASS parity fusion',count,'ADDs',len(out)//6,'records',flush=True)
+    return result
diff --git a/research/gen4-retiming-entrances/vendor/pr276/portable_bit.py b/research/gen4-retiming-entrances/vendor/pr276/portable_bit.py
new file mode 100644
index 0000000000..9d0355827f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/portable_bit.py
@@ -0,0 +1,55 @@
+"""Fresh gen4 local physical and complete five-stage global lowering (source527 integration, rebound).
+
+Inherited source-bound PR234 lowering, integrated with source527 using
+substantial OpenAI Codex assistance. Cover expansion is phase-major.
+"""
+from pathlib import Path
+import hashlib,importlib.util,sys,time,json
+sys.dont_write_bytecode=True
+if not __debug__:raise SystemExit('assertions required')
+HERE=Path(__file__).resolve().parent
+
+def load(name,path):
+ spec=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m);return m
+
+def phase_major_templates(lower):
+ """Expand all cover classes for each yielded phase before advancing."""
+ for stage in range(5):
+  yield('helper',stage,lambda s=stage:lower.iter_stage(s))
+  if stage in(1,2,4):
+   i={1:0,2:1,4:2}[stage]
+   yield('idle',i,lambda i=i:lower.iter_idle(i))
+   yield('bridge',i,lambda i=i:lower.iter_bridges(i))
+ yield('completion',0,lower.iter_completions)
+ yield('terminal_exchange',0,lower.iter_exchanges)
+
+def run(prepared_context=None,raw=None,output_dir=None,run_geometry=True,package_root=None):
+ begun=time.monotonic();package=Path(package_root or HERE).resolve()
+ if prepared_context is None:prepared_context=load('portable527_prepare',package/'prepare.py').prepare()
+ if raw is None:raw=load('portable527_raw_ledger',package/'raw_ledger.py').run(prepared_context)
+ physical_module=load('portable527_physical',package/'code/physical527.py');global_module=load('portable527_global',package/'code/global_lowering.py')
+ context=dict(prepared_context);source=context['SOURCE_TEXT']
+ producer_output=Path(output_dir)/'producer-bit' if output_dir is not None else None
+ producer=physical_module.run(context,source,output_dir=producer_output)
+ physical_run=load('portable527_parity',package/'parity_transform.py').run(producer,output_dir=output_dir)
+ raw=load('portable527_parity_raw',package/'raw_ledger.py').rebind_parity(raw,physical_run['parity_census'])
+ physical=physical_run['physical'];physical['source_head']=raw['source_head']
+ assert physical['source_heads']==raw['source_aliases']and physical['independent_dirty_registers']==raw['physical_R']
+ assert physical['paid_histogram']=={int(k):v for k,v in raw['one_stage_helper_histogram_including_copies'].items()}
+ assert physical['initial_independent_entrances']=={int(k):v for k,v in raw['auxiliary_entrance_rank_histogram'].items()}
+ lower=global_module.Lowerer(physical_run['records'],physical_run);global_result=global_module.verify(lower,raw)
+ assert global_result['paid_histogram']=={int(k):v for k,v in raw['five_stage_profile']['histogram'].items()}
+ global_result.update(source_head=raw['source_head'],scalar_projection_sha256=physical['scalar_projection_sha256'],local_tagged_sha256=physical['tagged_scalar_sha256'],weighted_stage_additions=global_result['opcode_counts'][global_module.ADD],bridge_additions=global_result['opcode_counts'][global_module.BRIDGE],total_weighted_additions=global_result['opcode_counts'][global_module.ADD]+global_result['opcode_counts'][global_module.BRIDGE],m=global_module.M,global_live=global_module.LIVE,external_work_family=global_module.WORK)
+ phases=[(name,index)for name,index,method in phase_major_templates(lower)]
+ assert phases==[('helper',0),('helper',1),('idle',0),('bridge',0),('helper',2),('idle',1),('bridge',1),('helper',3),('helper',4),('idle',2),('bridge',2),('completion',0),('terminal_exchange',0)]
+ geometry=None
+ if run_geometry:geometry=load('portable527_geometry',package/'code/geometry527.py').run(context,global_module)
+ result=dict(context=context,W=context['W'],C=context['C'],records=physical_run['records'],lower=lower,raw=raw,physical=physical,global_result=global_result,geometry=geometry,phase_major_schedule=phases,scalar_observer_result=physical_run['scalar_result'],seconds=time.monotonic()-begun)
+ if output_dir is not None:
+  out=Path(output_dir);out.mkdir(parents=True,exist_ok=True)
+  for name in('physical','global_result','geometry','raw'):
+   if result[name]is not None:(out/(name+'.json')).write_text(json.dumps(result[name],indent=2)+'\n')
+ return result
+
+def summary(result):
+ return dict(status='PASS_PORTABLE_GEN4_FRESH_PHYSICAL_GLOBAL_AND_GEOMETRY',source_head=result['raw']['source_head'],local_record_count=len(result['records'])//6,scalar_projection_sha256=result['physical']['scalar_projection_sha256'],physical_tagged_sha256=result['physical']['tagged_scalar_sha256'],global_result=result['global_result'],geometry=result['geometry'],phase_major_schedule=result['phase_major_schedule'],seconds=result['seconds'])
diff --git a/research/gen4-retiming-entrances/vendor/pr276/portable_complex.py b/research/gen4-retiming-entrances/vendor/pr276/portable_complex.py
new file mode 100644
index 0000000000..c068be3e1c
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/portable_complex.py
@@ -0,0 +1,151 @@
+#!/usr/bin/env python3
+"""Fresh complex label, scalar, splice and finite-guard checks from primary inputs.
+No saved PASS receipts, workstation paths, network or Lean rebuild are required.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha256
+from math import prod
+from pathlib import Path
+import gzip, importlib.util, json, sys
+sys.dont_write_bytecode = True
+
+PIN='f010392c923279e3dd59ef3aa5fedad23affc5fd'
+CHRONOLOGY=['stage0','stage1','climbA','bridgeA','stage2','climbB','bridgeB','stage3','stage4','final_climbs','bridgeC','terminal_shifts','signed_exchange']
+
+def need(ok, why):
+    if not ok: raise ValueError(why)
+
+def module(root, name):
+    spec=importlib.util.spec_from_file_location('portable_'+name,root/'code'/(name+'.py'))
+    result=importlib.util.module_from_spec(spec);spec.loader.exec_module(result)
+    return result
+
+def finite_guard(m, b, basis):
+    p=m['parameters'];l=m['ledger'];dim=p['m'];R=p['R'];h=p['h'];W=p['W_live']
+    need((dim,R,h,W)==(110,9412,22,14692),'complex family changed')
+    scalar=max(b[o]['totals']['real_component_primitive_steps'] for o in ['forward','backward'])
+    macros=max(b[o]['totals']['scalar_macros'] for o in ['forward','backward'])
+    scalar5=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps']
+    physical=W+R+h+1
+    adapters=8*(macros+m['checks']['invocation_calls']+p['invocation_live']+h)+32*dim
+    outside=8*(l['idle_calls']+6*p['v']+physical)+32*dim
+    compiler=64*(dim+1)**3
+    local=scalar+adapters*compiler
+    pervertex=scalar5+12*p['v']+(5*adapters+outside)*compiler+64*physical
+    group=(1<<(dim-1+(dim//2-1)**2))*prod((1<<(2*i))-1 for i in range(1,dim//2))
+    live_stock=group*W;physical_stock=group*physical;s=group*l['rank_mass']
+    K=group*pervertex+64;router=compiler*(K+1)*(physical_stock+1)**2
+    G,E,C0=1<<30000,1<<100000,1<<210000;B=s+E
+    literal=2*G*physical_stock**2+8*s+4*physical_stock+4+32*dim
+    need(local==213063694563472 and local<1<<48 and K<1<<6050,'fresh local/global bill')
+    need((group.bit_length(),live_stock.bit_length(),physical_stock.bit_length(),s.bit_length())==(5995,6009,6010,6016),'fresh cover/work stock')
+    need(router<G and literal<E and B<1<<100001,'fresh router/literal guard')
+    need(2*B*(dim-l['max_child'])-s-E==127*B,'completed-child induction')
+    need(32*dim*B*B<C0 and 2*B+18<C0 and 2*l['max_child']<dim,'semantic and half-shrink guard')
+    row=live_stock.bit_length()+9909+252;rowphysical=physical_stock.bit_length()+9909+252
+    need(row<=rowphysical<20161,'external rows')
+    gap=Q(10**6)-Q(51,25)*20161;need(gap>0,'row reserve gap')
+    need(2*(dim*(dim-1)+3*dim+dim+3*dim*(dim-1)//2+dim+1)+2*dim<compiler,'explicit quadratic-phase lowering')
+    for e in range(1,100001):need((e-1).bit_length()+1<=2*e,'grid-depth endpoint')
+    def validate(c):
+        need(c['physical']==c['live']+R+h+1,'missing work stock')
+        need(dim*c['live']-l['rank_mass']==l['deficit'],'wrong live normalization')
+        need(c['copy_calls']==5*h,'missing center child')
+        need(c['denominators']==[1,2,3,6],'unrecorded denominator')
+        need(physical_stock<1<<c['stock_exponent'],'false stock bound')
+    original=dict(physical=physical,live=W,copy_calls=5*h,denominators=[1,2,3,6],stock_exponent=6010)
+    validate(original);controls={}
+    for name,key,value in [('missing_tableau','physical',physical-R),('scratch_in_live','live',physical),('dropped_center','copy_calls',5*h-1),('unrecorded_divisor','denominators',[1,2,3,5,6]),('stale_stock_bound','stock_exponent',5208)]:
+        bad=dict(original);bad[key]=value
+        try:validate(bad)
+        except ValueError:controls[name]=True
+        else:raise ValueError('finite guard mutation accepted: '+name)
+    return dict(status='PASS_FRESH_EXACT_COMPLEX_GUARD',m=dim,live_per_vertex=W,physical_per_vertex=physical,
+        coefficient_denominators=[1,2,3,6],semantic_C1=1,complete_local_group_upper=local,
+        complete_local_group_bits=local.bit_length(),global_logical_groups_bits=K.bit_length(),
+        simple_global_logical_bound_exponent=6050,router_bits=router.bit_length(),G_exponent=30000,
+        literal_charge_bits=literal.bit_length(),E_exponent=100000,required_C0_bits=(32*dim*B*B).bit_length(),
+        C0_exponent=210000,induction_gap_multiple_of_B=127,group_bits=group.bit_length(),
+        live_stock_bits=live_stock.bit_length(),physical_stock_bits=physical_stock.bit_length(),
+        rank_mass_bits=s.bit_length(),live_row_coefficient=row,physical_row_overcharge_coefficient=rowphysical,
+        retained_row_coefficient=20161,retained_row_gap=str(gap),controls=controls,
+        binary_basis_count_tests=basis.gl_count_test(),
+        odd_denominator_grid='2^(-P)3^(-G(D+1)); no return rounding')
+
+def run(package_root=None, progress=lambda text:None):
+    root=Path(package_root).resolve() if package_root else Path(__file__).resolve().parent
+    labels=module(root,'complex_labels');scalar=module(root,'complex_scalars')
+    splice=module(root,'complex_splice');basis=module(root,'complex_basis')
+    pinpath=root/'inputs/complex/source-pins.json'
+    if not pinpath.is_file():pinpath=root/'inputs/complex-source-pins.json'
+    pins=json.loads(pinpath.read_text());verified={};by_upstream={}
+    for relative,spec in pins['files'].items():
+        path=root/relative;got=sha256(path.read_bytes()).hexdigest()
+        need(got==spec['sha256'],'primary proof input changed: '+relative)
+        verified[relative]=got;by_upstream[spec['upstream']]=(path,spec)
+    cp=pins['certificate'];z=(root/cp['path']).read_bytes()
+    need(sha256(z).hexdigest()==cp['compressed_sha256'],'compressed certificate binding')
+    raw=gzip.decompress(z);need(sha256(raw).hexdigest()==cp['uncompressed_sha256'],'expanded certificate binding')
+    verified[cp['path']]=sha256(z).hexdigest();c=json.loads(raw)
+    progress('Checking every complex source label and paid child.')
+    checks=labels.replay_label_counts(c)
+    H=Counter({int(k):5*n for k,n in checks['invocation_histogram'].items()})
+    v,R,h=c['v'],c['R'],c['h'];dim=5*h;W=4*v+R
+    for rank in [2*h-2,h-1,2*h+2,4]:H[rank]+=2*v
+    ledger=dict(histogram={str(k):n for k,n in sorted(H.items())},calls=sum(H.values()),
+        rank_mass=sum(k*n for k,n in H.items()),max_child=max(H),deficit=dim*W-sum(k*n for k,n in H.items()),
+        copy_calls=5*h,idle_calls=8*v)
+    need((ledger['calls'],ledger['rank_mass'],ledger['deficit'],ledger['max_child'])==(361405,1613040,3080,46),'fresh five-stage ledger')
+    source_path,source_spec=by_upstream['Work/GCert/Chain/NetDef.lean'];lines=source_path.read_text().splitlines();refs={}
+    for name in ['x01','y01','x12','y12','x23','y23','x34','y34','sfin','term']:
+        indices=[i for i,line in enumerate(lines) if name+' :' in line];need(indices,'missing exact matrix field '+name)
+        i=indices[-1] if name=='sfin' else indices[0]
+        text=' '.join(x.strip() for x in lines[i:i+(2 if name=='sfin' else 1)])
+        refs[name]=dict(source='Work/GCert/Chain/NetDef.lean',anchor=name+' :',line=i+1,declaration_line=text,
+            url='https://github.com/jacobalansussman/wht-power-saving-lean/blob/'+PIN+'/Work/GCert/Chain/NetDef.lean#L'+str(i+1))
+    m=dict(source_pin=PIN,parameters=dict(h=h,m=dim,v=v,R=R,W_live=W,invocation_live=2*v+R),
+        ledger=ledger,checks=checks,chronology=CHRONOLOGY,source_frame_equalities=refs)
+    progress('Deriving both complex scalar words and temporary lifetimes.')
+    A=scalar.flat(c['A']);B=scalar.flat(c['B']);b={};life={}
+    for orientation in ['forward','backward']:
+        b[orientation]=scalar.bill(scalar.inv_schedule(orientation,A,B,c))
+        life[orientation]=scalar.lifecycle(scalar.inv_schedule(orientation,A,B,c))
+    need((b['forward']['totals']['real_component_primitive_steps'],b['backward']['totals']['real_component_primitive_steps'])==(1492984,1549456),'fresh scalar expansion')
+    b['scratch_lifecycle_checks']=life;b['template_tests']=scalar.toy_checks()
+    b['five_invocation_scalar_primitives_per_vertex']=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps']
+    b['scratch']=dict(live_roles=W,physical_roles_per_cover=W+R+h+1,additional_recursive_calls=0,extra_external_row_coordinate=False)
+    progress('Merging scalar events, exact frames and all final climbs.')
+    programs={};controls=[]
+    for orientation in ['forward','backward']:
+        events=list(splice.emit(c,orientation));programs[orientation]=splice.validate(events,c,orientation,m,b)
+        controls.extend(splice.controls(events,c,orientation,m,b))
+    g=splice.global_contract(m);splice.validate_global(g,m)
+    mutations=[('wrong_helper_owner',lambda x:x['stage_recipe'][1].__setitem__('helper_owner','s1^(-1)(d)')),
+        ('rank_only_frame',lambda x:x['exact_frame_bindings']['x23'].__setitem__('declaration_line','same rank only')),
+        ('scratch_alias',lambda x:x['scratch_namespace'].__setitem__('centers',[14691,14713])),
+        ('wrong_live_normalization',lambda x:x.__setitem__('recursive_volume_denominator',24127)),
+        ('free_RAM',lambda x:x.__setitem__('primitive_policy','free_RAM')),
+        ('missing_tableau',lambda x:x.__setitem__('physical',14715))]
+    for name,fn in mutations:
+        bad=deepcopy(g);fn(bad)
+        try:splice.validate_global(bad,m)
+        except ValueError as error:controls.append(dict(name=name,rejected=True,reason=str(error)))
+        else:raise ValueError('global mutation accepted: '+name)
+    progress('Recomputing complex cover, router, precision and row inequalities.')
+    precision=finite_guard(m,b,basis)
+    need(labels.scalar_word([(1,0,1),(0,1,-1),(0,2,1),(3,1,-1),(1,0,1),(3,1,1),(0,2,-1),(2,3,-1),(3,2,1),(1,3,-1),(2,0,1)])==[[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]],'global scalar signed exchange')
+    return dict(status='PASS_FRESH_COMPLEX_LABEL_SCALAR_SPLICE_PRECISION',five_stage_histogram=ledger['histogram'],
+        label_checks=checks,ledger=ledger,scalar_bill=b,
+        splice=dict(program=programs,global_contract=g,controls=controls,source_pin=PIN,certificate_sha256=cp['compressed_sha256']),
+        precision_guard=precision,input_pins=verified,
+        inherited_theorem_dependencies=[
+            'Pinned hAi,hBi,hx,hy,hid establish the full scalar identity; this is not a fresh Lean or full scalar-column replay.',
+            'Pinned Lab.inv dirty lifting, exact gwinB/G0..G4 geometry, owner bijections and NetCert composition are inherited source theorems.',
+            'Retained general Clifford synthesis, compact complete-stream tape primitives, common-grid precision and complete-row proofs remain analytic dependencies.',
+            'The finite operational recipe is regenerated and checked; no astronomical cover enumeration or universal tape-machine execution is claimed.'])
+
+if __name__=='__main__':
+    result=run(progress=lambda text:print(text,file=sys.stderr))
+    print(json.dumps(result,indent=2))
diff --git a/research/gen4-retiming-entrances/vendor/pr276/prepare.py b/research/gen4-retiming-entrances/vendor/pr276/prepare.py
new file mode 100644
index 0000000000..952bd727b4
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/prepare.py
@@ -0,0 +1,63 @@
+"""Clean gen4 preparation: the arc-aware local-design paired-cube bit word with its physical layer.
+
+The bit word (gen4bit/selected/bit) is admitted by PR200's unmodified physical-word classes
+(gen4bit/bit/word.py, base_word.py) over PR168-v4's unmodified exact checker. The context exposes
+the interface of the retained source527 scalar program (scalar/word.py, byte-identical); every
+source527-specific selection (source loans, aggregation/rank/echelon groups, fresh and paired
+source reads, terminal sinks, early mixes, retimed prefixes) is empty for this word.
+No payload execution occurs here.
+Prepared by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from types import SimpleNamespace
+import hashlib,importlib.util,json,sys
+sys.dont_write_bytecode=True
+HERE=Path(__file__).resolve().parent
+WORD_SHA='e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42'
+
+def prepare():
+ G=HERE/'gen4bit'
+ spec=importlib.util.spec_from_file_location('gen4_pr200_physical_word',G/'bit/word.py');module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+ W=module.Candidate();C=W.C
+ # Exact decoder/geometry of the virtual graph, and every changed operation frame and alias handoff.
+ C.decoder();C.geometry();W.exact_frames()
+ W.changed_frames=[i for i,(a,b)in enumerate(zip(W.original_opframe,W.opframe))if a!=b]
+ W.endframe={r:W.opframe[ii[-1]]for r,ii in W.role_ops.items()}
+ assert W.R==17904 and len(W.pairs)==1494 and len(W.gauge)==3960 and W.v==1760 and W.h==24 and len(W.changed_frames)==1802
+ assert all(0<=W.readtime[s]<=W.first[s]for s in W.gauge)
+ assert all(W.last[d]<W.readtime[b]and C.sub(W.endframe[d],W.gauge[b]['frame'])for b,d in W.pairs)
+ assert all(not(set(W.gauge)&set(W.ops[i][:2]))for i in W.phase1)
+ # The centre prefix is exactly phase one, executed in its listed order.
+ schedule=dict(events=[dict(kind='gate',op=i)for i in W.phase1],center_prefix_events=list(range(len(W.phase1))),deferred_ops=[],new_phase1=list(W.phase1),new_untouched_roles=[])
+ selection=[];gauge_selection=[];new_gauge_selection=[];extra_selection=[];new_phase_roles=set()
+ borrow={};by_source={};omitted=set();early={};gauge_borrow={}
+ kpair={e['passive']:e for e in W.k['entries']};assert len(kpair)==880
+ adj=[{}for _ in range(W.R)]
+ for r,s in zip(W.g['roots'],W.w['rootroles']):
+  for t in r['targets']:adj[s][t]=adj[s].get(t,0)+1
+ for i in reversed(W.phase1+W.rest):
+  a,b,_=W.ops[i]
+  for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c
+ assert adj==W.adjoint()
+ assert all(set(adj[s])==set(z['targets'])for s,z in W.gauge.items()),'gauge targets are exact response supports'
+ terminal=[];removed=set();deletedroots=set();bywrite={};afterwrite={}
+ regs=sorted(set(W.phys.values())-set(borrow)-removed);idx={r:2*W.v+j for j,r in enumerate(regs)}
+ assert len(regs)==W.R-len(W.pairs)==16410
+ at=defaultdict(list)
+ for b in W.order:at[W.readtime[b]].append(b)
+ deliveries=defaultdict(list)
+ for e in W.k['entries']:deliveries[e['deliver_after_root']].append(e)
+ m=SimpleNamespace(W=W,C=C,schedule=schedule,selection=selection,gauge_selection=gauge_selection,new_gauge_selection=new_gauge_selection,
+  extra_selection=extra_selection,new_phase_roles=new_phase_roles,borrow=borrow,by_source=by_source,omitted=omitted,early=early,
+  gauge_borrow=gauge_borrow,kpair=kpair,adj=adj,terminal=terminal,removed=removed,deletedroots=deletedroots,bywrite=bywrite,
+  afterwrite=afterwrite,regs=regs,idx=idx,at=at,deliveries=deliveries,deferred=[],
+  agg=[],role_groups={},target_group={},read_frames={},extra_byrole={},rankgroups=[],rankowner={},echelon=[],eowner={},
+  fresh={},pair_byalias={},pair_bydirty={},pair_selection=[],zero=W.register([]),source_head='gen4')
+ # Names the retained scalar program reads from its preparation namespace.
+ m.Counter,m.defaultdict,m.json,m.sys,m.hashlib,m.Path=Counter,defaultdict,json,sys,hashlib,Path
+ m.SOURCE_TEXT=(HERE/'scalar/word.py').read_text()
+ assert hashlib.sha256(m.SOURCE_TEXT.encode()).hexdigest()==WORD_SHA
+ m.input_pins={str(p.relative_to(HERE)):hashlib.sha256(p.read_bytes()).hexdigest()for p in sorted(G.rglob('*'))if p.is_file()}
+ m.portable_source_pins=dict(m.input_pins)
+ return dict(m.__dict__)
diff --git a/research/gen4-retiming-entrances/vendor/pr276/prime_check.py b/research/gen4-retiming-entrances/vendor/pr276/prime_check.py
new file mode 100644
index 0000000000..a7151e2807
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/prime_check.py
@@ -0,0 +1,67 @@
+"""Recompute exact determinants for every physically consumed gen4 basis.
