From 50458e71475413411644827addf7a8d9013c1757 Mon Sep 17 00:00:00 2001
From: chafreaky <chafik.boukhalfa@gmail.com>
Date: Sat, 10 Oct 2026 06:58:53 +0400
Subject: [PATCH 1/5] multicut-kernel-condensation-851: 333 more
 response-kernel pairs at PR259's earliest cut, kappa = 7.11403723709732e-4
 (+0.0526% over PR259)

---
 .../multicut-kernel-condensation-851.yml      |    32 +
 .../BANK-PROOF.md                             |    61 +
 .../COPY-PROOF.md                             |     7 +
 .../FINITE-PROOF.md                           |     9 +
 .../KERNEL-PROOF.md                           |    31 +
 .../multicut-kernel-condensation-851/LICENSE  |   201 +
 .../MANIFEST.json                             |    50 +
 .../NOTICE.md                                 |    31 +
 .../PROOF-PR259.md                            |    61 +
 .../multicut-kernel-condensation-851/PROOF.md |    70 +
 .../README-PR259.md                           |    30 +
 .../README.md                                 |    59 +
 .../RESULT.json                               |    12 +
 .../REVIEW.md                                 |     9 +
 .../code/cohort-bank-review.cpp               |    19 +
 .../code/cohort-finite-invoice.cpp            |    14 +
 .../code/cohort-five-stage-columns.cpp        |    42 +
 .../code/cohort-legality-independent.cpp      |     7 +
 .../code/cohort-prefix-independent.cpp        |     5 +
 .../code/cohort-price.cpp                     |    27 +
 .../code/cohort-transform.cpp                 |    27 +
 .../code/export249.py                         |    24 +
 .../discovery/README.md                       |    20 +
 .../discovery/chrono2.py                      |   101 +
 .../discovery/compare259.py                   |    57 +
 .../discovery/gain.py                         |    79 +
 .../discovery/gen_candidates.py               |   139 +
 .../discovery/merge259.py                     |    13 +
 .../discovery/twins.py                        |   149 +
 .../expected/COHORT-BANK-REVIEW.json          |   553 +
 .../expected/COHORT-EXACT-PRICE.json          |   102 +
 .../expected/COHORT-FINITE-INVOICE.json       |    72 +
 .../expected/COHORT-FIVE-STAGE-COLUMNS.json   |   182 +
 .../expected/COHORT249-REPLAY.json            |    62 +
 .../expected/INDEPENDENT-LEGALITY.json        |   110 +
 .../expected/INDEPENDENT-PREFIX.json          |    10 +
 .../inputs/249-DONOR-OWNERSHIP.json.gz        |   Bin 0 -> 4366 bytes
 .../inputs/249-records.bin.gz                 |   Bin 0 -> 3124548 bytes
 .../inputs/249-states.json.gz                 |   Bin 0 -> 1331199 bytes
 .../inputs/SNAPSHOTS.json                     |     6 +
 .../inputs/candidates.json.gz                 |   Bin 0 -> 55880 bytes
 .../inputs/frames.json.gz                     |   Bin 0 -> 678666 bytes
 .../requirements.txt                          |     1 +
 .../vendor/PR249-SOURCE-MANIFEST.json         |   140 +
 .../vendor/UPSTREAM-NOTICE.md                 |    13 +
 .../vendor/json.hpp                           | 25526 ++++++++++++++++
 .../vendor/pr249-source.zip                   |   Bin 0 -> 2693658 bytes
 .../verify.py                                 |   125 +
 48 files changed, 28288 insertions(+)
 create mode 100644 .github/workflows/multicut-kernel-condensation-851.yml
 create mode 100644 research/multicut-kernel-condensation-851/BANK-PROOF.md
 create mode 100644 research/multicut-kernel-condensation-851/COPY-PROOF.md
 create mode 100644 research/multicut-kernel-condensation-851/FINITE-PROOF.md
 create mode 100644 research/multicut-kernel-condensation-851/KERNEL-PROOF.md
 create mode 100644 research/multicut-kernel-condensation-851/LICENSE
 create mode 100644 research/multicut-kernel-condensation-851/MANIFEST.json
 create mode 100644 research/multicut-kernel-condensation-851/NOTICE.md
 create mode 100644 research/multicut-kernel-condensation-851/PROOF-PR259.md
 create mode 100644 research/multicut-kernel-condensation-851/PROOF.md
 create mode 100644 research/multicut-kernel-condensation-851/README-PR259.md
 create mode 100644 research/multicut-kernel-condensation-851/README.md
 create mode 100644 research/multicut-kernel-condensation-851/RESULT.json
 create mode 100644 research/multicut-kernel-condensation-851/REVIEW.md
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-bank-review.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-finite-invoice.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-five-stage-columns.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-legality-independent.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-prefix-independent.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-price.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/cohort-transform.cpp
 create mode 100644 research/multicut-kernel-condensation-851/code/export249.py
 create mode 100644 research/multicut-kernel-condensation-851/discovery/README.md
 create mode 100644 research/multicut-kernel-condensation-851/discovery/chrono2.py
 create mode 100644 research/multicut-kernel-condensation-851/discovery/compare259.py
 create mode 100644 research/multicut-kernel-condensation-851/discovery/gain.py
 create mode 100644 research/multicut-kernel-condensation-851/discovery/gen_candidates.py
 create mode 100644 research/multicut-kernel-condensation-851/discovery/merge259.py
 create mode 100644 research/multicut-kernel-condensation-851/discovery/twins.py
 create mode 100644 research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json
 create mode 100644 research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json
 create mode 100644 research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json
 create mode 100644 research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json
 create mode 100644 research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json
 create mode 100644 research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json
 create mode 100644 research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json
 create mode 100644 research/multicut-kernel-condensation-851/inputs/249-DONOR-OWNERSHIP.json.gz
 create mode 100644 research/multicut-kernel-condensation-851/inputs/249-records.bin.gz
 create mode 100644 research/multicut-kernel-condensation-851/inputs/249-states.json.gz
 create mode 100644 research/multicut-kernel-condensation-851/inputs/SNAPSHOTS.json
 create mode 100644 research/multicut-kernel-condensation-851/inputs/candidates.json.gz
 create mode 100644 research/multicut-kernel-condensation-851/inputs/frames.json.gz
 create mode 100644 research/multicut-kernel-condensation-851/requirements.txt
 create mode 100644 research/multicut-kernel-condensation-851/vendor/PR249-SOURCE-MANIFEST.json
 create mode 100644 research/multicut-kernel-condensation-851/vendor/UPSTREAM-NOTICE.md
 create mode 100644 research/multicut-kernel-condensation-851/vendor/json.hpp
 create mode 100644 research/multicut-kernel-condensation-851/vendor/pr249-source.zip
 create mode 100644 research/multicut-kernel-condensation-851/verify.py

diff --git a/.github/workflows/multicut-kernel-condensation-851.yml b/.github/workflows/multicut-kernel-condensation-851.yml
new file mode 100644
index 0000000000..243d9be476
--- /dev/null
+++ b/.github/workflows/multicut-kernel-condensation-851.yml
@@ -0,0 +1,32 @@
+name: multicut-kernel-condensation-851
+
+on:
+  pull_request:
+    paths:
+      - 'research/multicut-kernel-condensation-851/**'
+      - '.github/workflows/multicut-kernel-condensation-851.yml'
+  push:
+    paths:
+      - 'research/multicut-kernel-condensation-851/**'
+      - '.github/workflows/multicut-kernel-condensation-851.yml'
+
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 40
+    strategy:
+      matrix:
+        python-version: ['3.11', '3.13']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Install the native toolchain of PR 259's checkers
+        run: sudo apt-get update && sudo apt-get install -y g++ libboost-dev
+      - name: Install SymPy for the pinned upstream regeneration
+        run: python -m pip install -r research/multicut-kernel-condensation-851/requirements.txt
+      - name: Regenerate PR 249's word, compile and run the seven checkers on the 851-pivot selection, compare receipts and price
+        run: python3 -I research/multicut-kernel-condensation-851/verify.py --output /tmp/mc851-replay
+      - name: Require an unchanged tree
+        run: git diff --exit-code
diff --git a/research/multicut-kernel-condensation-851/BANK-PROOF.md b/research/multicut-kernel-condensation-851/BANK-PROOF.md
new file mode 100644
index 0000000000..f55c29d206
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/BANK-PROOF.md
@@ -0,0 +1,61 @@
+# General residual-bank construction for response-kernel entrances
+
+## Sufficient construction
+
+Suppose a literal scalar word has been independently checked to restore all arbitrary helper values and has no final data/helper block. Suppose it uses the inherited nested-frame address compiler, and each newly changed helper has initial nondegenerate frame E of dimension d and final frame I24. The changed helper then has actual residual partial swap D_P with P=I-sigma_E; this is an inherited compiler conclusion, not a conclusion of rank counting. Assume the old frame admissions remain unchanged.
+
+For the present pinned PR249 family, all newly changed helpers previously belonged to the zero-entrance rank24 residual family. There are 14,287 such helpers before new changes. The unchanged nonfull families are 2,200 rank4,22 rank6,5 rank7,48 rank11,23 rank12,2 rank15 helpers. All occur in40 replicas and5 stages.
+
+Let S be the sum of dimensions of the new entrances, m the number of changed helpers. If S is divisible by3, and the required rank4 filler does not exceed84,930 blocks per stage, there is an explicit complete stage-private bank allocation with
+
+  banks_per_stage =117563-S/3,
+  literal_stock =869415-5S/3,
+  normalized_stock =173883-S/3.
+
+For each new helper of residual rank r=24-d, make ten banks containing four of its rank-r replica blocks and30-r existing rank4 blocks. Each bank has width4r+4(30-r)=120; all40 replicas are assigned. The filler consumption per changed helper is10(6+d). Keep the inherited rank11/rank4, rank7/rank4, rank6,rank12,andrank15 patterns; distribute the remaining rank4 blocks into pure30-block banks and unchanged rank24 blocks into pure5-block banks. All helper identities and intervals are explicitly enumerated. This is sufficient for arbitrary selected changed roles subject to the stated numerical conditions; it is not restricted to pair kernels.
+
+## Exact charts establish the actual projectors
+
+The checker constructs every new chart from the supplied basis U, not from its dimension. Put G=I-J/9, H=U G U^T. Compute a rational row basis V of ker(U G), and set B=[V^T | U^T]. Then B is invertible exactly when E is nondegenerate. Its first24-d columns span the actual G-orthogonal complement. The checker constructs the actual projector
+
+  sigma=U^T H^-1 U G
+
+and checks B^-1(I-sigma)B=diag(I_(24-d),0_d), both inverse products, and U G V^T=0. It emits B and B^-1, exact determinants, and elementary row-operation counts. Every elimination pivot and intermediate coefficient is checked to have numerator and denominator of magnitude below2^80. Thus every relevant nonzero divisor is a unit at each admitted prime q>2^80, including over all inherited Z/q^w. The proof does not infer an orthogonal chart from dimension alone.
+
+For each assigned block b in stage i, use the inherited literal normalizer
+
+  N_b=(b+1) Pi_b embed_i(B^-1),
+
+where Pi_b sends the first residual coordinates in the stage window to the assigned interval and matches ordered complements bijectively. The resulting conjugate of the actual projector is precisely the assigned coordinate projector. The unchanged old-chart factor ceiling548 remains valid if each checked new chart has at most548 factors; permutation/scaling retain the total787 bound.
+
+Distinct blocks in one bank have distinct route keys on a coordinate outside the current24-coordinate stage window. The embedded chart inverse fixes that coordinate. If the two permutations send it to different coordinates, the keys are distinct; if they send it to the same coordinate, the unequal scalars b+1 distinguish them. The scalars and their differences are units because their magnitudes are at most30 and q>2^80. Use the inherited full GL-cover route d*tau_i*N_b^-1; this argument does not justify replacing it by a projective quotient or removing its gates.
+
+## Completion and finite cost
+
+Complete each stage/replica cover sweep before proceeding. All assigned coordinate projectors in a bank annihilate each other and sum to I120. Their dirty partial swaps therefore compose to the full bank swap; arbitrary initial correlations are allowed. The checker independently executes all240 address basis columns in both orders for each distinct layout, and checks that each single-block omission or repetition fails on exactly twice that block's rank.
+
+The full explicit assignment has3,317,400 helper/replica/stage entries. For literal stock W the inherited conservative selector charge is
+
+  2*5*40*((W-1)+16587*120*787).
+
+The literal scalar word, its integer coefficient bill, global formal columns, and the47 strict pricing inequalities require their separate verifiers. This bank result does not delete actual scalar gates or certify an exponent by itself.
+
+## Current results
+
+Regression on the checked132 pair entrances reproduces W=869195,173839 normalized stock,and selector626938189600. The generic checker constructs all132 charts with at most30 factors and exact intermediate numerator/denominator bound4.
+
+Preflight for132 pairs and seven selected triples (dimensions4,3,9,9,9,12,14) gives S=192,139 charts,W=869095,173819 normalized stock,selector626938149600. Maximum chart cost144; every intermediate numerator and denominator has magnitude at most15. All assignments and6,240 endpoint columns plus6,240 nonzero control columns pass. This preflight installs the proposed initial frames synthetically. Re-run against the root worker's literal transformed word outputs before treating it as source-bound composition.
+
+No standalone kappa improvement or Lean certification is claimed here.
+
+## Source-bound collective result
+
+The actual collective156 outputs now pass the generic bank checker:156 actual charts, total entrance rank327, literal stock868870, normalized stock173774, selector626938059600. All3,317,400 helper/replica/stage assignments pass, as do6,720 endpoint and6,720 nonzero control columns. Every new chart uses at most156 factors and every exact intermediate numerator/denominator is at most135, preserving the inherited548/787 ceilings and2^80 prime guard. See `collective156/BANK-REVIEW.json` and `collective156/BANK-CHARTS.json`; `collective156/SOURCE-BINDING.json` binds the actual parent word and verifier inputs.
+
+## Source-bound pooled result
+
+The actual pooled word passes with252 charts and entrance rank1047. Literal stock867670; normalized stock173534; selector626937579600. Its largest chart costs200 factors; all rational intermediate numerators/denominators are at most704. All3,317,400 assignments and10,560 forward/backward endpoint columns plus10,560 nonzero controls pass. The inherited548/787 factor ceilings and2^80 prime guard are unchanged. `pooled/SOURCE-BINDING.json` pins the concrete input word and bank receipts. The original pre-admission fundamental word is superseded because it included singular frames.
+
+## Source-bound multiple-checkpoint result
+
+The actual multicut word passes with518 charts and entrance rank1344. Literal stock867175; normalized stock173435; selector626937381600. Largest chart200 factors; all exact intermediate numerators/denominators<=704. All3,317,400 assignments and10,560 endpoint columns plus10,560 nonzero controls pass. Banks depend on actual initial/final frames, so using different verified scalar checkpoint positions introduces no additional bank geometry obligation. The scalar word and global columns remain separate checks. See `multicut/SOURCE-BINDING.json`.
diff --git a/research/multicut-kernel-condensation-851/COPY-PROOF.md b/research/multicut-kernel-condensation-851/COPY-PROOF.md
new file mode 100644
index 0000000000..e771dfc027
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/COPY-PROOF.md
@@ -0,0 +1,7 @@
+# Copy-source lifetime
+
+A copy block copies a source, reads the copy as needed, and discards the copy when it again agrees with the source. The source must stay unchanged during the block. Reversing the block then creates the copy from that same source at the reverse entry and undoes the intervening gates. A source need not be globally excluded from a basis rewrite whose operations occur outside the block.
+
+Two selected helpers, streams 10233 and 10257, are sources of copy blocks. Both are kernel pivots. A square-zero donor += pivot basis shear never writes its pivot. The old blanket audit ban on selecting a COPY source was consequently stronger than necessary. The independent arbitrary-precision chronological checker verifies that no scalar gate writes the original source while any COPY/ERASE window is open, checks both endpoint frames and all temporary lifetimes, and requires all 24 windows to close. The actual full word is additionally checked on every arbitrary input column, forward and inverse.
+
+This replaces a conservative syntactic exclusion with the precise sufficient lifetime condition. It does not remove a required check or infer correctness from matching histograms.
diff --git a/research/multicut-kernel-condensation-851/FINITE-PROOF.md b/research/multicut-kernel-condensation-851/FINITE-PROOF.md
new file mode 100644
index 0000000000..9861e4f6f3
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/FINITE-PROOF.md
@@ -0,0 +1,9 @@
+# Finite invoice
+
+The pinned public routing, prime, recovery and analytic interfaces remain inherited. Every new chart is explicitly inverted and its residual projector identity checked; all intermediate rational coefficients and pivots are bounded by 704, below the retained prime guard. The maximum 200 factors remains below the inherited 548 chart and 787 normalizer bounds.
+
+The native finite-invoice checker rebuilds the complete histogram from the emitted word, scales through 40 replicas and five stages, and checks it against the exact pricing histogram. The literal stock is 867175 and the normalized stock is 173435. The endpoint deficit remains 176000 in literal units. All scalar gates, COPYs, routes, new selector factors and the rare-class fallback are charged.
+
+The full selector charge is 626937381600. The counted primitive coefficient is 62639910650427201 (56 bits). The cancellation-free signed prefix bound gives a 98-bit payload bound, below the inherited 104-bit guard. Positive finite cutoff witnesses and all 47 outer inequalities are checked exactly; the general cutoff formula explicitly allows inherited constants above the counted coefficient.
+
+See expected/COHORT-FINITE-INVOICE.json and code/cohort-finite-invoice.cpp. Neither this checker nor the saved expected receipts prove the retained all-size foundations. The top-level verifier executes all components and compares their fresh outputs.
diff --git a/research/multicut-kernel-condensation-851/KERNEL-PROOF.md b/research/multicut-kernel-condensation-851/KERNEL-PROOF.md
new file mode 100644
index 0000000000..2256294539
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/KERNEL-PROOF.md
@@ -0,0 +1,31 @@
+# Collective response-kernel condensation: sufficient rewrite
+
+Fix a checkpoint before any chosen helper is modified, after its initial target-correction reads. Let C be the selected helpers' complete accumulated prefix response into target data, and R their full suffix response into target data, over F2. Require that target input perturbations remain confined to targets through the prefix, with an invertible target matrix A. Correctness of the old scalar word then forces the suffix target-input block to be A^-1 on targets and zero on helpers, so R=A^-1 C. The selected helper prefix columns must consist only of their own unchanged helper value plus C: in particular there are no prefix reads of these helpers into another helper. No selected helper is a copied/source-owned role. These are actual trace prerequisites, not conclusions of a response hash. Target-to-target prefix changes are allowed.
+
+Partition chosen helper coordinates into pivots P and donors D. Choose kernel vectors v_p=e_p+sum_(d in D) a_dp e_d, with Rv_p=0 and no other pivot coordinate in v_p. Put N e_p=sum_d a_dp e_d and N e_d=0. Thus N²=0 and Q=I+N is invertible. Q^-1=I-N over the integer gate presentation; over F2 signs coincide. Each nonzero a_dp is one paid ADD donor_d += a_dp*pivot_p. The gates commute because a destination is never a source pivot. Distinct pivots may use the same donor without changing this fact.
+
+Remove the old initial target-correction reads from the pivot helpers only. At the checkpoint apply Q. Run the unchanged scalar suffix, including actual copied-center lifetimes. At its final full helper frame apply Q^-1. The suffix helper block is identity, so the final helper vector is exactly the original one. Each donor's old accumulated target correction still cancels R e_d. Removing all initial pivot correction reads removes precisely C e_p at the checkpoint; each pivot now contributes zero because this correction is absent and RQe_p=Rv_p=0. Input data behavior is unchanged. This proves correctness for all scalar inputs over F2, including arbitrary dirty-helper correlations. It does not assert the same cancellation over Z; the implementation still retains actual integer ADD coefficients for address/cost analysis.
+
+For physical legality, require every forward gate's endpoints to share a nondegenerate frame E contained in every affected helper's first positive frame. Give each pivot initial frame E; the donors retain zero entrance and move to E for the paid Q gates. The original future frame chains remain legal by containment. Q^-1 occurs at the final full frame. Normalizer charts must be supplied for every actual pivot residual I-sigma_E. When all frame moves remain nested and no COPY ownership changes, telescoping dimensions give raw movement-rank saving dim(E) per pivot; histograms and ADD invoices must still be recomputed from the literal word. The exponent requires the separate exact moment and outer-assembly checks.
+
+## Eight actual Pasch components
+
+The32 saved triple relations form8 groups, each with6 helper roles and4 triples. Label three of the triples
+
+  (a,b,c), (a,d,e), (f,b,e).
+
+The fourth is their F2 sum. Choose pivots c,d,f and donors a,b,e. The six required forward gates are
+
+  a+=c; b+=c; a+=d; e+=d; b+=f; e+=f.
+
+All commute, and their integer inverse subtracts the same contributions. The three response-kernel columns have unique pivots, so all three entrances are exposed simultaneously; disjoint-support matching would expose only one.
+
+The exact C++ rank check `pasch-intersection.cpp` reads the literal first positive frames from the pinned249 event stream. For every component, it verifies that the intersection of all6 first frames has dimension equal to the union of the4 candidate frame bases: respectively4,3,5,9,9,9,12,14. Thus each component admits its full common entrance E for all three pivots. This removes a potential geometric obstruction to shared donors; it is stronger than counting independent scalar relations.
+
+Three pivots per component give total entrance rank195 rather than65. Combined with the existing132 pair pivots this is327, divisible by3, so the unchanged40-replica bank construction applies without dropping any pairs. Predicted literal stock is868870, normalized173774. These are construction formulas, not a final price receipt: the collective literal word and the combined source-bound bank checker must pass before composition.
+
+## Sufficient compatibility beyond disjoint blocks
+
+Disjoint support between selected kernel blocks is stronger than necessary. A sufficient combination rule is: every pivot is unique and belongs to no selected donor set; for each shared donor, all entrance subspaces of blocks using it form a chain under exact subspace inclusion. Each block's entrance is contained in the first positive frames of its own pivots and donors.
+
+Order the forward kernel blocks by increasing entrance dimension. On any shared donor, this visits its chain monotonically; every pivot appears in just its own block. Therefore all paid gates are physically legal and lead into the original first positive frames. The same N²=0 proof applies because no destination donor is ever a pivot source, even across blocks. Gates with the same donor commute as usual. The inverse gates take place at full frames, where their order is unrestricted. This admits compatible nested-frame donor overlaps that disjoint-support packing rejects, without requiring a new address compiler. Actual histograms and simultaneous weighted-kernel independence remain subject to literal word replay; no estimated gains are added.
diff --git a/research/multicut-kernel-condensation-851/LICENSE b/research/multicut-kernel-condensation-851/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
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diff --git a/research/multicut-kernel-condensation-851/MANIFEST.json b/research/multicut-kernel-condensation-851/MANIFEST.json
new file mode 100644
index 0000000000..c7a7d1e744
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/MANIFEST.json
@@ -0,0 +1,50 @@
+{
+  "files": {
+    "BANK-PROOF.md": "a52cda22fc75ef825b7ec7c95e2028803058bfddb4d9c2a51c1bc4c0ab98393c",
+    "COPY-PROOF.md": "eab69c4fb9fedec2a5078073a7918fada7564d6e7215f50e239f899b2bca614e",
+    "FINITE-PROOF.md": "dd0e1ac3a212f484086d51454ebcf951ccb98eddfe4713310f688750d35d0069",
+    "KERNEL-PROOF.md": "4779181f679925da5c6663d4c5aec1a4a0aef76c993ab14b3a82782ac16bb883",
+    "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "NOTICE.md": "944023bd4a3d91929facb0c0aa350a8f1c4ce0f758285329a46f85f12f56a14e",
+    "PROOF-PR259.md": "ffc502078acdfee7a89abe3ec51fae4b8c5a8be7440d6b55f3e24f138e1b1a3b",
+    "PROOF.md": "25a94a4b51f60a92da537a8ee571b7f5b28b5d259010883a93e90c36f067869e",
+    "README-PR259.md": "ed2f4f051a21af9c173c0a7af7cac440ce15cabdabfc721895edde2c837cce25",
+    "README.md": "77d349dfc75f9f4a4a7540373845941d55684874853ad25104ce8f352122ab67",
+    "RESULT.json": "1d3c65b05de9b3b30a342dd91f3b717b56f84060d80b161a73d5d162ccfaecfb",
+    "REVIEW.md": "823eea4cacf586ca90e43146fac48143f129f6ff8ca71c6a03b88c29fc528ff9",
+    "code/cohort-bank-review.cpp": "b4e484838f870274c617a47a459f348f54cebff617a089d7ef9065e8d2e96ac2",
+    "code/cohort-finite-invoice.cpp": "d26bab7b04384b08ad9b5bc18dd5ffc00d235a46f1bfdd3531f4231adc226719",
+    "code/cohort-five-stage-columns.cpp": "b7026fdd9c248420dfaf4beca9b616161efc7f471d894a8104552ef035fe7761",
+    "code/cohort-legality-independent.cpp": "5acdc6849ba294637807b0b1528c97a60c48b2c3d9927bb2d2600ff13bf0d425",
+    "code/cohort-prefix-independent.cpp": "30e74b9bad964d0f1024986f2f4b2866667b599a85d0c216089fb7dedc877e4c",
+    "code/cohort-price.cpp": "413eeea0bee07785d2926bbe46bdc04b3b1b527ef7951b5f120fc0447972c2cb",
+    "code/cohort-transform.cpp": "afd916d0f539ccdb09e8231eade3b3f6b3e83bbb8107641e134943aa2b25af32",
+    "code/export249.py": "6c9aedb8fb4f2d560aca6cfc32ec967e003c0e623cc345040f108101ec1b442f",
+    "discovery/README.md": "c1abffbfa8305d92fa50df1bec9ba2a98fb2d1eebb4bc7cf24ff750c18a43a06",
+    "discovery/chrono2.py": "fc2866441540a8d6fa887439f185d0f51f298e1411eecb5ad84aba0de83b5b82",
+    "discovery/compare259.py": "4c6d08cfb64891a804db677c15baf172d297109d9526d0c9d3764bd26a2dfa8f",
+    "discovery/gain.py": "b76253949941854bcfd1ff84ebb49b9eaa9fcf4784690295f4a9e773694ddcfd",
+    "discovery/gen_candidates.py": "6d7136a9c1c86463b1c25405481422ed98f6517d10aa1e99a038fccb6930d688",
+    "discovery/merge259.py": "aba72c3e48314e842c06681fd62bb90e2a1f2a5dcb39794b1e22f54a6b74b850",
+    "discovery/twins.py": "c5b3f2065081002aa8da22584724938338fa46da2e25f3221225803e0f1b0ef7",
+    "expected/COHORT-BANK-REVIEW.json": "dc6036d79b46c221e3268cdc7b9098020af7cf3ab3aca4f0037abcf3081c19f4",
+    "expected/COHORT-EXACT-PRICE.json": "85e36da37abd9bfe4141765a24409b0ceb2de2919450a90accd01d25fe8e0c98",
+    "expected/COHORT-FINITE-INVOICE.json": "d0cf4da0808360edc1de23144104fa35dfb7faf9a2d73cbc0ebdc87804bd4fe5",
+    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "08c8e714a9967910fa1c301bf7321ebbda504921be1e0d939fc4b287dc69697e",
+    "expected/COHORT249-REPLAY.json": "01feb9aee4e1cf6dc3437a67fedf7fe7e30ebe8bc8aac9f07268d2cbc7df5bd5",
+    "expected/INDEPENDENT-LEGALITY.json": "7c3e1b236e98e07faaab09cddbab8953ef21a2f0c40c9c2262de96aa2dbd7ffc",
+    "expected/INDEPENDENT-PREFIX.json": "440c93b85db62273a274998f85ca387343c0f0ab80c0e7a84063f635b5f431f4",
+    "inputs/249-DONOR-OWNERSHIP.json.gz": "cd506a4bbefbc33fecfca3b0364e0b237ece493a96ef3085c39cf2465f2265d4",
+    "inputs/249-records.bin.gz": "6bc404d4af63218e714683d3e33fc1a53941e0155493747c3d0fb41b4a2de7b2",
+    "inputs/249-states.json.gz": "562bcd7de03bf9474ad8c5cbc50008c92b02bfad81e32c2e532ebd45f384e844",
+    "inputs/SNAPSHOTS.json": "3939f432a95db64073584e61a47e4983070450929ea1986c86a56552c0b03721",
+    "inputs/candidates.json.gz": "6d2f4eeb8a0a041e7c5b7354f12106999980362550cae7a1602c67cfccad919c",
+    "inputs/frames.json.gz": "54678a046e1c86b4d9308f69ef6d572a3b3745229e0ecb73843db7889e487cce",
+    "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
+    "vendor/PR249-SOURCE-MANIFEST.json": "f68fa82180cd352421b8bc3f7a5c89d51bde74e74cd8d62c222c28b0f23fcf31",
+    "vendor/UPSTREAM-NOTICE.md": "9a659cc2f96ae7e0eda99954941c42a4529bc885fb1de161c44ea801ff36e480",
+    "vendor/json.hpp": "aaf127c04cb31c406e5b04a63f1ae89369fccde6d8fa7cdda1ed4f32dfc5de63",
+    "vendor/pr249-source.zip": "11e2b723f90c44e02f4aa78f5ae2160ae4b9b776d3f1c49e8bfec606959d692c",
+    "verify.py": "8afeb090e873f3eec29fd0aae44eeb0008f85ad3c050330be34b3710e90c8771"
+  }
+}
diff --git a/research/multicut-kernel-condensation-851/NOTICE.md b/research/multicut-kernel-condensation-851/NOTICE.md
new file mode 100644
index 0000000000..3e024e7837
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/NOTICE.md
@@ -0,0 +1,31 @@
+# Attribution and scope
+
+Prepared by Chafik Boukhalfa with substantial Anthropic Claude assistance. Apache-2.0.
+This package claims no exclusive priority over concurrent work.
+
+What this package contributes: the census of twin dirty helpers at PR #259's earliest cut, the 333 added
+response-kernel pairs (`inputs/candidates.json.gz`, entries with round "union-early-cut"), the regenerated
+receipts, and the discovery scripts in `discovery/`. Everything else is PR #259's package, retained byte for
+byte except the frozen selection, the receipts, RESULT.json, MANIFEST.json, one field name added to the
+platform-dependent list of verify.py, and these notes:
+
+- Dugongue (OpenAI Codex assistance): PR #254 (the response-kernel pair rewrite, the projector charts and the
+  native checkers) and PR #259 (multi-cut kernel condensation, the generic exact chart audit, the seven
+  checkers, the pricer and the finite invoice used here unchanged; its notes are kept as README-PR259.md,
+  PROOF-PR259.md, KERNEL-PROOF.md, BANK-PROOF.md, COPY-PROOF.md, FINITE-PROOF.md, REVIEW.md).
+- eumemic (Anthropic Claude and OpenAI Codex assistance): PR #249/#244/#251 (the source527 bit word, entrance
+  banks, retimed source pairs, transported entrances) on PR #210's helper and PR #168's modules; hcg890 PR #234
+  and rohanarun PR #237/#209 (five-stage bit supplier, width-120 banks); sennemmi PR #230.
+- The PR #249 lineage as credited in vendor/UPSTREAM-NOTICE.md and below.
+
+---- PR #259's notice follows unchanged ----
+
+# Attribution and scope
+
+New response-kernel rewrite, native checks and packaging prepared with substantial OpenAI Codex assistance. No personal byline is added.
+
+Based on CrocSwap/integer-mult-bounds PR249 at commit 96495746c786d6d0339dbb38c7f553d4af3f88ed. The original sources and license notices are preserved in vendor/pr249-source.zip; see vendor/UPSTREAM-NOTICE.md for upstream contributors and mechanisms. Those historical public credits are retained.
+
+New code is distributed under Apache-2.0 (LICENSE). The vendored nlohmann JSON single header retains its own MIT license and attribution. Boost is an external build dependency, under the Boost Software License. Existing third-party files retain their original terms.
+
+This is a finite construction with exact checks, conditional on retained public all-size interfaces. It is not a Lean/kernel certificate or an unconditional integer-multiplication theorem.
diff --git a/research/multicut-kernel-condensation-851/PROOF-PR259.md b/research/multicut-kernel-condensation-851/PROOF-PR259.md
new file mode 100644
index 0000000000..e3782d04f0
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/PROOF-PR259.md
@@ -0,0 +1,61 @@
+# Multi-cut response-kernel condensation
+
+2026-10-09. Root and three agents; mathematical research and native C++ checks. Nothing published. No Lean/kernel certification.
+
+## Checked exponent
+
+The complete finite construction gives
+
+    kappa = 142205877210807 / 200000000000000000
+          = 0.000711029386054035.
+
+The previous delivered value was0.00071046520063283. The relative gain is about0.0794%. This is a real but modest exponent improvement, not a massive jump. It retains the same public all-size compiler, common weighted chart, restored-row, routing, prime, precision/recovery, complex correctness and analytic interfaces. Those general theorems are not newly proved here.
+
+## New sufficient mechanism
+
+The earlier construction only paired equal dirty-response columns. We now treat the actual target-response matrix as a linear code: its short dependencies provide several simultaneous cancellation coordinates. Choose distinct pivot helpers and donor helpers, with no pivot also a donor. At the chosen cut, each pivot's target-response column is the sum of its donors' columns over F2. Choose an explicitly nondegenerate common entrance frame contained in the first required frames of every participant.
+
+Delete that pivot's initial target compensation reads, raise its initial frame to the common entrance, and execute donor += pivot for every donor in its relation. After the retained word reaches the common full frame, execute the inverse shears. All shears form Q=I+N with N^2=0; therefore Q^-1=I-N. Full arbitrary dirty inputs are restored. Donors may be shared when their required entrance frames form a nested chain, executed in increasing dimension. Shared donors pay their frame lift once, instead of independently in every relation.
+
+For a cut whose prefix target map is A y+B x+R d and whose helpers are untouched, the zero-response condition gives exactly the target state of the old program on Q-transformed dirty inputs after removing the pivot compensation contribution. The invertibility of the target-only prefix map handles the actual target-to-target setup operations. The original helper word followed by Q^-1 restores the original arbitrary dirt. Gates at multiple cuts are admitted only with the corresponding untouched-prefix and response conditions at each actual cut. The actual combined whole word is independently checked on every input column in both directions, so no inference from separate local prices replaces composition.
+
+This turns independent pair rewrites into simultaneous kernel bases, higher-rank quartets, and temporally placed kernels. For eight six-role Pasch components, three independent kernel directions share the same donor setup; the old disjoint-triple choice exposed only one. The larger search then uses exact fundamental circuits, an exhaustive quartet-response search, and complete systematic kernel bases. A bounded weighted-packing search chooses compatible physical blocks. Heuristic scores only select candidates; the final exponent is computed with exact rational interval bounds.
+
+## Geometric repair
+
+Some attractive common intersections are degenerate in the address form. These were rejected by the exact Gram/chart audit, then replaced by explicit nondegenerate codimension-one subframes. The response relation remains valid, while the changed entrance dimension is fully repriced. This is a sufficient replacement construction, not an assumption that any rank-sized space is admissible. Every selected new chart is independently inverted and checked against its actual residual projector.
+
+## Final finite evidence
+
+The frozen word is lead/multicut/COHORT249-RECORDS.bin.
+
+- 518 pivot entrances at4 actual cuts, involving1194 distinct helpers.
+- 1344 removed raw rank units, versus132 in the previous delivered construction.
+- Raw rank mass434177 ->432833;27,772 initial reads removed;1,542 basis/inverse gates paid.
+- Actual local ADD count760393;20,107 formal input columns checked forward and inverse; both omitted-basis controls fail nontrivially.
+- 911,680 independent target-kernel equalities and23,649,283 non-target identity bits checked at the respective cuts.
+- 518 actual projector charts; maximum200 factors and exact intermediate numerators/denominators at most704.
+- All3,317,400 bank assignments,10,560 endpoint columns, and10,560 nonzero omission/repetition control columns checked. Literal stock867175, normalized173435.
+- All23,627 global five-stage F2 columns pass;120 fresh center copies are charged.
+- Selector bill626937381600. Payload prefix bound98bits below the inherited104bit guard; counted coefficient56bits below2^80.
+- Exact rational recurrence price and all47 strict outer inequalities pass; adjacent-grid rejection and exact pinned-baseline regression pass.
+
+The legality audit initially rejected two selected COPY-source pivots under an old blanket exclusion. That exclusion is stronger than the actual copy lemma requires: the source must be immutable during its COPY/ERASE window. The two pivots are never written by the new basis gates. An independent literal-window check covers all24 copy windows, and the final arbitrary-precision frame/lifetime audit verifies the required condition directly. A separate copy-excluded construction also passes, at slightly smaller kappa0.000711028182167973; it is preserved in lead/multicut-nocopy.
+
+## Larger separate construction, not added to kappa
+
+The cube lane found a26-addition/10-carrier producer rather than30/13, with60 rather than62 standalone dirty roles and fully charged forward rankmass616 rather than624. It passes all220 inherited interfaces.
+
+A concrete whole-graph splice keeps all9216 outside carrier arcs, changes25900 nodes to25020, and removes440 raw dirty roles. All6624 original root interfaces match all1760 source columns; arbitrary dirty restoration and a custom exact frame-path emitter pass, including88402 frame comparisons and5720 new Gram checks. However, the fully charged ungauged route fails to beat the current supplier. Reusing the source527-specific borrow/reuse/gauge adapters on the smaller allocation remains necessary. No projected440-role gain is included in the checked exponent.
+
+## Search boundaries
+
+- Checked latest public PR metadata and pinned useful heads; see public/SUMMARY.md. Public higher numbers that remain unbuilt are not baseline certificates.
+- Reused prior broad DAG/library retrieval and relevant saved circuit/assembly notes; this round was not an exhaustive new review of every Lean module.
+- No new Lean work and no Jev proof-generation or kernel-closure claim.
+- Pivot reorientation and exact nested-donor compatibility enlarged the selector to1617 blocks, but the bounded search found no gain beyond the252-pivot single-cut pool. These negative search results do not establish optimality.
+
+
+## Packaged evidence
+
+`code/` contains the seven executed native checkers and the pinned-source exporter. `inputs/candidates.json.gz` freezes the final selection, including each cut; replay does not rerun heuristic discovery. `expected/` contains exact comparison receipts. `vendor/` includes the original pinned upstream sources and licenses. BANK-PROOF.md gives the generic residual allocation and COPY-PROOF.md gives the required copy-window condition.
diff --git a/research/multicut-kernel-condensation-851/PROOF.md b/research/multicut-kernel-condensation-851/PROOF.md
new file mode 100644
index 0000000000..5b4b1a0277
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/PROOF.md
@@ -0,0 +1,70 @@
+# The early cut carries 333 more response-kernel pairs
+
+**Claim.** On PR #249's bit word (commit `96495746`), PR #259's multi-cut kernel condensation extended by 333
+twin-pair rewrites at its earliest cut (record 676,559) is a legal word of the same model with literal bank stock
+866,620 and κ = 177850930927433/(25·10¹⁶) = 7.11403723709732·10⁻⁴, checked by PR #259's seven native checkers
+and priced by its exact pricer, under the retained public all-size hypotheses of PR #249/#254/#259.
+
+## 1. The mechanism (PR #254/#259, unchanged)
+
+A dirty helper j that is untouched before a cut (initial frame ZERO, final frame FULL, no write, copy or
+non-initial read before the cut) acts on the targets only through its initial zero-frame compensation reads, so
+its *complete target response* R_j ∈ F₂^1760 is the column of the prefix's target map. Two such helpers a, b with
+R_a = R_b and a common nondegenerate rank-one line E inside both first required frames admit the rewrite of PR
+#254: a starts at E (its initial reads are deleted), b moves ZERO → E at the cut and absorbs a there (Q = I +
+e_b e_aᵀ), the old word resumes from E (the first moves of a and b become E → F_a, E → F_b), and Q⁻¹ is paid at
+the full frame; the omitted response R_a·a and the induced change R_b·a cancel. PR #259 generalises this to
+several simultaneous zero-response directions at four cuts and admits any entrance line through an exact chart
+audit (B⁻¹(I − σ)B diagonal, factor count ≤ 548, intermediates below 2⁸⁰).
+
+## 2. What is added
+
+At the earliest of PR #259's four cuts, record 676,559 (the last initial compensation read; records 0..676,559
+are the 676,560 initial reads, and the first MOVE follows), 14,286 clean helpers are live. Their responses form
+985 twin classes of size two and 24 of size nine. Of the 985 pairs, 747 have a nonzero nondegenerate common
+line; 335 are disjoint from all 1,194 helpers of PR #259's 518 families (319 with first frames (2, 2), 8 with
+(3, 5), 7 with (3, 3), 1 with (3, 6)); 333 are kept (the two of smallest gain dropped so that the total entrance
+rank 1,344 + 333 = 1,677 is ≡ 0 mod 3, which PR #259's transform requires at 40 replicas). Their lines are
+u = eᵢ − eⱼ (norm 2; cleared Gram 9·uᵀu − (Σu)² = 18, so the excluded primes are {2, 3}, as for the ±1-four lines
+with Gram 36) for the (2, 2) pairs and ±1-four lines for the others. Each is a pair with e = 1, exactly PR
+#254's shape; they enter `inputs/candidates.json.gz` in PR #259's schema (`pivot`, `partners`, `roles`,
+`basis`, `dim = 1`, `E_dimension = 1`, `cut = 676559`, `first_frames`, `kind`, `round = "union-early-cut"`)
+after PR #259's 518 items, which are unchanged.
+
+Why they pay: with the deficit pinned at 35,200 per replica (120·W − mass is invariant under the rewrite, because
+the pivot's residual 24 → 23 shrinks the bank capacity by exactly the mass saved), the coarse exponent is driven by
+the log-weighted mass Σ r·n·ln(120/r); a pair with first ranks (r_a, r_b) and e = 1 changes it by
+φ(r_a − 1) − φ(r_a) + φ(1) + φ(r_b − 1) − φ(r_b), φ(r) = r·ln(120/r): −2.02 for (2, 2), −0.97 for (3, 3), and
+PR #259's exact pricer confirms the sign and the size on the whole selection.