+Based on PR234's prime coverage check; substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from pathlib import Path
+import hashlib,importlib.util,json,time
+HERE=Path(__file__).resolve().parent
+
+def basis_hash(basis):return hashlib.sha256(json.dumps(basis,separators=(',',':')).encode()).hexdigest()
+
+def validate_record(row,dimension,determinant,allowed_primes):
+    assert type(row['dimension'])is int and type(row['determinant'])is int and type(row['residual'])is int,'exact integer witness fields'
+    assert row['dimension']==dimension and row['determinant']==determinant!=0,'exact determinant mismatch or singular basis'
+    assert 0<row['residual']<2**80,'retained prime lower bound'
+    product=row['residual']
+    for prime,exponent in row['factors'].items():
+        p=int(prime);assert p in allowed_primes and type(exponent)is int and exponent>0,'factor shape';product*=p**exponent
+    assert product==abs(determinant),'factor identity'
+
+def run(context,physical,progress=lambda text:None):
+    started=time.monotonic();w,c=context['W'],context['C']
+    p=HERE/'prime_witnesses.py';spec=importlib.util.spec_from_file_location('source527_exact_prime_validator',p);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+    required=set(w.opframe)|set(w.w['source_frame'])|set(w.w['root_frame'])|{w.w['full_frame'],w.register([])}
+    required.update(g['frame']for g in w.gauge.values())
+    for e in w.k['entries']:required.update((e['mix_frame'],e['deliver_frame']))
+    for t in range(w.v):required.add(w.register(w.module.kernel([c.cov[t]],w.h)[0]))
+    required.update(g['frame']for g in context['agg']+context['rankgroups']+context['echelon'])
+    required.update(r['mix_frame']for r in context['pair_selection'])
+    used=set();groups={}
+    for row in physical['used_frames']:
+        f=row['frame_id'];assert f not in used;used.add(f)
+        h=basis_hash(c.B[f]);assert h==row['basis_sha256'] and len(c.B[f])==c.dimf[f]==row['dimension'],'fresh physical basis identity'
+        groups.setdefault(h,f)
+    assert {basis_hash(c.B[f])for f in required}<=set(groups),'base and added transform coverage'
+    determinants={};largest=0;prime_factors=set();witnesses={}
+    for j,(h,f)in enumerate(sorted(groups.items())):
+        B=c.B[f];s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[k]for k,y in enumerate(B)]for i,x in enumerate(B)]
+        det=module.det(gram);powers,residual=module.factor_witness(det)
+        row=dict(dimension=len(B),determinant=det,residual=residual,factors={p:e for p,e in powers.items()if e})
+        validate_record(row,len(B),det,module.PRIMES);prime_factors.update(map(int,row['factors']));witnesses[h]=row
+        determinants[h]=det;largest=max(largest,abs(det).bit_length())
+        if j and j%5000==0:progress('Validated '+str(j)+' exact basis determinants')
+    ranks=Counter();bundle_bases=set()
+    for role,g in w.gauge.items():
+        if role in w.donor or role in context['borrow']:continue
+        a=g['dim'];h=basis_hash(c.B[g['frame']]);d=determinants[h]
+        assert 0<5*a<120 and d!=0;ranks[a]+=1;bundle_bases.add(h)
+        assert abs(d**5)==abs(d)**5
+    assert ranks=={20:2200,21:266}and len(bundle_bases)==370
+    assert 2*120**3*10**16<2**80
+    from copy import deepcopy
+    controls=[]
+    def reject(name,call):
+        try:call()
+        except AssertionError:controls.append(name)
+        else:raise AssertionError('invalid witness accepted: '+name)
+    first=next(iter(groups));row=witnesses[first];det=determinants[first]
+    missing=dict(witnesses);missing.pop(first)
+    def coverage(actual,wanted):assert set(actual)==set(wanted),'complete current basis coverage'
+    reject('missing current basis',lambda:coverage(groups,missing))
+    changed=deepcopy(row);changed['determinant']=det+1;reject('incorrect determinant',lambda:validate_record(changed,row['dimension'],det,module.PRIMES))
+    changed_factor=deepcopy(row);changed_factor['residual']+=1;reject('incorrect factor identity',lambda:validate_record(changed_factor,row['dimension'],det,module.PRIMES))
+    singular=deepcopy(row);singular['determinant']=0;reject('singular basis',lambda:validate_record(singular,row['dimension'],module.det([[1,2],[1,2]]),module.PRIMES))
+    huge=deepcopy(row);huge['residual']=2**80;reject('residual at prime lower bound',lambda:validate_record(huge,row['dimension'],det,module.PRIMES))
+    noninteger=deepcopy(row);noninteger['residual']=float(row['residual']);reject('noninteger residual',lambda:validate_record(noninteger,row['dimension'],det,module.PRIMES))
+    return dict(status='PASS_FRESH_ALL_ACTUAL_GEN4_BASIS_DETERMINANTS_AND_FIVEFOLD_BUNDLES',unique_bases=len(groups),current_frame_ids=len(used),basis_inventory_sha256=hashlib.sha256(json.dumps(sorted(groups),separators=(',',':')).encode()).hexdigest(),maximum_determinant_bits=largest,prime_factors=sorted(prime_factors),all_remaining_factors_below_2_power_80=True,independent_entrances=sum(ranks.values()),bundled_unique_bases=len(bundle_bases),entrance_rank_counts=dict(ranks),controls=controls,physical_inventory_bound=True,seconds=time.monotonic()-started,scope='Every actual physical basis of the gen4 word is freshly evaluated over exact integers; all source, gauge, operation, root, partner-mix, delivery and cap frames are covered. Five disjoint copies inherit nondegeneracy; compiler and prime supply remain theorem dependencies.')
diff --git a/research/gen4-retiming-entrances/vendor/pr276/prime_witnesses.py b/research/gen4-retiming-entrances/vendor/pr276/prime_witnesses.py
new file mode 100644
index 0000000000..7f16d93030
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/prime_witnesses.py
@@ -0,0 +1,99 @@
+"""Exact finite prime exclusions for the selected new rational bit frames.
+
+For integer basis B and G=I-J/9, det(9 B G B^t) is a nonzero integer.
+Excluding its prime divisors and 2,3,5 makes the reduced frame nondegenerate
+over every odd local ring Z/q^w. Projector denominators divide this determinant
+times fixed powers of 3. Retained frames retain their old exclusion witnesses.
+The selected q is an arbitrarily large fixed prime chosen after this finite
+set; this is not verification at a preselected numeric q.
+"""
+from pathlib import Path
+import argparse,gzip,hashlib,json,sys
+
+HERE=Path(__file__).resolve().parent
+
+def det(A):
+    A=[list(r) for r in A];n=len(A)
+    if not n:return 1
+    sign=1;previous=1
+    for k in range(n-1):
+        pivot=next((i for i in range(k,n) if A[i][k]),None)
+        if pivot is None:return 0
+        if pivot!=k:A[k],A[pivot]=A[pivot],A[k];sign=-sign
+        p=A[k][k]
+        for i in range(k+1,n):
+            for j in range(k+1,n):
+                v=A[i][j]*p-A[i][k]*A[k][j]
+                assert v%previous==0
+                A[i][j]=v//previous
+            A[i][k]=0
+        previous=p
+    return sign*A[-1][-1]
+
+PRIMES=(2,3,5,7,11,13,17,19,23,29,31)
+
+def factor_witness(determinant):
+    assert type(determinant) is int and determinant != 0
+    residual=abs(determinant);powers={}
+    for prime in PRIMES:
+        power=0
+        while residual%prime==0:residual//=prime;power+=1
+        powers[str(prime)]=power
+    validate_factor(determinant,powers,residual)
+    return powers,residual
+
+def validate_factor(determinant,powers,residual):
+    assert type(determinant) is int and determinant != 0
+    assert set(powers)==set(map(str,PRIMES))
+    assert all(type(x) is int and x>=0 for x in powers.values())
+    assert type(residual) is int and 0<residual<2**80
+    reconstructed=residual
+    for p in PRIMES:reconstructed*=p**powers[str(p)]
+    assert reconstructed==abs(determinant)
+
+def certificate(word=None):
+    if word is None:
+        from word import Candidate
+        word=Candidate()
+    C=word.C;h=word.h
+    used=set(word.opframe)|set(word.w['source_frame'])|set(word.w['root_frame'])|{word.w['full_frame']}
+    used.update(z['frame'] for z in word.w['gauges'])
+    for e in word.k['entries']:used.update((e['mix_frame'],e['deliver_frame']))
+    groups={}
+    for frame in sorted(used):
+        B=C.B[frame]
+        key=json.dumps(B,separators=(',',':'));groups.setdefault(key,[]).append(frame)
+    records=[]
+    for key,frames in sorted(groups.items()):
+        B=json.loads(key);s=list(map(sum,B))
+        gram=[[9*sum(a*b for a,b in zip(x,y))-s[i]*s[j] for j,y in enumerate(B)] for i,x in enumerate(B)]
+        determinant=det(gram);powers,residual=factor_witness(determinant)
+        records.append(dict(basis_sha256=hashlib.sha256(key.encode()).hexdigest(),
+            frame_ids=frames,dimension=len(B),cleared_gram_determinant=determinant,
+            small_prime_powers=powers,remaining_factor=residual,gram_denominator_power_of_9=len(B)))
+    controls=[];zeros={str(p):0 for p in PRIMES}
+    for name,args in (('zero determinant',(0,zeros,1)),('incorrect factor identity',(15,zeros,1)),
+        ('residual above retained prime lower bound',(2**80+7,zeros,2**80+7))):
+        try:validate_factor(*args)
+        except AssertionError:controls.append(name)
+        else:raise ValueError('Invalid prime witness accepted: '+name)
+    return dict(status='PASS exact prime witnesses for every used physical frame',h=h,
+        source_commit='4a3c769e5c5430e7114c4d3e099ff34664677f17',
+        input_sha256={str(p.relative_to(HERE.parents[2])):hashlib.sha256(p.read_bytes()).hexdigest() for p in word.input_paths},
+        script_sha256=hashlib.sha256(Path(__file__).read_bytes()).hexdigest(),
+        stripped_primes=list(PRIMES),frame_witnesses=records,unique_used_bases=len(records),
+        total_used_frames=len(used),total_operation_frames=len(word.changed_frames),
+        maximum_determinant_bits=max(abs(z['cleared_gram_determinant']).bit_length() for z in records),
+        all_remaining_factors_below_retained_prime_lower_bound=True,adverse_controls=controls,
+        rule='Every q>2^80 avoids every nonzero used-frame determinant, so the original prime range is unchanged.',
+        scope='Exact integer cleared-Gram factors for all physical frames including every changed operation, gauge, source, root, partner-mix, delivery and ambient frame. Uniform split-rank and fallback arguments remain the retained local-ring interface.')
+
+def main():
+    assert not sys.flags.optimize
+    ap=argparse.ArgumentParser();ap.add_argument('--write',action='store_true');args=ap.parse_args()
+    record=certificate();target=HERE/'prime-witnesses.json.gz'
+    if args.write:target.write_bytes(gzip.compress((json.dumps(record,sort_keys=True,separators=(',',':'))+'\n').encode(),mtime=0))
+    else:assert record==json.loads(gzip.decompress(target.read_bytes())),'Exact prime witnesses changed'
+    print(json.dumps({k:v for k,v in record.items() if k!='frame_witnesses'}))
+
+if __name__=='__main__':main()
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md b/research/gen4-retiming-entrances/vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md
new file mode 100644
index 0000000000..42a585d742
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/FINITE_BIT_ACCOUNTING.md
@@ -0,0 +1,126 @@
+# Portable five-stage BIT finite bill
+
+The executable `finite_check.run` accepts the freshly reconstructed source
+ledger, physical tags, independently checked scalar projection, exact current
+basis-prime result, exact moment calculation and optional global lowering
+result. It reads no saved execution receipt. Source expectations are checked
+against those computed objects, not substituted for them. The complete
+package runner is responsible for generating its inputs before this call.
+
+## Quantifiers and inherited primitive hypotheses
+
+Fix this candidate and an eligible odd prime q>2^80 before the input widths
+n,w are chosen. All represented determinant and route exclusions lie in
+{2,3,5,7}. The primitive constant C may depend on q, the fixed source recipe,
+the finite bootstrap level and the retained primitive implementations. It
+does not depend on n,w, ancestor values or unrelated spectator widths except
+through logical volume V.
+
+The three byte-pinned public sources supplied here are
+`three-stage-cover-bit.tex`, `three-stage-cover-rows.tex`, and
+`copied-centers-lemma.tex`. Their exact-tape, completed ordinary-leaf and
+complete-stream hypotheses are retained. All high matrix fibers are batched;
+prefix descriptor preparation has fixed polynomial cost in w and is paid
+over the complete q^w target fiber. Unrelated spectators use ripple counters.
+Fresh child role fields never enter the ancestor weight descriptor. Finite
+low-type tables, initialization and sequential scans are charged in C.
+There is no unit-cost random-access oracle or new numerical Turing-machine
+constant requirement.
+
+## Actual finite recipe
+
+Let m=120, W=23,683, E=495,304, v=1,760, R=16,643, d=m^2 and
+J=20v+10R+4v=208,670. The last 4v=7,040 families pay the explicit final
+complete-stream exchange; they are not equal-frame payload shears.
+
+The check derives from the fresh word 12,858,690 weighted additions or
+21,787,770 unit additions, including all six bridge families. Its
+cancellation-free prefix lift is
+64*37,623^3*9,430,154^2=303,094,329,841,208,644,962,256,113,408<2^98.
+No old defining-integer endpoint is imposed on the F2 supplier.
+
+The actual rational 48-dimensional route is reconstructed, eliminated and
+inversely replayed: 195 additions, 44 swaps and 27 scalings, with denominator
+set {1,2,3,6}. A missing addition fails reconstruction. Coordinate
+permutations and embedding give the other ports and stages.
+
+Per route, pay at most 23,707*|GL_120(F_q)| low-role transpositions and
+16*(d+1)^2 high affine factors. Per good edge, pay at most 8m^2+8 elementary
+normalizer wrappers. The same compiler pays all exterior completions.
+There are 120 copied-center episodes. Their recursive rank-22 calls and
+their scalar reads are already included in E and the scalar count; their
+copy/erase and parking passes are separately paid by the complete-stream
+primitive, using one additional work stream.
+
+For a bad edge with N=2m=240, the exact inherited Gaussian fallback uses at
+most 6N(N-1)+3N+6(N-1)=346,314<32m^2=460,800 children. Keep the entire
+larger allowance in the moment. Coefficient preparation uses only unit
+pivot inversions. Allocate 128N^3 ring operations per edge per low class:
+four 8N^3 elimination/inversion allocations and sixteen 2N^3 matrix products
+give 64N^3; the remaining 64N^3 pays extraction, copying, generic tests,
+factor output and the bad-branch elimination. Matrix bit costs and descriptor
+arithmetic are paid by the inherited primitive theorem. Invertibility testing
+of each candidate low matrix additionally gets 16m^3 operations.
+
+Overcharging every finite recipe item over every low matrix gives
+
+    B(q) <= [unit+J*16(d+1)^2+J*(W+24)+E*(8m^2+8)
+             +E*128(2m)^3+16m^3+120+E+1]*q^14400
+         = 1,568,901,757,016,837*q^14400 < q^14401.
+
+These are explicit ring/recipe counts, not single-step machine costs. All
+fixed-tape, table, setup and selector constants stay in C_primitive, giving
+the normalized toll C*n+C*w^(1-a_old) after increasing one finite C.
+No recursive child is absorbed into this nonrecursive constant.
+
+## Weighted induction and rows
+
+Set c=704197288590873/10^18 and tau=1-c. Exact interval recomputation,
+adding the entire 10^-16*32m^2 fallback envelope per edge, proves
+
+    1-mu_tau > 774/10^21,
+    1-mu_1 = 107421874442783/69383789062500000 > 0.
+
+For the retained recurrence
+T(n,w)<=sum_r c_r*T(r*floor(n/120),w)+C*n+C*w^(1-a_old),
+take A=C*(1+1/(1-mu_1)+1/(1-mu_tau)). Induction bounds T by
+A*(n+n^tau*w^(1-a_old)): the linear and stopped gaps separately pay the
+two tolls; the leaves follow A>=C. Floors only decrease the child sizes.
+
+The maximum ratio is 5/6, so four levels halve. The depth bound
+4*ceil(log2(max(2,n))) changes stock, not the one-level moment. Paying all
+24 temporary roles gives per-level log_q stock below 14400w+1. Add the
+inherited old-leaf reserve. The new contribution is at most
+57,604w*ceil(log2(max(2,n))). Borrow and restore these complete high digits;
+successive residuals and the two-call ordinary wrapper reuse the reserve.
+One outer row padding factor is below two; binary-radix padding costs less
+than q^2 in logical volume. The temporary roles never enter the denominator W.
+
+## Finite ordinary bootstrap and cutoff
+
+Starting with completed ordinary a0=384599/10^10, set beta=c and repeat
+a_(j+1)=(1-c)c+c*a_j exactly three times. The finite result is
+
+    a3=704197288358392787581160456097840009769165126434639147437106139267359/10^72.
+
+At each stage, the paid exponents are 1-c, 1-a_(j+1), c with a logarithm,
+and c(1-a_j). The exact positive gaps are c-a_(j+1),
+1-a_(j+1)-c, 1-a_(j+1)-c(1-a_j), and 1-c (for row fitting).
+
+Choose a finite integer C>=1 dominating that stage's already fixed primitive,
+recurrence, wrapper, row, setup, padding and previous ordinary constants.
+Let delta be the minimum positive gap and
+
+    L=ceil(max(1,36/delta^2,2*(4+ceil(log2 C))/delta)), e0=2^L.
+
+For e>=e0, C(1+log2 e)e^(-delta)<=1/16. Indeed for t=log2 e,
+log2(1+t)<=3sqrt(t)<=delta*t/2 and log2 C+4<=delta*t/2.
+Thus every lower-order toll is covered and the borrowed high part fits.
+Below e0 use the previously completed ordinary algorithm. A finite next
+constant is C_large+C_old*2^(L*(a_(j+1)-a_j)). This choice is sequential,
+not circular, and uniform in the input and complete spectators.
+
+This proves the finite-accounting and ordinary-bootstrap step at the same
+conditional theorem level as the retained public baseline. It does not claim
+an independent proof of those inherited primitives, a measured universal
+machine constant, or execution at every input width.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/INTEGRATED_PROOF.md b/research/gen4-retiming-entrances/vendor/pr276/proof/INTEGRATED_PROOF.md
new file mode 100644
index 0000000000..c624da6c5c
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/INTEGRATED_PROOF.md
@@ -0,0 +1,87 @@
+# Source-bound five-stage compositional candidate
+
+9 October 2026. This is an isolated research admission branch. Its executable checks immutable finite receipts and recomputes exact scalar moments, a finite ordinary bootstrap, and all 47 balanced outer inequalities. It additionally binds fresh public-source bit preparation, raw-ledger construction, and the complete globally lowered physical event stream. It does not repeat the exhaustive F2 column proof, run the Lean kernel or universal tape machine, or claim Mac qualification or publication.
+
+## 1. Meaning of admission here
+
+The branch is an explicit conjunction of constructive source theorems and finite source-bound evidence. It does not replace any proof with a numerical root or infer source correctness from a PASS string. The new family names are `new5stageF2` and `baseline5stageComplex`; the old dimension-72 entry point and written bounds are kept byte-identical. The branch has no general-purpose dimension override.
+
+The executable's semantic guards reject a wrong source, omitted copied centers, a rank-only complex frame contract, a work/live denominator substitution, omitted final climbs, incorrect reverse-copy lowering, and a one-level bit-halving substitution. The source lock identifies the exact evidence, code, and primary proof files consumed. The more detailed emitted-program verifiers exercise local chronology and addresses, beyond these top-level schema controls.
+
+## 2. Raw source471 provenance
+
+The saved raw helper ledger pins an older screen.py. The older screen bytes are unavailable; no byte-delta assertion is made. The rebind verifier reruns the current exact geometry/ledger construction with all writes suppressed and a hash-verified cached certificate in place of its redundant network fetch. Every semantic field, all 471 source paths, and all 1,760 target paths agree. The saved ledger is not rewritten.
+
+The apparent target-prefix duplication is resolved by the actual chronology: screen.py removes the two latest loan prefixes for its predecessor positive controls; raw_ledger.py puts those two prefixes back. There are exactly eight restored target reads. Current-source dependency hashes and the canonical semantic-payload digest make this equivalence independently inspectable. The sole historical pin exception is specifically this screen.py field and is allowed only with the exact rebind witness.
+
+## 3. Local bit helper and global lowering
+
+The source is PR210 df95878d11190518e45ef9717c9ee05011f88ace. The independently recorded local scalar word has 2,569,626 weighted events. Its projection is fixed by SHA256 e74e43692685ad5f716b41b363acb8b443c2c90096634a55f0e3728980713944. Both literal forward and signed inverse pass all 20,163 F2 columns, including arbitrary targets and 16,643 independent dirty helpers. The 471 borrowed sources are source aliases, never extra independent dirty coordinates.
+
+The tagged physical word has digest 614f19da4288021cd5c10a575ec7759c069962a6030bf30edb047573ed76edf6 and realizes the telescope Dout M Din^-1. Its input frames are X:Pq, Y:0, Z:sigma and output frames X:H, Y:H-Pq, Z:H. Thus a completed invocation has no data/helper cross blocks and each independent helper residual is D_(H-sigma). This is a full arbitrary-input operator identity, not just zero-dirt testing.
+
+The five-stage compiler maps every local live index through the stage owner injection, maps every local temporary to external family 23,683, and applies the stage's data or helper cover bijection. The active source/target pairs are (X1,Y1), (Y1,X1), (X1,Y1), (Y2,X2), (X2,Y2). The unused pair stays parked. A data route is right multiplication by the exact rational rho_i,S; a helper route is the whole-block exchange tau_i. Both are bijections of the eligible GL cover. They are charged address movements, not dense payload arithmetic.
+
+Cover expansion is strictly phase-major: complete every cover class in stage i before starting the next routed stage or boundary phase. The same rule applies separately to idle, bridge, completion and terminal-exchange phases. Running all five stages for one class before proceeding to another class would be incorrect because rho and tau refer to other classes. The callable stage and boundary iterators specify the phases; a flattened one-class-per-phase template is not a class-major execution schedule. The admission contract rejects that alternative loop ordering.
+
+For backward stages the compiler reverses the complete local event order, negates scalar coefficients, and replaces local P by H-P. A copied-center block is lowered afresh: copy the original at H-U, transform the copy to H, perform reverse signed scatter, and erase it. It is forbidden to invert an erased temporary. Every original center also retains its complementary live climb. Copy/live index injectivity is checked for all stage orientations.
+
+The global lowering artifact must emit bridges, idle children, independent gauge completions, and the final signed bank exchange. That exchange is an explicitly paid complete-stream role permutation, not a same-frame shear. A stage-descriptor string alone does not meet this obligation.
+
+## 4. Rational five-window geometry and prime eligibility
+
+Take H=Q^24, G=I-J/9 and a triple line q*. Its projector has denominator 6; coordinate permutations supply the port isometries. The two-block involution rho_i,S fixes the two port lines and exchanges their complementary spaces. With Q_i the direct sum of the first i copied complements, the frame is D_[g rho_i,S(P direct_sum Q_i)rho_i,S^-1 g^-1]. The four elementary two-block projector identities imply all eight bank boundary equalities. Rational complements are I-P.
+
+The exact rational partial swap is D_P=[[I-P,P],[P,I-P]]. It is involutory. Every same-frame scalar gate telescopes exactly, all idle transitions are nested actual projectors, and D_I D_Pq=D_(I-Pq) gives the terminal all-data address endpoint after the scalar exchange. No Pauli or Fourier phase claim is imported from the complex compiler into this bit proof.