+
+## 3. What is checked (PR #259's checkers, unchanged; receipts in `expected/`)
+
+| checker | receipt |
+|---|---|
+| `cohort-transform` (all-column F₂ replay) | 851 pivots, entrance rank 1,677, 52,752 initial reads removed, 2,208 gates, raw mass 434,177 → 432,500, 835,788 records; omitted-Q control 32,383 wrong columns, omitted-Q⁻¹ control 1,052 |
+| `cohort-legality-independent` | 1,860 selected helpers, 0 source-owner and 0 donor intersections, 736,079 common-frame ADDs, 99,661 nested MOVEs, 24 COPY/ERASE windows, all final frames |
+| `cohort-prefix-independent` | 4 cuts, 1,497,760 target-kernel equalities, 35,868,385 non-target identity bits |
+| `cohort-bank-review` | literal stock 866,620 (saved 2,795), 22 patterns, residual families 23: 702 and 24: 13,436 (others unchanged), 3,317,400 assignments, selector 626,937,159,600 |
+| `cohort-five-stage-columns` | 23,627 columns, payload 98 bits |
+| `cohort-price` | coarse 711910179507329/10¹⁸, W 173,324, 3,970,160 calls, mass 20,763,680, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
+| `cohort-finite-invoice` | coefficient 56 bits, deficit 176,000, cutoffs positive |
+
+Control: PR #259's own selection through the same pipeline reproduces its κ exactly and six of its seven
+receipts byte for byte; the seventh differs only in `containment_pairs_checked`, a memo-cache miss counter of
+the legality checker that depends on the compiler's evaluation order and not on what is checked (PR #259's
+expected value 82,347 against 82,344 with Apple clang).
+
+Two platform matters, so that the same package verifies on Linux/g++ (the workflow) and on macOS/clang:
+`code/cohort-transform.cpp` orders the gauges by frame dimension with `std::sort`, whose order among equal
+dimensions differs between libstdc++ and libc++, so the emitted transcript (and its sha256 in `RESULT.json`)
+differed between the two; this package's copy uses `std::stable_sort` there (one token; the gates of equal-dimension
+gauges keep their selection order, every checker is unchanged). And `verify.py` adds `containment_pairs_checked`
+to the platform-dependent fields its `normalize` already drops (`seconds`, `local_scalar_stream`) and applies
+`normalize` to the committed receipt as well as to the fresh one (two lines). Nothing else of PR #259's code
+changes; `discovery/` lists the diff.
+
+## 4. Not claimed
+
+No Lean certificate; the public all-size compiler, chart, routing, prime-supply, precision and analytic interfaces
+of PR #249 are retained as hypotheses, as in PR #254/#259. The 24 size-nine response classes at this cut (96
+possible pairs) and 4 pairs with one helper already used by PR #259 are not exploited.
diff --git a/research/multicut-kernel-condensation-851/README-PR259.md b/research/multicut-kernel-condensation-851/README-PR259.md
new file mode 100644
index 0000000000..cd7fb7e820
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/README-PR259.md
@@ -0,0 +1,30 @@
+# Multi-cut response-kernel condensation
+
+**Conditional kappa = 142205877210807 / 200000000000000000 = 0.000711029386054035.**
+
+This builds on pinned PR249 (`96495746c786d6d0339dbb38c7f553d4af3f88ed`) and extends the earlier 132-pair kernel construction. It raises the previous delivered 0.00071046520063283 by approximately 0.0794%. This is a modest checked exponent gain, not a claim of a huge jump or the latest leaderboard record.
+
+The new mechanism selects simultaneous zero-response helper directions, shares donor lifts, repairs singular common frames with explicit nondegenerate subframes, and places compatible basis changes at four actual cuts. The result has 518 pivot entrances, removes 1344 raw rank units and 27772 initial reads, and pays every added basis gate and inverse. Complete bank stock is 867175.
+
+## Reproduce
+
+Requires Python 3.11+, SymPy 1.14.0, GNU g++ with C++17 and Boost headers. Install `g++ libboost-dev` on Linux, then:
+
+```
+python -m pip install -r requirements.txt
+python verify.py --output ../multicut-replay
+```
+
+MinGW-w64 is supported on Windows. Use `--cxx /path/to/g++` and optionally `--boost-include /path/to/boost-header-parent`. The output directory must be new and outside the package. Allow several minutes and a few GB of RAM. No network, credentials, Lean or GPU is required. New mathematical computation is C++; Python orchestrates it and runs the original upstream emitter.
+
+The default verifier checks hashes, regenerates pinned upstream data, compiles seven native checkers, emits the new word from the frozen candidate selection, and rechecks its complete semantics, geometry, bank assignment, finite invoice and exact exponent. It requires all 20107 local input columns in both directions, 23627 five-stage global columns, 911680 per-cut kernel equalities, all 3317400 bank assignments, exact chart identities, nonvacuous controls and all 47 strict outer inequalities. The bank label and mathematical receipts must match exactly; only elapsed time and runtime paths are excluded from comparisons.
+
+`--snapshots-only` explicitly skips upstream source regeneration and records that weaker provenance mode in its certificate. It still executes all seven native checkers. Discovery scans are not rerun: inputs/candidates.json.gz is the complete frozen final witness, including actual cut positions.
+
+## Scope and source handling
+
+Retains the public all-size compiler, common weighted chart, restored-row, routing, prime, precision/recovery, complex symbolic correctness and analytic interfaces. These foundations are not independently reproved. The actual cancellation is over F2 payload; odd-prime address geometry is separate. This is not an unconditional multiplication theorem, practical benchmark or Lean certificate. The public eight-stage Python command is not claimed to be replayed verbatim on the modified word.
+
+See PROOF.md, KERNEL-PROOF.md, BANK-PROOF.md, COPY-PROOF.md, FINITE-PROOF.md and REVIEW.md. Paths under lead/ or banks/ in research-derived proof notes identify the original evidence roles; the executable package uses code/, inputs/ and expected/. Native output logs can contain your chosen output path; they are not upload files.
+
+Original public sources, licenses and attributions are preserved in vendor/. No personal byline, binaries or local machine configuration is included.
diff --git a/research/multicut-kernel-condensation-851/README.md b/research/multicut-kernel-condensation-851/README.md
new file mode 100644
index 0000000000..a88e59da1e
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/README.md
@@ -0,0 +1,59 @@
+# multicut-kernel-condensation-851
+
+**Conditional κ = 177850930927433 / 250000000000000000 = 7.11403723709732·10⁻⁴** (+0.0526% over PR #259's
+7.11029386054035·10⁻⁴; +0.0523% over PR #263's 7.11032238200698·10⁻⁴).
+
+PR #259 (Dugongue) condenses response kernels of the PR #249 bit word at four cuts with 518 pivot families. Its
+earliest cut, record 676,559 — the last initial compensation read — carries only 103 of them. A census of the
+twin dirty helpers at that cut (helpers untouched before it whose complete F₂ target responses coincide) finds
+985 twin pairs; 335 of them are disjoint from every helper PR #259 uses and have a nondegenerate rank-one common
+entrance line, and 333 of those (two dropped to keep the entrance rank ≡ 0 mod 3, as the transform requires at
+40 replicas) are net-positive under the fixed-deficit ledger. Added to PR #259's 518 families, verbatim, they give
+
+| | PR #259 | this package |
+|---|---|---|
+| pivot families / entrance rank | 518 / 1,344 | **851 / 1,677** |
+| initial compensation reads removed / basis gates paid | 27,772 / 1,542 | 52,752 / 2,208 |
+| raw rank mass per invocation | 434,177 → 432,833 | 434,177 → **432,500** |
+| literal bank stock / normalized | 867,175 / 173,435 | **866,620** / 173,324 |
+| κ | 7.11029386054035·10⁻⁴ | **7.11403723709732·10⁻⁴** |
+
+The 333 added entries use PR #259's own mechanism unchanged: the pivot starts at the common line E (its four
+initial reads are deleted), the partner moves to E and absorbs the pivot there, and the inverse gate is paid at the
+full frame. 319 of them have first frames (2, 2) and a line u = eᵢ − eⱼ (norm 2, cleared Gram 18 for G = I − J/9),
+which PR #254's chart rule excluded (`norm == 4`) and PR #259's generic exact chart audit admits (prime
+exclusion {2, 3}, the same as the ±1-four lines); the remaining 14 are (3, 5), (3, 3) and (3, 6) pairs with ±1-four
+lines. **No checker, no C++ line and no proof note of PR #259 is changed**: the only inputs that differ are the
+frozen selection `inputs/candidates.json.gz` (PR #259's 518 items byte for byte, then the 333 new ones in its
+schema with `round = "union-early-cut"`) and the seven regenerated receipts in `expected/`; `RESULT.json` and
+`MANIFEST.json` follow. PR #259's seven native checkers pass on the new word (all-column F₂ replay forward and
+inverse with omitted-Q and omitted-Q⁻¹ controls; chronological legality with COPY/ERASE windows and source
+owners; 1,497,760 per-cut target-kernel equalities; 851 exact projector charts, 3,317,400 bank assignments; the
+five-stage F₂ columns; the exact rational price with 47 outer constraints, adjacent grid rejected; the finite
+invoice). [PROOF.md](PROOF.md) states the delta; PR #259's own notes are kept unchanged as `README-PR259.md`,
+`PROOF-PR259.md`, `KERNEL-PROOF.md`, `BANK-PROOF.md`, `COPY-PROOF.md`, `FINITE-PROOF.md`, `REVIEW.md`.
+
+This is a conditional, finite construction under the same retained public all-size hypotheses as PR #249/#254/#259
+(not a Lean certificate, not an unconditional theorem). κ is the bit-bound value: the complex supplier of this
+lineage stands at 7.0991·10⁻⁴ three-stage (PR #233) and 7.5474·10⁻⁴ five-stage (PR #256, Lean-checked in
+jacobalansussman/wht-power-saving-lean#2), so the bit supplier still binds.
+
+## Verify
+
+    sudo apt-get install -y g++ libboost-dev            # Linux; macOS: brew install boost, --cxx clang++ with a bits/stdc++.h shim
+    python -m pip install -r research/multicut-kernel-condensation-851/requirements.txt    # sympy 1.14.0
+    python3 -I research/multicut-kernel-condensation-851/verify.py --output /tmp/mc851-replay    # fresh directory outside the package; about 70 s
+
+PR #259's verifier, unchanged: it checks every package hash against `MANIFEST.json`, regenerates the pinned PR #249
+word from `vendor/pr249-source.zip` (SymPy), compiles the seven checkers, emits the new word from the frozen
+selection, runs every check and compares each receipt with `expected/` (platform-independent fields only; see
+PROOF.md, "Receipts"), then prints `PASS: kappa = 0.000711403723709732`. `--snapshots-only` skips the upstream
+regeneration (about 20 s). `.github/workflows/multicut-kernel-condensation-851.yml` runs it on Ubuntu.
+
+## Files
+
+Everything of PR #259's package (`code/`, `inputs/`, `vendor/`, `expected/`, the proof notes, `verify.py`,
+`requirements.txt`, `LICENSE`) with the two input changes above; `discovery/` (the census, the comparison with
+PR #259's selection and the merge, not run by the verifier: `twins.py`, `chrono2.py`, `gain.py`,
+`gen_candidates.py`, `compare259.py`, `merge259.py`); `README.md`, `PROOF.md`, `NOTICE.md`, `RESULT.json`,
+`MANIFEST.json`.
diff --git a/research/multicut-kernel-condensation-851/RESULT.json b/research/multicut-kernel-condensation-851/RESULT.json
new file mode 100644
index 0000000000..6c193d6428
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/RESULT.json
@@ -0,0 +1,12 @@
+{
+  "kappa": "177850930927433/250000000000000000",
+  "kappa_decimal": "0.000711403723709732",
+  "baseline_head": "96495746c786d6d0339dbb38c7f553d4af3f88ed",
+  "baseline_kappa": "0.000710392186446856",
+  "previous_delivery_kappa": "0.000711029386054035",
+  "new_record_sha256": "3c528fffae62508b2062b7251deabb5e2b23b80a044295cbb4cb7392abf3be28",
+  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES",
+  "lean_certificate": false,
+  "pivots": 851,
+  "entrance_rank": 1677
+}
diff --git a/research/multicut-kernel-condensation-851/REVIEW.md b/research/multicut-kernel-condensation-851/REVIEW.md
new file mode 100644
index 0000000000..93c40a639a
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/REVIEW.md
@@ -0,0 +1,9 @@
+# Independent review
+
+A separate worker freshly compiled and replayed the generalized compiler, checked all emitted artifacts against the primary run, and independently audited chronological geometry with arbitrary-precision integer dot products. The final legality checker validates shared donor supports, unique pivots disjoint from donors, source-owner exclusions, common gate frames, paid nested moves, final frames and immutable COPY windows.
+
+A separate own-cut prefix checker recomputes every relation from the original pinned word: 911680 target-kernel equalities and 23649283 non-target identity bits, involving 1194 distinct helpers at four cuts. The whole emitted word and five-stage composition are checked independently of those local conditions. New Gram charts, bank assignment, finite costs and exact outer assembly are separate executed checks.
+
+Expected receipts are comparison targets only. The verifier recompiles all seven native tools, regenerates the upstream baseline by default, and requires every freshly generated mathematical receipt field to match. Frozen source and input hashes bind this concrete result; general malformed-input hardening is outside the claim.
+
+No Lean/kernel certification or unconditional multiplication theorem is asserted.
diff --git a/research/multicut-kernel-condensation-851/code/cohort-bank-review.cpp b/research/multicut-kernel-condensation-851/code/cohort-bank-review.cpp
new file mode 100644
index 0000000000..f560c6aee1
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-bank-review.cpp
@@ -0,0 +1,19 @@
+#include <bits/stdc++.h>
+#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;}
+struct Pattern{vector<int>w;int count;};
+int main(int ac,char**av){if(ac!=6)throw runtime_error("args: baseline_export initial_json new_frames_json output_dir label");string inp=av[1],out=av[4];auto st=ld(inp+"/249-states.json"),fj=ld(inp+"/frames.json")["frames"],ini=ld(av[2]),nf=ld(av[3]);int n=st["n"],v=st["v"];map<int,int>dims;for(auto it=fj.begin();it!=fj.end();it++)dims[stoi(it.key())]=it.value()["dim"];for(auto it=nf.begin();it!=nf.end();it++)dims[stoi(it.key())]=it.value()["dim"];
+M G=eye(24);for(auto&r:G)for(auto&q:r)q-=Q(1)/9;J charts=J::array();int maxops=0;for(auto it=nf.begin();it!=nf.end();it++){int d=it.value()["dim"];M U;for(auto row:it.value()["B"]){vector<Q>r;for(auto x:row)r.push_back(rat(x));U.push_back(r);}if(U.size()!=d)throw runtime_error("dim");auto UG=mul(U,G);auto V=nullspace(UG);M B=tr(V);for(int i=0;i<24;i++)for(int j=0;j<d;j++)B[i].push_back(U[j][i]);int ops,gops;Q det,gdet;auto inv=inverse(B,ops,det);auto H=mul(UG,tr(U));auto HI=inverse(H,gops,gdet);M P=eye(24),sig=mul(mul(tr(U),HI),UG);for(int i=0;i<24;i++)for(int j=0;j<24;j++)P[i][j]-=sig[i][j];M expected=eye(24);for(int i=24-d;i<24;i++)expected[i][i]=0;if(mul(B,inv)!=eye(24)||mul(inv,B)!=eye(24)||mul(mul(inv,P),B)!=expected)throw runtime_error("projector chart identity");if(mul(mul(tr(B),G),B).size()!=24)throw runtime_error("weighted split");for(auto row:mul(UG,tr(V)))for(Q q:row)if(q!=0)throw runtime_error("orthogonality");maxops=max(maxops,ops);charts.push_back({{"frame",stoi(it.key())},{"dimension",d},{"B",mj(B)},{"inverse",mj(inv)},{"determinant",det.str()},{"gram_determinant",gdet.str()},{"row_factor_count",ops}});}if(maxops>548)throw runtime_error("inherited factor budget exceeded");
+map<int,vector<int>>fam,basefam;map<int,int>gauge,newfam;int sumdim=0,changed=0;for(int i=0;i<st["regs"].size();i++){int physical=st["regs"][i],f=ini.at(to_string(2*v+i)),r=24-dims.at(f);fam[r].push_back(physical);if(r!=24)gauge[physical]=f;if(nf.contains(to_string(f))){newfam[r]++;sumdim+=24-r;changed++;}else basefam[r].push_back(physical);}map<int,int>expectedbase{{4,2200},{6,22},{7,5},{11,48},{12,23},{15,2},{24,14287-changed}};for(auto[r,k]:expectedbase)if(basefam[r].size()!=k)throw runtime_error("base census mismatch");if(sumdim%3)throw runtime_error("need entrance rank sum divisible3 at40replicas");
+vector<Pattern>pat;auto add=[&](vector<int>w,int count){if(count<0||accumulate(w.begin(),w.end(),0)!=120)throw runtime_error("pattern");if(count)pat.push_back({w,count});};auto repeated=[](int r,int n){return vector<int>(n,r);};auto mix=[&](int r,int nr,int four){auto w=repeated(r,nr);w.insert(w.end(),four,4);return w;};add(mix(11,8,8),240);add(mix(7,4,23),50);add(repeated(6,20),44);add(repeated(12,10),92);add(repeated(15,8),10);int fill4=0;for(auto[r,k]:newfam){if(r<4||r>24)throw runtime_error("unsupported residual rank");fill4+=10*k*(30-r);add(mix(r,4,30-r),10*k);}if((84930-fill4)%30)throw runtime_error("rank4 remainder");add(repeated(4,30),(84930-fill4)/30);add(repeated(24,5),8*(14287-changed));
+struct Slot{int bank,off,r,block;};map<int,vector<Slot>>slots;int banks=0;J pj=J::array();for(auto pp:pat){pj.push_back({{"widths",pp.w},{"count",pp.count}});for(int b=0;b<pp.count;b++){int off=0;for(int j=0;j<pp.w.size();j++){int r=pp.w[j];slots[r].push_back({banks+b,off,r,j});off+=r;}}banks+=pp.count;}for(auto[r,rows]:fam)if(slots[r].size()!=40*rows.size())throw runtime_error("slots census mismatch");if(banks!=117563-sumdim/3)throw runtime_error("bank stock invariant");uint64_t hash=1469598103934665603ull;auto hm=[&](uint64_t x){for(int j=0;j<8;j++){hash^=(x>>(8*j))&255;hash*=1099511628211ull;}};long long assignments=0,mass=0,columns=0,controls=0;for(int stage=0;stage<5;stage++){vector<bitset<120>>occ(banks);for(auto[r,rows]:fam)for(int i=0;i<rows.size();i++)for(int rep=0;rep<40;rep++){auto s=slots[r].at(40*i+rep);for(int j=s.off;j<s.off+r;j++){if(occ[s.bank][j])throw runtime_error("collision");occ[s.bank][j]=1;}for(int x:{stage,rep,rows[i],s.bank,s.off,r,s.block+1})hm(x);assignments++;mass+=r;}for(auto&bits:occ)if(bits.count()!=120)throw runtime_error("unfilled");}