+
+For each independent physical helper, the five routed residuals occupy different H_i. Their supported projectors have pairwise zero products. Their product is D_(I-sum_i sigma_i), so one paid child D_(sum_i sigma_i) completes D_I. This is one correction for each helper, not a packing of unrelated dirty rows. The 2,279 independent entrances have ranks {12:18,13:48,18:13,20:2200}; the 31 source-owned gauge entrances receive no extra completion.
+
+All 26,750 used physical frame IDs (26,380 distinct bases) have exact determinant witnesses. Their factors lie in {2,3,5,7}; the 231 distinct gauge-bundle bases use {2,3,5}. Window-map denominators also use {2,3,5}. Hence every retained q>2^80 preserves these ranks. General GL charts use gPg^-1, not a recomputed Euclidean orthogonal projection.
+
+The weighted generic normalizer allows every proper rank, including 60,65,90,100 in dimension120. Its cleared pivot-polynomial degree is at most m r(r+1)/2 < m^3. Thus the bad fraction is at most2m^3/q<10^-16. Each bad edge retains the full invertible local-ring residual and is paid 32m^2=460,800 rank-one fallback children. No field elimination at nonunit pivots is substituted.
+
+## 5. Exact bit ledger and ordinary finite recurrence
+
+One invocation has 95,789 positive-rank children and rank mass435,846. Its24 rank22 center copies are included once, as are each original center's live climbs. With H this histogram,
+
+n5 = 5H + 3520(delta4+delta23+delta46+delta50)
+     +18delta60+48delta65+13delta90+2200delta100.
+
+Thus m=120, W=23,683, calls495,304, mass2,837,560, deficit4,400. Work streams do not enlarge the live moment denominator. Five invocations retain all120 rank22 centers.
+
+The counted finite-bit adapter pays the literal scalar word, six bridge families, weighted good-edge wrappers, bad-class residuals, copy/read/erase, class routing, selector arithmetic, and fixed-tape movement. Its retained primitive theorem fixes the eligible prime and finite source recipe before varying width, so its finite constant may depend on that prime and recipe. It cannot depend on width, ancestor payload values or unrelated spectators except through complete volume. This is the correct quantifier order; an invented numerical Turing-machine constant is unnecessary.
+
+The largest child ratio is5/6. Three levels do not halve and four do: (5/6)^4=625/1296<1/2. The same one-level weighted moment induction remains valid; the factor4 is used only in depth/descriptor/borrowed-row bounds. Even paying24 simultaneous temporaries gives physical stock23,707 per GL cover vertex and log_q Wphysical(w)<14400w+1. The resulting internal log_q row charge is at most4ceil(log2(max(2,n)))(14400w+1), plus the old-leaf reserve. High digits are borrowed and restored internally; this is not a new external q-adic group factor.
+
+The defining-integer lift need not equal the older supplier's decoder endpoint. A safe cancellation-free prefix bound is64*37623^3*9430154^2<2^98. It uses neither signed integer restoration nor commutation between stage-dependent decoder channels. F2 payload exactness does not require complex floating precision.
+
+Let c=704197288590873/10^18. The freshly enclosed full bit moment, including all bad fallback charges, has a strictly positive gap. Start from the retained completed ordinary leaf a0=384599/10^10. Three finite levels with atom exponent beta=c give
+
+a_(j+1)=(1-c)c+c a_j,
+a3=.000704197288358392787581160456097840009769165126434639147437106139267359.
+
+At every level a_j<a_(j+1)<c<1-a_(j+1). The actual finite-cutoff witness binds the positive moment and lower-order toll gaps to the new finite recipe. This is not an infinite limiting bootstrap or a packed-profile substitution.
+
+## 6. Complex source, complete splice and finite guard
+
+The complex source is f010392c923279e3dd59ef3aa5fedad23affc5fd. The published gcert/1 gzip and expanded JSON identities are checked directly. Its pinned scalar identities and GBridge2 matrix equalities are reused as source theorems, including phases; no same-rank substitute or changed-185 helper is admitted.
+
+The source-defined old-response and cleanup maps are realized by filtered, reversed and transposed literal helper words. Their scalar projections are checked against complete schedule hashes. Old-response uses a9,412-stream temporary tableau, cleared before all recursive children. The coefficient work stream is also cleared after use. The emitted label/scalar splice preserves13,798 phaseA transitions,46,937 phaseB transitions, and9,412 final climbs, totaling70,147 live transitions. It retains22 center children. Final climbs occur after B, followed by exact final-frame adapters and then cleanup.
+
+The five-stage source theorem supplies all ten exact matrix fields x01/y01 through x34/y34, sfin and term, the actual cover owner bijections, all idle banks and final signed exchange. The complete finite compiler uses the retained two-rank-zero-factor construction around each exact recursive C^r child. Rank-zero phase/permutation operations are charged selected-bit and complete-stream tape primitives, not free RAM lookups.
+
+The exact scalar primitive counts are1,492,984 forward and1,549,456 backward, totaling7,577,864 for three forward plus two backward invocations. All361,405 recursive children, including110 rank20 centers, remain charged. The profile has m110, W14692, mass1,613,040, deficit3,080 and maxchild46.
+
+Physical work stock is24,127|O(110,2)|, with6010 bits; live recursion stock has6009 bits. The proved local operation bill is below2^48 and the complete fixed-program bound below2^6050. Router and literal guards fit G=2^30000 and E=2^100000. Coefficients use only denominators1,2,3,6, so the exact common grid2^-P 3^-G(D+1) introduces no return rounding. Completed child semantics give C1=1, induction gap127B, and C0=2^210000>32mB^2. The complex half-shrink requirement is preserved:2*46<110.
+
+The physical row overcharge16,171 remains below20,161. Degree1,000,000 and suffix slope4,000,000 retain exact row gap23,971,789/25. These constants come from the changed stock and counted program, not from simply replacing72 by110 in the old guard.
+
+## 7. Fresh outer47 arithmetic and completion boundary
+
+Use complex saving747454944651775/10^18, strictly inside its freshly re-enclosed moment. The bit saving is the exact finite a3 above. Both moment gaps exceed7.7e-19. With eta=10^-12 and stopping fraction10^-9, the unchanged retained balanced assembly produces47 positive strict constraints and7 margins.
+
+The isolated candidate is kappa=703701743496697/10^18, or.000703701743496697. The minimum outer margin exceeds it by approximately7.3899e-19. This arithmetic value exceeds the retained frontier. Exact rational gaps, rather than printed decimals, are the evidence.
+
+The certificate remains a receipt-bound compositional research candidate with explicit source-theorem dependencies. The clean loader consumes 22 pinned public files and agrees in 23 exact semantic components with the audited context. Its fresh raw ledger and complete five-stage histogram agree; an empty-directory extraction passes all 10 focused tests. The clean-root global emitter regenerates all 12,858,690 weighted additions, 495,304 paid children, 120 fresh copies and erasures, 2,279 helper completions, and 3,520 final pair exchanges. Source-bound global lowering, exact h24 geometry, clean-loader qualification, and finite closure supplements are all mandatory before the entry point emits its PASS certificate.
+
+These fresh computations do not pretend that the inherited exhaustive F2 columns, exact determinant archive, or complex source theorems were independently reproved. Full portable packaging and Mac qualification remain separate delivery checks. The pinned comparison frontier is df95878's .000694782719690783; the subsequently reported public head31f4ccc1c16c538749845f9244b24747f1cf93dd claims .000695191451687307, which is a separate comparator pending independent validation and is not substituted into this source freeze.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/PARITY-CONTRACT.md b/research/gen4-retiming-entrances/vendor/pr276/proof/PARITY-CONTRACT.md
new file mode 100644
index 0000000000..fad6150b1f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/PARITY-CONTRACT.md
@@ -0,0 +1,45 @@
+# Parity-even payload gate removal: inherited contract audit
+
+Conclusion: removing an even-coefficient pointwise payload ADD is valid for the bit supplier. The odd-prime address arithmetic remains unchanged. A new paid profile still requires the actual filtered word and full frame schedule; this conclusion alone does not certify a new kappa value.
+
+## Primary source evidence
+
+The bundled, unmodified primary section [`primary/03-motifs.tex`](primary/03-motifs.tex) states the following. Its exact source, attribution, and file hashes are recorded in [`primary/PROVENANCE.md`](primary/PROVENANCE.md).
+
+* Line50: in the bit construction scalars lie in F2.
+* Lines149–177: replace a scalar by an array in R^Omega, with R the scalar ring of the network. Common R-linear frames give the exact operator `D_out S_Omega D_in^-1`.
+* Around line223: the scalar domain need not equal the label field. Bit labels are rational subspaces even though the payload scalars are binary.
+* Lines483–493: rational-address frames are F2-linear permutations of array entries; the bit network uses pointwise XOR gates.
+
+The byte-pinned [`copied-centers-lemma.tex`](copied-centers-lemma.tex) in this package opens with its scalar restoration identity explicitly over F2. Its copy contract preserves the complete role stream, controls and spectators; each copy's frame change and erasure remain paid.
+
+The retained PR234 [`INTEGRATED_PROOF.md`](INTEGRATED_PROOF.md), line56, explicitly says: "The defining-integer lift need not equal the older supplier's decoder endpoint" and the majorant "uses neither signed integer restoration nor commutation between stage-dependent decoder channels." The package's signed integer decoder checks are stronger supplier evidence; the inherited bit interface does not impose their particular integer endpoint on a newly synthesized F2-equivalent word.
+
+The retained weighted bit theorem, [`three-stage-cover-bit.tex`](three-stage-cover-bit.tex), uses the odd-prime local ring Z/q^w for address fields and weighted address interchanges. Its rational projectors, unit-pivot tests, route matrices and fallback coefficients are address geometry. They are not the F2 payload ADD coefficients.
+
+## Operator proof
+
+Fix the finite complete address set Omega and let one stream be a vector in F2^Omega. A payload gate is `x_a <- x_a + (c mod2) x_b`. For even c this is the identity on every input, including arbitrary correlated dirty streams and spectators. Removing any number of these identity gates leaves the complete scalar operator S_Omega unchanged. Negative odd coefficients and coefficient3 also reduce to1, though the simplest experimental witness can retain their original signed integer representatives.
+
+Retain each original input/output frame and every remaining gate's original common frame. The common-frame identity then gives the same `D_out S_Omega D_in^-1` for the filtered word. In particular, every independent helper still has its required partial-swap residual and the existing completed-bank proof still applies. No integer identity of the new lift is needed to conclude this F2 operator identity.
+
+## Safe frame compression
+
+Deleting an ADD removes its operand-frame alignment requirement. For a given stream, collect successive MOVE operations between surviving uses. A use includes any surviving ADD, COPY read/write, ERASE or required phase/endpoint boundary. No use may be crossed merely because another stream is idle.
+
+Suppose the original local frames form a nested chain U0 <= U1 <= ... <= Uk. Their exact address changes telescope to `D_Uk D_U0^-1`. Their orthogonal increments are disjoint commuting projectors, so this is one allowed residual of rank dim(Uk)-dim(U0). In the reflected orientation the chain is the reversed complementary chain; the same endpoint difference and rank follow exactly. The ambient stage background cancels. Rebuild both ledgers from the actual surviving uses and actual basis inclusions; do not infer this from summed ranks alone.
+
+Keep every physical input/output family and its endpoint, all stage boundaries, all data routes/bridges, and every copied-center lifetime. For source527 the120 center copies in the five-stage construction have odd scatter coefficients, so parity filtering does not itself remove those episodes. The shared work stream cannot be used before COPY or after ERASE. A COPY is a barrier even if its original register has no intervening ADD.
+
+## Required finite admission
+
+1. Filter actual emitted ADD records by the literal coefficient modulo2; retain all odd-coefficient records in their original order. Check all20107 formal F2 source, target and dirty columns against the admitted shear. The expected local event counts before any further resynthesis are1,783,196 removed and786,621 retained.
+2. Generate the actual complemented inverse schedule, with fresh reverse copies as before, and verify every formal F2 column again. Do not reverse an erasure.
+3. Compute cancellation-free prefix bounds for the new literal signed forward/inverse projections. Recompute the five-stage bound and finite bill. Failure to reproduce the previous integer decoder is not itself a contract failure; a missing F2 dirty restoration is.
+4. Regenerate exact monotone forward/reflected physical paths and the complete paid histogram. Every fused residual's actual endpoints must be checked. Keep all remaining recursive children, copied-center calls, fallback allowance, data idle edges and stock.
+5. Rebind the completed banks and final global address lowering to the new word and tags. Their actual rational address projectors, odd-q routes and normalizers must not be reduced modulo2.
+6. Rerun actual basis/prime coverage, finite ordinary-leaf assembly, both rational moment engines and all47 outer inequalities before claiming a result.
+
+For simple monotone MOVE fusion the paid rank mass and physical stock remain unchanged; combining positive increments can improve the concave moment while reducing the number of children. Any different deficit or stock must be explained by a separate exact endpoint change. The displayed bound is still conditional on the retained all-size compiler, selectors, common ancestor charts, restored rows, routing, prime and analytic interfaces.
+
+Prepared with OpenAI Codex assistance. This audit is independent of the physical parity-filter/fusion implementation owned by the complex research lane.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/README.md b/research/gen4-retiming-entrances/vendor/pr276/proof/README.md
new file mode 100644
index 0000000000..19751671be
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/README.md
@@ -0,0 +1,8 @@
+# Retained proof documents
+
+The `.tex` files are byte-pinned theorem sources. `finite_check.py` checks their hashes and phrases.
+
+`INTEGRATED_PROOF.md`, `FINITE_BIT_ACCOUNTING.md` and `PARITY-CONTRACT.md` are retained verbatim from the
+PR234 and source527 packages. Their arguments apply to this package unchanged. Their numerical instances,
+such as R, W, stock, bills and digests, describe the earlier source471 and source527 helpers, not gen4.
+The gen4 values are recomputed by `verify.py` and stated in `../PROOF.md` and `../BANK-PROOF.md`.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/copied-centers-lemma.tex b/research/gen4-retiming-entrances/vendor/pr276/proof/copied-centers-lemma.tex
new file mode 100644
index 0000000000..8933aaf508
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/copied-centers-lemma.tex
@@ -0,0 +1,103 @@
+\subsection{Scalar, frame and temporary-stream contracts}
+The retained source-copy, reversible mixer and scatter maps satisfy
+$JLV=I$. Over $\mathbb F_2$ the chronological word
+\[
+ L,\ J,\ L^{-1},\ V,\ L,\ J,\ L^{-1},\ V
+\]
+adds the input to the target and restores every arbitrary auxiliary.
+Over Gaussian dyadics use its corresponding old-value subtraction and
+new-value addition. A designated retained output has a distinct terminal
+output-use carrier: a matching may feed that carrier, but cannot merge
+two designated terminals or append a later middle-producer consumer.
+Its remaining uses before cleanup are its scatter reads, all of which
+leave its scalar value unchanged.
+
+Within one tensor invocation suppress the fixed future line and put
+\[
+ D_0=B\otimes F_h,\quad D_1=A\otimes F_h,\quad
+ A=B\mathbin{\perp}P,\quad D_U=D_0\mathbin{\perp}(P\otimes U),
+\]
+where $P$ and the suppressed future factor are one-dimensional and
+$U$ is a nondegenerate retained-center space of dimension $r$.
+Thus a local change of rank $d$ has ambient rank $d$.
+Write $\mathcal F_Q$ for the address frame: it is the rational partial
+swap $D_Q$ in the bit construction, and the binary phase $C_Q$ in the
+complex construction. Changing a copy from frame $Q_1$ to $Q_2$ means
+applying $\mathcal F_{Q_2}\mathcal F_{Q_1}^{-1}$ to its physical stream.
+Orthogonal backgrounds cancel in this quotient.
+
+Copies use Paureel's retained copy/transform/read/discard interface
+\cite{paureel,pr29}. A copy has precisely the original complete role
+stream, including all control and spectator ranges, and volume $V/W$.
+It is processed while inactive original streams are parked on the fixed
+depth-first stack tapes. Copying, pointwise reads and erasure are linear
+in that stream's volume. Sequential processing needs one additional
+fixed work stream, not an independently varying row coordinate.
+
+\begin{lemma}[Copied retained-center schedule]
+In either invocation orientation a designated retained center's
+physical rank profile can be changed from $z^r+z^h$ to
+$z^r+z^{h-r}$, with the same scalar action, original role endpoints,
+and arbitrary-scratch restoration. The rank-$r$ transform on the copy
+is included in the recursive call list.
+\end{lemma}
+\begin{proof}
+In the forward orientation the original center has scalar value $w$
+at frame $D_U$ after the middle mixer. Its old sequence was
+$D_U\to D_0\to D_1$: scatter at $D_0$, then cleanup at $D_1$,
+with ranks $r,h$.
+Keep the original at $D_U$, copy its physical stream, and transform
+only the copy to $D_0$, paying rank $r$. Supply every scatter read
+from that transformed copy while its data targets remain at their
+unchanged common frame $D_0$, then erase the temporary. The reads
+are exactly those of $w$ in the old schedule. Since they do not change
+$w$, move the original directly from $D_U$ to $D_1$ before its first
+cleanup incidence; this costs $h-r$. Every subsequent original gate
+therefore receives the same scalar value at its required frame.
+
+In the reverse complementary orientation the old sequence was
+$D_0\to D_1\to D_{U^\perp}$, with ranks $h,r$ and scatter at $D_1$.
+After the preceding all-$D_0$ operations, advance the original directly
+to $D_{U^\perp}=D_0\mathbin{\perp}(P\otimes U^\perp)$, paying
+$h-r$. Copy it and transform the copy to $D_1$, paying $r$.
+Use that copy for all early scatter reads, then erase it. The original
+already has the exact frame and unchanged scalar value required by the
+following inverse mixer. Terminal output-use separation ensures no
+intervening producer consumer has been bypassed.
+
+For partial swaps either direction of the rank-$r$ change is the same
+involution. For complex phases the forward copy uses $C_U^{-1}$,
+the direct original growth uses $C_{U^\perp}$, and the reverse copy
+uses $C_FC_{U^\perp}^{-1}=C_U$. These are the same charged ranks,
+implemented by the retained forward/inverse residual interface.
+All tensor backgrounds cancel as stated. Every original scalar
+incidence, final source-copy cancellation and auxiliary source/sink
+operator is unchanged. Thus the scalar identity and all endpoints
+remain exact on arbitrary initial auxiliary values.
+\end{proof}
+
+For the selected centers $r=h-1$, and there are $h$ distinct retained
+output uses per invocation. Their old histogram has rank mass
+$hR_h+2\ell_h$, where $\ell_h=h(h-1)$. The new histogram is exactly
+\[
+ H'_{h,1}=H_{h,1}+h,\qquad H'_{h,h}=H_{h,h}-h,
+ \qquad H'_{h,r}=H_{h,r}\quad(r\ne1,h),
+\]
+and hence $\sum_r rH'_{h,r}=hR_h+\ell_h$.
+Every old rank-$(h-1)$ residual remains as a paid transform of a copy;
+its projector and ordinary bit pivot profile are unchanged. Only the
+full-rank original transition becomes the rank-one complement.
+The physical role count $R_h$ is unchanged.
+
+For two factors, put $N=v_av_b$, $B_a=v_bR_a$, $B_b=v_aR_b$,
+$W=2N+B_a+B_b$ and $L=v_b\ell_a+v_a\ell_b$.
+All exterior, data-front and endpoint-correction calls remain in place.
+The resulting complete rank mass is
+\[
+ s=Wm-N+L,\qquad Wm-s=N-L.
+\]
+This follows by subtracting exactly $L$ from the retained two-stage
+physical mass $Wm-N+2L$. The $N$ rank-one endpoint-copy calls are
+separate and remain fully charged. Because center copies retain the
+same complete role-volume fraction $1/W$, the existing complete-row,
+integer-width remainder and fixed-tape recurrence proofs apply.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/primary/03-motifs.tex b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/03-motifs.tex
new file mode 100644
index 0000000000..cdb0ba527a
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/03-motifs.tex
@@ -0,0 +1,700 @@
+\section{Two finite networks with a rank saving}
+\label{sec:finite-networks}
+
+We construct two fixed linear networks that exchange two banks of values
+while restoring every auxiliary value.  When the values are replaced by
+arrays, a common representation on all wires at a gate lets that gate act
+pointwise without disturbing the representation.  We explain this invariant
+before constructing the subspace labels that make changes of representation
+cheap.  The first network uses bit values and rational subspaces; the second
+uses Gaussian dyadic values and binary subspaces.  The scalar domain specifies
+the values combined at a gate, while the subspace labels are used to construct operators
+on each wire's address-indexed array.
+
+Put
+\[
+ h=100,\qquad v=\binom h3=161700,\qquad
+ N=v^3=4227952113000000,\qquad m=h^3=1000000.
+\]
+Let $\mathcal T$ be the set of three-element subsets of $[h]$.
+There are two data banks $X_a,Y_a$, indexed by
+$a=(a_1,a_2,a_3)\in\mathcal T^3$.
+A wire carries one scalar.  A gate is a fixed linear map on a specified
+set of wires; untouched wires retain their values.  The vertices on a
+wire are its source, the gates that touch it in time order, and its sink;
+its edges join consecutive vertices.  We call the name of a wire its
+\emph{role}, so that we can distinguish a fixed place in the network
+from the value currently carried there.
+
+\subsection{Scalar operations and restored auxiliary values}
+
+There are three stages.  At stage $j$, fix the other two coordinates and
+operate on the $v$ values in each bank obtained by varying coordinate $j$.  Thus
+there are $v^2$ separate invocations at each stage.
+Each such invocation has its own auxiliary wires, distinct from all
+other invocations, including those in other stages.  There are
+\[
+ I=3v^2=78440670000
+\]
+invocations.  In a forward invocation, write $x_T$ for the data used as
+controls and $y_S$ for the data to be updated; $S,T\in\mathcal T$ are
+their varying $j$th coordinates.  These are the logical source and
+target banks of the invocation.  For each ordered pair $(S,T)$ that is
+neighboring under the rule below, there is an auxiliary wire $A_{ST}$.
+There are also central wires $C_i$, $i\in[h]$, and in the second
+construction a wire $C_\ast$.  We call all these auxiliary wires
+\emph{scratch wires}; their initial values may be arbitrary.
+
+The following maps specify the construction.
+\begin{itemize}
+\item In the bit construction, scalars lie in $\mathbb F_2$, and
+$S,T$ are neighbors when $|S\cap T|=1$.
+The copy map adds $x_T$ to $A_{ST}$ for each neighbor pair.
+The side injection adds $\sum_{T:\,|S\cap T|=1}A_{ST}$ to $y_S$.
+The gather adds $\sum_{T\ni i}x_T$ to $C_i$, and the scatter adds
+$\sum_{i\in S}C_i$ to $y_S$.
+\item In the complex construction, scalars lie in
+$\mathbb Z[i,1/2]$, and neighbors are distinct triples with even
+intersection.  Copy is unchanged.  Side injection adds
+\[
+ -\sum_{T\text{ neighboring }S}\frac{|S\cap T|-1}{2}A_{ST}
+\]
+to $y_S$.  Gather adds $\sum_{T\ni i}x_T$ to $C_i$ and
+$\sum_Tx_T$ to $C_\ast$.  Scatter adds
+$(\sum_{i\in S}C_i-C_\ast)/2$ to $y_S$.
+\end{itemize}
+Each update leaves its control wires unchanged.  The first two rows of
+the following schedule remove the effect of the old scratch values;
+the next four introduce the source values and add their effect to the
+target; the last two restore the scratch values.
+This cancellation of arbitrary initial scratch values is a linear
+instance of the restoration construction for transparent computation in
+Buhrman, Cleve, Kouck\'y, Loff and Speelman~\cite[Section~3]{BuhrmanCleveKouckyLoffSpeelman2014}.
+The forward schedule is
+\begin{equation}
+\begin{array}{c|l|l}
+\text{row}&\text{operation}&\text{gate grouping}\\ \hline
+0&\text{subtract side injection}&\text{one gate per target}\\
+1&\text{subtract scatter}&\text{one gate on targets and center}\\
+2&\text{copy}&\text{one gate per source}\\
+3&\text{gather}&\text{one gate on sources and center}\\
+4&\text{scatter}&\text{one gate on targets and center}\\
+5&\text{side injection}&\text{one gate per target}\\
+6&\text{undo gather}&\text{one gate on sources and center}\\
+7&\text{undo copy}&\text{one gate per source}.
+\end{array}
+\label{eq:motif-schedule}
+\end{equation}
+
+\begin{lemma}\label{lem:scalar-motifs}
+For arbitrary initial values of its auxiliary wires, a forward
+invocation changes $y_S$ to $y_S+x_S$ and leaves every other value
+unchanged.  Performing a forward invocation from $X$ to $Y$ at stage 1,
+the inverse forward schedule from $Y$ to $X$ at stage 2, and a forward
+invocation from $X$ to $Y$ at stage 3 sends
+\[
+ (X_a,Y_a)\longmapsto(-Y_a,X_a)
+\]
+and restores every auxiliary value.  In the bit construction this is the
+permutation exchanging $X_a$ and $Y_a$.
+\end{lemma}
+
+\begin{proof}
+Write $\mathcal V$ for copy, $\mathcal G$ for gather,
+$\mathcal J$ for side injection and $\mathcal R$ for scatter.
+If the initial side and central vectors are $a,c$, the first two rows
+subtract $\mathcal J a+\mathcal R c$ from $y$.  Rows 2 and 3 change
+them to $a+\mathcal Vx,c+\mathcal Gx$.  Rows 4 and 5 therefore add
+$\mathcal R(c+\mathcal Gx)+\mathcal J(a+\mathcal Vx)$.
+Rows 6 and 7 restore $c,a$.  The net target change is
+$(\mathcal J\mathcal V+\mathcal R\mathcal G)x$, independently of
+$a,c$.
+
+In the bit case, the central coefficient from $x_T$ to $y_S$ is
+$|S\cap T|\bmod2$.  The side contribution cancels exactly the
+intersection-one cases; distinct triples with intersection zero or two
+already have coefficient zero, and the self coefficient is one.
+In the complex case, the central coefficient is $(|S\cap T|-1)/2$.
+The side cancels it for distinct triples with intersection zero or two;
+intersection one contributes zero, and the self coefficient is one.
+Thus both net maps are $y\gets y+x$.
+
+The inverse schedule with logical source $Y$ and target $X$ effects
+$X\gets X-Y$.  Starting from $(x,y)$, the three stages give
+$(x,y+x)$, then $(-y,y+x)$, then $(-y,x)$.
+Each invocation restores its own auxiliary wires.
+\end{proof}
+
+A fixed triple has
+\[
+ z_{\rm b}=3\binom{97}{2}=13968,\qquad
+ z_{\rm c}=\binom{97}{3}+3\cdot97=147731
+\]
+neighbors in the two constructions, respectively.  The second count
+separates intersection zero and intersection two.  Ordered pairs must
+be counted: there are $vz$ side wires in each invocation, not $vz/2$.
+With $c_{\rm b}=100$ and $c_{\rm c}=101$ central wires per invocation,
+the total wire counts are
+\begin{align}
+ W_{\rm b}&=2N+I(vz_{\rm b}+c_{\rm b})
+          =177176569091445000000,\label{eq:bit-wire-count}\\
+ W_{\rm c}&=2N+I(vz_{\rm c}+c_{\rm c})
+          =1873807244643542670000.\label{eq:complex-wire-count}
+\end{align}
+All these numbers are fixed, independently of any eventual input length.
+
+\subsection{From scalar values to arrays}
+
+We record the representation principle before choosing the labels.  Let
+$R$ be the scalar ring of either network and let $\Omega$ be a finite address
+set common to all wires.  Replace each scalar by an array in $R^\Omega$, and
+apply each scalar gate pointwise at every address.  Write $\mathsf S_\Omega$
+for the resulting network on the vector of wire arrays.
+
+At each source, gate and sink $v$, assign an invertible $R$-linear operator
+$D_v$ on $R^\Omega$, called its \emph{frame}.  A frame acts on the values
+indexed by addresses within one wire's array and may mix them; a gate instead
+combines wire values at each fixed address.  All incoming and outgoing
+incidences of one gate use the same $D_v$.  On an edge from $u$ to $v$, apply
+$D_vD_u^{-1}$ to that wire's array.  Define the operators on all input and
+output roles by
+\[
+ D_{\rm in}=\bigoplus_w D_{\mathrm{source}(w)},\qquad
+ D_{\rm out}=\bigoplus_w D_{\mathrm{sink}(w)}.
+\]
+For a supplied physical input $f$, define its logical interpretation to be
+$g=D_{\rm in}^{-1}f$; this definition requires no physical preprocessing.
+At a vertex $v$, the invariant is that the stored array equals $D_v$ applied
+to the logical array there.  It holds at the sources by definition.  On an
+edge whose logical array is $\varphi$, the edge operator changes $D_u\varphi$
+to $D_v\varphi$.  At a gate with logical input arrays $\varphi_j$,
+$R$-linearity gives
+$\sum_j c_jD_v\varphi_j=D_v(\sum_j c_j\varphi_j)$ for each output combination, with
+$c_j\in R$.  Thus the common frame commutes with the pointwise gate, and
+the invariant continues to the sinks.  The implemented operator is therefore
+\begin{equation}
+ D_{\rm out}\,\mathsf S_\Omega\,D_{\rm in}^{-1}.
+ \label{eq:common-frame-identity}
+\end{equation}
+In particular, if the scalar network is a signed role permutation that
+sends input role $w$ to output role $\rho(w)$ with scalar sign
+$\varepsilon_w$, that route applies
+$\varepsilon_wD_{\mathrm{sink}(\rho(w))}
+D_{\mathrm{source}(w)}^{-1}$ to its input array.  All roles, including
+the auxiliary roles, enter this identity.  Once the scalar routing is fixed,
+the endpoint frames determine the array operator on each route; the
+intermediate frames can then be chosen to make each edge change inexpensive.
+
+Figure~\ref{fig:frame-compatibility} summarizes this invariant.
+\begin{figure}[ht]
+\centering
+\input{figures/proof-map.tex}
+\caption{An edge changes the representation of one role's logical array
+$g_w$. At the next gate $G$, all $t$ input arrays have the common frame
+$D_v$, so the pointwise linear gate commutes with that frame. The same
+$D_v$ acts on each output component.}
+\label{fig:frame-compatibility}
+\end{figure}
+
+\subsection{Subspaces attached to the gates}
+
+The scalar network already has the required signed exchange. We now
+choose its intermediate labels to make the changes of frame inexpensive.
+A label is a nondegenerate subspace of a fixed bilinear space. On every
+edge one label will contain the other. For such an edge, the
+\emph{orthogonal residual} is the orthogonal complement of the smaller label inside
+the larger one; its dimension is the absolute change in label dimension.
+The saving will come from keeping the total dimension lost on decreasing
+edges small relative to $N$.
+
+For the bit network, let $F=\mathbb Q^h$ with bilinear form
+\[
+ \langle x,y\rangle=x^{\mathsf T}(I-J/9)y,
+\]
+where $J$ is the all-one matrix.  This form has eigenvalues $1$ and
+$1-h/9=-91/9$, so it is nondegenerate.  For a triple $T$ let $t_T$ be
+its indicator vector.  Then
+\[
+ \langle t_S,t_T\rangle=|S\cap T|-1,
+ \qquad \langle t_T,t_T\rangle=2.
+\]
+For the complex network, take instead $F=\mathbb F_2^h$ with the
+ordinary dot product; here $t_T\cdot t_T=1$.
+Thus every triple line is nondegenerate, and neighboring triple lines
+are orthogonal, in the label field belonging to either construction.
+The scalar domain need not equal the label field.
+These degree-one intersection formulas specialize the construction
+described by Alon~\cite[Section~3, remark after Theorem~1.1]{Alon1998}
+to the prime $2$, with the ground-set size changed to $h=100$.
+
+The ambient label space is $\mathcal F=F^{\otimes3}$ with its tensor
+bilinear form.  It has dimension $m$ and is nondegenerate.  Write
+\[
+ u_a=t_{a_1}\otimes t_{a_2}\otimes t_{a_3},\qquad U_a=\langle u_a\rangle.
+\]
+The prescribed terminal labels are
+\[
+\begin{array}{c|cc}
+\text{role}&\text{source label}&\text{sink label}\\ \hline
+X_a&U_a&\mathcal F\\
+Y_a&0&U_a^\perp\\
+\text{each scratch role}&0&\mathcal F.
+\end{array}
+\]
+Write $W$ for the wire count in the construction under consideration.
+The source dimensions sum to $N$ and the sink dimensions to $Wm-N$.
+Thus the signed dimension changes will sum to $Wm-2N$, because the
+contributions at gates cancel. If decreasing edges lose a total
+dimension $L$, the sum of absolute changes is $Wm-2N+2L$.
+We will obtain $L<N/2$. The rational interface below will require
+an additional $N$ source ranks, so this inequality will leave a strict
+saving in both constructions.
+
+At stage $j$, fix an invocation.  Put
+\[
+ A=F^{\otimes(j-1)},\qquad
+ P=\langle t_{a_1}\otimes\cdots\otimes t_{a_{j-1}}\rangle,
+ \qquad B=P^\perp\subset A.
+\]
+An empty tensor product is the one-dimensional ground field; thus
+$B=0$ at stage 1.  Let
+$Q=\langle t_{a_{j+1}}\otimes\cdots\otimes t_{a_3}\rangle
+\subset F^{\otimes(3-j)}$, again using the empty tensor product at
+stage 3.  Since $P$ is nondegenerate,
+$A=B\mathbin{\perp}P$.  
+We prescribe the following transition for each data wire in the stage,
+where $t$ is the indicator of that wire's $j$th triple:
+\[
+\begin{array}{c|c|c}
+ &\text{incoming label}&\text{outgoing label}\\ \hline
+ X&A\otimes\langle t\rangle\otimes Q&(A\otimes F)\otimes Q\\
+ Y&B\otimes\langle t\rangle\otimes Q&
+ \bigl((B\otimes F)\mathbin{\perp}(P\otimes t^\perp)\bigr)\otimes Q.
+\end{array}
+\]
+The outgoing $Y$ label can also be written
+$(P\otimes\langle t\rangle)^\perp_{A\otimes F}\otimes Q$.
+These transitions expose one tensor factor at each stage. To see that
+they fit together, for $j<3$ write
+$Q=\langle t_{a_{j+1}}\rangle\otimes Q'$. The next stage has
+\[
+ A'=A\otimes F,\qquad
+ P'=P\otimes\langle t\rangle,\qquad
+ B'=(P')^\perp_{A'}
+    =(B\otimes F)\mathbin{\perp}(P\otimes t^\perp).
+\]
+Thus the prescribed outgoing labels are
+$A'\otimes\langle t_{a_{j+1}}\rangle\otimes Q'$ on $X$ and
+$B'\otimes\langle t_{a_{j+1}}\rangle\otimes Q'$ on $Y$, exactly
+the next incoming labels. At stage 1 they start at $U_a$ on $X_a$
+and zero on $Y_a$; at stage 3 they end at $\mathcal F$ on $X_a$
+and $U_a^\perp$ on $Y_a$, as prescribed at the terminals.
+
+The gate labels are organized by the decomposition
+\[
+ A\otimes F=(B\otimes F)\mathbin{\perp}(P\otimes F),
+\]
+with the common summand $B\otimes F$ and the remaining summand
+$P\otimes F$ of dimension $h$. Suppress the one-dimensional factor
+$Q$ for the moment. On a side wire joining neighboring physical triples
+with indicators $t_X,t_Y$, the common component grows to $B\otimes F$,
+while the remaining component passes through
+\[
+ P\otimes\langle t_X\rangle
+ \ \subset\ P\otimes t_Y^\perp
+ \ \subset\ P\otimes F.
+\]
+The first inclusion is possible because $t_X\perp t_Y$.
+For the central gates we assign $A\otimes F$ on the physical $X$
+bank and $B\otimes F$ on the physical $Y$ bank. A central wire
+returns once from the former label to the latter, losing exactly
+$P\otimes F$. The gate order below confines all decreases to this
+return, while the other edges realize the prescribed stage transitions.
+
+Number the successive times in an invocation by
+$r=0,\ldots,7$. At stages 1 and 3, time $r$ uses row $r$ of the scalar
+schedule~\eqref{eq:motif-schedule}. At stage 2 it uses the inverse of
+row $7-r$, with the logical banks exchanged. In either case the gates
+touch the physical wires in the order
+\[
+ Y\text{-side},\quad Y\text{-center},\quad X\text{-side},\quad
+ X\text{-center},\quad Y\text{-center},\quad Y\text{-side},\quad
+ X\text{-center},\quad X\text{-side}.
+\]
+A side wire still joins neighboring physical triples in stage 2 because
+the neighbor relation is symmetric. The following table assigns the
+common gate labels. It suppresses the tensor factor $Q$; for a gate
+indexed by a physical bank triple, $t$ denotes that triple's indicator.
+
+\begin{equation}
+\begin{array}{c|l|l}
+\text{time}&\text{physical wires}&\text{common gate label}\\ \hline
+0&Y,\ \text{its side wires}&B\otimes\langle t\rangle\\
+1&Y,\ \text{all center wires}&B\otimes F\\
+2&X,\ \text{its side wires}&(B\otimes F)\mathbin{\perp}(P\otimes\langle t\rangle)\\
+3&X,\ \text{all center wires}&A\otimes F\\
+4&Y,\ \text{all center wires}&B\otimes F\\
+5&Y,\ \text{its side wires}&(B\otimes F)\mathbin{\perp}(P\otimes t^\perp)\\
+6&X,\ \text{all center wires}&A\otimes F\\
+7&X,\ \text{its side wires}&A\otimes F.
+\end{array}
+\label{eq:motif-labels}
+\end{equation}
+All labels are tensored by $Q$ and viewed as subspaces of $\mathcal F$.
+Every displayed summand is nondegenerate.
+
+All scratch sources have label zero and all scratch sinks have label
+$\mathcal F$, as prescribed above. The next lemma verifies the stage
+boundaries and all intervening edge changes, including these scratch
+edges.
+
+\begin{lemma}\label{lem:motif-residuals}
+Every edge joins comparable nondegenerate labels.  The only decreasing
+edges are the central-wire edges from time 3 to time 4; their dimension
+loss is $h$.  Consequently, if $c$ is the number of central wires per
+invocation and $W$ the total number of wires, then
+\begin{equation}
+ L=Ich,\qquad
+ \sum_{e}\bigl|\dim U_{\mathrm{head}(e)}-
+                       \dim U_{\mathrm{tail}(e)}\bigr|
+ =Wm-2N+2L.                                      \label{eq:rank-budget-labels}
+\end{equation}
+For the binary label space, every nonzero orthogonal residual of an
+edge has an orthonormal basis.
+\end{lemma}
+
+\begin{proof}
+Write $a=\dim A=h^{j-1}$ and $f=h^{3-j}$.  In the table below,
+$\mathrm{in}$ denotes the preceding vertex on that data wire: its source
+at stage 1, and its last gate in the preceding stage otherwise.  The
+interstage calculation above gives its label.  The table lists the
+orthogonal residual and its dimension for every edge except the final
+data edges to their sinks, whose labels agree and whose residuals are zero.
+Tensor each residual by $Q$, except in the last row.  The symbols $t_X,t_Y$ are
+the indicators of the neighboring physical triples joined by a side wire.
+\[
+\begin{array}{l|l|r}
+\text{wire and edge}&\text{orthogonal residual}&\text{dimension}\\ \hline
+X:\ \mathrm{in}\to2&B\otimes t_X^\perp&(a-1)(h-1)\\
+X:\ 2\to3&P\otimes t_X^\perp&h-1\\
+X:\ 3\to6,\ 6\to7&0&0\\
+Y:\ \mathrm{in}\to0&0&0\\
+Y:\ 0\to1&B\otimes t_Y^\perp&(a-1)(h-1)\\
+Y:\ 1\to4&0&0\\
+Y:\ 4\to5&P\otimes t_Y^\perp&h-1\\
+\mathrm{center}:\ \mathrm{source}\to1&B\otimes F&(a-1)h\\
+\mathrm{center}:\ 1\to3&P\otimes F&h\\
+\mathrm{center}:\ 3\to4&P\otimes F&h\\
+\mathrm{center}:\ 4\to6&P\otimes F&h\\
+\mathrm{side}:\ \mathrm{source}\to0&B\otimes\langle t_Y\rangle&a-1\\
+\mathrm{side}:\ 0\to2&(B\otimes t_Y^\perp)\mathbin{\perp}(P\otimes\langle t_X\rangle)
+ &(a-1)(h-1)+1\\
+\mathrm{side}:\ 2\to5&P\otimes\langle t_X,t_Y\rangle^\perp&h-2\\
+\mathrm{side}:\ 5\to7&P\otimes\langle t_Y\rangle&1\\
+\mathrm{scratch}:\ \mathrm{last}\to\mathrm{sink}
+ &(A\otimes F)\otimes Q^\perp&ah(f-1).
+\end{array}
+\]
+The last gate on a central wire is at time 6, and the last gate on a side
+wire is at time 7.  Both have label $(A\otimes F)\otimes Q$.  Enlarging it
+to $\mathcal F$ at the sink gives the last residual in the table, with
+$Q^\perp$ taken in the entire future tensor space.
+The side edge $2\to5$ uses the neighbor relation
+essentially.  Since $t_X\perp t_Y$, we have
+$\langle t_X\rangle\subset t_Y^\perp$.  Hence its two labels satisfy
+\[
+ (B\otimes F)\mathbin{\perp}(P\otimes\langle t_X\rangle)
+ \ \subset\
+ (B\otimes F)\mathbin{\perp}(P\otimes t_Y^\perp).
+\]
+The complement of $\langle t_X\rangle$ inside $t_Y^\perp$ is
+$\langle t_X,t_Y\rangle^\perp$, of dimension $h-2$; tensoring by
+$P$ and then by $Q$ gives the residual in the table.  The other entries
+follow directly by splitting $A=B\mathbin{\perp}P$ and
+$F=\langle t\rangle\mathbin{\perp}t^\perp$.
+Label dimension is nondecreasing along every edge except center $3\to4$, which removes
+$P\otimes F\otimes Q$.  The table includes the interstage edges through
+$\mathrm{in}$, and the initial and final data labels match their terminals,
+so no other dimension changes occur.
+
+The signed sum of dimension changes telescopes at every gate: each
+touched wire has one incoming and one outgoing incidence with the same
+gate label.  The sum of source dimensions is $N$, while the sum of
+sink dimensions is $Wm-N$.  The signed increase is therefore $Wm-2N$.
+There are $Ic$ decreasing edges, each of loss $h$; replacing signed
+changes by absolute changes adds $2L$.
+
+Now work over $\mathbb F_2$.  A nondegenerate symmetric bilinear space
+is nonalternating precisely when it contains a vector of norm one.
+The lines $P,Q$ have such vectors.  If $B\ne0$, a coordinate unit
+outside the support of the earlier tensor vector belongs to $B$:
+that support has size $3^{j-1}<h^{j-1}$ when $j>1$.
+The same argument gives a unit vector in $Q^\perp$ when it is nonzero.
+A triple complement, and the complement of two neighboring triple
+lines, contain coordinate units outside supports of sizes at most
+three and six, respectively.  Full tensor spaces contain coordinate
+units as well.  In each nonzero tensor summand, tensoring these chosen
+norm-one vectors gives a norm-one vector; placing it in that orthogonal
+summand gives one in the whole residual.  Each residual is nondegenerate
+by the decompositions above.  Thus every nonzero residual is nonalternating.
+
+For completeness, every nondegenerate nonalternating binary symmetric
+space has an orthonormal basis.  Split off unit lines until the
+remaining space is alternating.  A nonzero nondegenerate alternating
+space splits into planes with bases $a,b$ satisfying
+$a\cdot a=b\cdot b=0$, $a\cdot b=1$; this follows by choosing a
+nonzero $a$, choosing $b$ with $a\cdot b=1$, and taking the orthogonal
+complement of their nondegenerate plane.  Retain one unit vector $w$
+from the lines already split off.  A plane orthogonal to $w$ can be
+absorbed into that line: the three vectors
+\[
+ w+a,\qquad w+b,\qquad w+a+b
+\]
+are independent, pairwise orthogonal, and have norm one.
+Use one of these new unit vectors in place of $w$ for the next plane;
+the remaining planes are still orthogonal to it.  Repeating this
+operation absorbs every alternating plane.
+\end{proof}
+
+The loss ratios have the exact values
+\[
+ \frac{L_{\rm b}}{N}=\frac{100}{539},\qquad
+ \frac{L_{\rm c}}{N}=\frac{101}{539}.
+\]
+In particular, both are smaller than $1/2$.  We now turn the dimension
+count into the two interfaces needed later.
+
+\subsection{The rational matrix interface}
+
+For a nondegenerate rational subspace $U\subset\mathcal F$, write
+$P_U$ for the projection onto $U$ along $U^\perp$.  Assign $P_U$ to
+each gate or sink with label $U$.  Assign the source matrix $-P_{U_a}$
+to $X_a$ and zero to every other source.
+These are fixed rational $m\times m$ matrices; write $M_v$ for the matrix
+at vertex $v$.  Define
+$\rho(X_a)=Y_a$, $\rho(Y_a)=X_a$, and let $\rho$ fix every auxiliary
+wire.
+
+In the tape application, two address chunks are written as vectors $H,D$
+of $m$ fields.  For a matrix $M$, the frame $\Phi_M$ moves the array entry
+at $(H,D)$ to $(H+MD,D)$, leaving the other address fields unchanged.
+The fields use a radix coprime to the fixed denominators, and addition is
+modulo their common range.  Hence $\Phi_M$ is an invertible
+$\mathbb F_2$-linear permutation of array entries, and
+$\Phi_{M'}\Phi_M=\Phi_{M'+M}$.  Using $D_v=\Phi_{M_v}$
+in \eqref{eq:common-frame-identity}, the endpoint matrix difference on each
+routed role is exactly the shear applied to that role.  The following identity
+makes it the same shear $H\gets H+D$ on every role;
+Section~\ref{sec:tape-interchange} turns that shear into a field interchange
+and implements an edge change with one smaller interchange per unit of its
+rational rank.
+
+\begin{proposition}\label{prop:bit-motif-interface}
+The bit network has $W_{\rm b}$ wires, uses only pointwise XOR gates,
+and sends its input vector to the permutation $\rho$ of that vector.