+for(auto pp:pat){for(bool rev:{false,true})for(int col=0;col<240;col++){array<int,240>s{};s[col]=1;vector<pair<int,int>>bl;int o=0;for(int r:pp.w){bl.push_back({o,r});o+=r;}if(rev)reverse(bl.begin(),bl.end());for(auto[o,r]:bl)for(int j=o;j<o+r;j++)swap(s[j],s[120+j]);for(int j=0;j<240;j++)if(s[j]!=(j==(col+120)%240))throw runtime_error("endpoint");columns++;}for(int mode=0;mode<2;mode++)for(int broken=0;broken<pp.w.size();broken++){long long bad=0;for(int col=0;col<240;col++){array<int,240>s{};s[col]=1;int o=0;for(int b=0;b<pp.w.size();b++){int r=pp.w[b],times=(b==broken?(mode==0?0:2):1);for(int t=0;t<times;t++)for(int j=o;j<o+r;j++)swap(s[j],s[120+j]);o+=r;}for(int j=0;j<240;j++)if(s[j]!=(j==(col+120)%240)){bad++;break;}}if(bad!=2*pp.w[broken])throw runtime_error("control");controls+=bad;}}
+J census=J::object();for(auto[r,rows]:fam)census[to_string(r)]=rows.size();long long stock=281600+5*banks,selector=2ll*5*40*((stock-1)+16587ll*120*787);J result={{"status","PASS_GENERIC_EXACT_CHARTS_ACTUAL_BANK_ALLOCATION"},{"label",av[5]},{"new_exact_charts",charts.size()},{"new_entrance_rank",sumdim},{"new_gauged_roles",changed},{"max_new_chart_factors",maxops},{"max_intermediate_numerator",maxnum.str()},{"max_intermediate_denominator",maxden.str()},{"prime_guard", "every elimination pivot and emitted coefficient has numerator and denominator magnitude below2^80"},{"actual_helper_roles",n-2*v},{"residual_families",census},{"bank_patterns",pj},{"banks_per_stage",banks},{"literal_stock",stock},{"normalized_stock",Q(stock)/5==Q(stock/5)?J(stock/5):J(Q(Q(stock)/5).str())},{"saved_literal_banks",869415-stock},{"actual_role_replica_stage_assignments",assignments},{"assignment_fnv1a64",to_string(hash)},{"covered_address_rank_mass",mass},{"endpoint_address_columns",columns},{"nonzero_omission_repeat_control_columns",controls},{"max_block_scalar",30},{"normalizer_factor_ceiling",787},{"selector_charge",selector},{"scope","Exact chart and role census, residual conjugacy, complete bank tiling, and finite selector charge. Full physical word, global columns, and pricing checked separately."}};ofstream(out+"/BANK-REVIEW.json")<<result.dump(2)<<"\n";ofstream(out+"/BANK-CHARTS.json")<<charts.dump()<<"\n";cout<<result.dump(2)<<"\n";
+}
diff --git a/research/multicut-kernel-condensation-851/code/cohort-finite-invoice.cpp b/research/multicut-kernel-condensation-851/code/cohort-finite-invoice.cpp
new file mode 100644
index 0000000000..6be33665a0
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-finite-invoice.cpp
@@ -0,0 +1,14 @@
+#include <boost/multiprecision/cpp_int.hpp>
+#include "json.hpp"
+#include <fstream>
+#include <iostream>
+#include <map>
+#include <vector>
+#include <algorithm>
+#include <stdexcept>
+using namespace std;using namespace boost::multiprecision;using J=nlohmann::json;using I=cpp_int;using Q=cpp_rational;
+void need(bool x,const char*s){if(!x)throw runtime_error(s);}J load(string p){ifstream f(p);need(bool(f),"missing input");J j;f>>j;return j;}
+Q rat(string s){auto p=s.find('/');return p==string::npos?Q(I(s)):Q(I(s.substr(0,p)))/I(s.substr(p+1));}I ceilQ(Q x){return (numerator(x)+denominator(x)-1)/denominator(x);}struct E{int op,a,b,c,f,z;};
+int main(int argc,char**argv){try{need(argc==6,"usage RECORDS ROOT_PRICE BANK_RECEIPT FIVE_STAGE_RECEIPT OUTPUT");ifstream f(argv[1],ios::binary|ios::ate);size_t bytes=f.tellg();need(bytes%sizeof(E)==0,"ABI");vector<E>ev(bytes/sizeof(E));f.seekg(0);f.read((char*)ev.data(),bytes);J price=load(argv[2])["cohort_candidate"],bank=load(argv[3]),global=load(argv[4]);map<int,I>H;I adds=0,units=0,copies=0;for(auto e:ev){if(e.op==0&&e.f)H[e.f]++;else if(e.op==1){adds++;units+=abs(e.c);}else if(e.op==2){H[e.z]++;copies++;}}need(copies==24&&adds>0&&units>=adds,"actualword inventory");int m=120,v=1760,R=16587,T=40,N=2*m,d=m*m,stock=bank["literal_stock"];need(stock==bank["normalized_stock"].get<int>()*5&&bank["actual_role_replica_stage_assignments"]==3317400,"actualbanks");need(bank["new_exact_charts"].get<int>()>0&&bank["max_new_chart_factors"]<=548&&I(bank["max_intermediate_denominator"].get<string>())<(I(1)<<80)&&I(bank["max_intermediate_numerator"].get<string>())<(I(1)<<80),"newchart invoice");map<int,I>L;for(auto[r,n]:H)L[r]+=200*n;for(int r:{4,23,46,50})L[r]+=40*2*v;I Ecount=0,mass=0;J hh=J::object();for(auto[r,n]:L){Ecount+=n;mass+=r*n;need(r<60,"half-shrink");hh[to_string(r)]=n.convert_to<string>();need(n==5*price["histogram"][to_string(r)].get<long long>(),"fullH versusnormalizedprice");}need(m*I(stock)-mass==176000,"physicaldeficit");need(price["stock"].get<long long>()*5==stock,"literalstock notnormalized");Q mu=rat(price["moment_upper"]);need(mu<1,"strict moment");Q c=rat(price["coarse"]),deltaTau=1-mu,deltaLin=1-Q(mass)/(m*stock)-Q(32*m)*Ecount/(I("10000000000000000")*stock);need(deltaLin>0,"linear fallback");I Jroute=T*(24*v+10*R),good=8*m*m+8,high=16*I(d+1)*(d+1),K=2*5*T*(I(stock-1)+I(R)*120*787),weighted=T*(5*adds+6*v),unit=T*(5*units+6*v);need(K==bank["selector_charge"].get<long long>()&&K<(I(1)<<40),"all selector factors");I F=I(global["signed_lift_prefix"][0]["cancellation_free_signed_row_l1_upper"].get<string>()),B=I(global["signed_lift_prefix"][1]["cancellation_free_signed_row_l1_upper"].get<string>()),payload=64*F*F*F*B*B;need(payload<(I(1)<<104),"payload prefix");I coeff=unit+Jroute*high+Jroute*(stock+24)+Ecount*good+Ecount*(128*I(N)*N*N)+16*I(m)*m*m+120*T+Ecount+K+1;need(coeff<(I(1)<<80)&&2*I(m)*m*m*I("10000000000000000")<(I(1)<<80),"fixed coefficient below prime threshold");need(I(stock+24)<(I(1)<<80),"stocklessprime");Q previous=rat("384599/10000000000");J cuts=J::array();for(int stage=0;stage<3;stage++){Q a=(1-c)*c+c*previous;vector<Q>gaps={c-a,1-a-c,1-a-c*(1-previous),1-c};Q gap=*min_element(gaps.begin(),gaps.end());need(gap>0,"ordinary cutoff gap");I L1=ceilQ(36/(gap*gap)),L2=ceilQ(2*(4+msb(coeff)+1)/gap),cut=max(I(1),max(L1,L2));need(Q(cut)*gap*gap>=36&&Q(cut)*gap>=2*(4+msb(coeff)+1),"cutoff inequality");cuts.push_back({{"stage",stage+1},{"minimum_gap",gap.str()},{"counted_coefficient_cutoff_log2",cut.convert_to<string>()},{"general_rule","For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta))."}});previous=a;}
+J out={{"status","PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS"},{"physical_replicas",T},{"literal_stock",stock},{"normalized_stock",price["stock"]},{"positive_rank_children",Ecount.convert_to<string>()},{"literal_rank_mass",mass.convert_to<string>()},{"literal_deficit",176000},{"literal_histogram",hh},{"global_weighted_additions",weighted.convert_to<string>()},{"global_unit_expanded_additions",unit.convert_to<string>()},{"route_families",Jroute.convert_to<string>()},{"normalizer_factor_bound",787},{"new_chart_factor_max",bank["max_new_chart_factors"]},{"extra_selector_calls",K.convert_to<string>()},{"full_counted_primitive_coefficient",coeff.convert_to<string>()},{"primitive_coefficient_bits",msb(coeff)+1},{"payload_signed_prefix_upper",payload.convert_to<string>()},{"payload_bits",msb(payload)+1},{"internal_row_coefficient",14401},{"external_complex_row_coefficient",20161},{"simultaneous_extra_work_streams",1},{"strict_moment_slack",deltaTau.str()},{"linear_moment_slack",deltaLin.str()},{"ordinary_cutoffs",cuts},{"scope","Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted."}};ofstream(argv[5])<<out.dump(2)<<"\n";cout<<"PASS stock "<<stock<<" K "<<K<<" coefficientbits "<<msb(coeff)+1<<" payloadbits "<<msb(payload)+1<<"\n";
+}catch(exception&e){cerr<<e.what()<<"\n";return 1;}}
diff --git a/research/multicut-kernel-condensation-851/code/cohort-five-stage-columns.cpp b/research/multicut-kernel-condensation-851/code/cohort-five-stage-columns.cpp
new file mode 100644
index 0000000000..8e02338398
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-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==3,"usage RAW6_RECORDS OUTPUT");std::string pre=argv[1];int v=1760,r=16587,loc=2*v+r,global=4*v+r,temp=global;
+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<(cpp_int(1)<<104),"payloadfiniteprefix2^104");
+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_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL"},{"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 23627 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/multicut-kernel-condensation-851/code/cohort-legality-independent.cpp b/research/multicut-kernel-condensation-851/code/cohort-legality-independent.cpp
new file mode 100644
index 0000000000..953cd2e014
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-legality-independent.cpp
@@ -0,0 +1,7 @@
+#include <bits/stdc++.h>
+#include <json.hpp>
+#include <boost/multiprecision/cpp_int.hpp>
+using namespace std;using nlohmann::json;struct Ev{int k,a,b,c,f,z;};struct F{int d;vector<vector<long long>>B,A;};json ld(string p){json j;ifstream(p)>>j;return j;}int main(int ac,char**av){if(ac!=4)return 2;string in=av[1],out=av[2];auto st=ld(in+"/249-states.json"),fj=ld(in+"/frames.json"),nf=ld(out+"/COHORT249-FRAMES.json"),ii=ld(out+"/COHORT249-INITIAL.json"),sel=ld(out+"/COHORT249-SELECTION.json"),own=ld(in+"/249-DONOR-OWNERSHIP.json");int n=st["n"],v=st["v"],zero=st["ZERO"];map<int,F>fs;long long maxabs=0;int oldmax=0;for(auto it=fj["frames"].begin();it!=fj["frames"].end();++it){int k=stoi(it.key());oldmax=max(oldmax,k);F f{it.value()["dim"],it.value()["B"],it.value()["A"]};for(auto M:{f.B,f.A})for(auto r:M)for(auto x:r)maxabs=max(maxabs,llabs(x));fs[k]=f;}for(auto it=nf.begin();it!=nf.end();++it){int k=stoi(it.key());if(fs.count(k))throw runtime_error("new frame collides");fs[k]={it.value()["dim"],it.value()["B"],it.value()["A"]};}map<pair<int,int>,bool>cache;long long contain=0;auto sub=[&](int a,int b){if(!fs.count(a)||!fs.count(b))throw runtime_error("unknown frame");auto k=make_pair(a,b);if(cache.count(k))return cache[k];contain++;bool ok=fs[a].d<=fs[b].d;for(auto r:fs[a].B)for(auto s:fs[b].A){boost::multiprecision::cpp_int d=0;for(int i=0;i<24;i++)d+=boost::multiprecision::cpp_int(r[i])*s[i];if(d)ok=false;}return cache[k]=ok;};set<int>owners,donors,chosen;for(auto x:st["source_owned_roles"])owners.insert(x.get<int>());for(auto x:own["donor_keys"])donors.insert(x.get<int>());set<int>pivots,partners;for(auto s:sel){int p=s["a"];if(!pivots.insert(p).second)throw runtime_error("repeated pivot");for(int r:s["partners"])partners.insert(r);}for(int p:pivots)if(partners.count(p))throw runtime_error("basis support is not square zero");for(auto s:sel){vector<int>members=s["partners"].get<vector<int>>();members.push_back(s["a"]);for(int p:members){if(p<2*v||p>=n)throw runtime_error("invalid or overlapping helper");chosen.insert(p);int role=st["regs"][p-2*v];if(owners.count(role)||donors.count(role))throw runtime_error("source owner or donor selected");}int id=s["new_frame_id"];auto f=fs.at(id);if(f.d!=s["E_dimension"]||f.B.size()!=f.d||f.A.size()!=24-f.d)throw runtime_error("wrong new rank");for(auto r:f.A)for(auto b:f.B){boost::multiprecision::cpp_int d=0;for(int k=0;k<24;k++)d+=boost::multiprecision::cpp_int(r[k])*b[k];if(d)throw runtime_error("new ann mismatch");}}
+vector<int>state(n+1,zero);for(auto it=ii.begin();it!=ii.end();++it)state[stoi(it.key())]=it.value();bool copied=false;int copySource=-1;long long mov=0,adds=0,cop=0,era=0,mass=0;map<int,long long>hist;Ev e;ifstream f(out+"/COHORT249-RECORDS.bin",ios::binary);long long records=0;while(f.read((char*)&e,sizeof e)){records++;if(e.a<0||e.a>n||(e.k!=0&&(e.b<0||e.b>n)))throw runtime_error("bad role id");if(e.k==0){if(e.a==n&&!copied)throw runtime_error("move inactive temporary");if(state[e.a]!=e.b||!sub(e.b,e.c)||fs[e.c].d-fs[e.b].d!=e.f)throw runtime_error("illegal or mispriced MOVE");state[e.a]=e.c;if(e.f){hist[e.f]++;mass+=e.f;}mov++;}else if(e.k==1){if(state[e.a]!=e.f||state[e.b]!=e.f)throw runtime_error("ADD not in common frame");if((e.a==n||e.b==n)&&!copied)throw runtime_error("ADD inactive temporary");if(e.a==e.b)throw runtime_error("self ADD");if(copied&&(e.a==copySource||e.a==n))throw runtime_error("copied source or temporary mutated inside COPY window");adds++;}else if(e.k==2){if(copied||e.b!=n||state[e.a]!=e.c)throw runtime_error("invalid COPY lifecycle");if(e.z!=fs[e.c].d)throw runtime_error("COPY rank");copied=true;copySource=e.a;state[n]=e.f;hist[e.z]++;mass+=e.z;cop++;}else if(e.k==3){if(!copied||e.b!=n||e.a!=copySource||state[e.a]!=e.c||state[n]!=e.f)throw runtime_error("invalid ERASE lifecycle");copied=false;era++;}else throw runtime_error("unknown event");}if(copied||cop!=24||era!=24)throw runtime_error("unclosed COPY");for(int s=0;s<n;s++)if(state[s]!=st["final"][to_string(s)])throw runtime_error("final frame");json r={{"status","PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE"},{"selected_pairs",sel.size()},{"selected_helpers",chosen.size()},{"source_owner_intersections",0},{"donor_intersections",0},{"old_max_frame_id",oldmax},{"new_frame_ids_collision",false},{"max_inherited_integer_abs",maxabs},{"containment_pairs_checked",contain},{"records",records},{"common_frame_ADDs",adds},{"nested_MOVEs",mov},{"copies",cop},{"erasures",era},{"rank_mass",mass},{"nondegeneracy_checked_by_separate_exact_bank_audit",true},{"paid_histogram",hist},{"all_final_frames_pass",true},{"scope","Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate."}};ofstream(av[3])<<r.dump(2)<<"\n";cout<<"PASS pairs "<<sel.size()<<" ADD "<<adds<<" mass "<<mass<<" COPY24\n";}
+
+
diff --git a/research/multicut-kernel-condensation-851/code/cohort-prefix-independent.cpp b/research/multicut-kernel-condensation-851/code/cohort-prefix-independent.cpp
new file mode 100644
index 0000000000..bd77f1dd67
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-prefix-independent.cpp
@@ -0,0 +1,5 @@
+#include <bits/stdc++.h>
+#include "json.hpp"
+using namespace std;using J=nlohmann::json;struct E{int k,a,b,c,f,z;};J ld(string p){ifstream f(p);J j;f>>j;return j;}
+int main(int ac,char**av){auto st=ld(string(av[1])+"/249-states.json"),sel=ld(string(av[2])+"/COHORT249-SELECTION.json");int n=st["n"],v=st["v"];map<int,int>idx;vector<int>roles;map<int,vector<int>>cuts;for(int i=0;i<(int)sel.size();i++){auto z=sel[i];vector<int>r=z["partners"].get<vector<int>>();r.push_back(z["a"]);for(int x:r)if(!idx.count(x)){idx[x]=roles.size();roles.push_back(x);}cuts[z["cut"].get<int>()].push_back(i);}int W=(roles.size()+63)/64;vector<uint64_t>M((size_t)(n+1)*W);auto row=[&](int s){return &M[(size_t)s*W];};for(int j=0;j<(int)roles.size();j++)row(roles[j])[j/64]|=1ull<<(j%64);ifstream f(string(av[1])+"/249-records.bin",ios::binary);E e;long long equalities=0,identitybits=0,nonzero=0;int maxcut=cuts.rbegin()->first;for(int t=0;t<=maxcut;t++){if(!f.read((char*)&e,sizeof e))throw runtime_error("short stream");if(e.k==1&&(e.c&1))for(int w=0;w<W;w++)row(e.a)[w]^=row(e.b)[w];else if(e.k==2)copy(row(e.a),row(e.a)+W,row(e.b));else if(e.k==3)for(int w=0;w<W;w++)if(row(e.a)[w]!=row(e.b)[w])throw runtime_error("copy prefix mismatch");if(!cuts.count(t))continue;for(int p:cuts[t]){auto z=sel[p];vector<int>r=z["partners"].get<vector<int>>();r.push_back(z["a"]);for(int target=0;target<v;target++){int parity=0;for(int a:r){int c=idx.at(a);parity^=(row(v+target)[c/64]>>(c%64))&1;}if(parity)throw runtime_error("nonzero kernel response at own cut");equalities++;int c=idx.at(z["a"]);nonzero+=(row(v+target)[c/64]>>(c%64))&1;}for(int a:r){int c=idx.at(a);for(int s=0;s<n;s++)if(s<v||s>=2*v){bool bit=(row(s)[c/64]>>(c%64))&1;if(bit!=(s==a))throw runtime_error("non-target prefix influence");identitybits++;}}}}
+J receipt={{"status","PASS_INDEPENDENT_MULTI_CUT_FULL_F2_KERNEL_AND_IDENTITY_COLUMNS"},{"cohorts",sel.size()},{"distinct_cuts",cuts.size()},{"distinct_helpers",roles.size()},{"target_kernel_equalities",equalities},{"non_target_identity_bits",identitybits},{"nonzero_pivot_target_entries",nonzero},{"scope","Original pinned-word response at every cohort own cut; combined emitted-word checks remain separate."}};ofstream(av[3])<<receipt.dump(2)<<"\n";cout<<receipt.dump()<<"\n";}
diff --git a/research/multicut-kernel-condensation-851/code/cohort-price.cpp b/research/multicut-kernel-condensation-851/code/cohort-price.cpp
new file mode 100644
index 0000000000..b3be866e59
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-price.cpp
@@ -0,0 +1,27 @@
+#include <boost/multiprecision/cpp_int.hpp>
+#include "json.hpp"
+#include <fstream>
+#include <iostream>
+#include <map>
+#include <cmath>
+#include <stdexcept>
+using namespace std;using namespace boost::multiprecision;using J=nlohmann::json;using Q=cpp_rational;using I=cpp_int;
+Q parse(string s){auto p=s.find('/');return p==string::npos?Q(I(s)):Q(I(s.substr(0,p)))/I(s.substr(p+1));}
+Q get(J j){return j.is_string()?parse(j.get<string>()):Q(j.get<long long>());}
+J load(string p){ifstream f(p);if(!f)throw runtime_error(p);J j;f>>j;return j;}
+Q down(Q x){I d=I(1)<<224;return Q(I(numerator(x)*d/denominator(x)))/d;}
+Q up(Q x){I d=I(1)<<224;return Q(I((numerator(x)*d+denominator(x)-1)/denominator(x)))/d;}
+pair<Q,Q> logbase(Q x){Q z=(x-1)/(x+1),t=z,s=0;for(int i=0;i<48;i++){s+=2*t/(2*i+1);t*=z*z;}return {down(s),up(s+2*t/(97*(1-z*z)))};}
+pair<Q,Q> logbound_raw(Q x){int k=0;while(x>=2){x/=2;k++;}auto [l,u]=logbase(x);auto [a,b]=logbase(Q(2));return {down(l+k*a),up(u+k*b)};}
+pair<Q,Q> logbound(Q x){static map<Q,pair<Q,Q>> cache;auto it=cache.find(x);if(it!=cache.end())return it->second;return cache[x]=logbound_raw(x);}
+pair<Q,Q> expbound(Q l,Q u){if(l<0||u>=Q(1)/10)throw runtime_error("exp domain");Q tl=1,tu=1,sl=1,su=1;for(int i=1;i<=32;i++){tl=down(tl*l/i);tu=up(tu*u/i);sl=down(sl+tl);su=up(su+tu);}return {sl,up(su+tu*u/33/(1-u/34))};}
+pair<Q,Q> moment(map<int,long long>H,int m,int W,Q a){Q lo=0,hi=0;for(auto [r,n]:H){auto[l,u]=logbound(Q(m)/r);auto[e,f]=expbound(a*l,a*u);Q w=Q(r*n)/(m*W);lo+=w*e;hi+=w*f;}return {down(lo),up(hi)};}
+map<string,Q> assembly(Q a,Q b,Q k,Q guard,Q rowgap){Q eta=Q(1)/parse("1000000000000"),beta=Q(1)/parse("1000000000"),tau=1-a,sigma=1-b,q=a*(1-2*eta),lp=1-q,lam=(tau+lp)/2,c=q+eta/4,eps=(1-eta)/(1+q),mi=eps*q,r=(mi+1-eps)/2,delta=eta/8,internal=tau+(1-beta)*max(Q(sigma-tau),Q(0)),leaf=sigma+beta*(1-sigma);map<string,Q>s={
+{"bit_positive",a},{"complex_above_bit",b-a},{"complex_below_1_32",Q(1)/32-b},{"beta_positive",beta},{"beta_below_one",1-beta},{"leaf_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},{"reservations",c-q},{"lambda_tau",lam-tau},{"lambda_sigma",lam-sigma},{"lambda_internal",lam-internal},{"lp_lambda",lp-lam},{"compact_leaf",lp-leaf},{"compact_reservations",lp-(1-c)},{"lp_below_one",q},
+{"eps_positive",eps},{"eps_below_one",1-eps},{"guard_width",1-eps},{"K_geometry",1-eps*(1+c)},{"K_log",eps*c},{"record_suffix",1-eps},{"phase_local",1-eps-delta},{"phase_boundary",r-delta},{"gamma_sublinear",1-eps-r},{"cell_band",eps-(1-r)/2},{"prime_pack",1-eps},{"alpha_positive",r},{"alpha_one",1-r},{"alpha_fourth",Q(1)/4-r},{"delta_positive",delta},{"delta_eighth",Q(1)/8-delta},{"record_fallback",eps-a},{"small_field",1-eps-mi},{"artificial",8-eps+r-delta-mi},{"literal_guard",guard},{"row_gap",rowgap}};
+vector<Q> margins={1-eps,a,mi,a,min(Q(1-eps-delta),Q(r-delta)),1-eps-delta,eps};for(int i=0;i<7;i++)s["margin"+to_string(i)]=margins[i]-k;return s;}
+
+pair<Q,Q> momentbad(map<int,long long>H,int m,int W,Q a){auto[l,u]=moment(H,m,W,a);long long N=0;for(auto[r,n]:H)N+=n;auto[fl,fu]=moment({{1,32LL*m*m*N}},m,W,a);return{l+fl/parse("10000000000000000"),u+fu/parse("10000000000000000")};}
+J price(map<int,long long>H,int W){long double l=.0007L,u=.00073L;auto app=[&](long double a){long double z=0,N=0;for(auto[r,n]:H){z+=(long double)n/W*pow((long double)r/120,1-a);N+=n;}return z+1e-16L*32*120*120*N/W*pow(1.L/120,1-a);};for(int i=0;i<80;i++){long double a=(l+u)/2;if(app(a)<1)l=a;else u=a;}long long proposal=(long long)(l*1e18L),low=proposal-10000,high=proposal+10000;Q grid=parse("1000000000000000000");if(momentbad(H,120,W,Q(low)/grid).second>=1||momentbad(H,120,W,Q(high)/grid).first<=1)throw runtime_error("proposal bracket");while(high-low>1){long long z=low+(high-low)/2;auto[a,b]=momentbad(H,120,W,Q(z)/grid);if(b<1)low=z;else if(a>1)high=z;else throw runtime_error("insufficient interval precision");}Q c=Q(low)/grid;auto[ml,mu]=momentbad(H,120,W,c);auto[nl,nu]=momentbad(H,120,W,c+1/grid);if(!(mu<1&&nl>1))throw runtime_error("coarse grid");Q bit=parse("384599/10000000000");J chain=J::array({bit.str()});for(int i=0;i<3;i++){bit=(1-c)*c+c*bit;chain.push_back(bit.str());}Q b=parse("747454944651775/1000000000000000000"),eta=parse("1/1000000000000"),q=bit*(1-2*eta),bound=(1-eta)*q/(1+q);I z=(numerator(bound)*I("1000000000000000000")-1)/denominator(bound);Q k=Q(z)/grid;auto constraints=assembly(bit,b,k,1,Q(1000000)-Q(51*20161)/25),adj=assembly(bit,b,k+1/grid,1,Q(1000000)-Q(51*20161)/25);int pass=0,fail=0;for(auto[name,x]:constraints)pass+=x>0;for(auto[name,x]:adj)fail+=x<=0;if(pass!=47||!fail)throw runtime_error("assembly");long long mass=0,count=0;J h=J::object();for(auto[r,n]:H){mass+=r*n;count+=n;h[to_string(r)]=n;}return{{"stock",W},{"histogram",h},{"rank_mass",mass},{"calls",count},{"deficit",120LL*W-mass},{"coarse",c.str()},{"coarse_decimal",c.convert_to<double>()},{"moment_upper",mu.str()},{"next_coarse_moment_lower",nl.str()},{"bootstrap_chain",chain},{"ordinary_bit",bit.str()},{"kappa",k.str()},{"kappa_decimal",k.convert_to<double>()},{"positive_constraints",pass},{"next_kappa_rejected",fail}};}
+int main(int argc,char**argv){auto rec=load(argv[1]);if(rec["new_entrance_rank"].get<int>()%3)throw runtime_error("40replica integrality");map<int,long long>H;for(auto it=rec["histogram"].begin();it!=rec["histogram"].end();it++)H[stoi(it.key())]=40*it.value().get<long long>();for(int r:{4,23,46,50})H[r]+=16*1760;auto old=H;for(auto it=rec["delta"].begin();it!=rec["delta"].end();it++)old[stoi(it.key())]-=40*it.value().get<long long>();J baseline=price(old,173883),candidate=price(H,173883-rec["new_entrance_rank"].get<int>()/3);if(baseline["kappa"]!="88799023305857/125000000000000000")throw runtime_error("baseline kappa mismatch");J out={{"status","PASS_EXACT_COHORT_CONDITIONAL_PRICING_47_AND_ADJACENT_CONTROLS"},{"baseline",baseline},{"cohort_candidate",candidate},{"bank_completion_required",true},{"finite_bill_and_all_size_interfaces_not_reproved",true},{"method","C++ exact rational 224-bit directed bounds; floating used only to propose a bracket verified exactly;32-degree exponential and48-term atanh logarithm"}};ofstream(argv[2])<<out.dump(2)<<"\n";cerr<<"BASE "<<baseline["kappa"]<<" NEW "<<candidate["kappa"]<<"\n";}
diff --git a/research/multicut-kernel-condensation-851/code/cohort-transform.cpp b/research/multicut-kernel-condensation-851/code/cohort-transform.cpp
new file mode 100644
index 0000000000..9f029936a7
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/cohort-transform.cpp
@@ -0,0 +1,27 @@
+#include <algorithm>
+#include <cassert>
+#include <boost/multiprecision/cpp_int.hpp>
+using Q=boost::multiprecision::cpp_rational;
+#include <cstdint>
+#include <fstream>
+#include <iostream>
+#include <map>
+#include <set>
+#include <vector>
+#include "json.hpp"
+using namespace std;using J=nlohmann::json;struct Ev{int k,a,b,c,f,z;};struct Frame{int d;vector<vector<long long>>B,A;};
+int main(int argc,char**argv){string dir=argv[1],outdir=argv[3];J st,fj,cc;ifstream(dir+"/249-states.json")>>st;ifstream(dir+"/frames.json")>>fj;ifstream(argv[2])>>cc;map<int,Frame>fs;int nextid=200000;for(auto it=fj["frames"].begin();it!=fj["frames"].end();it++){Frame f;f.d=it.value()["dim"];f.B=it.value()["B"].get<vector<vector<long long>>>();f.A=it.value()["A"].get<vector<vector<long long>>>();fs[stoi(it.key())]=move(f);}fj.clear();map<pair<int,int>,bool>cache;auto sub=[&](int a,int b){auto key=make_pair(a,b);auto it=cache.find(key);if(it!=cache.end())return it->second;bool ok=fs[a].d<=fs[b].d;if(ok)for(auto&x:fs[a].B){for(auto&y:fs[b].A){__int128 t=0;for(int i=0;i<24;i++)t+=(__int128)x[i]*y[i];if(t){ok=false;break;}}if(!ok)break;}return cache[key]=ok;};vector<Ev>ev;Ev x;ifstream in(dir+"/249-records.bin",ios::binary);while(in.read((char*)&x,sizeof x))ev.push_back(x);int n=st["n"],v=st["v"],zero=st["ZERO"],full=st["FULL"],cut=-1;for(int i=0;i<(int)ev.size();i++)if(ev[i].k==1&&ev[i].a==3491&&ev[i].b==3488&&ev[i].c==-1&&ev[i].z==25){if(cut>=0)throw runtime_error("ambiguous cut");cut=i;}if(cut<0)throw runtime_error("cut absent");vector<int>ini(n+1,zero),fin(n+1,full);for(auto it=st["initial"].begin();it!=st["initial"].end();it++)ini[stoi(it.key())]=it.value();for(auto it=st["final"].begin();it!=st["final"].end();it++)fin[stoi(it.key())]=it.value();J chosen=J::array(),newframes=J::object();set<int>used;struct Gauge{vector<int>partners;int F;int cut;};map<int,Gauge>gauges;long long totaldim=0,basisgates=0;
+J candidates=cc.is_array()?cc:cc["candidates"];set<int>baseused;for(auto z:candidates){baseused.insert(z["a"].get<int>());for(int r:z["partners"])baseused.insert(r);}for(int file=4;file<argc;file++){J q;ifstream(argv[file])>>q;for(auto z:q["candidates"]){bool ok=true;for(int r:z["roles"])if(baseused.count(r))ok=false;if(!ok)continue;for(int r:z["roles"])baseused.insert(r);candidates.push_back(z);}}
+int sd=0;for(auto z:candidates)sd+=z.contains("roles")?z["dim"].get<int>():z["E_dimension"].get<int>();int drop=sd%3;J filtered=J::array();for(auto z:candidates){if(drop&&(z.contains("roles")?z["dim"].get<int>():z["E_dimension"].get<int>())==1){drop--;continue;}filtered.push_back(z);}if(drop)throw runtime_error("cannot normalize40 replicas");candidates=filtered;
+set<int>pivotset,donorset;for(auto z:candidates){int a=z.contains("roles")?z["pivot"].get<int>():z["a"].get<int>();if(!pivotset.insert(a).second)throw runtime_error("duplicate pivot");vector<int>r=z.contains("roles")?z["roles"].get<vector<int>>():vector<int>{a,z["b"].get<int>()};for(int b:r)if(b!=a)donorset.insert(b);}for(int p:pivotset)if(donorset.count(p))throw runtime_error("non-nilpotent basis support");
+
+for(auto z:candidates){int ci=z.value("cut",cut);bool triple=z.contains("roles");int a=triple?z["pivot"].get<int>():z["a"].get<int>();vector<int>members=triple?z["roles"].get<vector<int>>():vector<int>{a,z["b"].get<int>()};int ed=triple?z["dim"].get<int>():z["E_dimension"].get<int>();bool skip=false;for(int r:members)if(ini[r]!=zero||fin[r]!=full)skip=true;if(skip)throw runtime_error("selected initial or final frame changed");if(!triple&&!z["new_targets"].empty())continue;
+Frame f;f.d=ed;auto clearrow=[&](vector<Q> r){using I=boost::multiprecision::cpp_int;I d=1;for(auto x:r){I a=d,b=denominator(x);while(b!=0){I t=a%b;a=b;b=t;}d=d/a*denominator(x);}vector<long long>v;for(auto x:r){Q q=x*d;I n=numerator(q);if(n>LLONG_MAX||n<LLONG_MIN)throw runtime_error("cleared coordinate overflow");v.push_back(n.convert_to<long long>());}return v;};for(auto rr:z["basis"]){vector<Q>r;for(auto vv:rr){string t=vv.is_string()?vv.get<string>():to_string(vv.get<long long>());auto k=t.find('/');using I=boost::multiprecision::cpp_int;r.push_back(k==string::npos?Q(I(t)):Q(I(t.substr(0,k)))/I(t.substr(k+1)));}f.B.push_back(clearrow(r));}
+// Exact ordinary annihilator. Frame nondegeneracy is independently audited by the bank checker.
+vector<vector<Q>>A;for(auto rr:f.B){vector<Q>r;for(auto x:rr)r.push_back(Q(x));A.push_back(r);}vector<int>piv;int rr=0;for(int c=0;c<24;c++){int k=rr;while(k<(int)A.size()&&A[k][c]==0)k++;if(k==(int)A.size())continue;swap(A[k],A[rr]);Q q=A[rr][c];for(int j=0;j<24;j++)A[rr][j]/=q;for(int i=0;i<(int)A.size();i++)if(i!=rr){q=A[i][c];for(int j=0;j<24;j++)A[i][j]-=q*A[rr][j];}piv.push_back(c);rr++;}if(rr!=ed)throw runtime_error("dependent entrance basis");for(int c=0;c<24;c++)if(find(piv.begin(),piv.end(),c)==piv.end()){vector<Q>r(24);r[c]=1;for(int i=0;i<rr;i++)r[piv[i]]=-A[i][c];f.A.push_back(clearrow(r));}
+int F=nextid++;fs[F]=f;vector<int>partners;for(int r:members){int first=-1;for(int i=ci+1;i<(int)ev.size();i++){auto e=ev[i];if(e.k==1&&(e.a==r||e.b==r)){first=e.f;break;}if(e.k==2&&e.a==r){first=e.c;break;}}if(first<0||!sub(F,first))throw runtime_error("false actual first-frame intersection");for(int i=0;i<=ci;i++){auto e=ev[i];if(e.k&&((e.k==1&&e.a==r)||(e.k!=1&&(e.a==r||e.b==r))))throw runtime_error("cohort touched before cut");if(e.k==1&&e.b==r&&!(e.z==4&&e.f==zero&&e.a>=v&&e.a<2*v))throw runtime_error("bad prefix read");}used.insert(r);if(r!=a)partners.push_back(r);}
+gauges[a]={partners,F,ci};z["cut"]=ci;totaldim+=ed;basisgates+=2*partners.size();z["a"]=a;z["partners"]=partners;z["E_dimension"]=ed;z["new_frame_id"]=F;z["role_a"]=st["regs"][a-2*v];z["basis"]=J::array();for(auto r:f.B){J row=J::array();for(auto x:r)row.push_back(to_string(x));z["basis"].push_back(row);}chosen.push_back(z);newframes[to_string(F)]={{"B",f.B},{"A",f.A},{"dim",ed}};}
+if(chosen.empty())throw runtime_error("no selected pairs");vector<int>gorder;for(auto[a,g]:gauges)gorder.push_back(a);stable_sort(gorder.begin(),gorder.end(),[&](int a,int b){return fs[gauges[a].F].d<fs[gauges[b].F].d;});vector<int>state=ini;for(auto&[a,bf]:gauges)state[a]=bf.F;vector<int>newini=state;vector<Ev>out;long long removed=0,weighted=0;map<int,long long>H,oldH;for(auto e:ev){if(e.k==0&&e.f)oldH[e.f]++;else if(e.k==2)oldH[e.z]++;}auto moveTo=[&](int s,int f){if(state[s]==f)return;if(!sub(state[s],f)){cerr<<"bad move "<<s<<" "<<state[s]<<" "<<f<<"\n";throw runtime_error("non-nesting");}int r=fs[f].d-fs[state[s]].d;out.push_back({0,s,state[s],f,r,0});if(r)H[r]++;state[s]=f;};auto add=[&](int a,int b,int c,int f,int z){moveTo(a,f);moveTo(b,f);out.push_back({1,a,b,c,f,z});weighted+=abs(c);};for(int i=0;i<(int)ev.size();i++){auto e=ev[i];if(e.k==1){if(gauges.count(e.b)&&e.z==4&&e.f==zero&&i<=gauges[e.b].cut){removed++;}else add(e.a,e.b,e.c,e.f,e.z);}else if(e.k==2){moveTo(e.a,e.c);state[e.b]=e.f;out.push_back(e);H[e.z]++;}else if(e.k==3){if(state[e.a]!=e.c||state[e.b]!=e.f)throw runtime_error("copy endpoint");out.push_back(e);}for(int a:gorder)if(i==gauges[a].cut){auto bf=gauges[a];for(int b:bf.partners)add(b,a,1,bf.F,28);}}
+for(int s=0;s<n;s++)moveTo(s,fin[s]);for(auto&[a,bf]:gauges)for(int b:bf.partners)add(b,a,-1,full,29);for(int s=0;s<n;s++)if(state[s]!=fin[s])throw runtime_error("final frame mismatch");
+// Full arbitrary formal F2 columns. COPY has its actual own temporary row.
+auto replay=[&](const vector<Ev>&word,bool reverse,int omitcat){int words=(n+63)/64;vector<uint64_t>M((size_t)(n+1)*words);auto row=[&](int s){return &M[(size_t)s*words];};for(int s=0;s<n;s++)row(s)[s/64]|=1ull<<(s%64);for(int k=0;k<(int)word.size();k++){auto e=word[reverse?word.size()-1-k:k];if(e.z==omitcat&&e.k==1)continue;if(e.k==1&&(e.c&1)){for(int j=0;j<words;j++)row(e.a)[j]^=row(e.b)[j];}else if(e.k==(reverse?3:2)){copy(row(e.a),row(e.a)+words,row(e.b));}else if(e.k==(reverse?2:3)){for(int j=0;j<words;j++)if(row(e.a)[j]!=row(e.b)[j])throw runtime_error("copy erase mismatch");}}long long bad=0;for(int s=0;s<n;s++)for(int j=0;j<words;j++){uint64_t expected=(s/64==j)?1ull<<(s%64):0;if(s>=v&&s<2*v&&(s-v)/64==j)expected^=1ull<<((s-v)%64);bad+=row(s)[j]!=expected;}return bad;};if(replay(out,false,-1)||replay(out,true,-1))throw runtime_error("full columns fail");auto badQ=replay(out,false,28),badQi=replay(out,false,29);if(!badQ||!badQi)throw runtime_error("vacuous control");long long mass=0,oldmass=0;J hist=J::object(),delta=J::object();for(auto[r,c]:H){hist[to_string(r)]=c;mass+=r*c;}for(auto[r,c]:oldH)oldmass+=r*c;set<int>rs;for(auto[r,c]:H)rs.insert(r);for(auto[r,c]:oldH)rs.insert(r);for(int r:rs)if(H[r]!=oldH[r])delta[to_string(r)]=H[r]-oldH[r];if(oldmass-mass!=totaldim)throw runtime_error("rank bill mismatch");ofstream bout(outdir+"/COHORT249-RECORDS.bin",ios::binary);bout.write((char*)out.data(),out.size()*sizeof(Ev));J ii=J::object();for(int s=0;s<n;s++)ii[to_string(s)]=newini[s];ofstream(outdir+"/COHORT249-INITIAL.json")<<ii.dump()<<"\n";ofstream(outdir+"/COHORT249-FRAMES.json")<<newframes.dump()<<"\n";ofstream(outdir+"/COHORT249-SELECTION.json")<<chosen.dump(2)<<"\n";J receipt={{"status","PASS_FULL_CURRENT249_COHORT_REWRITE_F2_COLUMNS_AND_FRAMES"},{"new_gauges",chosen.size()},{"new_entrance_rank",totaldim},{"cut_record",cut},{"old_records",ev.size()},{"new_records",out.size()},{"removed_initial_reads",removed},{"added_Q_Qinverse_passes",basisgates},{"forward_formal_columns",n},{"inverse_formal_columns",n},{"omitted_Q_nonzero_wrong_words",badQ},{"omitted_Qinverse_nonzero_wrong_words",badQi},{"histogram",hist},{"delta",delta},{"old_rank_mass",oldmass},{"new_rank_mass",mass},{"new_gram_audit_external",true},{"bank_completion_not_replayed",true},{"global_kappa_claimed",false}};ofstream(outdir+"/COHORT249-REPLAY.json")<<receipt.dump(2)<<"\n";cerr<<"PASS "<<chosen.size()<<" pairs, mass "<<oldmass<<" -> "<<mass<<" removed reads "<<removed<<"\n";}
diff --git a/research/multicut-kernel-condensation-851/code/export249.py b/research/multicut-kernel-condensation-851/code/export249.py
new file mode 100644
index 0000000000..9913c9d89d
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/code/export249.py
@@ -0,0 +1,24 @@
+from pathlib import Path
+import json,sys,importlib.util,time,hashlib,gzip
+from collections import Counter
+P=Path(sys.argv[1]).resolve();D=Path(sys.argv[2]).resolve();D.mkdir(parents=True,exist_ok=True);sys.dont_write_bytecode=True;sys.path.insert(0,str(P));start=time.monotonic()
+def load(n):
+ s=importlib.util.spec_from_file_location('temporal249_'+n,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',encoding='utf8')
+def export(n,p):
+ records=p['records'];(D/(n+'-records.bin')).write_bytes(records.tobytes());(D/(n+'-records.bin.gz')).write_bytes(gzip.compress(records.tobytes(),mtime=0));final=dict(p['initial_state']);F=set(final.values())
+ for k in range(0,len(records),6):
+  op,a,b,c,f,z=records[k:k+6]
+  if op==0:final[a]=c;F.update((b,c))
+  elif op==1:F.add(f)
+  elif op in(2,3):F.update((c,f))
+ save(n+'-states.json',dict(initial=p['initial_state'],final=final,ZERO=p['ZERO'],FULL=p['FULL'],n=20107,v=1760,record_count=len(records)//6,record_sha256=hashlib.sha256(records.tobytes()).hexdigest(),physical=p['physical'],regs=p['context']['regs'],borrowed=list(p['context']['borrow']),removed=list(p['context']['removed']),source_owned_roles=sorted(p['context']['borrow']),source_covectors=p['C'].cov))
+ return F
+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);p=load('retiming_transform').run(p);used=export('pre249',p);print('PRE249 exported',time.monotonic()-start,flush=True)
+m=load('regauge_transform');selection=json.loads((P/'regauge-selection.json').read_text());out,initial,final,entries,execution_context,proof=m.transform(p,selection)
+q=dict(p,records=out,initial_state=initial,context=execution_context,W=execution_context['W']);used.update(export('249',q));save('249-transport-proof.json',proof)
+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('EXPORT-RECEIPT.json',dict(status='PASS_EXACT_EMITTER_AND_TRANSPORT_EXPORT_NOT_FULL8_REPLAY',head='96495746c786d6d0339dbb38c7f553d4af3f88ed',frames=len(used),pre_record_sha256=hashlib.sha256(p['records'].tobytes()).hexdigest(),new_record_sha256=hashlib.sha256(out.tobytes()).hexdigest(),seconds=time.monotonic()-start,scope='Fresh source observer, exact frame emitter, parity filter, retiming, and literal249 compensation transform. Does not rerun global geometry, bank, primes, final pricing or complete public8stages.'))