+Its rational matrices are common to all incidences of a gate and obey
+\[
+ M_{\mathrm{sink}(\rho(w))}-M_{\mathrm{source}(w)}=I_m
+ \quad\text{for every input role }w.
+\]
+The sum of the rational ranks of all edge differences is
+\begin{align}
+ s_{\rm b}
+ &=\sum_{e}\operatorname{rank}_{\mathbb Q}
+      (M_{\mathrm{head}(e)}-M_{\mathrm{tail}(e)})\\
+ &=W_{\rm b}m-N+2L_{\rm b}
+  =177176569088785861287000000<W_{\rm b}m.
+\end{align}
+\end{proposition}
+
+\begin{proof}
+Lemma~\ref{lem:scalar-motifs} gives the scalar permutation, including
+all auxiliary roles.  For $U\subset V$ nondegenerate,
+$P_V-P_U$ is the identity on $V\cap U^\perp$ and zero on its
+orthogonal complement.  Its rank is $\dim V-\dim U$; reversing the
+edge negates the matrix without changing its rank.
+The only exceptions are the $N$ negative source projections.
+At stage 1, $B=0$, and the first gate on $X_a$ has label exactly $U_a$.
+Its first edge matrix is therefore $2P_{U_a}$, of rational rank one,
+where the corresponding dimension change was zero.
+Lemma~\ref{lem:motif-residuals} consequently gives the stated rank sum.
+Its deficit from $W_{\rm b}m$ is $N-2L_{\rm b}>0$.
+
+For an input $X_a$ the endpoint difference is
+$P_{U_a^\perp}-(-P_{U_a})=I_m$.  Every other role has zero source
+matrix and identity sink matrix.  This proves the interface.
+\end{proof}
+
+\subsection{The binary phase interface}
+
+Use the complex scalar network and binary labels.  For a binary vector
+$x$, let $\operatorname{wt}(x)$ denote its integer Hamming weight, and
+write $[b]\in\{0,1\}$ for the integer representative of $b\in\mathbb F_2$.
+For a label $U$, let
+\[
+ q_U(x)=\operatorname{wt}(P_Ux)\pmod4.
+\]
+The projection here is over $\mathbb F_2$.
+Let
+\[
+ H=\frac1{\sqrt2}\begin{pmatrix}1&1\\1&-1\end{pmatrix},\quad
+ C=H\begin{pmatrix}1&0\\0&i\end{pmatrix}H
+   =aI+bX,\qquad a=\frac{1+i}{2},\quad b=\frac{1-i}{2},
+\]
+where $X$ interchanges the two coordinates.  On functions of
+$x\in\mathbb F_2^m$ define
+\[
+ \mathcal C_U=H^{\otimes m}\operatorname{diag}_x(i^{q_U(x)})H^{\otimes m}.
+\]
+The use of $H$ in this definition is an identity of matrices.  Each entry
+of $\mathcal C_U$ and its inverse is a Gaussian integer divided by $2^m$,
+so both preserve arrays over $\mathbb Z[i,1/2]$.  The kernels implemented
+below have Gaussian dyadic coefficients.
+
+To apply the scalar network to these functions, replace the scalar on
+each wire $w$ by an array
+$f_w:\mathbb F_2^m\to\mathbb Z[i,1/2]$.  At each address, a gate
+applies its scalar linear map to the values on the wires it touches.
+The frame in \eqref{eq:common-frame-identity} is $D_v=\mathcal C_U$ at a
+vertex with label $U$.  On an edge from label $U$ to label $V$, apply
+$\mathcal C_V\mathcal C_U^{-1}$ to that wire's array.
+All frames are diagonalized by the same matrix $H^{\otimes m}$.
+For an integer $k\ge1$, an address for $k$ columns is
+$(x^{(1)},\ldots,x^{(k)})\in(\mathbb F_2^m)^k$; every frame and edge
+operator is then the tensor product of its one-column version over
+these $k$ coordinates.  Each scalar gate is still applied once at each
+joint address, to the vector of values on the roles it touches.
+
+\begin{proposition}\label{prop:complex-motif-interface}
+For each edge of the complex network, write $U,V$ for its tail and
+head labels.  Its phase-frame difference
+$\mathcal C_V\mathcal C_U^{-1}$ is a product of one translation
+kernel $aI+bX_v$, or its inverse, per vector in an orthonormal basis
+of the edge residual.  Here $(X_vf)(x)=f(x+v)$.
+The sum of these basis lengths is
+\[
+ s_{\rm c}=W_{\rm c}m-2N+2L_{\rm c}
+ =1873807244636671267308000000<W_{\rm c}m.
+\]
+After source and sink diagonal corrections, and undoing the signed
+bank exchange, telescoping these phase frames gives $C^{\otimes m}$
+on every role, including auxiliary roles.  The same assertion holds
+on any positive number of columns by taking tensor products over columns.
+\end{proposition}
+
+\begin{proof}
+For binary vectors $z,w$,
+\[
+ \operatorname{wt}(z+w)
+ =\operatorname{wt}(z)+\operatorname{wt}(w)
+       -2|\operatorname{supp}(z)\cap\operatorname{supp}(w)|.
+\]
+If $z\cdot w=0$, the intersection cardinality is even, so weight is
+additive modulo four.  If $V=U\mathbin{\perp}E$ and $\mathcal B$
+is an orthonormal basis of $E$, it follows that
+\[
+ q_V(x)-q_U(x)=\sum_{v\in\mathcal B}
+                 \operatorname{wt}(v)[v\cdot x]\pmod4.
+\]
+For a decreasing edge the right side is negated.
+Each $v$ has norm one, so $\operatorname{wt}(v)$ is odd.  Its
+coefficient in the phase, including the sign for the edge direction,
+is therefore some $\varepsilon\in\{1,-1\}$ modulo four.  The function
+$i^{\varepsilon[v\cdot x]}$ equals
+\[
+ \frac{1+i^\varepsilon}{2}
+ +\frac{1-i^\varepsilon}{2}(-1)^{v\cdot x}.
+\]
+The identity $H\operatorname{diag}(1,-1)H=X$, tensored over the
+coordinates in $\operatorname{supp}(v)$, sends the diagonal character
+$(-1)^{v\cdot x}$ to translation $X_v$.  The displayed phase therefore
+becomes $aI+bX_v$ or its inverse.  The nonzero residuals have such
+bases by Lemma~\ref{lem:motif-residuals}; for a zero residual use the
+empty basis.  The same lemma gives the count $s_{\rm c}$.
+The deficit is $2N-2L_{\rm c}>0$.
+
+For an edge $e$, write $\mathcal B_e$ for its residual basis and
+$K_{e,v}$ for the forward or inverse translation kernel associated
+with $v\in\mathcal B_e$.  Taking tensor products preserves their
+product, so on $k$ columns
+\[
+ \bigl(\mathcal C_V\mathcal C_U^{-1}\bigr)^{\otimes k}
+ =\prod_{v\in\mathcal B_e}K_{e,v}^{\otimes k}.
+\]
+Thus each residual vector contributes one factor acting on all $k$
+columns, and there are $s_{\rm c}$ such factors over the network.
+
+Let $\rho$ denote the underlying permutation of the complex roles: it
+exchanges $X_a,Y_a$ and fixes each scratch role.
+By Lemma~\ref{lem:scalar-motifs}, the pointwise scalar network sends an input array at
+$X_a$ to $Y_a$ with sign $+1$, an input at $Y_a$ to $X_a$ with sign
+$-1$, and each scratch input to its own output with sign $+1$.
+Applying \eqref{eq:common-frame-identity} with $D_v=\mathcal C_{U_v}$,
+where $U_v$ is the label at vertex $v$, shows that an input role $w$ reaches
+output role $\rho(w)$ with that sign and with operator
+$\mathcal C_{U_{\mathrm{sink}(\rho(w))}}
+ \mathcal C_{U_{\mathrm{source}(w)}}^{-1}$.
+For $k$ columns, use $D_v=\mathcal C_{U_v}^{\otimes k}$ on the joint
+address set in the same identity.  The route operator is then the $k$th
+tensor power of the displayed address operator, multiplied by its scalar
+route sign once.
+The zero label has frame $I$, while the full label has frame
+$C^{\otimes m}$ because $q_{\mathcal F}(x)=\operatorname{wt}(x)$.
+Every pair except $X_a\to Y_a$ has these zero and full labels.
+For the remaining pair, write $u=u_a$.  Its binary norm is one and
+its weight is $3^3=27$.  Orthogonal weight additivity yields
+\begin{align*}
+ q_{U_a^\perp}(x)-q_{U_a}(x)
+ &=\operatorname{wt}(x)-2\operatorname{wt}(u)[u\cdot x]\\
+ &=\operatorname{wt}(x)+2[u\cdot x]\pmod4.
+\end{align*}
+Since $2[u\cdot x]\equiv2\sum_{j\in\operatorname{supp}(u)}x_j
+\pmod4$, the operator on $X_a\to Y_a$ is the tensor of $C^{-1}$ on the
+27 coordinates of $\operatorname{supp}(u)$ and $C$ elsewhere.
+Put $Z=\operatorname{diag}(1,-1)$.  Direct multiplication gives
+\[
+ C=iZC^{-1}Z,\qquad C^{-1}=-iZCZ.
+\]
+For $k$ columns, let $Z_{a,k}$ be the tensor product of $Z$ on
+those 27 coordinates in every column and the identity elsewhere.
+Apply $Z_{a,k}$ before the network at $X_a$, and apply
+$i^{27k}Z_{a,k}$ after the network at $Y_a$; the latter scalar is
+applied once to the whole role.  There are $27k$ inverse factors, so
+the identity $C=iZC^{-1}Z$ turns each of them into $C$.  The operator
+on this pair is therefore $C^{\otimes mk}$ as well.
+Only the physical $X$ outputs still carry the minus sign of the
+scalar exchange.  Negate those outputs and send output role $\rho(w)$
+back to role $w$.  Every role, including every scratch role, now has
+the required forward tensor product.
+\end{proof}
+
+\subsection{Explicit rational bounds for the two recurrences}
+
+The relative rank deficits are
+\[
+ \eta_{\rm b}=\frac{W_{\rm b}m-s_{\rm b}}{W_{\rm b}m}
+       =\frac{339}{22587335000000},\qquad
+ \eta_{\rm c}=\frac{W_{\rm c}m-s_{\rm c}}{W_{\rm c}m}
+       =\frac{73}{19906842167500}.
+\]
+For both recurrences we may use the fixed rational exponent
+\begin{equation}
+ \tau=\sigma=1-2^{-50}.
+ \label{eq:explicit-motif-exponents}
+\end{equation}
+Both exact deficits displayed above are greater than $20\cdot2^{-50}$.
+Since $m<2^{20}$ and $\log 2<1$, we have $\log m<20$, whence
+\[
+ m^{1-2^{-50}}
+ =m\exp(-2^{-50}\log m)
+ >m(1-20\cdot2^{-50})>m(1-\eta)
+\]
+for either $\eta=\eta_{\rm b}$ or $\eta=\eta_{\rm c}$.
+Consequently
+\[
+ \frac{s_{\rm b}}{W_{\rm b}}<m^\tau,
+ \qquad \frac{s_{\rm c}}{W_{\rm c}}<m^\sigma,
+ \qquad 0<\tau=\sigma<1.
+\]
+Here $\sigma$ is a rational upper bound for the logarithmic exponent
+of the complex recurrence.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/primary/LICENSE b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/primary/PROVENANCE.md b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/PROVENANCE.md
new file mode 100644
index 0000000000..bebdb72910
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/PROVENANCE.md
@@ -0,0 +1,23 @@
+# Primary bit-scalar and common-frame contract
+
+The three unmodified source files in this directory are carried by Henry Grant / hcg890's PR234 snapshot:
+
+- Repository: https://github.com/hcg890/integer-mult-bounds
+- PR: https://github.com/CrocSwap/integer-mult-bounds/pull/234
+- Exact snapshot commit: `af3fe331ca60c936229e060681ffccbc1c208678`
+- Primary section path in that snapshot: `upstream/build/sections/03-motifs.tex`
+- Accompanying source paths: `upstream/README.md` and `upstream/LICENSE`
+
+The accompanying README identifies the primary work as **OpenAI, Integer multiplication below n log n, September 23, 2026** and records its original citation and publication link. It is retained as `UPSTREAM-README.md`. This is attribution to the primary source; the snapshot commit above belongs to the carrying repository and is not asserted to be an original OpenAI commit. These credits do not imply review or endorsement of this contribution.
+
+The accompanying Apache-2.0 license is retained without modification as `LICENSE`. These files have not been edited, excerpted, or reformatted. The exact content hashes are:
+
+| Bundled file | SHA256 |
+| --- | --- |
+| `03-motifs.tex` | `ed76761194988a01af77ead0ea6469cb5dcd29690ab985a0b5a4006b0f2b69bb` |
+| `UPSTREAM-README.md` | `8d1ceff898a4e0e681679f91c4def485820be9e99f04e4861f2ce601a364723e` |
+| `LICENSE` | `c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4` |
+
+`03-motifs.tex` supplies the bit scalar ring at line50, the common-frame identity at lines149–177, the distinction between scalar and label fields at line225, and the rational-address bit frame contract at lines483–493. It is bundled as theorem evidence, not as a standalone compilable document. The accompanying [`../PARITY-CONTRACT.md`](../PARITY-CONTRACT.md) proves the parity-filter adaptation and records the finite verification obligations. No theorem dependency in that parity argument requires a machine-local path.
+
+This provenance note and the parity contract were prepared with substantial OpenAI Codex assistance. Original source authorship and assistance disclosures remain separate from that disclosure.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/primary/UPSTREAM-README.md b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/UPSTREAM-README.md
new file mode 100644
index 0000000000..c8cb3c3857
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/primary/UPSTREAM-README.md
@@ -0,0 +1,17 @@
+# [Integer multiplication below n log n](paper.pdf)
+
+**Author:** OpenAI
+
+**Date:** September 23, 2026
+
+## Citation
+
+```bibtex
+@misc{OAI:Integer-multiplication-below-n-log-n-September-23-2026,
+  author = {{OpenAI}},
+  title = {{Integer multiplication below $n\log n$}},
+  howpublished = {OpenAI Math Release preprint
+                  \href{https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf}{OAI:Integer-multiplication-below-n-log-n-September-23-2026}},
+  year = {2026}
+}
+```
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/three-stage-cover-bit.tex b/research/gen4-retiming-entrances/vendor/pr276/proof/three-stage-cover-bit.tex
new file mode 100644
index 0000000000..f05225d21f
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/three-stage-cover-bit.tex
@@ -0,0 +1,264 @@
+\subsection{Atom contract and common endpoint}
+Fix an odd prime $q$, chosen below, and put $R_w=\mathbb Z/q^w\mathbb Z$.
+An atom is a complete consecutive $w$-digit address field. Write $C_n$ for
+reversal of the $n$ atom positions, without reversing digits inside an atom.
+The recursive contract is the involution
+\[
+ F_A(H,D)=(AC_nD,C_nA^{-1}H),
+\]
+where $A$ is a diagonal array of units on the head atoms. Its entries may
+depend on exposed ancestor row fields and the atom index, but not on the
+fresh role fields of this invocation or on the head/data values. Only the
+polynomial-time descriptors generated by the construction are required;
+no constant-cost oracle for arbitrary functions of a prefix is assumed.
+Every call preserves all complete spectator fields and restores its row
+coordinate. The original unweighted call has $A=I$.
+
+For a split idempotent $P$ on the head coordinates set
+\[
+ D_P=\begin{pmatrix}I-P&PC_n\\C_nP&I-C_nPC_n\end{pmatrix},
+ \qquad F=D_I.
+\]
+These are involutions, and $D_P-I$ has split rank $\operatorname{rank}P$.
+Nested commuting-projector identities are polynomial identities and require
+no symmetry of $P$. For $n=mf$ and $G=g\otimes I_f$ define
+\[
+ Q_g=\operatorname{diag}(G,C_nGC_n).
+\]
+Then $Q_gF=FQ_g$ and $Q_gD_PQ_g^{-1}=D_{GPG^{-1}}$.
+Consequently conjugating every base frame by any $g\in\operatorname{GL}_m(R_w)$
+leaves the same full physical endpoint $F$.
+
+Put $Q_A=\operatorname{diag}(A,I)$. Conjugate the entire completed scalar
+word by $Q_A$. Scalar gates mix roles having the same address map, so they
+commute with $Q_A$. A current role routing also commutes with $Q_A$, since
+it changes only fresh fields. Thus only address residuals change, and the
+completed endpoint is $Q_AFQ_A^{-1}=F_A$. More explicitly, when a port
+changes charts from $g$ to $gR_s$, its local label changes from $M$ to
+$R_s^{-1}MR_s$, and
+\[
+ (gR_s)(R_s^{-1}MR_s)(gR_s)^{-1}=gMg^{-1}.
+\]
+This routing is a change of row/chart, not an uncharged dense address map.
+The adapted chart $Q_AQ_gQ_A^{-1}$ commutes with $F_A$. None of these
+conjugations is executed as an extra normalization pass.
+
+\subsection{Explicit rational three-stage geometry}
+Use the retained PR97 local producer with
+\[
+ h=23,\qquad v=1771,\qquad R_{\rm loc}=28866,\qquad \ell=506.
+\]
+Its physical projector ranks and scalar word are unchanged. On
+$\mathcal A=\mathbb Q^{23}$ take the form $H_0=(I-J/9)/2$.
+For a triple $S$ let $q_S=\chi_S$; then $q_S^tH_0q_S=1$.
+Fix $q_0=\chi_{\{1,2,3\}}$ and $K=q_0^\perp$. A rational basis is
+\[
+ k_i=e_i-(e_i^tH_0q_0)q_0,\qquad 2\le i\le23.
+\]
+Projection along $q_0$ is injective on the span of $e_2,\ldots,e_{23}$,
+since $q_0$ has nonzero first coordinate. Thus this is indeed a basis.
+Let $\mathcal B,\mathcal C$ be orthogonal copies of $K$ and put
+$\mathcal E=\mathcal A\perp\mathcal B\perp\mathcal C$, of dimension $m=67$.
+
+Choose a coordinate permutation $\pi_S$ taking $\{1,2,3\}$ to $S$.
+It preserves $H_0$. The rational isometry $R_{12,S}$ fixes $q_S$ and
+$\mathcal C$, and exchanges $\pi_Sk_i\in q_S^\perp\subset\mathcal A$
+with $k_i\in\mathcal B$. Define $R_{23,S}$ by exchanging the same vectors
+with their copies in $\mathcal C$, fixing $q_S$ and $\mathcal B$.
+Both maps are involutions. A hyperedge $(g,S)$ uses the invocations
+$gR_{12,S},g,gR_{23,S}$, with active spaces
+\[
+ g(\mathcal B+\mathbb Qq_S),\qquad g\mathcal A,
+ \qquad g(\mathcal C+\mathbb Qq_S).
+\]
+Their projectors commute; their pairwise and common intersection is the
+projector $P_{gq_S}$, and their sum is $I+2P_{gq_S}$.
+This follows from the orthogonal decomposition
+$\mathbb Qq_S\perp q_S^\perp\perp\mathcal B\perp\mathcal C$ before
+conjugation. These are the cumulative-projector three-stage transfer
+identities: the three scalar shears complete the interchange, with zero
+interstage connectors and no rank-one endpoint correction. Each port
+family visits the full cover bijectively, by right multiplication with
+its displayed involution. The physical ledger is therefore three copies
+of the local auxiliary, data and center histograms, and three copies of
+the exterior histogram $m-\text{nullity}$.
+
+\subsection{One weighted child on a generic residue class}
+Work first on one atom column. Let $g$ be its weighted residual involution,
+of split rank $r$ relative to $I$. If the cross block has generic northeast
+rank profile, unit lower row and column elimination, without normalizing
+pivots, gives
+\[
+ Lg_{XY}R=ED_pF_0^t,
+ \quad E=(e_1,\ldots,e_r),\quad
+ F_0=(e_m,\ldots,e_{m-r+1}),
+\]
+with invertible diagonal $D_p$. Conjugate by $\operatorname{diag}(L,R^{-1})$.
+Split rank and the unit pivot minor give a factorization
+\[
+ g-I=\binom EB(A_0,D_pF_0^t),\qquad
+ A_0E+D_pF_0^tB=-2I_r.
+\]
+For clarity, if $g-I=UV$, then $g^2=I$ gives
+$U(VU+2I)V=0$. The unit minor supplies a left inverse of $U$ and a right
+inverse of $V$, proving the identity over the local ring itself.
+Set
+\[
+ K=-(B+F_0D_p^{-1})E^t+F_0D_p^{-1}A_0(I-EE^t),
+ \qquad S=\begin{pmatrix}I&0\\K&I\end{pmatrix}.
+\]
+The identities $KE=-B-F_0D_p^{-1}$ and
+$D_pF_0^tK=A_0+E^t$ give
+\[
+ SgS^{-1}=\begin{pmatrix}
+ I-EE^t&ED_pF_0^t\\F_0D_p^{-1}E^t&I-F_0F_0^t
+ \end{pmatrix}.
+\]
+This is one weighted reversed interchange on the first $r$ head and last
+$r$ tail coordinates. All other factors are unit lower intrabank maps or
+lower cross-bank additive maps. Thus variable diagonal units remain in
+the child's weight array rather than becoming unsupported routing passes.
+
+For $n=mf$, group atoms by coarse coordinate $i$ and column $j$.
+If $L_P,R_P,D_P$ are unweighted normalizers for the current projector and
+$A_j=\operatorname{diag}(A[if+j])$, then
+$L_j=A_jL_PA_j^{-1}$ and $R_j=R_P$ are unit lower normalizers for
+$A_jPC_m$. The child's exact contiguous index rule is
+\[
+ A_{\rm child}[kf+j]=A[i_kf+j]D_P[k].
+\]
+The cross-bank atom pairing is reversed, and $C_r\otimes C_f=C_{rf}$.
+Hence the middle operation is exactly one $rf$-atom call of the same
+contract, with no interleaving or gathering. Its coefficients depend only
+on parent prefix fields, which become ancestor spectators at the child;
+the child's fresh roles come from disjoint unused row stock.
+
+All unit lower adapters require $O(n)$ atom passes. The retained ordered
+affine lemma implements each later-target shear in $O(V)$, including
+prefix-controlled offsets. The generated descriptors have polynomial cost
+in $w$: good-class evaluation follows one ancestral index per level;
+fallback evaluation branches by a constant per level. Since depth is
+$O(\log e)$ and $w=\lceil e^{1/1000}\rceil$, this costs $e^{O(1)}=w^{O(1)}$.
+Stored ancestor data use $O(w\log e)$ bits. The proof of the ordered affine
+lemma still applies with these controls: polynomial preparation per prefix
+is absorbed by the complete $q^w$ target fiber. Unrelated spectator counters
+are incremented by ripple counting rather than read in their entirety.
+
+\subsection{Weighted leaves and a genuine local-ring fallback}
+At one atom write $J_a=\left(\begin{smallmatrix}0&a\\a^{-1}&0\end{smallmatrix}\right)$,
+$U(a)=\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)$ and
+$L(b)=\left(\begin{smallmatrix}1&0\\b&1\end{smallmatrix}\right)$.
+Then
+\[
+ J_a=\operatorname{diag}(1,-1)U(a)L(-a^{-1})U(a),
+ \qquad U(a)=J_1L(a)J_1.