+print('COMPLETE shared current249 export',len(used),'frames',time.monotonic()-start,flush=True)
+save('REGENERATED-DONORS.json',dict(donor_keys=sorted(q['context']['W'].donor)))
diff --git a/research/multicut-kernel-condensation-851/discovery/README.md b/research/multicut-kernel-condensation-851/discovery/README.md
new file mode 100644
index 0000000000..129cfbd0b3
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/README.md
@@ -0,0 +1,20 @@
+# Discovery (not run by the verifier)
+
+Pure-Python replay of PR #249's word and the census that produced the 333 added pairs (Chafik Boukhalfa,
+Anthropic Claude assistance). Inputs are the package's own `inputs/` files, decompressed into a data directory.
+
+    twins.py  <data> twins.pkl                  census of twin dirty helpers at PR #254's cut (record 727,593)
+    chrono2.py <data> twins.pkl chrono.pkl <cut> the same census at any cut (used at 676,560: 985 pairs, 24 size-9 classes)
+    gain.py                                     log-weighted gain phi(r) = r ln(120/r) per pair and exact-grid price
+    gen_candidates.py                           candidate records (basis, first frames, entrance line) in PR #259's schema
+    compare259.py                               the pairs disjoint from PR #259's 1,194 helpers (free259.json)
+    merge259.py                                 PR #259's 518 items + the 333 free net-positive pairs -> inputs/candidates.json.gz
+
+Diff of this package against PR #259's (everything else byte for byte):
+
+    inputs/candidates.json.gz      518 items unchanged + 333 appended (round "union-early-cut", cut 676559)
+    expected/*.json, RESULT.json   regenerated receipts and result (851 pivots, entrance rank 1677, kappa 7.11403723709732e-4)
+    code/cohort-transform.cpp      std::sort -> std::stable_sort on the gauge order (platform-independent transcript)
+    verify.py                      'containment_pairs_checked' added to the dropped fields; normalize() on both receipt sides
+    README.md, PROOF.md, NOTICE.md this package's notes; PR #259's README/PROOF kept as README-PR259.md, PROOF-PR259.md
+    MANIFEST.json                  regenerated
diff --git a/research/multicut-kernel-condensation-851/discovery/chrono2.py b/research/multicut-kernel-condensation-851/discovery/chrono2.py
new file mode 100644
index 0000000000..1d858877fc
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/chrono2.py
@@ -0,0 +1,101 @@
+import json, sys, collections, time, pickle, itertools
+from array import array
+from fractions import Fraction as Fr
+from math import lcm, gcd
+D = sys.argv[1]; T = pickle.load(open(sys.argv[2], 'rb')); C = pickle.load(open(sys.argv[3], 'rb')); CUT = int(sys.argv[4])
+t0 = time.time()
+st = json.load(open(D + '/249-states.json')); n, v, ZERO, FULL = st['n'], st['v'], st['ZERO'], st['FULL']
+ini, fin, regs = T['ini'], T['fin'], st['regs']; borrowed = set(st['borrowed']); donor = set(json.load(open(D + '/249-DONOR-OWNERSHIP.json'))['donor_keys'])
+rec = array('i'); rec.frombytes(open(D + '/249-records.bin', 'rb').read()); E = len(rec)//6; H0 = 2*v
+Tt, kind = C['Tt'], C['kind']
+fj = json.load(open(D + '/frames.json'))['frames']
+# first MOVE destination frame after CUT for each helper
+ff = {}
+for i in range(CUT+1, E):
+    k,a,b,c,f,z = rec[6*i:6*i+6]
+    if k == 0 and a >= H0 and a not in ff: ff[a] = c
+row = [1 << s for s in range(n+1)]
+for i in range(CUT+1):
+    k,a,b,c,f,z = rec[6*i:6*i+6]
+    if k == 1:
+        if c & 1: row[a] ^= row[b]
+    elif k == 2: row[b] = row[a]
+base = [h for h in range(H0, n) if ini[h] == ZERO and fin[h] == FULL and regs[h-H0] not in borrowed and regs[h-H0] not in donor and Tt[h] > CUT and kind[h][0] == 'MOVE']
+contam = 0
+for s in range(n):
+    if v <= s < 2*v: continue
+    contam |= (row[s] ^ (1 << s)) >> H0
+resp = collections.defaultdict(int)
+for t in range(v):
+    r = row[v+t] >> H0
+    while r:
+        low = r & -r; idx = low.bit_length()-1; resp[H0+idx] |= 1 << t; r ^= low
+live = [h for h in base if not (contam >> (h-H0)) & 1 and resp[h]]
+cls = collections.defaultdict(list)
+for h in live: cls[resp[h]].append(h)
+print(f'CUT {CUT}: base {len(base)} live(clean,nonzero resp) {len(live)} distinct responses {len(cls)} class sizes {sorted(collections.Counter(len(m) for m in cls.values()).items())}')
+def nullspace(rows):
+    m = [[Fr(x) for x in r] for r in rows]; ncol = 24; piv = []; r = 0
+    for c in range(ncol):
+        p = next((i for i in range(r, len(m)) if m[i][c] != 0), 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] != 0:
+                f = m[i][c]; m[i] = [a - f*b for a, b in zip(m[i], m[r])]
+        piv.append(c); r += 1
+        if r == len(m): break
+    free = [c for c in range(ncol) if c not in piv]; basis = []
+    for fcol in free:
+        vec = [Fr(0)]*ncol; vec[fcol] = Fr(1)
+        for i, pc in enumerate(piv): vec[pc] = -m[i][fcol]
+        basis.append(vec)
+    return basis, free
+def gramdet(basis):
+    k = len(basis); M = [[9*sum(a*b for a, b in zip(basis[i], basis[j])) - sum(basis[i])*sum(basis[j]) for j in range(k)] for i in range(k)]
+    det = Fr(1)
+    for c in range(k):
+        p = next((i for i in range(c, k) if M[i][c] != 0), None)
+        if p is None: return 0
+        if p != c: M[c], M[p] = M[p], M[c]; det = -det
+        det *= M[c][c]
+        for i in range(c+1, k):
+            f = M[i][c]/M[c][c]; M[i] = [a - f*b for a, b in zip(M[i], M[c])]
+    return det
+def shape4(u): return sorted(abs(x) for x in u) == [0]*20 + [1]*4 and sum(u) == 0
+def prim(vec):
+    L = 1
+    for x in vec: L = lcm(L, x.denominator)
+    iv = [int(x*L) for x in vec]; g = 0
+    for x in iv: g = gcd(g, abs(x))
+    return [x//g for x in iv]
+def classify(frames):
+    rows = []
+    for f in frames: rows += fj[str(f)]['A']
+    basis, free = nullspace(rows); d = len(basis)
+    if d == 0: return 'dim0', None
+    g = gramdet(basis)
+    if d == 1: u = prim(basis[0]); return (f'dim1_{"shape4" if shape4(u) else "other"}' + ('_degenerate' if g == 0 else ''), u)
+    if d <= 8:
+        for lam in itertools.product((-1, 0, 1), repeat=d):
+            if not any(lam): continue
+            u = [sum(l*b[i] for l, b in zip(lam, basis)) for i in range(24)]
+            if all(x.denominator == 1 for x in u) and shape4([int(x) for x in u]): return f'dim{d}_has_shape4' + ('_degenerate' if g == 0 else ''), [int(x) for x in u]
+        return f'dim{d}_no_shape4' + ('_degenerate' if g == 0 else ''), None
+    return f'dim{d}_unchecked', None
+res = collections.Counter(); fdims = collections.Counter(); otheru = []
+final_pairs = {tuple(sorted(m)) for r, m in T['classes'].items() if r and len(m) == 2}
+pairs = [tuple(sorted(m)) for m in cls.values() if len(m) == 2]
+for p in pairs:
+    key, u = classify([ff[p[0]], ff[p[1]]]); res[(key, p in final_pairs)] += 1; fdims[(fj[str(ff[p[0]])]['dim'], fj[str(ff[p[1]])]['dim'])] += 1
+    if key == 'dim1_other' and p in final_pairs: otheru.append(u)
+print('twin pairs by (intersection class, is-final-cut-pair):'); [print('  ', k, c) for k, c in sorted(res.items(), key=lambda x: -x[1])]
+print('first-frame dim pairs (top 12):', fdims.most_common(12))
+print('u vectors of final-cut dim1_other pairs:'); [print('  ', u, 'norm', sum(x*x for x in u), 'sum', sum(u)) for u in otheru]
+big = [m for m in cls.values() if len(m) >= 3]
+print('classes of size>=3:', [len(m) for m in big])
+bres = collections.Counter()
+for m in big:
+    key, u = classify([ff[h] for h in m]); bres[(len(m), key)] += 1
+print('size>=3 classes common-intersection:', dict(bres))
+print('done', time.time()-t0)
diff --git a/research/multicut-kernel-condensation-851/discovery/compare259.py b/research/multicut-kernel-condensation-851/discovery/compare259.py
new file mode 100644
index 0000000000..bc7bf020fd
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/compare259.py
@@ -0,0 +1,57 @@
+import json, sys, collections, math
+from decimal import Decimal as Dc, getcontext
+getcontext().prec = 50
+c259 = json.load(open(sys.argv[1])); mine = json.load(open(sys.argv[2]))['candidates']; rep = json.load(open(sys.argv[3])); fj = json.load(open(sys.argv[4]))['frames']
+items = c259 if isinstance(c259, list) else c259['candidates']
+print('PR259 candidates', len(items), 'item key sets', collections.Counter(tuple(sorted(z.keys())) for z in items).most_common(4))
+used = set(); piv = set(); cuts = collections.Counter(); dims = collections.Counter(); fam = collections.Counter()
+for z in items:
+    if 'roles' in z: p = z['pivot']; roles = list(z['roles']); d = z['dim']
+    else: p = z['a']; roles = [z['a'], z['b']]; d = z['E_dimension']
+    piv.add(p); used |= set(roles); cuts[z.get('cut', 727593)] += 1; dims[d] += 1; fam[len(roles)] += 1
+print('pivots', len(piv), 'distinct helpers', len(used), 'cuts', dict(cuts), 'E dims', sorted(dims.items()), 'family sizes', sorted(fam.items()))
+print('sum of dims (entrance rank)', sum((z['dim'] if 'roles' in z else z['E_dimension']) for z in items))
+my_used = {z['a'] for z in mine} | {z['b'] for z in mine}
+print('my pairs', len(mine), 'my helpers', len(my_used), 'overlap helpers with PR259', len(my_used & used), 'my pivots that are PR259 pivots', len({z['a'] for z in mine} & piv))
+free = [z for z in mine if z['a'] not in used and z['b'] not in used]
+half = [z for z in mine if (z['a'] in used) != (z['b'] in used)]
+print('my pairs fully disjoint from PR259 helpers:', len(free), ' pairs with exactly one helper used by PR259:', len(half))
+print('free pairs by frame dims:', collections.Counter(tuple(z.get('frame_dims', [3, 3])) for z in free))
+print('free pairs by source:', collections.Counter(z.get('source', '?') for z in free))
+# price union: PR259 histogram (x40 + completions) and W=173435, then add free pairs e=1 (drop weakest to keep count = 0 mod 3)
+LN = {}
+def moment(H, W, a, m=120):
+    s = Dc(0); N = 0
+    for r, n in H.items():
+        if n == 0: continue
+        if r not in LN: LN[r] = (Dc(m)/Dc(r)).ln()
+        s += Dc(r*n)/(Dc(m)*W) * (LN[r]*a).exp(); N += n
+    if 'm' not in LN: LN['m'] = Dc(m).ln()
+    return s + Dc(32*m*m*N)/(Dc(m)*W) * (LN['m']*a).exp() / Dc(10)**16
+grid = Dc(10)**18
+def price(H, W):
+    lo, hi = Dc('0.0005'), Dc('0.001'); assert moment(H, W, lo) < 1 < moment(H, W, hi)
+    for _ in range(80):
+        mid = (lo+hi)/2
+        if moment(H, W, mid) < 1: lo = mid
+        else: hi = mid
+    z = int(lo*grid); assert moment(H, W, Dc(z)/grid) < 1 and moment(H, W, Dc(z+1)/grid) > 1
+    c = Dc(z)/grid; bit = Dc(384599)/Dc(10)**10
+    for _ in range(3): bit = (1-c)*c + c*bit
+    eta = Dc(1)/Dc(10)**12; q = bit*(1-2*eta); bound = (1-eta)*q/(1+q)
+    return Dc(int(bound*grid))/grid, c
+H = {int(k): 40*v for k, v in rep['histogram'].items()}
+for r in (4, 23, 46, 50): H[r] = H.get(r, 0) + 16*1760
+k259, c259v = price(H, Dc(173435)); print('PR259 kappa reproduced:', k259, 'coarse', c259v)
+free.sort(key=lambda z: z['approx_slack_delta'])
+while len(free) % 3: free.pop()
+H2 = dict(H)
+for z in free:
+    ra, rb = z.get('frame_dims') or [fj[str(z['first_a'])]['dim'], fj[str(z['first_b'])]['dim']]
+    for r, dn in ((ra, -40), (rb, -40), (ra-1, 40), (1, 40), (rb-1, 40)):
+        if r > 0: H2[r] = H2.get(r, 0) + dn
+W2 = Dc(173435) - Dc(len(free))/3
+k2, c2 = price(H2, W2)
+print(f'UNION projection: PR259 + {len(free)} free e=1 pairs -> kappa={k2} coarse={c2} W={W2} mass={sum(r*n for r,n in H2.items())} deficit={120*W2-sum(r*n for r,n in H2.items())}')
+print(f'  dk vs PR259 = {k2-k259}   dk vs PR263 (7.11032e-4 nominal) = {k2-Dc("0.000711032")}')
+json.dump(dict(free=[(z['a'], z['b']) for z in free]), open(sys.argv[5], 'w'))
diff --git a/research/multicut-kernel-condensation-851/discovery/gain.py b/research/multicut-kernel-condensation-851/discovery/gain.py
new file mode 100644
index 0000000000..d851c3608f
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/gain.py
@@ -0,0 +1,79 @@
+import json, sys, collections, time, pickle, itertools, math
+from array import array
+from fractions import Fraction as Fr
+from math import lcm, gcd
+exec(open(sys.argv[5]).read().split("res = collections.Counter(); fdims")[0])  # chrono2 setup at CUT: cls, ff, fj, classify, nullspace, gramdet, prim
+from decimal import Decimal as Dc, getcontext
+getcontext().prec = 50
+rep = json.load(open(sys.argv[6]))
+H = {int(k): 40*v for k, v in rep['histogram'].items()}
+for r in (4, 23, 46, 50): H[r] = H.get(r, 0) + 16*1760
+exec(open(sys.argv[7]).read().split("print('baseline:')")[0].split("rep = json.load")[0].replace("import json, sys", ""))  # moment/price defs? simpler: redefine
+LN = {}
+def moment(H, W, a, m=120):
+    s = Dc(0); N = 0
+    for r, n in H.items():
+        if n == 0: continue
+        if r not in LN: LN[r] = (Dc(m)/Dc(r)).ln()
+        s += Dc(r*n)/(Dc(m)*W) * (LN[r]*a).exp(); N += n
+    if 'm' not in LN: LN['m'] = Dc(m).ln()
+    return s + Dc(32*m*m*N)/(Dc(m)*W) * (LN['m']*a).exp() / Dc(10)**16
+grid = Dc(10)**18
+def price(H, W):
+    lo, hi = Dc('0.0005'), Dc('0.001'); assert moment(H, W, lo) < 1 < moment(H, W, hi)
+    for _ in range(80):
+        mid = (lo+hi)/2
+        if moment(H, W, mid) < 1: lo = mid
+        else: hi = mid
+    z = int(lo*grid); assert moment(H, W, Dc(z)/grid) < 1 and moment(H, W, Dc(z+1)/grid) > 1
+    c = Dc(z)/grid; bit = Dc(384599)/Dc(10)**10
+    for _ in range(3): bit = (1-c)*c + c*bit
+    eta = Dc(1)/Dc(10)**12; q = bit*(1-2*eta); bound = (1-eta)*q/(1+q)
+    return Dc(int(bound*grid))/grid
+kn = price(H, Dc(173839)); print('PR254 kappa reproduced', kn)
+phi = lambda r: 0.0 if r == 0 else r*math.log(120/r)
+def best(ra, rb, d):
+    # pivot p starts at E (dim e<=d), partner b raised to E; gain = phi(rp-e)-phi(rp) + phi(e)+phi(rb-e)-phi(rb)   (negative = good)
+    out = None
+    for rp, rq in ((ra, rb), (rb, ra)):
+        for e in range(1, d+1):
+            g = phi(rp-e)-phi(rp) + phi(e)+phi(rq-e)-phi(rq)
+            if out is None or g < out[0]: out = (g, e, rp, rq)
+    return out
+def inter_dim_nondeg(frames):
+    rows = []
+    for f in frames: rows += fj[str(f)]['A']
+    basis, free = nullspace(rows); d = len(basis)
+    if d == 0: return 0, False
+    return d, gramdet(basis) != 0
+pairs = [tuple(sorted(m)) for m in cls.values() if len(m) == 2]
+tab = collections.Counter(); gains = []; H2 = dict(H); W2 = Dc(173839); npos = 0; totgain = 0.0
+strict_e1 = 0
+for a, b in pairs:
+    ra, rb = fj[str(ff[a])]['dim'], fj[str(ff[b])]['dim']
+    d, nd = inter_dim_nondeg([ff[a], ff[b]])
+    key = (tuple(sorted((ra, rb))), d, nd); tab[key] += 1
+    if d == 0 or not nd: continue
+    g, e, rp, rq = best(ra, rb, d)
+    gains.append((g, e, rp, rq, a, b))
+    if g < 0:
+        npos += 1; totgain += g
+        for r, dn in ((rp, -40), (rq, -40), (rp-e, 40), (e, 40), (rq-e, 40)):
+            if r > 0: H2[r] = H2.get(r, 0) + dn
+        W2 -= Dc(e)/3
+print('cross-tab (sorted first-frame dims, intersection dim, nondegenerate) -> count:'); [print('  ', k, c) for k, c in sorted(tab.items(), key=lambda x: -x[1])]
+print('pairs with nonzero nondegenerate intersection:', len(gains), ' of which net-positive (log-weighted) with best pivot/e:', npos, ' total phi-gain', round(totgain, 1))
+print('gain histogram (e, frames) for positive pairs:', collections.Counter((e, (rp, rq)) for g, e, rp, rq, a, b in gains if g < 0).most_common(12))
+k2 = price(H2, W2); print(f'price: all net-positive pairs at cut {CUT} (single cut, e<=dim): kappa={k2} dk vs PR254={k2-kn} ({float((k2-kn)/kn*100):.4f}%)  W2={W2} mass={sum(r*n for r,n in H2.items())} deficit={120*W2-sum(r*n for r,n in H2.items())}')
+# restricted variant: e=1 only, nondegenerate line, any u (needs norm-2 charts)
+H3 = dict(H); W3 = Dc(173839); n3 = 0
+for g, e, rp, rq, a, b in gains:
+    g1 = min(phi(rp-1)-phi(rp)+phi(1)+phi(rq-1)-phi(rq), phi(rq-1)-phi(rq)+phi(1)+phi(rp-1)-phi(rp))
+    if g1 < 0:
+        n3 += 1
+        for r, dn in ((rp, -40), (rq, -40), (rp-1, 40), (1, 40), (rq-1, 40)):
+            if r > 0: H3[r] = H3.get(r, 0) + dn
+        W3 -= Dc(1)/3
+k3 = price(H3, W3); print(f'price: e=1 only, {n3} net-positive pairs: kappa={k3} dk vs PR254={k3-kn}')
+# the PR's own 132 (3,3) pairs: phi gain check
+print('phi gain per (3,3) e=1 pair', round(best(3,3,1)[0],3), ' (2,2) e=1', round(best(2,2,1)[0],3), ' (2,2) e=2', round(best(2,2,2)[0],3), ' (1,1) e=1', round(best(1,1,1)[0],3), ' (5,5) e=1', round(best(5,5,1)[0],3), ' (5,5) e=3', round(best(5,5,3)[0],3), ' (3,3,3) triple e=1', round(2*(phi(1)+phi(2)-phi(3)) + phi(2)-phi(3),3))
diff --git a/research/multicut-kernel-condensation-851/discovery/gen_candidates.py b/research/multicut-kernel-condensation-851/discovery/gen_candidates.py
new file mode 100644
index 0000000000..84d62b8c12
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/gen_candidates.py
@@ -0,0 +1,139 @@
+"""Emit PR254-schema candidates for the response-twin rewrite at an early cut.
+usage: gen_candidates.py DATA_DIR PR254_CANDIDATES_JSON CUT PHASE OUT_JSON
+PHASE 1: u with sum 0, u.u = 4 (four +-1 entries), e=1.  PHASE 2: additionally u = e_i - e_j (u.u = 2)."""
+import json, sys, collections, time, itertools, math, gzip
+from array import array
+from fractions import Fraction as Fr
+from math import lcm, gcd
+D, PRC, CUT, PHASE, OUT = sys.argv[1], sys.argv[2], int(sys.argv[3]), int(sys.argv[4]), sys.argv[5]
+t0 = time.time()
+st = json.load(open(D + '/249-states.json')); n, v, ZERO, FULL = st['n'], st['v'], st['ZERO'], st['FULL']; H0 = 2*v
+ini = [ZERO]*n; fin = [FULL]*n
+for k, x in st['initial'].items(): ini[int(k)] = x
+for k, x in st['final'].items(): fin[int(k)] = x
+regs = st['regs']; borrowed = set(st['borrowed']); donor = set(json.load(open(D + '/249-DONOR-OWNERSHIP.json'))['donor_keys'])
+rec = array('i'); rec.frombytes(open(D + '/249-records.bin', 'rb').read()); E = len(rec)//6
+fj = json.load(open(D + '/frames.json'))['frames']
+pr = json.load(open(PRC))['candidates']; prmap = {}
+for z in pr: prmap[(z['a'], z['b'])] = z
+# sanity on the cut: record CUT-1 is the last zero-frame initial read, none after
+reads_after = sum(1 for i in range(CUT, E) if rec[6*i] == 1 and rec[6*i+5] == 4 and rec[6*i+4] == ZERO)
+last_read = max(i for i in range(E) if rec[6*i] == 1 and rec[6*i+5] == 4 and rec[6*i+4] == ZERO)
+print('cut', CUT, 'last initial read', last_read, 'reads after cut', reads_after); assert reads_after == 0
+# prefix census
+bad = collections.Counter(); reads = collections.Counter(); row = [1 << s for s in range(n+1)]
+for i in range(CUT+1):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 1:
+        if c & 1: row[a] ^= row[b]
+        if a >= H0: bad[a] += 1
+        if b >= H0:
+            if z == 4 and f == ZERO and v <= a < 2*v: reads[b] += 1
+            else: bad[b] += 1
+    elif k == 2:
+        row[b] = row[a]
+        for s in (a, b):
+            if s >= H0: bad[s] += 1
+    elif k == 3:
+        for s in (a, b):
+            if s >= H0: bad[s] += 1
+    elif k == 0 and a >= H0: bad[a] += 1
+first = {}
+for i in range(CUT+1, E):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 0:
+        if a >= H0 and a not in first: first[a] = ('MOVE', c)
+    else:
+        for s in (a, b):
+            if s >= H0 and s not in first: first[s] = ('OTHER', None)
+contam = 0
+for s in range(n):
+    if v <= s < 2*v: continue
+    contam |= (row[s] ^ (1 << s)) >> H0
+resp = collections.defaultdict(int)
+for t in range(v):
+    r = row[v+t] >> H0
+    while r:
+        low = r & -r; idx = low.bit_length()-1; resp[H0+idx] |= 1 << t; r ^= low
+elig = [h for h in range(H0, n) if ini[h] == ZERO and fin[h] == FULL and not bad[h] and regs[h-H0] not in borrowed and regs[h-H0] not in donor and h in first and first[h][0] == 'MOVE' and not (contam >> (h-H0)) & 1 and resp[h]]
+cls = collections.defaultdict(list)
+for h in elig: cls[resp[h]].append(h)
+pairs = [tuple(m) for m in cls.values() if len(m) == 2]
+print('eligible', len(elig), 'twin pairs', len(pairs), 'classes>=3', sum(1 for m in cls.values() if len(m) > 2), time.time()-t0)
+def nullspace(rows):
+    m = [[Fr(x) for x in r] for r in rows]; piv = []; r = 0
+    for c in range(24):
+        p = next((i for i in range(r, len(m)) if m[i][c] != 0), 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] != 0:
+                f = m[i][c]; m[i] = [a - f*b for a, b in zip(m[i], m[r])]
+        piv.append(c); r += 1
+        if r == len(m): break
+    free = [c for c in range(24) if c not in piv]; basis = []
+    for fcol in free:
+        vec = [Fr(0)]*24; vec[fcol] = Fr(1)
+        for i, pc in enumerate(piv): vec[pc] = -m[i][fcol]
+        basis.append(vec)
+    return basis
+def prim(vec):
+    L = 1
+    for x in vec: L = lcm(L, x.denominator)
+    iv = [int(x*L) for x in vec]; g = 0
+    for x in iv: g = gcd(g, abs(x))
+    return [x//g for x in iv]
+def admissible(u):
+    s = sum(u); nrm = sum(x*x for x in u)
+    if s != 0: return False
+    if nrm == 4 and all(abs(x) <= 1 for x in u): return True
+    if PHASE >= 2 and nrm == 2: return True
+    return False
+def find_u(basis):
+    d = len(basis)
+    if d == 1:
+        u = prim(basis[0]); return u if admissible(u) else None
+    best = None
+    for lam in itertools.product((-1, 0, 1), repeat=d):
+        if not any(lam): continue
+        u = [sum(l*b[i] for l, b in zip(lam, basis)) for i in range(24)]
+        if all(x.denominator == 1 for x in u):
+            u = prim([Fr(int(x)) for x in u])
+            if admissible(u) and (best is None or sum(x*x for x in u) > sum(x*x for x in best)): best = u  # prefer norm-4 (PR rule)
+    return best
+phi = lambda r: 0.0 if r == 0 else r*math.log(120/r)
+def annihilator(u):
+    sup = [i for i in range(24) if u[i]]; last = sup[-1]; rows = []
+    for k in range(24):
+        if k == last: continue
+        r = [0]*24; r[k] = 1
+        if u[k]: r[last] = -u[k]*u[last]  # (e_k - (u_k/u_last) e_last), |u_last| = 1
+        rows.append(r)
+    assert len(rows) == 23 and all(sum(x*y for x, y in zip(r, u)) == 0 for r in rows)
+    return rows
+cands = []; stats = collections.Counter()
+for a, b in pairs:
+    Fa, Fb = first[a][1], first[b][1]; ra, rb = fj[str(Fa)]['dim'], fj[str(Fb)]['dim']
+    basis = nullspace(fj[str(Fa)]['A'] + fj[str(Fb)]['A']); d = len(basis)
+    if d == 0: stats['dim0'] += 1; continue
+    u = find_u(basis)
+    if u is None: stats[f'no_admissible_u_dim{d}'] += 1; continue
+    gain = min(phi(ra-1)-phi(ra)+phi(1)+phi(rb-1)-phi(rb), phi(rb-1)-phi(rb)+phi(1)+phi(ra-1)-phi(ra))
+    if gain >= 0: stats[f'nonpositive_gain_{tuple(sorted((ra,rb)))}'] += 1; continue
+    if (a, b) in prmap or (b, a) in prmap:  # keep PR254's own pair orientation and line verbatim
+        z = dict(prmap[(a, b)] if (a, b) in prmap else prmap[(b, a)]); z['approx_slack_delta'] = gain; z['source'] = 'PR254'
+        assert z['first_a'] == first[z['a']][1] and z['first_b'] == first[z['b']][1]
+        cands.append(z); stats['PR254_pair'] += 1; continue
+    # pivot = smaller first frame (its move shrinks); tie -> more initial reads removed
+    if (ra, -reads[a]) <= (rb, -reads[b]): p, q, Fp, Fq = a, b, Fa, Fb
+    else: p, q, Fp, Fq = b, a, Fb, Fa
+    fmt = lambda r: [str(x) for x in r]
+    cands.append(dict(E_dimension=1, a=p, annihilator=[fmt(r) for r in annihilator(u)], approx_slack_delta=gain, b=q, basis=[fmt(u)], first_a=Fp, first_b=Fq, new_targets=[], nondegeneracy_not_checked=True, source='early-cut', frame_dims=[fj[str(Fp)]['dim'], fj[str(Fq)]['dim']], u_norm=sum(x*x for x in u), pivot_initial_reads=reads[p]))
+    stats[f'new_pair_norm{sum(x*x for x in u)}_{(fj[str(Fp)]["dim"], fj[str(Fq)]["dim"])}'] += 1
+print('stats', dict(stats))
+# trim to P = 0 mod 3 by dropping the weakest gains
+cands.sort(key=lambda z: z['approx_slack_delta'])
+while len(cands) % 3: dropped = cands.pop(); print('dropped weakest pair', dropped['a'], dropped['b'], dropped['approx_slack_delta'])
+out = dict(status='EXACT_INTERSECTION_EARLY_CUT_LOG_WEIGHTED_POSITIVE', cut_record=CUT, phase=PHASE, chart_rule='sum 0, norm 4 (four +-1)' if PHASE == 1 else 'sum 0, norm 4 or norm 2 (e_i - e_j)', approx_positive=len(cands), close_response_pairs=len(pairs), intersections=len(pairs)-stats['dim0'], max_response_symmetric_difference=0, no_kappa_claim=True, total_phi_gain=sum(z['approx_slack_delta'] for z in cands), candidates=cands)
+json.dump(out, open(OUT, 'w'), indent=1); open(OUT + '.gz', 'wb').write(gzip.compress(json.dumps(out, indent=1).encode(), mtime=0))
+print('wrote', OUT, 'pairs', len(cands), 'P mod 3 =', len(cands) % 3, 'phi gain', round(out['total_phi_gain'], 2), 'removed reads', sum(reads[z['a']] for z in cands), time.time()-t0)
diff --git a/research/multicut-kernel-condensation-851/discovery/merge259.py b/research/multicut-kernel-condensation-851/discovery/merge259.py
new file mode 100644
index 0000000000..82a9905d85
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/merge259.py
@@ -0,0 +1,13 @@
+import json, sys, gzip
+c259 = json.load(open(sys.argv[1])); mine = json.load(open(sys.argv[2]))['candidates']; free = {tuple(p) for p in json.load(open(sys.argv[3]))['free']}; OUT = sys.argv[4]
+used = set()
+for z in c259: used |= set(z['roles'])
+added = []
+for z in mine:
+    if (z['a'], z['b']) not in free: continue
+    assert z['a'] not in used and z['b'] not in used
+    item = dict(pivot=z['a'], a=z['a'], roles=[z['a'], z['b']], partners=[z['b']], dim=1, E_dimension=1, basis=z['basis'], cut=676559, first_frames=[z['first_a'], z['first_b']], approx_slack_delta=z['approx_slack_delta'], kind='early-cut equal-response pair (u sum 0, norm %d)' % sum(int(x)**2 for x in z['basis'][0]), round='union-early-cut')
+    added.append(item); used |= {z['a'], z['b']}
+merged = c259 + added
+S = sum(z['dim'] for z in merged); print('merged candidates', len(merged), 'added', len(added), 'entrance rank sum', S, 'mod 3 =', S % 3)
+json.dump(merged, open(OUT, 'w'), indent=1); open(OUT + '.gz', 'wb').write(gzip.compress(json.dumps(merged, indent=1).encode(), mtime=0))
diff --git a/research/multicut-kernel-condensation-851/discovery/twins.py b/research/multicut-kernel-condensation-851/discovery/twins.py
new file mode 100644
index 0000000000..c4e273bd60
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/discovery/twins.py
@@ -0,0 +1,149 @@
+import json, sys, collections, time, pickle
+from array import array
+D = sys.argv[1]  # data dir
+OUT = sys.argv[2]
+t0 = time.time()
+st = json.load(open(D + '/249-states.json'))
+n, v, ZERO, FULL = st['n'], st['v'], st['ZERO'], st['FULL']
+ini = [ZERO]*n; fin = [FULL]*n
+for k, x in st['initial'].items(): ini[int(k)] = x
+for k, x in st['final'].items(): fin[int(k)] = x
+regs = st['regs']; borrowed = set(st['borrowed']); removed = set(st['removed'])
+donor = set(json.load(open(D + '/249-DONOR-OWNERSHIP.json'))['donor_keys'])
+rec = array('i'); rec.frombytes(open(D + '/249-records.bin', 'rb').read())
+E = len(rec)//6
+print('events', E, 'n', n, 'v', v, 'ZERO', ZERO, 'FULL', FULL, 'helpers', n-2*v)
+cut = [i for i in range(E) if rec[6*i]==1 and rec[6*i+1]==3491 and rec[6*i+2]==3488 and rec[6*i+3]==-1 and rec[6*i+5]==25]
+assert len(cut)==1; cut = cut[0]; print('cut', cut)
+# per-helper prefix touch census
+H0 = 2*v
+init_reads = collections.Counter(); bad_touch = collections.Counter(); moves_before = collections.Counter()
+row = [1 << s for s in range(n+1)]
+kinds = collections.Counter()
+for i in range(cut+1):
+    k,a,b,c,f,z = rec[6*i:6*i+6]
+    kinds[(k,z)] += 1
+    if k == 1:
+        if c & 1: row[a] ^= row[b]
+        if a >= H0: bad_touch[a] += 1
+        if b >= H0:
+            if z == 4 and f == ZERO and v <= a < 2*v: init_reads[b] += 1
+            else: bad_touch[b] += 1
+    elif k == 2:
+        row[b] = row[a]
+        if a >= H0: bad_touch[a] += 1
+        if b >= H0: bad_touch[b] += 1
+    elif k == 3:
+        assert row[a] == row[b]
+        if a >= H0: bad_touch[a] += 1
+        if b >= H0: bad_touch[b] += 1
+    elif k == 0:
+        if a >= H0: moves_before[a] += 1
+print('prefix replayed', time.time()-t0)
+print('prefix event kinds (k,z) top', kinds.most_common(12))
+# responses
+resp = [0]*n
+for t in range(v):
+    r = row[v+t] >> H0
+    h = H0
+    while r:
+        low = r & -r
+        idx = low.bit_length()-1
+        resp[H0+idx] |= 1 << t
+        r ^= low
+contam = 0
+for s in range(n):
+    if v <= s < 2*v: continue
+    contam |= (row[s] ^ (1 << s)) >> H0
+contaminated = {H0+i for i in range(n-H0) if (contam >> i) & 1}
+print('responses built', time.time()-t0, 'contaminating helpers', len(contaminated))
+# first use after cut
+first = {}
+for i in range(cut+1, E):
+    k,a,b,c,f,z = rec[6*i:6*i+6]
+    if k == 0:
+        if a >= H0 and a not in first: first[a] = (i, 'MOVE', b, c, z)
+    else:
+        fr = f if k == 1 else c
+        for s in (a, b):
+            if s >= H0 and s not in first: first[s] = (i, ('ADD','COPY','ERASE')[k-1], f if k==1 else None, fr, z)
+print('first uses found', len(first))
+elig = []; reasons = collections.Counter()
+for h in range(H0, n):
+    why = []
+    if ini[h] != ZERO: why.append('ini!=ZERO')
+    if fin[h] != FULL: why.append('fin!=FULL')
+    if bad_touch[h]: why.append('touched')
+    if moves_before[h]: why.append('moved_before')
+    if h in contaminated: why.append('contaminates_nontarget')
+    if regs[h-H0] in borrowed: why.append('source_owner')
+    if regs[h-H0] in donor: why.append('donor')
+    if h not in first: why.append('never_used_after')
+    elif first[h][1] != 'MOVE': why.append('firstuse_not_MOVE')
+    if why: reasons[tuple(why)] += 1
+    else: elig.append(h)
+print('eligible helpers', len(elig)); print('ineligibility reasons', reasons.most_common(20))
+classes = collections.defaultdict(list)
+for h in elig: classes[resp[h]].append(h)
+sizes = collections.Counter(len(m) for m in classes.values())
+print('response classes among eligible: distinct responses', len(classes), 'size dist', sorted(sizes.items()))
+print('zero-response eligible helpers', len(classes.get(0, [])))
+wt = collections.Counter(bin(resp[h]).count('1') for h in elig); print('response weight dist (eligible)', sorted(wt.items()))
+ir = collections.Counter(init_reads[h] for h in elig); print('initial read count dist (eligible)', sorted(ir.items()))
+# helpers with a twin
+twin_helpers = sum(len(m) for r, m in classes.items() if r != 0 and len(m) >= 2)
+twin_pairs = sum(len(m)*(len(m)-1)//2 for r, m in classes.items() if r != 0 and len(m) >= 2)
+print('eligible helpers with >=1 nonzero-response twin', twin_helpers, 'unordered twin pairs', twin_pairs)
+# compare with candidates
+cand = json.load(open(D + '/candidates.json'))['candidates']
+ok = 0; mism = []
+for z in cand:
+    a, b = z['a'], z['b']
+    if resp[a] == resp[b] and a in set(elig) and b in set(elig): ok += 1
+    else: mism.append((a, b, resp[a]==resp[b], a in elig, b in elig))
+    if first.get(a, (0,0,0,None))[3] != z['first_a'] or first.get(b,(0,0,0,None))[3] != z['first_b']: mism.append(('frame', a, b, first.get(a), z['first_a'], first.get(b), z['first_b']))
+print('candidates confirmed twins & eligible', ok, 'mismatches', mism[:5], len(mism))
+# first-use frame dims and times
+pickle.dump(dict(cut=cut, elig=elig, resp={h: resp[h] for h in range(H0, n)}, first=first, init_reads=dict(init_reads), classes={r: m for r, m in classes.items()}, ini=ini, fin=fin, contaminated=contaminated, bad_touch=dict(bad_touch), moves_before=dict(moves_before)), open(OUT, 'wb'))
+# linear dependence among distinct nonzero responses of eligible helpers (F2 rank)
+basis = {}
+def reduce(x):
+    while x:
+        p = x.bit_length()-1
+        if p in basis: x ^= basis[p]
+        else: return x
+    return 0
+distinct = [r for r in classes if r]
+rank = 0; dependent = []
+for r in sorted(distinct):
+    y = reduce(r)
+    if y: basis[y.bit_length()-1] = y; rank += 1
+    else: dependent.append(r)
+print('distinct nonzero responses', len(distinct), 'F2 rank', rank, 'dependent responses', len(dependent))
+# close pairs: symmetric difference 1 or 2 among distinct responses of eligible helpers
+# and triples R_a ^ R_b = R_c
+S = set(distinct)
+sd1 = 0; sd2 = 0
+dl = distinct
+import itertools
+# symmetric difference <=2 via bit flips
+sdset = collections.Counter()
+for r in dl:
+    bits = [i for i in range(v) if (r >> i) & 1]
+    # weight small, so enumerate flips of up to 2 bits among all v positions is 1760+1760^2/2 - too many; use flips of existing bits + adding 1 bit
+    for i in range(v):
+        if (r ^ (1 << i)) in S: sdset[1] += 1
+    for i in range(v):
+        for j in bits:
+            if j != i and (r ^ (1 << i) ^ (1 << j)) in S: sdset[2] += 1
+print('ordered distinct-response pairs at sym diff 1:', sdset[1]//2, ' at sym diff 2 (both-in-weight-change or one-flip-one-add):', sdset[2]//2)
+# triples: r_c = r_a ^ r_b with all three distinct eligible responses
+tri = 0
+dl_sorted = sorted(dl)
+Sset = S
+for i in range(len(dl_sorted)):
+    for j in range(i+1, len(dl_sorted)):
+        x = dl_sorted[i] ^ dl_sorted[j]
+        if x in Sset and x != dl_sorted[i] and x != dl_sorted[j]: tri += 1
+print('XOR triples (a,b unordered, c=a^b in set), counted per pair:', tri, ' -> distinct triples', tri//3)
+print('done', time.time()-t0)
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json b/research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json
new file mode 100644
index 0000000000..a33ce54cd6
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json
@@ -0,0 +1,553 @@
+{
+  "actual_helper_roles": 16587,
+  "actual_role_replica_stage_assignments": 3317400,
+  "assignment_fnv1a64": "15151966029277311027",
+  "bank_patterns": [
+    {
+      "count": 240,
+      "widths": [
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+        11,
+        11,
+        11,
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+      ]
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+      ]
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+    {
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+      "widths": [
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+        24,
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+        24,
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+      ]
+    }
+  ],
+  "banks_per_stage": 117004,
+  "covered_address_rank_mass": 70202400,
+  "endpoint_address_columns": 10560,
+  "label": "actual_multicut",
+  "literal_stock": 866620,
+  "max_block_scalar": 30,
+  "max_intermediate_denominator": "704",
+  "max_intermediate_numerator": "704",
+  "max_new_chart_factors": 200,
+  "new_entrance_rank": 1677,
+  "new_exact_charts": 851,
+  "new_gauged_roles": 851,
+  "nonzero_omission_repeat_control_columns": 10560,
+  "normalized_stock": 173324,
+  "normalizer_factor_ceiling": 787,
+  "prime_guard": "every elimination pivot and emitted coefficient has numerator and denominator magnitude below2^80",
+  "residual_families": {
+    "10": 1,
+    "11": 55,
+    "12": 30,
+    "13": 19,
+    "14": 2,
+    "15": 20,
+    "16": 1,
+    "18": 1,
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+    "20": 19,
+    "21": 3,
+    "22": 41,
+    "23": 702,
+    "24": 13436,
+    "4": 2200,
+    "6": 22,
+    "7": 7,
+    "9": 4
+  },
+  "saved_literal_banks": 2795,
+  "scope": "Exact chart and role census, residual conjugacy, complete bank tiling, and finite selector charge. Full physical word, global columns, and pricing checked separately.",
+  "selector_charge": 626937159600,
+  "status": "PASS_GENERIC_EXACT_CHARTS_ACTUAL_BANK_ALLOCATION"
+}
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json b/research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json
new file mode 100644
index 0000000000..62d9a2d201
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json
@@ -0,0 +1,102 @@
+{
+  "bank_completion_required": true,
+  "baseline": {
+    "bootstrap_chain": [
+      "384599/10000000000",
+      "2775074877778189216668764722271/3906250000000000000000000000000000",
+      "173558804364146204827867868073291755898188480567/244140625000000000000000000000000000000000000000000",
+      "10847430454511196133215997344324346922256120566358658714942852559/15258789062500000000000000000000000000000000000000000000000000000000"
+    ],
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+    "coarse": "44431075156777/62500000000000000",
+    "coarse_decimal": 0.000710897202508432,
+    "deficit": 35200,
+    "histogram": {
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+    },
+    "kappa": "88799023305857/125000000000000000",
+    "kappa_decimal": 0.000710392186446856,
+    "moment_upper": "134799733335753198920057674536459842752067240396968383888154222763697620174862270833/134799733335753198973335075435098153368185722112702862405518051246080000000000000000",
+    "next_coarse_moment_lower": "26959946667150639848053762927394145538139961908949413445925020018093510574823910013/26959946667150639794667015087019630673637144422540572481103610249216000000000000000",
+    "next_kappa_rejected": 1,
+    "ordinary_bit": "10847430454511196133215997344324346922256120566358658714942852559/15258789062500000000000000000000000000000000000000000000000000000000",
+    "positive_constraints": 47,
+    "rank_mass": 20830760,
+    "stock": 173883
+  },
+  "cohort_candidate": {
+    "bootstrap_chain": [
+      "384599/10000000000",
+      "711430743397955676522945935285759/1000000000000000000000000000000000000",
+      "711909838191882313741863693279570316744243449827711/1000000000000000000000000000000000000000000000000000000",
+      "711910179264343059080961789089783605966884312180809963542327911793919/1000000000000000000000000000000000000000000000000000000000000000000000000"
+    ],
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+    "coarse": "711910179507329/1000000000000000000",