+\]
+Thus a weighted leaf uses four old ordinary atom interchanges, three
+prefix-controlled shifts and one fixed sign. With
+$a_{\rm old}=384599/10^{10}$ it costs $O(Vw^{1-a_{\rm old}})$.
+This constant occurs only at stopped leaves.
+
+A bad residue class cannot be treated by field Bruhat elimination:
+an entry zero modulo $q$ need not vanish modulo $q^w$. Instead Gaussian
+eliminate the full invertible residual of size $N_0=2m$ with unit pivots.
+Each invertible Schur complement has a unit in its next pivot column;
+row swaps and unnormalized additions clear that column. There are at most
+$N_0(N_0-1)$ additions and $N_0$ swaps. Pivot choices are determined by
+the unweighted low residue class: diagonal conjugation scales every
+Schur-complement row and column by units and preserves its zero pattern.
+The final diagonal has product a fixed sign, since the residual has
+determinant $(-1)^r$ and row swaps change only the sign.
+
+A lower addition is a paid additive adapter. An upper addition is
+conjugated into a lower addition by two ordinary coarse-field swaps.
+For a field of $f$ atoms, let $R_{\rm tail}$ reverse the later field.
+Then the ordinary weighted swap is
+\[
+ J_A=R_{\rm tail}F_AR_{\rm tail},\qquad
+ J_A(H,D)=(AD,A^{-1}H).
+\]
+Each $R_{\rm tail}$ is one unweighted reversed call on the first and last
+$\lfloor f/2\rfloor$ atoms, fixing a possible middle atom. Thus $J_A$
+costs at most three children of widths $f,\lfloor f/2\rfloor,
+\lfloor f/2\rfloor$. A paired diagonal scaling is $J_aJ_1$, at most six
+children. The full diagonal is a product of $N_0-1$ such pairs and a fixed
+sign. Across the two banks the reversed pairing already makes the swaps
+and diagonal pairs directly reversed calls; the preceding ordinary bounds
+remain conservative. Reindexing a tail weight by $j\mapsto f-1-j$ changes
+only its descriptor. Charging every addition as upper therefore gives
+\[
+ 6N_0(N_0-1)+3N_0+6(N_0-1)<32m^2.
+\]
+Every child has width at most $f$, hence ratio at most $1/m$. Coefficients
+are computed from constant-sized local-ring matrices and parent weight
+descriptors; only units are inverted. This proves the fallback cost,
+including its actual reversals, rather than assuming nonunit pivots away.
+
+\subsection{Finite covers, batching, and the strict moment}
+Take $q>2^{80}$ avoiding all fixed rational denominators and rank witnesses.
+At atom width $w$ use the finite cover $\operatorname{GL}_m(R_w)$ and its
+right-multiplication edges $g\mapsto gR_s$. Every vertex has the unique chart
+\[
+ g=g_0+qG_1,\quad g_0\in\operatorname{GL}_m(\mathbb F_q),
+ \quad G_1\in(\mathbb Z/q^{w-1}\mathbb Z)^{m^2},
+\]
+using fixed representatives for $g_0$. Right multiplication permutes $g_0$
+and acts affinely on $G_1$, with a carry determined by $g_0$. Its fixed
+dimensional rational linear part factors into fixed scalings, ordered
+shifts and a constant number of old width-$O(w)$ interchanges. Thus each
+fixed port routing costs $O(Vw^{1-a_{\rm old}})$.
+
+Let $W_0=|\operatorname{GL}_m(\mathbb F_q)|(2v+3R_{\rm loc})$.
+The full role count is $W(w)=W_0q^{m^2(w-1)}$. Split preceding rows into
+low role type, high matrix and unused stock. Batch \emph{all} high matrices
+for each low type in one stream. A frame edge is one child on this whole
+batch, of volume $V/W_0$, and routing is executed once per fixed operation
+type. Consequently neither the number of tapes nor the number of child
+programs grows with $w$. High cardinality cancels in the normalized moment,
+but its $m^2(w-1)$ digits are charged in the row reserve.
+
+For each fixed projector require the leading minors of sizes $1$ through
+$r$ to be units. Each cleared minor polynomial in $g_0$ is nonzero:
+similarity to $\operatorname{diag}(I_r,0)$ supplies a witness after the
+fixed rank is preserved modulo $q$. Their total degree is at most $m^3$.
+The polynomial zero bound and conditioning on invertibility (a factor at
+most two) give bad fraction at most $2m^3/q<10^{-16}$ for each edge type.
+No simultaneous union bound over edge types is needed, since their moments
+are averaged separately. Good classes use the whole-rank child; bad
+classes use the full $32m^2$-child fallback just proved.
+
+Let $H_r$ be the three-stage histogram described above and
+$W=2v+3R_{\rm loc}=90140$. The retained ledger gives
+\[
+ \sum_r rH_r=6037356,\qquad Wm-\sum_r rH_r=2024=2v-3\ell,
+ \qquad \max\{r:H_r>0\}=66.
+\]
+For $a=747/2000000$, $\tau=1-a$, and $b=10^{-16}$ the conservative moment is
+\[
+ \mu_\tau\le
+ \sum_r\frac{H_r}{W}(r/m)^\tau+
+ b\frac{32m^2\sum_rH_r}{W}(1/m)^\tau<1.
+\]
+The entire fallback is added; no displaced good contribution is subtracted.
+The exact script \path{scripts/three_stage_cover_network.py} and certificate
+\path{certificates/three-stage-cover-network.json}, from the retained axis
+\path{certificates/three-stage-cover-bit-input.json}, give
+$1-\mu_\tau>6.3397366396\cdot10^{-7}$.
+The certificate uses the 32-term positive atanh logarithm series with its
+geometric tail, $\exp(u)\le1+u+u^2/(2(1-u/3))$, and upward rounding to
+the grid $2^{-120}$. All inputs have $0\le u<3$; these are rational upper
+bounds, not floating-point root estimates. Since every child ratio is at
+most one and $\tau<1$, this same strict bound implies $\mu_1<1$.
+
+With $T(n,w)$ denoting time divided by logical volume, the fixed low-type
+profile $\{c_r\}$, including fallback classes, satisfies
+\[
+ T(n,w)\le\sum_rc_rT(r\lfloor n/m\rfloor,w)+Cn+Cw^{1-a_{\rm old}}
+ \quad(n\ge m),\qquad
+ T(n,w)\le Cw^{1-a_{\rm old}}\quad(n<m).
+\]
+Peeling fewer than $m$ leftover atoms uses the weighted leaf algorithm.
+The constants are independent of $w,n$ and ancestor values. Induction,
+using $\mu_1<1$ for the linear term and $\mu_\tau<1$ for the stopped term,
+gives $T(n,w)=O(n+n^\tau w^{1-a_{\rm old}})$. The maximum proper ratio
+$66/67$ has halving degree $47$, so recursion depth is $O(\log n)$.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/proof/three-stage-cover-rows.tex b/research/gen4-retiming-entrances/vendor/pr276/proof/three-stage-cover-rows.tex
new file mode 100644
index 0000000000..590da4b892
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/proof/three-stage-cover-rows.tex
@@ -0,0 +1,95 @@
+\subsection{Internal row reserve and ordinary conversion}
+The finite cover requires a row divisor $W(w)$ at each coarse level.
+All children have ratio at most $66/67$ and depth
+$D(n)\le47\lceil\log_2\max(2,n)\rceil+O(1)$.
+A sufficient common divisor is $W(w)^{D(n)}$ times the inherited old-leaf
+reserve. The old supplier has its retained complete-row contract and
+logarithmic reserve. Therefore a sufficient integer $S(e,w)$ satisfies
+\[
+ \log_qS(e,w)=O(w\log e).
+\]
+Unused stock is divided only into fresh descendant role fields; exposed
+parent low/high fields are spectator prefixes. Their weights cannot depend
+on those fresh roles. Every completed call restores its row coordinate,
+so successive residuals and the outer wrapper reuse one reserve instead
+of multiplying reserves for sequential calls.
+
+The unweighted reversed endpoint $F_n(H,D)=(C_nD,C_nH)$ converts to an
+ordinary interchange by the chronological sequence
+\[
+ D\leftarrow D-H;\quad F_n;\quad D\leftarrow D+H;\quad
+ F_n;\quad D\leftarrow H-D.
+\]
+Indeed the successive values are $(H,D-H)$, $(C_n(D-H),C_nH)$,
+$(C_n(D-H),C_nD)$, $(D,D-H)$, and $(D,H)$.
+The three additive maps cost $O(Vn)$ in the atom model. The two calls
+reuse restored rows; their constant multiplicity is outside the recursion
+and does not multiply its characteristic moment.
+
+\subsection{Borrowing and restoring the stock}
+Set $\beta=1/1000$, $w=\lceil e^\beta\rceil$, and
+$k=\lceil\log_qS(e,w)\rceil=O(w\log e)$, using the depth bound for the
+original width $e$. For sufficiently large $e$, $k<e/2$. Write the two
+original complete radix-$q$ chunks as $H=(H_{\rm hi},H_{\rm body})$ and
+$D=(D_{\rm hi},D_{\rm body})$, both high parts having $k$ digits. The
+physical order, including arbitrary original complete spectators $Z$, is
+\[
+ H_{\rm hi},\ H_{\rm body},\ Z,\ D_{\rm hi},\ D_{\rm body}.
+\]
+The complete $q^k$ range of $H_{\rm hi}$ already precedes both bodies.
+Reinterpret it as a preceding row field; $D_{\rm hi}$ remains an intervening
+spectator. Pad only this row range to $\lceil q^k/S\rceil S$. As $q^k\ge S$,
+the padding factor is less than two.
+
+Execute the completed \emph{ordinary} body wrapper with this row reserve,
+then remove the padding. Each row is restored, so the genuine row range
+is invariant at the completed endpoint. The order of values is now
+\[
+ H_{\rm hi},\ D_{\rm body},\ Z,\ D_{\rm hi},\ H_{\rm body}.
+\]
+One inherited ordinary width-$k$ interchange of the two high parts,
+with the bodies and $Z$ as spectators, gives
+\[
+ D_{\rm hi},\ D_{\rm body},\ Z,\ H_{\rm hi},\ H_{\rm body}.
+\]
+This is precisely the original full-chunk interchange. Its extra cost is
+$O(Vk^{1-a_{\rm old}})\le O(Vw\log e)$, conservatively. No full body is
+moved once per borrowed digit. Padding occurs only in this outer wrapper;
+it contributes one volume constant, not a recursive branching factor.
+The wrapper does not rely on a raw reversed call preserving borrowed high
+positions. Small widths use the retained supplier directly.
+
+\subsection{Uniform saving and return to binary addresses}
+Select atom width from the original $e$. Since $k=o(e)$, the body width
+$e-k$ has the same asymptotic powers as $e$. Apply the ordinary wrapper to
+its complete atom body and the old ordinary supplier to fewer than $w$
+remaining digits. The stopped recurrence and the borrowing cost give
+\[
+ O\!\left(V\left[e^{1-\beta}+
+ e^{(1-\beta)(1-a)+\beta(1-a_{\rm old})}+e^\beta\log e\right]\right).
+\]
+Here $a=747/2000000$ and $a_{\rm old}=384599/10^{10}$. Set
+\[
+ a_{\rm bit}=(1-\beta)a+\beta a_{\rm old}
+ =\frac{3731649599}{10^{13}}=0.0003731649599.
+\]
+The inequalities $\beta>a_{\rm bit}$ and $\beta<1-a_{\rm bit}$ make both
+the atom-adapter and borrowing terms lower order. The remainder cost
+$O(Vw^{1-a_{\rm old}})$ is also covered. Thus the ordinary radix-$q$
+interchange has cost $O(Ve^{1-a_{\rm bit}})$, without an externally supplied
+superpolynomial stock of rows.
+
+For an original binary chunk range $[2^e]$, let
+$t=\lceil e/\log_2q\rceil$ and embed it numerically into $[q^t]$.
+Pad both exchanged ranges while retaining every spectator. The total
+logical-volume increase is below $q^2$. Execute the completed ordinary
+radix-$q$ interchange, then remove the padding. Its endpoint preserves the
+rectangular genuine set $[2^e]\times[2^e]$; intermediate maps may mix genuine
+and padded addresses, which does not affect this endpoint justification.
+As $q$ is fixed and $t=\Theta(e)$, the binary interchange has the same
+saving exponent. All schedules use a fixed number of finite-alphabet
+tapes; low residue tables and port types are fixed independently of $w$.
+
+The conclusion retains the original local-producer, ordered-affine,
+ordinary-leaf and multiplication-framework hypotheses. It adds no free
+unit-scaling, dense chart transformation, or external row-stock primitive.
diff --git a/research/gen4-retiming-entrances/vendor/pr276/raw_ledger.py b/research/gen4-retiming-entrances/vendor/pr276/raw_ledger.py
new file mode 100644
index 0000000000..b55b02fd11
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/raw_ledger.py
@@ -0,0 +1,189 @@
+"""Independent fresh gen4 physical path census, including both reflections.
+Derived from the source527 census (eumemic); constants rebound to the gen4 word.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+No saved receipt, search script, or historical profile is consumed.
+"""
+from collections import Counter,defaultdict
+from types import SimpleNamespace
+
+def run(context):
+ m=SimpleNamespace(**context);W=m.W;C=m.C;chosen=m.pair_selection;fresh=m.fresh;pair_byalias=m.pair_byalias;pair_bydirty=m.pair_bydirty
+ compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ zero=W.register([]);compact=lambda h:{str(k):v for k,v in sorted(h.items())if v}
+ # Exact raw event sequence, with every actual extra source included.
+ events=[]
+ for j,op in enumerate(W.rest):
+  for s in m.at[j]:events.append(dict(kind='gauge',ref=s,frame=W.gauge[s]['frame'],targets=list(m.adj[s])))
+  if op in m.bywrite:events.append(dict(kind='terminalwrite',ref=op,frame=W.opframe[op],targets=[m.bywrite[op]['pivot']]))
+  if op in m.afterwrite:events.append(dict(kind='terminalread',ref=op,frame=m.afterwrite[op]['root_frame'],targets=m.afterwrite[op]['targets']))
+ for s in m.at[len(W.rest)]:events.append(dict(kind='gauge',ref=s,frame=W.gauge[s]['frame'],targets=list(m.adj[s])))
+ endgauge=len(events)
+ for j,r in enumerate(W.g['roots']):
+  if r['kind']=='side'and j not in m.deletedroots:events.append(dict(kind='root',ref=j,frame=W.w['root_frame'][j],targets=r['targets']))
+  for e in m.deliveries[j]:events.append(dict(kind='K',ref=e['passive'],frame=e['deliver_frame'],targets=e['receivers']))
+ for t in range(W.v):events.append(dict(kind='endpoint',ref=t,frame=W.register(W.module.kernel([C.cov[t]],W.h)[0]),targets=[t]))
+ 
+ def histogram(t,path):
+  h=Counter();rev=Counter();assert path[0]==zero and C.dimf[path[-1]]==W.h-1
+  for f in path:assert C.nondeg(f)and all(W.module.dot(C.cov[t],b)==0 for b in C.B[f]),('cap/nondeg',t,f)
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b),('forward inclusion',t,a,b)
+   d=C.dimf[b]-C.dimf[a];assert d>=0
+   if d:h[d]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]),('reflected inclusion',t,a,b)
+   d=len(C.A[b])-len(C.A[a]);assert d>=0
+   if d:rev[d]+=1
+  assert h==rev and sum(k*v for k,v in h.items())==W.h-1
+  return h
+ 
+ def paths(agg,readframes,echelon,rankgroups):
+  rankowner={t:k for k,g in enumerate(rankgroups)for t in g['targets']}
+  out=[[zero]for _ in range(W.v)];owner={t:k for k,g in enumerate(agg)for t in g['targets']};roles=defaultdict(list)
+  for k,g in enumerate(agg):
+   for s in g['roles']:roles[s].append(k)
+  active=set(range(len(agg)));rankactive=set(range(len(rankgroups)));echactive=set(range(len(echelon)));seen=[set()for _ in echelon];restores=[]
+  for j,e in enumerate(events):
+   if j>=endgauge:assert not active and not rankactive and not echactive
+   s=e['ref'];T=set(e['targets'])
+   if e['kind']=='gauge':
+    if s in pair_byalias:continue
+    if s in fresh:
+     for t,c in fresh[s]['transformed_response'].items():
+      if c:out[int(t)].append(W.gauge[s]['frame'])
+     continue
+    skip=set()
+    for k,g in enumerate(echelon):
+     if k not in echactive:continue
+     if s not in g['roles']:
+      if T&set(g['targets']):
+       assert seen[k]==g['roles'];restores.append(dict(group=k,before_role=s,event=j))
+       for t in g['targets']:out[t].append(g['frame'])
+       echactive.remove(k)
+      continue
+     seen[k].add(s);skip.update(g['targets'])
+     for t,a in g['response'].items():
+      if a.get(s,0):out[t].append(W.gauge[s]['frame'])
+    for k in sorted({rankowner[t]for t in T if t in rankowner}):
+     if k in rankactive and s not in rankgroups[k]['roles']:
+      for t in rankgroups[k]['targets']:out[t].append(rankgroups[k]['frame'])
+      rankactive.remove(k)
+    for k in sorted({owner[t]for t in T if t in owner}):
+     if k in active and s not in agg[k]['roles']:
+      for t in agg[k]['targets']:out[t].append(agg[k]['frame'])
+      active.remove(k)
+    for k in roles[s]:
+     assert k in active;g=agg[k];out[g['pivot']].append(readframes[s,k]);skip.update(g['targets'])
+    for t in e['targets']:
+     if t in skip:continue
+     rk=rankowner.get(t)
+     if rk in rankactive and t in rankgroups[rk]['dependent']:continue
+     out[t].append(e['frame'])
+   else:
+    assert not(T&{t for k in active for t in agg[k]['targets']})
+    assert not(T&{t for k in echactive for t in echelon[k]['targets']})
+    for t in e['targets']:out[t].append(e['frame'])
+  H=Counter()
+  for t,p in enumerate(out):H.update(histogram(t,p))
+  return out,H,restores
+ 
+ newpaths,target,restores=paths(m.agg,m.read_frames,m.echelon,m.rankgroups)
+ # Recover raw literal adjoint independently, respecting all omitted copies.
+ adj=[{}for _ in range(W.R)]
+ for root,role in zip(W.g['roots'],W.w['rootroles']):
+  for t in root['targets']:adj[role][t]=adj[role].get(t,0)+1
+ for i in reversed(W.phase1+W.rest):
+  if i in m.omitted:continue
+  a,b,_=W.ops[i]
+  for t,c in adj[a].items():adj[b][t]=adj[b].get(t,0)+c
+ assert adj==m.adj
+ oldused={r[k]for r in m.selection+m.gauge_selection if r['role']not in pair_byalias for k in('source','partner')}
+ assert len({r[k]for r in chosen for k in('source','partner')})==2*len(chosen)==0 and not oldused&{r[k]for r in chosen for k in('source','partner')}
+ for r in chosen:
+  b=r['aliased_role'];response=Counter(adj[b])
+  for a,c in r['retained_dirty_coefficients'].items():
+   for t,v in adj[a].items():response[t]+=c*v
+  assert not any(response.values())
+ # Complete physical source and auxiliary census, including all alias handoffs.
+ recipient={d:b for b,d in W.pairs};roots=defaultdict(list)
+ for j,s in enumerate(W.w['rootroles']):roots[s].append(W.w['root_frame'][j])
+ source_role={s:n for n,s in W.source.items()};plainborrow={r['role']:r for r in m.selection};gauges={r['role']:r for r in m.gauge_selection}
+ assert len(plainborrow)==0 and len(gauges)==0 and len(m.borrow)==0
+ seq={s:[('op',i,W.opframe[i])for i in W.role_ops[s]]+[('root',j,f)for j,f in enumerate(roots[s])]for s in range(W.R)}
+ def physical_path(s):
+  a=list(seq[s])
+  if s in pair_bydirty:a=[('paired-source-injection',s,pair_bydirty[s]['mix_frame'])]+a
+  if s in recipient:
+   b=recipient[s];a+=[('alias',b,W.gauge[b]['frame'])]+seq[b]
+  return a+[('full',s,W.w['full_frame'])]
+ count=0
+ 
+ def census_hist(start,events):
+  nonlocal count
+  count+=1;prev=start;dim=C.dimf[start]if start is not None else 0;out=Counter();chain=[]if start is None else[start]
+  for _,_,f in events:
+   assert C.nondeg(f)and(prev is None or C.sub(prev,f));d=C.dimf[f]-dim;assert d>=0
+   if d:out[d]+=1
+   prev=f;dim=C.dimf[f];chain.append(f)
+  assert dim==24;reflected=Counter()
+  for a,b in zip(reversed(chain),list(reversed(chain))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);d=len(C.A[b])-len(C.A[a]);assert d>=0
+   if d:reflected[d]+=1
+  if start is None:
+   d=24-len(C.A[chain[0]])
+   if d:reflected[d]+=1
+  assert reflected==out
+  return out,chain
+ internal=Counter();sources=Counter();pathrows={};sourcepaths={};dirtypaths={}
+ for s in m.regs:
+  start=W.gauge[s]['frame']if s in W.gauge else W.w['source_frame'][source_role[s]]if s in source_role else None
+  H,chain=census_hist(start,physical_path(s))
+  if s in source_role:H[1]+=1
+  internal.update(H);pathrows['a'+str(s)]=compact(H)
+  if s in pair_bydirty:dirtypaths[str(s)]=[zero]+chain
+ for j,r in enumerate(W.g['roots']):
+  if r['kind']=='center':internal[C.dimf[W.w['root_frame'][j]]]+=1
+ for entry in W.k['entries']:
+  carrier,n=entry['carrier'],entry['passive'];H,chain=census_hist(entry['carrier_chain'][0],[('carrier',j,f)for j,f in enumerate(entry['carrier_chain'][1:])]);sources.update(H)
+  if n not in m.by_source:
+   H,chain=census_hist(entry['passive_chain'][0],[('passive',j,f)for j,f in enumerate(entry['passive_chain'][1:])]);sources.update(H);pathrows['s'+str(n)]=compact(H);continue
+  r=m.by_source[n];s=r['role'];events=physical_path(s)
+  if s in plainborrow:
+   r=plainborrow[s];events=[x for x in events if not(x[0]=='op'and x[1]==r['omit_copy'])];at=next(i for i,x in enumerate(events)if x[0]=='op'and x[1]==r['early']);events.insert(at,('mix',n,entry['mix_frame']))
+  else:
+   assert s in gauges;events=[('mix',n,entry['mix_frame']),('gauge',s,W.gauge[s]['frame'])]+events
+  H,chain=census_hist(W.w['source_frame'][n],events);sources.update(H);pathrows['s'+str(n)]=compact(H)
+  if s in m.extra_byrole:sourcepaths[str(s)]=chain
+ assert count==18170 and len(sourcepaths)==0 and len(dirtypaths)==0 and sum(k*v for k,v in sources.items())==1760*23
+ gauges=Counter(z['dim']for s,z in W.gauge.items()if s not in W.donor and s not in m.borrow)
+ assert gauges=={20:2200,21:266}
+ copies=Counter(C.dimf[W.w['root_frame'][j]]for j,r in enumerate(W.g['roots'])if r['kind']=='center');assert copies=={22:24}
+ withoutcopies=internal.copy();withoutcopies.subtract(copies);assert min(withoutcopies.values())>=0
+ helper=internal+sources+target;h=24;v=1760;R=len(m.regs);M=120;stock=4*v+R
+ assert R==16410 and len(m.borrow)==0
+ assert sum(k*n for k,n in helper.items())==h*R+2*v*(h-1)+sum(k*n for k,n in copies.items())-sum(k*n for k,n in gauges.items())
+ idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)});five=Counter({r:5*n for r,n in helper.items()});five.update(idle)
+ for r,n in gauges.items():five[5*r]+=n
+ mass=sum(k*n for k,n in five.items());assert M*stock-mass==4400
+ raw=dict(schema='gen4-fresh-raw-ledger/1',source_head=context.get('source_head','gen4'),h=h,v=v,physical_R=R,source_aliases=len(m.borrow),terminal_sinks=len(m.terminal),physical_donor_recipient_identifications=len(W.pairs),physical_internal_excluding_center_copies=compact(withoutcopies),paid_center_copy_histogram=compact(copies),physical_source_histogram=compact(sources),physical_target_histogram=compact(target),one_stage_helper_histogram_including_copies=compact(helper),auxiliary_entrance_rank_histogram=compact(gauges),auxiliary_entrance_count=sum(gauges.values()),helper_rank_mass=sum(k*n for k,n in helper.items()),five_stage_profile=dict(m=M,W=stock,histogram=compact(five),idle_histogram=compact(idle),calls=sum(five.values()),rank_mass=mass,deficit=M*stock-mass,maxchild=max(five)),source_aux_paths=count,target_paths=1760,extra_source_paths=len(sourcepaths),paired_dirty_paths=len(dirtypaths),all_reflected_ledgers=True,all_zero_response_relations=True,scope='Fresh complete gen4 raw physical source/internal/target and copied-center ledger. Both reflected chains checked; no saved execution receipt consumed.')
+ assert raw['five_stage_profile']['calls']==487546 and mass==2809600
+ return raw
+
+def rebind_parity(raw,receipt):
+ """Bind the fresh required-use census to the retained producer source ledger."""
+ from copy import deepcopy
+ def hist(x):return Counter({int(r):n for r,n in x.items()if n})
+ assert receipt['status']=='PASS_FRESH_PARITY_FUSION_AND_INDEPENDENT_REQUIRED_FRAME_CENSUS'
+ assert receipt['both_reflected_ledgers']and receipt['unchanged_all_input_output_frames']
+ source=hist(receipt['source_histogram']);target=hist(receipt['target_histogram']);internal=hist(receipt['internal_histogram_including_copies']);copies=hist(receipt['copied_center_histogram'])
+ assert source==hist(raw['physical_source_histogram'])
+ assert internal==hist(raw['physical_internal_excluding_center_copies'])+copies
+ delta=target.copy();delta.subtract(hist(raw['physical_target_histogram']));assert {r:n for r,n in delta.items()if n}=={}
+ producer=deepcopy(raw);helper=source+target+internal;five=Counter({r:5*n for r,n in helper.items()});five.update(hist(raw['five_stage_profile']['idle_histogram']))
+ for a,n in hist(raw['auxiliary_entrance_rank_histogram']).items():five[5*a]+=n
+ assert sum(five.values())==487546 and sum(r*n for r,n in five.items())==2809600
+ raw['schema']='gen4-parity-fused-fresh-raw-ledger/1';raw['producer_ledger']=producer
+ raw['physical_target_histogram']={str(r):n for r,n in sorted(target.items())};raw['one_stage_helper_histogram_including_copies']={str(r):n for r,n in sorted(helper.items())}
+ raw['five_stage_profile'].update(histogram={str(r):n for r,n in sorted(five.items())},calls=sum(five.values()))
+ raw['parity_transform']=receipt;raw['scope']='Fresh gen4 producer ledger plus independently rebuilt actual surviving-use ledger after F2 payload identity elision and same-stream nested MOVE fusion. Both reflected endpoint inclusions checked. No address arithmetic reduced modulo2.'
+ return raw
diff --git a/research/gen4-retiming-entrances/vendor/pr276/requirements.txt b/research/gen4-retiming-entrances/vendor/pr276/requirements.txt
new file mode 100644
index 0000000000..1ca5fd0616
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/requirements.txt
@@ -0,0 +1 @@
+sympy==1.14.0
diff --git a/research/gen4-retiming-entrances/vendor/pr276/scalar/word.py b/research/gen4-retiming-entrances/vendor/pr276/scalar/word.py
new file mode 100644
index 0000000000..95b9affd44
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/scalar/word.py
@@ -0,0 +1,263 @@
+def replay(mode='F2',direction=1,bits=24,mutation=None):
+ major=mode=='bound';binary=mode=='F2';v=W.v
+ unit=(lambda i:1)if major else(lambda i:1<<i)if binary else(lambda i:1<<(bits*i))
+ def add(x,c,y):return x+abs(c)*y if major else x^y if binary and c&1 else x if binary else x+c*y
+ target_frames=[None]*v;target_paths=[[]for _ in range(v)];center_reads=[];target_hist=Counter()
+ aggregation_active=[True]*len(agg);aggregation_read=[set()for _ in agg];aggregation_restores=[];aggregation_pivot_reads=0
+ rank_active=set(range(len(rankgroups)));rank_seen=[set()for _ in rankgroups];rank_restores=[];rank_skipped=0
+ echelon_active=set(range(len(echelon)));echelon_seen=[set()for _ in echelon];echelon_restores=[];echelon_reads=0
+ def target_move(t,f):
+  previous=target_frames[t];assert previous is None or C.sub(previous,f),('actual target chronology',t,previous,f)
+  assert all(W.module.dot(C.cov[t],b)==0 for b in C.B[f]),('actual target cap',t,f)
+  d=C.dimf[f]-(0 if previous is None else C.dimf[previous]);assert d>=0
+  if d:target_hist[d]+=1
+  target_frames[t]=f;target_paths[t].append(f)
+ X0=[unit(i)for i in range(v)];Y0=[unit(v+i)for i in range(v)];Z0={r:unit(idx[r])for r in regs};x=X0[:];y=Y0[:];z=Z0.copy();top=1;done=[]
+ def track(value):
+  nonlocal top
+  if major:top=max(top,value)
+  return value
+ def value(s):
+  s=W.phys[s];return x[borrow[s]]if s in borrow else z[s]
+ def assign(s,val):
+  s=W.phys[s]
+  if s in borrow:x[borrow[s]]=track(val)
+  else:z[s]=track(val)
+ source_paths={role:[W.w['source_frame'][r['source']],r['mix_frame']]for role,r in extra_byrole.items()}
+ pair_dirty_paths={r:[zero]for r in pair_bydirty}
+ def source_move(s,f):
+  role=W.phys[s]
+  if role in pair_dirty_paths:
+   assert C.sub(pair_dirty_paths[role][-1],f),('paired dirty chronology',role,pair_dirty_paths[role][-1],f)
+   pair_dirty_paths[role].append(f)
+  if role not in source_paths:return
+  assert C.sub(source_paths[role][-1],f),('orderedsource chronology',s,role,source_paths[role][-1],f)
+  source_paths[role].append(f)
+ responses=W.adjoint() if mutation=='old_adjoint' else adj
+ def aggregate_restore(k,trigger):
+  if not aggregation_active[k]:return
+  group=agg[k];pivot=group['pivot'];assert aggregation_read[k]==set(group['roles']),('early aggregation inverse',k,trigger,aggregation_read[k])
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_aggregation_inverse' or k!=39:
+   for t in group['targets']:
+    if t!=pivot:y[t]=track(add(y[t],1,y[pivot]))
+  aggregation_active[k]=False;aggregation_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def rank_restore(k,trigger):
+  group=rankgroups[k];assert k in rank_active and rank_seen[k]==group['roles']
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_rank_inverse'or k!=0:
+   for t,cs in group['dependent'].items():
+    for p,c in cs.items():y[t]=track(add(y[t],c,y[p]))
+  rank_active.remove(k);rank_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def echelon_restore(k,trigger):
+  group=echelon[k];assert echelon_seen[k]==group['roles']
+  for t in group['targets']:target_move(t,group['frame'])
+  if mutation!='omit_echelon_inverse'or k!=0:
+   for t,p,c in reversed(group['moves']):y[t]=track(add(y[t],-c,y[p]))
+  echelon_active.remove(k);echelon_restores.append(dict(group=k,before_role=trigger,frame=group['frame']))
+ def read(s):
+  nonlocal aggregation_pivot_reads,rank_skipped,echelon_reads
+  if s in pair_byalias:
+   if mutation=='subtract_paired_alias'and s==next(iter(pair_byalias)):
+    for t,c in adj[s].items():y[t]=track(add(y[t],-direction*c,value(s)))
+   return
+  if s in fresh:
+   if mutation=='omit_transformed_source_read'and s==next(iter(fresh)):return
+   for t,c in fresh[s]['transformed_response'].items():
+    t=int(t);source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame']);y[t]=track(add(y[t],-direction*c,value(s)))
+   return
+  echelon_skip=set()
+  if s in W.gauge:
+   for k,group in enumerate(echelon):
+    if k not in echelon_active:continue
+    if s not in group['roles']:
+     if set(responses[s])&set(group['targets']):echelon_restore(k,s)
+     continue
+    echelon_seen[k].add(s);echelon_skip.update(group['targets'])
+    for t,a in group['response'].items():
+     c=a.get(s,0)
+     if not c:continue
+     if mutation=='flip_echelon_sign'and k==0 and c<0:c=-c
+     source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame']);y[t]=track(add(y[t],-direction*c,value(s)));echelon_reads+=1
+  if s in W.gauge:
+   for k in sorted({rankowner[t]for t in responses[s]if t in rankowner}):
+    if k not in rank_active:continue
+    if s not in rankgroups[k]['roles']:rank_restore(k,s)
+    else:rank_seen[k].add(s)
+  if mutation=='omit_gauge_compensation'and s==new_gauge_selection[-1]['role']:return
+  if mutation=='omit_extra_compensation'and s==extra_selection[0]['role']:return
+  grouped=role_groups.get(s,[])
+  for k in sorted({target_group[t]for t in responses[s]if t in target_group}) if s in W.gauge else []:
+   if k not in grouped:aggregate_restore(k,s)
+  skipped=set()
+  for k in grouped:
+   group=agg[k];pivot=group['pivot'];assert aggregation_active[k]
+   assert set(group['targets'])<=set(responses[s])and len({responses[s][t]for t in group['targets']})==1
+   c=responses[s][pivot];source_move(s,read_frames[s,k]);target_move(pivot,read_frames[s,k]);y[pivot]=track(add(y[pivot],-direction*c,value(s)))
+   if mutation=='repeat_aggregation_read'and k==39:
+    t=next(t for t in group['targets']if t!=pivot);target_move(t,read_frames[s,k]);y[t]=track(add(y[t],-direction*c,value(s)))
+   skipped.update(group['targets']);aggregation_read[k].add(s);aggregation_pivot_reads+=1
+  for t,c in responses[s].items():
+   if t in skipped or t in echelon_skip:continue
+   rk=rankowner.get(t)
+   if s in W.gauge and rk in rank_active and t in rankgroups[rk]['dependent']:
+    rank_skipped+=1
+    if mutation!='repeat_rank_read'or rk!=0:continue
+   if s in W.gauge:source_move(s,W.gauge[s]['frame']);target_move(t,W.gauge[s]['frame'])
+   else:assert target_frames[t]is None,'initial correction leaves target atD0'
+   y[t]=track(add(y[t],-direction*c,value(s)))
+ def gate(i,sign):
+  a,b,_=W.ops[i]
+  if sign==1:
+   source_move(a,W.opframe[i]);source_move(b,W.opframe[i])
+  assign(a,add(value(a),sign,value(b)))
+ for s in range(W.R):
+  if s not in W.gauge and s not in borrow and s not in removed:read(s)
+ for n,s in W.source.items():assign(s,add(value(s),1,x[n]))
+ for r in gauge_selection:
+  if mutation=='omit_transformed_source_mix'and r is next(iter(fresh.values())):continue
+  if mutation=='omit_extra_mix'and r is extra_selection[0]:continue
+  if mutation!='omit_gauge_mix' or r is not new_gauge_selection[-1]:x[r['partner']]=track(add(x[r['partner']],1,x[r['source']]))
+ def forward(i):
+  if i not in omitted:gate(i,1);done.append(i)
+ for k in schedule['center_prefix_events']:
+  event=schedule['events'][k];i=event['op']
+  if event['kind']=='early_mix':
+   r=early[i];a,b=r['partner'],r['source']
+   if mutation!='omit_early_mix' or r is not selection[0]:x[a]=track(add(x[a],1,x[b]))
+  else:forward(i)
+ for r,s in zip(W.g['roots'],W.w['rootroles']):
+  if r['kind']=='center':
+   for t in r['targets']:
+    assert all(f is None for f in target_frames),'copied centers scatter before any nonzero target movement'
+    center_reads.append((s,t));y[t]=track(add(y[t],direction,value(s)))
+ for k,group in enumerate(echelon):
+  assert all(target_frames[t]is None for t in group['targets'])
+  if mutation!='omit_echelon_setup'or k!=0:
+   for t,p,c in group['moves']:y[t]=track(add(y[t],c,y[p]))
+ for k,group in enumerate(rankgroups):
+  assert all(target_frames[t]is None for t in group['targets'])
+  if mutation!='omit_rank_setup'or k!=0:
+   for t,cs in group['dependent'].items():
+    for p,c in cs.items():y[t]=track(add(y[t],-c,y[p]))
+ for k,group in enumerate(agg):
+  assert all(target_frames[t]is None for t in group['targets']), 'aggregation setup after all D0 center scatters'
+  if mutation!='omit_aggregation_setup'or k!=39:
+   for t in group['targets']:
+    if t!=group['pivot']:y[t]=track(add(y[t],-1,y[group['pivot']]))
+ for e in terminal:
+  assert all(target_frames[t]is None for t in e['targets']),'terminal setup afterD0center scatter'
+  for t in e['targets']:
+   if t!=e['pivot']:y[t]=track(add(y[t],-1,y[e['pivot']]))
+ # Original dirty compensation happened at D0 before these source injections.
+ for r in pair_selection:
+  b,f=r['aliased_role'],r['mix_frame']
+  for a,c in r['retained_dirty_coefficients'].items():
+   source_move(a,f);source_move(b,f)
+   if mutation=='omit_sparse_anchor'and r is pair_selection[14]and a==next(iter(r['retained_dirty_coefficients'])):continue
+   if mutation=='wrong_sparse_sign'and r is pair_selection[14]and a==next(iter(r['retained_dirty_coefficients'])):c=-c
+   if mutation!='omit_pair_initialization'or r is not pair_selection[0]:assign(a,add(value(a),c,value(b)))
+ for j,i in enumerate(W.rest):
+  for s in at[j]:
+   if mutation!='late_phase1_gauge' or s not in new_phase_roles:read(s)
+  if mutation=='late_phase1_gauge'and j==168:
+   for s in sorted(new_phase_roles):read(s)
+  if i in bywrite:
+   e=bywrite[i];a,b,n=W.ops[i];source_move(b,W.opframe[i]);target_move(e['pivot'],W.opframe[i]);y[e['pivot']]=track(add(y[e['pivot']],direction,value(b)))
+  else:forward(i)
+  if i in afterwrite:
+   e=afterwrite[i]
+   for t in e['targets']:
+    target_move(t,e['root_frame'])
+    if t!=e['pivot']:y[t]=track(add(y[t],1,y[e['pivot']]))
+ for s in at[len(W.rest)]:read(s)
+ assert not any(aggregation_active),'all quotient inverses precede original side/K reads'
+ assert not rank_active,'rank quotient inverses precede side/K reads'
+ assert not echelon_active,'echelon inverses precede side/K reads'
+ for j,(r,s)in enumerate(zip(W.g['roots'],W.w['rootroles'])):
+  if r['kind']=='side' and j not in deletedroots:
+   for k in sorted({target_group[t]for t in r['targets']if t in target_group}):aggregate_restore(k,('root',j))
+   source_move(s,W.w['root_frame'][j])
+   for t in r['targets']:target_move(t,W.w['root_frame'][j]);y[t]=track(add(y[t],direction,value(s)))
+  for e in deliveries[j]:
+   a,b=e['carrier'],e['passive']
+   if b not in by_source:x[a]=track(add(x[a],1,x[b]))
+   for k in sorted({target_group[t]for t in e['receivers']if t in target_group}):aggregate_restore(k,('K',j))
+   for t in e['receivers']:target_move(t,e['deliver_frame']);y[t]=track(add(y[t],direction,x[a]))
+ assert not any(aggregation_active),'all target inverses completed beforecleanup'
+ for e in W.k['entries']:
+  if e['passive']not in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ if mutation=='undo_before_restore':
+  for e in W.k['entries']:
+   if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ for role in source_paths:source_move(role,W.w['full_frame'])
+ for role in pair_dirty_paths:source_move(role,W.w['full_frame'])
+ for i in reversed(done):gate(i,-1)
+ for r in reversed(pair_selection):
+  b=r['aliased_role']
+  for a,c in reversed(list(r['retained_dirty_coefficients'].items())):
+   c=-c
+   if mutation=='wrong_pair_restore_sign'and r is pair_selection[0]:c=-c
+   if mutation!='omit_pair_restoration'or r is not pair_selection[0]:assign(a,add(value(a),c,value(b)))
+ if mutation!='undo_before_restore':
+  for e in W.k['entries']:
+   if e['passive']in by_source:x[e['carrier']]=track(add(x[e['carrier']],-1,x[e['passive']]))
+ for n,s in W.source.items():assign(s,add(value(s),-1,x[n]))
+ if binary:want=[Y0[t]^X0[t]for t in range(v)]
+ else:
+  want=Y0[:];cache={}
+  for root in W.g['roots']:
+   n=root['node']
+   if n not in cache:
+    mask=C.sup[n];val=0
+    while mask:low=mask&-mask;mask-=low;val=add(val,1,X0[low.bit_length()-1])
+    cache[n]=val
+   for t in root['targets']:want[t]=add(want[t],direction,cache[n])
+  for e in W.k['entries']:
+   val=add(X0[e['carrier']],1,X0[e['passive']])
+   for t in e['receivers']:want[t]=add(want[t],direction,val)
+ # Finish every local target at its codimension-one cap, then reverse the exact
+ # annihilator stream. All copied-center scatters lie before these movements,
+ # hence atD0 forward and atD1 after the complementary movements reverse.
+ reflected=Counter()
+ for t,chain in enumerate(target_paths):
+  assert chain
+  d=W.h-1-C.dimf[chain[-1]];assert d>=0
+  if d:target_hist[d]+=1
+  previous=[C.cov[t]];dimension=1
+  for f in reversed(chain):
+   assert all(W.module.dot(a,b)==0 for a in previous for b in C.B[f])
+   basis=C.A[f];step=len(basis)-dimension;assert step>=0
+   if step:reflected[step]+=1
+   previous=basis;dimension=len(basis)
+  if W.h>dimension:reflected[W.h-dimension]+=1
+ assert reflected==target_hist
+ assert len(center_reads)==sum(len(r['targets'])for r in W.g['roots']if r['kind']=='center')
+ assert sum(k*n for k,n in target_hist.items())==W.v*(W.h-1)
+ source_histogram=Counter();source_reflected=Counter()
+ for role,path in source_paths.items():
+  assert C.dimf[path[0]]==1 and C.dimf[path[-1]]==W.h
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b)and C.nondeg(a)and C.nondeg(b)
+   step=C.dimf[b]-C.dimf[a]
+   if step:source_histogram[step]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);step=len(C.A[b])-len(C.A[a]);assert step>=0
+   if step:source_reflected[step]+=1
+ assert source_histogram==source_reflected and sum(k*n for k,n in source_histogram.items())==len(source_paths)*(W.h-1)
+ paired_hist=Counter();paired_reflected=Counter()
+ for role,path in pair_dirty_paths.items():
+  assert C.dimf[path[0]]==0 and C.dimf[path[-1]]==W.h
+  for a,b in zip(path,path[1:]):
+   assert C.sub(a,b)and C.nondeg(a)and C.nondeg(b)
+   d=C.dimf[b]-C.dimf[a]
+   if d:paired_hist[d]+=1
+  for a,b in zip(reversed(path),list(reversed(path))[1:]):
+   assert all(W.module.dot(x,y)==0 for x in C.A[a]for y in C.B[b]);d=len(C.A[b])-len(C.A[a])
+   if d:paired_reflected[d]+=1
+ assert paired_hist==paired_reflected and sum(k*n for k,n in paired_hist.items())==len(pair_dirty_paths)*W.h
+ if major:return max(top,max(a+b for a,b in zip(y,want)),max(z[r]+Z0[r]for r in regs),max(a+b for a,b in zip(x,X0)))
+ assert y==want,('wrong targets',mode,[t for t in range(v)if y[t]!=want[t]][:10])
+ assert x==X0,('source restoration',mode,[s for s in range(v)if x[s]!=X0[s]][:10])
+ assert z==Z0,('dirty restoration',mode)
+ return dict(mode=mode,direction=direction,formal_columns=2*v+len(regs),sources=v,targets=v,dirty=len(regs),all_targets=True,all_source_and_dirty_restored=True,copied_center_target_reads=len(center_reads),all_forward_centers_at_D0=True,all_reflected_centers_at_D1=True,actual_target_histogram={str(k):n for k,n in sorted(target_hist.items())},actual_reflected_target_histogram={str(k):n for k,n in sorted(reflected.items())},aggregation_groups=len(agg),aggregation_pivot_reads=aggregation_pivot_reads,aggregation_restores=aggregation_restores,actual_extra_source_paths=source_paths,rank_groups=len(rankgroups),rank_targets=len(rankowner),rank_restores=rank_restores,rank_removed_reads=rank_skipped,actual_extra_source_histogram=dict(source_histogram),actual_extra_reflected_source_histogram=dict(source_reflected),echelon_restores=echelon_restores,echelon_reads=echelon_reads,paired_dirty_paths=pair_dirty_paths,paired_dirty_histogram=dict(paired_hist),paired_dirty_reflected_histogram=dict(paired_reflected))
diff --git a/research/gen4-retiming-entrances/vendor/pr276/scalar_check.py b/research/gen4-retiming-entrances/vendor/pr276/scalar_check.py
new file mode 100644
index 0000000000..cd33eefeaa
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/scalar_check.py
@@ -0,0 +1,125 @@
+"""Fresh F2 source proof, independent literal projection/inverse and controls.
+No saved execution receipt is accepted. Uses the actual clean source context
+and freshly emitted local physical records. Assisted with ChatGPT (source527).
+Rebound to the gen4 word: 19930 formal columns; the controls corrupt the actual
+gen4 context (responses, read chronology, alias reads, gates, centres, partner
+deliveries, injections and signs) instead of absent source527 selections.
+Gen4 rebinding and controls by DreamingOfClouds with Anthropic Claude assistance.
+"""
+from collections import Counter,defaultdict
+from copy import copy
+import hashlib,json,time
+
+EXPECTED_EVENT='c0f4da07311f1998e0813b39098da9015969c180fa55d72f281e45cdd50aaba8'
+N=19930;V=1760;EVENTS=626360;COUNTS={1:624600,3:1760}
+
+
+def events(records,reverse=False):
+    center=None
+    for k in (range(len(records)-6,-1,-6) if reverse else range(0,len(records),6)):
+        op,a,b,c,f,z=records[k:k+6]
+        if op==1:
+            if b==N:
+                assert center is not None
+                b=center
+            assert 0<=a<N and 0<=b<N and a!=b
+            yield a,b,-c if reverse else c
+        elif op==(3 if reverse else 2):
+            assert center is None and b==N
+            center=a
+        elif op==(2 if reverse else 3):
+            assert center==a and b==N
+            center=None
+    assert center is None
+
+
+def replay_projection(records,reverse=False,omit_event=None):
+    n=N;v=V
+    columns=[1<<i for i in range(n)];norms=[1]*n
+    wanted=columns[:]
+    for i in range(v):wanted[v+i]^=1<<i
+    largest=1;counts=Counter();digest=hashlib.sha256();count=0
+    for event_index,(a,b,c) in enumerate(events(records,reverse)):
+        if event_index==omit_event:continue
+        if c&1:columns[a]^=columns[b]
+        norms[a]+=abs(c)*norms[b];largest=max(largest,norms[a])
+        counts[abs(c)]+=1
+        digest.update(json.dumps([a,b,c],separators=(',',':')).encode());digest.update(b'\n');count+=1
+    assert columns==wanted,'independent literal all-column endpoint'
+    assert count==EVENTS and counts==COUNTS
+    if not reverse:assert digest.hexdigest()==EXPECTED_EVENT
+    return dict(all_formal_columns=n,all_source_and_dirty_restored=True,
+                arbitrary_target_contents_preserved=True,
+                event_sha256=digest.hexdigest(),weighted_additions=count,
+                coefficient_counts=dict(counts),literal_unit_additions=sum(c*n for c,n in counts.items()),
+                max_intermediate_row_l1=largest,final_source_row_l1=max(norms[:v]),
+                final_target_row_l1=max(norms[v:2*v]),final_dirty_row_l1=max(norms[2*v:]))
+
+
+def mutated_namespaces(context):
+    """Actual-context corruptions; each must make the unchanged scalar program fail."""
+    W=context['W'];adj=context['adj'];at=context['at']
+    recipients={b:d for b,d in W.pairs}
+    plain_gauge=next(s for s in W.order if s not in recipients and adj[s])
+    recipient=next(b for b in W.order if b in recipients and adj[b])
+    dirty=next(s for s in range(W.R) if s not in W.gauge and s in set(W.phys.values()) and adj[s] and s not in context['borrow'])
+    def with_adj(role,row):
+        a=list(adj);a[role]=row;return dict(adj=a)
+    def drop_first(role):
+        t=next(iter(adj[role]));return with_adj(role,{u:c for u,c in adj[role].items() if u!=t})
+    def move_read(role,time):
+        a=defaultdict(list,{k:list(v) for k,v in at.items()})
+        a[W.readtime[role]].remove(role);a[time].append(role);return dict(at=a)
+    def proxy(**changes):
+        P=copy(W);P.__dict__.update(changes);return dict(W=P)
+    yield 'omit_gauge_compensation','F2',drop_first(plain_gauge)
+    yield 'omit_dirty_compensation','F2',drop_first(dirty)
+    yield 'omit_alias_recipient_compensation','F2',drop_first(recipient)
+    t=next(iter(adj[plain_gauge]));other=(t+1)%V
+    while other in adj[plain_gauge]:other=(other+1)%V
+    row=dict(adj[plain_gauge]);row[other]=row.pop(t)
+    yield 'misrouted_gauge_response','F2',with_adj(plain_gauge,row)
+    row=dict(adj[plain_gauge]);row[t]=-row[t]
+    yield 'flipped_gauge_compensation_sign','Z',with_adj(plain_gauge,row)
+    position={i:j for j,i in enumerate(W.rest)}
+    def last_write(d):
+        js=[position[i] for i in W.role_ops[d] if W.ops[i][0]==d and i in position]
+        return max(js) if js else None
+    written=next(b for b in W.order if b in recipients and adj[b] and last_write(recipients[b]) is not None)
+    yield 'alias_read_before_donor_last_write','F2',move_read(written,last_write(recipients[written]))
+    yield 'gauge_read_after_first_use','F2',move_read(plain_gauge,W.first[plain_gauge]+1)
+    gate=next(i for i in W.rest if W.ops[i][0] not in W.gauge)
+    yield 'omitted_gate','F2',dict(omitted={gate})
+    roots=[dict(r) for r in W.g['roots']];j=next(k for k,r in enumerate(roots) if r['kind']=='center');roots[j]['targets']=roots[j]['targets'][1:]
+    yield 'omitted_centre_scatter','F2',proxy(g=dict(W.g,roots=roots))
+    deliveries=defaultdict(list,{k:list(v) for k,v in context['deliveries'].items()});k=next(k for k,v in sorted(deliveries.items()) if v);deliveries[k]=deliveries[k][1:]
+    yield 'omitted_partner_delivery','F2',dict(deliveries=deliveries)
+    source=dict(W.source);source.pop(next(iter(source)))
+    yield 'omitted_source_injection','F2',proxy(source=source)
+
+
+def run(context,records,progress=lambda text:None):
+    import gc
+    started=time.monotonic();ns=dict(context);source=ns['SOURCE_TEXT']
+    assert hashlib.sha256(source.encode()).hexdigest()=='e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42'
+    exec(compile(source,'retained source527 exact scalar word','exec'),ns)
+    progress('Checking all19930 source, target and arbitrary dirty F2 columns')
+    exact=ns['replay']('F2');assert exact['formal_columns']==N and exact['all_targets']and exact['all_source_and_dirty_restored']
+    progress('Checking independent literal physical projection and inverse')
+    forward=replay_projection(records);inverse=replay_projection(records,True)
+    assert forward['max_intermediate_row_l1']==21725 and inverse['max_intermediate_row_l1']==1850360
+    try:replay_projection(records,omit_event=EVENTS-1)
+    except AssertionError:filtered_control='omitted surviving odd payload ADD rejected'
+    else:raise AssertionError('filtered odd payload omission accepted')
+    bound=ns['replay']('bound');bits=8*((bound.bit_length()+2+7)//8);assert 1<<bits>2*bound
+    progress('Checking the signed integer source decoder and dirty restoration')
+    integer=[]
+    for direction in(1,-1):integer.append(ns['replay']('Z',direction,bits));gc.collect()
+    controls={}
+    for name,mode,changes in mutated_namespaces(context):
+        bad=dict(context);bad.update(changes);exec(compile(source,'retained source527 exact scalar word','exec'),bad)
+        try:bad['replay'](mode,bits=bits)
+        except AssertionError as error:controls[name]=dict(rejected=True,reason=str(error)[:200])
+        else:raise AssertionError('invalid gen4 context mutation accepted: '+name)
+    assert len(controls)==11
+    return dict(status='PASS_FRESH_GEN4_PRODUCER_SIGNED_DECODER_AND_PARITY_FUSED_F2_INVERSE_AND_CONTROLS',filtered_control=filtered_control,F2=exact,integer=integer,majorant=dict(residual_bound=bound,packing_bits=bits),forward=forward,inverse=inverse,controls=controls,source_sha256=hashlib.sha256(source.encode()).hexdigest(),seconds=time.monotonic()-started,scope='The retained source527 scalar program, run on the gen4 context, proves the signed defining-integer decoder in both directions and rejects11 actual-context corruptions. The emitted parity-filtered word is independently checked on all19930formal F2columns and literalreverse, with its own cancellation-free signed-lift prefix bounds. Its integer endpoint is not asserted equal to the producer decoder; F2payload identity supplies the bit contract. Odd-prime address arithmetic is unchanged.')
diff --git a/research/gen4-retiming-entrances/vendor/pr276/verify.py b/research/gen4-retiming-entrances/vendor/pr276/verify.py
new file mode 100644
index 0000000000..6b1a5fa662
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/verify.py
@@ -0,0 +1,83 @@
+#!/usr/bin/env python3
+"""Immutable gen4 five-stage banks: regenerate every mandatory finite stage.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import sys
+if not __debug__:raise SystemExit('Assertions required; refusing-O')
+sys.dont_write_bytecode=True
+from pathlib import Path
+from datetime import datetime,timezone
+from fractions import Fraction
+import argparse,hashlib,importlib.util,json,time,traceback
+ROOT=Path(__file__).resolve().parent
+REQUIRED={'virtual','raw','bit','scalar','primes','banks','complex','math','finite'}
+
+def progress(message):print(datetime.now(timezone.utc).strftime('%H:%M:%S UTC')+'  '+message,flush=True)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def serial(x):
+ if isinstance(x,Fraction):return str(x)
+ if isinstance(x,dict):return {str(k):serial(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return list(map(serial,x))
+ return x
+
+def load(name):
+ s=importlib.util.spec_from_file_location('source527_'+name,ROOT/(name+'.py'));m=importlib.util.module_from_spec(s);sys.modules[s.name]=m;s.loader.exec_module(m);return m
+
+def integrity():
+ p=ROOT/'MANIFEST.json';m=json.loads(p.read_text());actual={}
+ for q in ROOT.rglob('*'):
+  assert not q.is_symlink(),'Symlink in package'
+  if q.is_file()and q.name!='MANIFEST.json':actual[q.relative_to(ROOT).as_posix()]=sha(q)
+ # Nested source manifests are also ordinary pinned inputs.
+ for q in ROOT.rglob('MANIFEST.json'):
+  if q!=p:actual[q.relative_to(ROOT).as_posix()]=sha(q)
+ assert actual==m['files'],'Missing, changed or unpinned package/source file'
+ return sha(p),len(actual)
+
+def validate_required(results):
+ assert set(results)==REQUIRED,'Missing mandatory proof stage'
+ assert all(isinstance(results[k],dict)and results[k]for k in REQUIRED)
+
+def controls():
+ out=[];good={k:{'present':True}for k in REQUIRED}
+ for k in sorted(REQUIRED):
+  bad=good.copy();bad.pop(k)
+  try:validate_required(bad)
+  except AssertionError:out.append('omitted '+k+' stage')
+  else:raise AssertionError('Missingstageaccepted')
+ return out
+
+def main():
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--output',type=Path,required=True);args=ap.parse_args()
+ import sympy
+ assert sys.version_info>=(3,11)and sympy.__version__=='1.14.0'
+ digest,count=integrity();output=args.output.resolve();assert not output.is_relative_to(ROOT)and not output.exists(),'Output must be new and outside package';output.mkdir(parents=True)
+ results={};timings={};start=time.monotonic()
+ def save(name,value):(output/name).write_text(json.dumps(serial(value),sort_keys=True,indent=2)+'\n')
+ def stage(name,call):
+  t=time.monotonic();value=call();results[name]=value;timings[name]=time.monotonic()-t;save(name+'.json',value);progress(name+' PASS '+format(timings[name],'.1f')+'s');return value
+ try:
+  progress('Admitting the pinned gen4 physical bit word')
+  stage('virtual',lambda:load('virtual_check').run(output,progress))
+  context=load('prepare').prepare()
+  raw=stage('raw',lambda:load('raw_ledger').run(context))
+  portable=load('portable_bit');bit=portable.run(prepared_context=context,raw=raw,output_dir=output,run_geometry=True,package_root=ROOT);raw=bit['raw'];results['raw']=raw;save('raw.json',raw);results['bit']=portable.summary(bit);timings['bit']=bit['seconds'];save('bit.json',results['bit']);progress('bit physical/global/geometry PASS')
+  scalar=stage('scalar',lambda:load('scalar_check').run(context,bit['records'],progress))
+  primes=stage('primes',lambda:load('prime_check').run(context,bit['physical'],progress))
+  bankresult=stage('banks',lambda:load('bank_check').run(context,bit['global_result'],bit['lower']))
+  banks=bankresult['banks'];banked=bankresult['banked_result']
+  complex_result=stage('complex',lambda:load('portable_complex').run(package_root=ROOT,progress=progress))
+  assert complex_result['precision_guard']['retained_row_coefficient']==20161
+  math=stage('math',lambda:load('math_check').run(raw,complex_result['five_stage_histogram'],banks,bit['global_result']))
+  finite=stage('finite',lambda:load('finite_check').run(raw,bit['physical'],scalar,primes,math,banks,banked,bit['global_result']))
+  assert math['mathematics']['finite_bridge']['rows']['coefficient']==complex_result['precision_guard']['retained_row_coefficient']==finite['row_reserve']['external_complex_coefficient']
+  validate_required(results);assert len(scalar['controls'])==11 and len(primes['controls'])==6
+  assert math['mathematics']['kappa']=='144573965469499/200000000000000000'
+  after,_=integrity();assert after==digest,'Package changed during replay'
+  certificate=dict(schema='gen4-parity-fused-five-stage-banks/1',**math['mathematics'],scope='Conditionalfiniteconstruction; inheritedallsizecompiler,weightedselector,commonancestorchart,restoredrow,routing,prime,recovery,complexsymbolicandanalyticinterfacesremainassumptions.')
+  save('certificate.json',certificate)
+  report=dict(status='PASS_IMMUTABLE_PARITY_FUSED_GEN4_FIVE_STAGE_BANKED_CONSTRUCTION',manifest_sha256=digest,files=count,kappa=math['mathematics']['kappa'],kappa_scientific=math['mathematics']['kappa_scientific'],fresh_stages=sorted(REQUIRED),inputs_unchanged=True,timings=timings,seconds=time.monotonic()-start,negative_controls=controls())
+  save('verification.json',report);print(json.dumps(report),flush=True)
+ except BaseException as exc:
+  save('failure.json',dict(status='FAIL',error=str(exc),completed_stages=sorted(results),timings=timings,traceback=traceback.format_exc()));raise
+if __name__=='__main__':main()
diff --git a/research/gen4-retiming-entrances/vendor/pr276/virtual_check.py b/research/gen4-retiming-entrances/vendor/pr276/virtual_check.py
new file mode 100644
index 0000000000..8538bd1297
--- /dev/null
+++ b/research/gen4-retiming-entrances/vendor/pr276/virtual_check.py
@@ -0,0 +1,63 @@
+"""Retained admissions of the gen4 bit word: PR168-v4 package checker and PR200 physical-word proof.
+
+1. eumemic's unmodified PR168-v4 check_paired_cube_bit.py on the virtual (node-frame, unaliased) word:
+   exact frames, mod-2 decoder with stars and side parts, geometry (source lines, root caps, operand
+   nesting, star spans), role and target chains, partner chronology, G-nondegeneracy, a literal F2
+   dirty-scratch replay and the ledger recount, with its five mutation controls.
+2. Chafik Boukhalfa's unmodified PR200 physical-word classes, run as PR200's bit/prove.py runs them:
+   exact changed operation frames and handoffs, the physical row (phase one = centre closure, actual
+   addition operands, gauge supports, partner chronology, nested physical role and target chains,
+   telescoping deficit), the physical word on every formal column over F2 and the defining integer
+   decoder, and its adverse controls (omitted compensation, missing partner delivery, stale recipient
+   read, zero operation frame).
+Gen4 integration by DreamingOfClouds with Anthropic Claude assistance; Apache-2.0.
+"""
+from pathlib import Path
+import gzip,hashlib,importlib.util,json,shutil,time
+HERE=Path(__file__).resolve().parent
+
+def load(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod);return mod
+
+def run(output_dir,progress=lambda text:None):
+    begun=time.monotonic();src=HERE/'gen4bit/selected/bit';d=Path(output_dir)/'virtual-bit';d.mkdir(parents=True)
+    for name in ('graph','kchron','profile'):shutil.copyfile(src/(name+'_p12.json'),d/(name+'_p12.json'))
+    for name in ('word','frames'):(d/(name+'_p12.json')).write_bytes(gzip.decompress((src/(name+'_p12.json.gz')).read_bytes()))
+    p=HERE/'gen4bit/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py'
+    mod=load('gen4_pr168_v4_checker',p)
+    progress('Running the PR168-v4 package checker on the gen4 virtual word')
+    result=mod.Checker(d,12).run()
+    assert result==dict(frames=26058,roles=17904,W=21424,m=72,deficit=1936,children=293416)
+    controls={}
+    for m in ('broken_mix','outside_cap','below_level','dropped_star','non_nested'):
+        try:mod.Checker(d,12,mutate=m).run()
+        except mod.Fail as error:controls[m]=str(error)
+        else:raise AssertionError('PR168 mutation control accepted: '+m)
+    assert len(controls)==5
+    progress('Running the PR200 physical-word proof on the gen4 physical word')
+    word=load('gen4_pr200_physical_word_admission',HERE/'gen4bit/bit/word.py').Candidate()
+    word.exact_frames();row=word.row()
+    reference=json.loads((src/'profile_p12.json').read_text())
+    assert row['reused_registers']==len(word.pairs)==1494 and row['virtual_R']==reference['R']==17904
+    assert row['R']==16410 and row['W_per_vertex']==19930 and row['deficit_per_vertex']==reference['deficit_per_vertex']==1936 and row['loss']==reference['loss']==528
+    assert row['changed_operation_frames']==1802 and row['selected_roles']==2466 and row['selected_rank_histogram']=={20:2200,21:266}
+    formal=[word.formal(r) for r in (2,0)]
+    assert formal[0]['identity'] and all(f['defining_decoder'] and f['all_dirty_and_source_columns_restored'] and f['formal_variables']==19930 for f in formal)
+    physical_controls=[]
+    for tamper in ('omit_compensation','missing_partner','stale'):
+        try:word.formal(2,tamper)
+        except ValueError:physical_controls.append(tamper)
+        else:raise AssertionError('PR200 adverse word control accepted: '+tamper)
+    i=word.changed_frames[0];old=word.opframe[i];word.opframe[i]=word.register([])
+    try:word.exact_frames()
+    except ValueError:physical_controls.append('zero_operation_frame')
+    else:raise AssertionError('zero operation frame accepted')
+    word.opframe[i]=old
+    assert len(physical_controls)==4
+    row={k:(dict(v) if isinstance(v,dict) else v) for k,v in row.items()}
+    return dict(status='PASS_PR168_V4_VIRTUAL_AND_PR200_PHYSICAL_ADMISSION_OF_GEN4',virtual=result,virtual_controls_rejected=controls,
+        physical_row=row,physical_formal=formal,physical_controls_rejected=physical_controls,
+        checker_sha256=hashlib.sha256(p.read_bytes()).hexdigest(),
+        pr200_classes_sha256={n:hashlib.sha256((HERE/'gen4bit/bit'/n).read_bytes()).hexdigest() for n in ('word.py','base_word.py')},
+        seconds=time.monotonic()-begun,
+        scope='The pinned word is admitted by both retained checkers exactly as PR200 admitted its own word (its terminal-sink and prime steps have no gen4 counterpart here; primes are rechecked by prime_check).')
diff --git a/research/gen4-retiming-entrances/verify.py b/research/gen4-retiming-entrances/verify.py
new file mode 100644
index 0000000000..cb5b980aa7
--- /dev/null
+++ b/research/gen4-retiming-entrances/verify.py
@@ -0,0 +1,60 @@
+#!/usr/bin/env python3
+"""Fresh, network-free admission of the composed conditional gen4 construction."""
+import sys
+if not __debug__: raise SystemExit('Assertions required; refusing -O')
+sys.dont_write_bytecode = True
+import argparse, hashlib, json, os, shlex, shutil, subprocess, time
+from pathlib import Path
+ROOT = Path(__file__).resolve().parent
+BASE_MANIFEST = '6381aa8d881a4a89cf6c40db5bcd705b928a27599540a270bf3cd15f604c705d'
+WORD = '71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48'
+def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest()
+def integrity():
+    manifest = ROOT/'MANIFEST.json'
+    files = {}
+    for p in ROOT.rglob('*'):
+        assert not p.is_symlink(), 'Symlink in immutable package'
+        if p.is_file() and p != manifest: files[p.relative_to(ROOT).as_posix()] = sha(p)
+    assert files == json.loads(manifest.read_text())['files'], 'Changed, missing or unpinned source'
+    assert sha(ROOT/'vendor/pr276/MANIFEST.json') == BASE_MANIFEST
+    return sha(manifest)
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--output',type=Path,required=True)
+    a=ap.parse_args(); out=a.output.resolve()
+    assert not out.exists() and not out.is_relative_to(ROOT), 'Use a fresh output outside package'
+    import sympy
+    assert sys.version_info >= (3,11) and sympy.__version__ == '1.14.0'
+    digest=integrity(); out.mkdir(parents=True); start=time.monotonic(); stages=[]
+    env=dict(os.environ, PYTHONDONTWRITEBYTECODE='1')
+    def run(name,args):
+        print(name, flush=True); t=time.monotonic()
+        with (out/(name+'.log')).open('w') as log:
+            subprocess.run([str(x) for x in args],check=True,stdout=log,stderr=subprocess.STDOUT,env=env)
+        stages.append({'stage':name,'seconds':time.monotonic()-t})
+    py=[sys.executable,'-B']; code=ROOT/'code'; base=ROOT/'vendor/pr276'
+    try:
+        run('01-baseline',py+[base/'verify.py','--output',out/'baseline'])
+        run('02-export',py+[code/'export.py','--base',base,'--output',out/'export'])
+        run('03-retime',py+[code/'retime.py','--export-dir',out/'export','--output',out/'retimed'])
+        run('04-cleanup',py+[code/'cleanup.py','--source-dir',out/'retimed','--export-dir',out/'export','--output',out/'cleanup'])
+        run('05-entrances',py+[code/'entrances.py','--source-dir',out/'cleanup','--export-dir',out/'export','--output',out/'candidate'])
+        assert sha(out/'candidate/COHORT249-RECORDS.bin') == WORD
+        compiler=shlex.split(os.environ.get('CXX','c++'))
+        for name in ['five-stage-columns','charts']:
+            run('compile-'+name,compiler+['-std=c++17','-O2','-I'+str(ROOT/'vendor'),code/(name+'.cpp'),'-o',out/name])
+        run('06-columns',[out/'five-stage-columns',out/'candidate/COHORT249-RECORDS.bin',out/'candidate/COHORT-FIVE-STAGE-COLUMNS.json','1760','16410'])
+        # The binary and chart output directory must have distinct names.
+        chartdir=out/'chart-audit'; chartdir.mkdir()
+        run('07-charts',[out/'charts',out/'export',out/'candidate',chartdir])
+        run('08-price',py+[code/'price.py',out/'candidate','--base',base,'--output',out/'PRICE.json'])
+        run('09-admission',py+[code/'admit.py',out/'candidate','--export',out/'export','--baseline',out/'baseline','--charts',chartdir/'COMBINED-CHART-AUDIT.json','--price',out/'PRICE.json','--output',out/'admission'])
+        assert integrity()==digest
+        price=json.loads((out/'PRICE.json').read_text())
+        report={'status':'PASS_IMMUTABLE_COMPOSED_GEN4_CONSTRUCTION','manifest_sha256':digest,'word_sha256':WORD,'kappa':price['kappa'],'kappa_decimal':price['kappa_decimal'],'inputs_unchanged':True,'fresh_stages':stages,'seconds':time.monotonic()-start,'scope':'Conditional finite construction. Inherited all-size compiler, common weighted chart, restored rows, selectors, routing, prime supply, precision/recovery, complex symbolic correctness and analytic interfaces remain assumptions. No claim about the latest public comparator is inferred by this offline verifier.'}
+        (out/'VERIFICATION.json').write_text(json.dumps(report,indent=2)+'\n')
+        print('PASS kappa = '+price['kappa_decimal'],flush=True)
+    except BaseException as e:
+        (out/'FAILURE.json').write_text(json.dumps({'status':'FAIL','error':str(e),'completed':stages},indent=2)+'\n')
+        raise
+if __name__=='__main__': main()