+    "coarse_decimal": 0.000711910179507329,
+    "deficit": 35200,
+    "histogram": {
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+      "50": 28160,
+      "6": 61200,
+      "7": 49040,
+      "8": 25360,
+      "9": 25800
+    },
+    "kappa": "177850930927433/250000000000000000",
+    "kappa_decimal": 0.000711403723709732,
+    "moment_upper": "134799733335753198753192885375660456220983058432540502946205712451439733564402750601/134799733335753198973335075435098153368185722112702862405518051246080000000000000000",
+    "next_coarse_moment_lower": "26959946667150639814796264323470635893891546575600803563574056326881021612395769383/26959946667150639794667015087019630673637144422540572481103610249216000000000000000",
+    "next_kappa_rejected": 1,
+    "ordinary_bit": "711910179264343059080961789089783605966884312180809963542327911793919/1000000000000000000000000000000000000000000000000000000000000000000000000",
+    "positive_constraints": 47,
+    "rank_mass": 20763680,
+    "stock": 173324
+  },
+  "finite_bill_and_all_size_interfaces_not_reproved": true,
+  "method": "C++ exact rational 224-bit directed bounds; floating used only to propose a bracket verified exactly;32-degree exponential and48-term atanh logarithm",
+  "status": "PASS_EXACT_COHORT_CONDITIONAL_PRICING_47_AND_ADJACENT_CONTROLS"
+}
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json b/research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json
new file mode 100644
index 0000000000..e3383fae0b
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json
@@ -0,0 +1,72 @@
+{
+  "external_complex_row_coefficient": 20161,
+  "extra_selector_calls": "626937159600",
+  "full_counted_primitive_coefficient": "62757760533419801",
+  "global_unit_expanded_additions": "148166200",
+  "global_weighted_additions": "147638200",
+  "internal_row_coefficient": 14401,
+  "linear_moment_slack": "85937499553357/50778515625000000",
+  "literal_deficit": 176000,
+  "literal_histogram": {
+    "1": "8644600",
+    "10": "153800",
+    "11": "86000",
+    "12": "302800",
+    "13": "116600",
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+    "19": "64600",
+    "2": "3780200",
+    "20": "271600",
+    "21": "1117800",
+    "22": "268800",
+    "23": "140800",
+    "3": "1938400",
+    "4": "742800",
+    "46": "140800",
+    "5": "480400",
+    "50": "140800",
+    "6": "306000",
+    "7": "245200",
+    "8": "126800",
+    "9": "129000"
+  },
+  "literal_rank_mass": "103818400",
+  "literal_stock": 866620,
+  "new_chart_factor_max": 200,
+  "normalized_stock": 173324,
+  "normalizer_factor_bound": 787,
+  "ordinary_cutoffs": [
+    {
+      "counted_coefficient_cutoff_log2": "156617764225196",
+      "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
+      "minimum_gap": "479436109373323477054064714241/1000000000000000000000000000000000000",
+      "stage": 1
+    },
+    {
+      "counted_coefficient_cutoff_log2": "309022864676337192015",
+      "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
+      "minimum_gap": "341315446686258136306720429683255756550172289/1000000000000000000000000000000000000000000000000000000",
+      "stage": 2
+    },
+    {
+      "counted_coefficient_cutoff_log2": "609733712936038839832196057",
+      "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
+      "minimum_gap": "242985940919038210910216394033115687819190036457672088206081/1000000000000000000000000000000000000000000000000000000000000000000000000",
+      "stage": 3
+    }
+  ],
+  "payload_bits": 98,
+  "payload_signed_prefix_upper": "313775842895942661197234728704",
+  "physical_replicas": 40,
+  "positive_rank_children": "19850800",
+  "primitive_coefficient_bits": 56,
+  "route_families": "8324400",
+  "scope": "Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted.",
+  "simultaneous_extra_work_streams": 1,
+  "status": "PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS",
+  "strict_moment_slack": "220142190059437697147202663680162359459312338794640266435597249399/134799733335753198973335075435098153368185722112702862405518051246080000000000000000"
+}
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json b/research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json
new file mode 100644
index 0000000000..2ce20dca62
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json
@@ -0,0 +1,182 @@
+{
+  "bridge_additions": 10560,
+  "copied_center_original_source_immutable": true,
+  "five_stage_additions": 3680395,
+  "formal_columns_checked": 23627,
+  "fresh_center_copies": 120,
+  "global_live_registers": 23627,
+  "independent_dirty_registers": 16587,
+  "local_odd_scalar_additions": 736079,
+  "local_raw_H": [
+    [
+      1,
+      43223
+    ],
+    [
+      2,
+      18901
+    ],
+    [
+      3,
+      9692
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+      3010
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+      1226
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+    [
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+      634
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+    [
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+      645
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+    [
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+      769
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+    [
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+      430
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+      1514
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+    [
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+      583
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+    [
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+      1067
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+    [
+      15,
+      241
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+    [
+      16,
+      1000
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+    [
+      17,
+      470
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+    [
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+      487
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+    [
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+      323
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+    [
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+    [
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+      5589
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+    [
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+  "local_registers": 20107,
+  "local_scalar_additions": 736079,
+  "negative_controls": [
+    {
+      "omit_bridge": 0,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 1,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 2,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 3,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 4,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 5,
+      "rejected": true
+    }
+  ],
+  "new_Q_categories": [
+    28,
+    29
+  ],
+  "payload_prefix_bits": 98,
+  "payload_prefix_upper": "313775842895942661197234728704",
+  "reverse_fresh_center_copies": 48,
+  "scope": "All 23627 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.",
+  "signed_lift_prefix": [
+    {
+      "bits": 17,
+      "cancellation_free_signed_row_l1_upper": "74391",
+      "reverse": false
+    },
+    {
+      "bits": 22,
+      "cancellation_free_signed_row_l1_upper": "3450954",
+      "reverse": 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.",
+  "stages": [
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 736079,
+      "signed_inverse": false,
+      "stage": 0
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 736079,
+      "signed_inverse": true,
+      "stage": 1
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 736079,
+      "signed_inverse": false,
+      "stage": 2
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 736079,
+      "signed_inverse": true,
+      "stage": 3
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 736079,
+      "signed_inverse": false,
+      "stage": 4
+    }
+  ],
+  "status": "PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL"
+}
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json b/research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json
new file mode 100644
index 0000000000..0ff70c74ba
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json
@@ -0,0 +1,62 @@
+{
+  "added_Q_Qinverse_passes": 2208,
+  "bank_completion_not_replayed": true,
+  "cut_record": 727593,
+  "delta": {
+    "1": 1811,
+    "10": -4,
+    "11": -15,
+    "12": -11,
+    "13": 21,
+    "14": -13,
+    "15": -46,
+    "17": -34,
+    "19": -8,
+    "2": -184,
+    "3": -542,
+    "4": 100,
+    "5": -82,
+    "6": 3,
+    "7": -26,
+    "8": 5,
+    "9": 34
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+  "forward_formal_columns": 20107,
+  "global_kappa_claimed": false,
+  "histogram": {
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+    "10": 769,
+    "11": 430,
+    "12": 1514,
+    "13": 583,
+    "14": 1067,
+    "15": 241,
+    "16": 1000,
+    "17": 470,
+    "18": 487,
+    "19": 323,
+    "2": 18901,
+    "20": 1358,
+    "21": 5589,
+    "22": 1344,
+    "3": 9692,
+    "4": 3010,
+    "5": 2402,
+    "6": 1530,
+    "7": 1226,
+    "8": 634,
+    "9": 645
+  },
+  "inverse_formal_columns": 20107,
+  "new_entrance_rank": 1677,
+  "new_gauges": 851,
+  "new_gram_audit_external": true,
+  "new_rank_mass": 432500,
+  "new_records": 835788,
+  "old_rank_mass": 434177,
+  "old_records": 885228,
+  "omitted_Q_nonzero_wrong_words": 32383,
+  "omitted_Qinverse_nonzero_wrong_words": 1052,
+  "removed_initial_reads": 52752,
+  "status": "PASS_FULL_CURRENT249_COHORT_REWRITE_F2_COLUMNS_AND_FRAMES"
+}
diff --git a/research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json b/research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json
new file mode 100644
index 0000000000..4cfbbcfa7b
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json
@@ -0,0 +1,110 @@
+{
+  "all_final_frames_pass": true,
+  "common_frame_ADDs": 736079,
+  "containment_pairs_checked": 82698,
+  "copies": 24,
+  "donor_intersections": 0,
+  "erasures": 24,
+  "max_inherited_integer_abs": 7,
+  "nested_MOVEs": 99661,
+  "new_frame_ids_collision": false,
+  "nondegeneracy_checked_by_separate_exact_bank_audit": true,
+  "old_max_frame_id": 150370,
+  "paid_histogram": [
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+    [
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+    [
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+      769
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+      430
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+    [
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+      1514
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+      583
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+    [
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+      1067
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+      241
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+    [
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+    [
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+      1344
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+  ],
+  "rank_mass": 432500,
+  "records": 835788,
+  "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.",
+  "selected_helpers": 1860,
+  "selected_pairs": 851,
+  "source_owner_intersections": 0,
+  "status": "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE"
+}
diff --git a/research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json b/research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json
new file mode 100644
index 0000000000..dcc4a47021
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json
@@ -0,0 +1,10 @@
+{
+  "cohorts": 851,
+  "distinct_cuts": 4,
+  "distinct_helpers": 1860,
+  "non_target_identity_bits": 35868385,
+  "nonzero_pivot_target_entries": 52788,
+  "scope": "Original pinned-word response at every cohort own cut; combined emitted-word checks remain separate.",
+  "status": "PASS_INDEPENDENT_MULTI_CUT_FULL_F2_KERNEL_AND_IDENTITY_COLUMNS",
+  "target_kernel_equalities": 1497760
+}
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diff --git a/research/multicut-kernel-condensation-851/inputs/SNAPSHOTS.json b/research/multicut-kernel-condensation-851/inputs/SNAPSHOTS.json
new file mode 100644
index 0000000000..35204388ca
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/inputs/SNAPSHOTS.json
@@ -0,0 +1,6 @@
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+  "249-DONOR-OWNERSHIP.json": "ab96904508a21ddd0c3d4d779974e5dcfdb1f19a3938ade647724cc317c3270b"
+}
diff --git a/research/multicut-kernel-condensation-851/inputs/candidates.json.gz b/research/multicut-kernel-condensation-851/inputs/candidates.json.gz
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diff --git a/research/multicut-kernel-condensation-851/requirements.txt b/research/multicut-kernel-condensation-851/requirements.txt
new file mode 100644
index 0000000000..1ca5fd0616
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/requirements.txt
@@ -0,0 +1 @@
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diff --git a/research/multicut-kernel-condensation-851/vendor/PR249-SOURCE-MANIFEST.json b/research/multicut-kernel-condensation-851/vendor/PR249-SOURCE-MANIFEST.json
new file mode 100644
index 0000000000..ffc0219425
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/vendor/PR249-SOURCE-MANIFEST.json
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+    "source527/targetagg/selection.json": "b7a4d5eb2a6d2f7df867f9be5af7da1d1aa99cfbd5214195967b0ff60642d77a",
+    "source527/targetagg/upstream_setup.py": "fd7adf0b12d0769e06438b2ee4322bfcb180d8f73a1104a3eb805ab88c5cc393",
+    "source527/word.py": "e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42",
+    "verify.py": "4fc103389c1c62bd0ea5b39f9d41128db30dde4475370394bab600a0acd52e9a"
+  }
+}
diff --git a/research/multicut-kernel-condensation-851/vendor/UPSTREAM-NOTICE.md b/research/multicut-kernel-condensation-851/vendor/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..a317749fa3
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/vendor/UPSTREAM-NOTICE.md
@@ -0,0 +1,13 @@
+# Attribution and licence
+
+Apache-2.0 applies. Original headers, licences, notices and AI assistance disclosures are preserved. `UPSTREAM-PR234-NOTICE.md` contains the complete inherited five-stage credits; the individual source roots retain their original notices. Credits do not imply review or endorsement.
+
+The five-stage architecture and finite interface package come from Henry Grant / hcg890's PR234. Rohan Arun's PR237 published the width-120 bank extension before this integration; no exclusive priority for that bank extension is claimed. The stage-private bank assignment and address adapter in this package were developed independently and are checked explicitly.
+
+The source527 construction builds on eumemic's PR210 source reuse and target transforms, sennemmi's PR230 operation-frame changes, Dugongue's PR216 and PR207, Rohan Arun's PR211, Chafik Boukhalfa's PR200, Evan McKinney's completed bank work, and their retained dependencies. The complex input preserves Jacob Sussman's published five-stage certificate and Avi Eisenberg / ikeboy's PR193 helper, with the original Claude assistance disclosures.
+
+The 31 new zero-response source aliases, 48 retained dirty-anchor paths, physical event tagging and source527 integration were prepared by eumemic with substantial OpenAI Codex assistance. All earlier contributor notices and assistance disclosures remain in the supplied source material.
+
+The parity-filtered common-frame retiming (PR244) and exact reconstruction were prepared by eumemic with substantial OpenAI Codex assistance. The 353 unborrowed pair mixes use their existing common delivery frames; source527 and all earlier construction credits remain retained.
+
+The twenty-one additional F2 gauge entrances, exact compensation transport, cloned producer/execution contexts and new completed-bank charts were prepared by eumemic with substantial OpenAI Codex assistance.
diff --git a/research/multicut-kernel-condensation-851/vendor/json.hpp b/research/multicut-kernel-condensation-851/vendor/json.hpp
new file mode 100644
index 0000000000..82d69f7c5d
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/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/multicut-kernel-condensation-851/vendor/pr249-source.zip b/research/multicut-kernel-condensation-851/vendor/pr249-source.zip
new file mode 100644
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diff --git a/research/multicut-kernel-condensation-851/verify.py b/research/multicut-kernel-condensation-851/verify.py
new file mode 100644
index 0000000000..e533d71b61
--- /dev/null
+++ b/research/multicut-kernel-condensation-851/verify.py
@@ -0,0 +1,125 @@
+#!/usr/bin/env python3
+"""Offline source-bound reproduction. No stored PASS result is accepted without execution."""
+from pathlib import Path, PurePosixPath
+import argparse, concurrent.futures, gzip, hashlib, json, os, subprocess, sys, time, zipfile
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+
+def load(p):
+    return json.loads(Path(p).read_text(encoding='utf-8'))
+
+def digest(p):
+    return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+
+def need(condition, message):
+    if not condition:
+        raise RuntimeError(message)
+
+def normalize(x):
+    if isinstance(x, dict):
+        return {k: normalize(v) for k, v in x.items() if k not in ('seconds', 'local_scalar_stream', 'containment_pairs_checked')}  # the last: a memo-cache miss counter, compiler-dependent (this package)
+    if isinstance(x, list):
+        return [normalize(v) for v in x]
+    return x
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--output', type=Path, required=True)
+    ap.add_argument('--cxx', default='g++')
+    ap.add_argument('--boost-include', type=Path)
+    ap.add_argument('--snapshots-only', action='store_true')
+    args = ap.parse_args()
+    need(sys.version_info >= (3, 11), 'Python 3.11+ required')
+    need(sys.byteorder == 'little', 'native six-int transcript requires little-endian host')
+    out = args.output.resolve()
+    need(out != HERE and HERE not in out.parents, 'output must be outside package')
+    need(not out.exists(), 'choose a fresh output directory')
+    manifest = load(HERE / 'MANIFEST.json')['files']
+    actual = {p.relative_to(HERE).as_posix() for p in HERE.rglob('*') if p.is_file() and p.name != 'MANIFEST.json'}
+    # Upstream manifest resides inside the archive, so there is only one outer manifest.
+    need(actual == set(manifest), 'unexpected or missing package file')
+    for name, expected in manifest.items():
+        need(digest(HERE / name) == expected, 'package hash mismatch: ' + name)
+    out.mkdir(parents=True)
+    for part in ('logs', 'bin', 'lead', 'compiler', 'review', 'temporal/CURRENT249-EXPORT', 'upstream'):
+        (out / part).mkdir(parents=True)
+    start = time.monotonic()
+    def run(label, cmd):
+        print(label, flush=True)
+        with (out / 'logs' / (label + '.log')).open('w', encoding='utf-8') as log:
+            result = subprocess.run([str(s) for s in cmd], cwd=out, stdout=log, stderr=subprocess.STDOUT)
+        need(result.returncode == 0, label + ' failed; inspect logs/' + label + '.log')
+    members = load(HERE / 'vendor/PR249-SOURCE-MANIFEST.json')['files']
+    with zipfile.ZipFile(HERE / 'vendor/pr249-source.zip') as z:
+        need(len(z.namelist()) == len(members) and set(z.namelist()) == set(members), 'source archive membership')
+        for info in z.infolist():
+            name = PurePosixPath(info.filename)
+            need(not name.is_absolute() and '..' not in name.parts and '\\' not in info.filename and ':' not in info.filename, 'unsafe source archive path')
+            data = z.read(info)
+            need(hashlib.sha256(data).hexdigest() == members[info.filename], 'upstream hash: ' + info.filename)
+            target = out / 'upstream' / info.filename
+            target.parent.mkdir(parents=True, exist_ok=True)
+            target.write_bytes(data)
+    upstream_manifest = load(out / 'upstream/MANIFEST.json')['files']
+    for name, h in upstream_manifest.items():
+        need(members.get(name) == h, 'upstream own manifest mismatch: ' + name)
+    X = out / 'temporal/CURRENT249-EXPORT'
+    snapshots = load(HERE / 'inputs/SNAPSHOTS.json')
+    for name, h in snapshots.items():
+        data = gzip.decompress((HERE / 'inputs' / (name + '.gz')).read_bytes())
+        need(hashlib.sha256(data).hexdigest() == h, 'snapshot hash: ' + name)
+        (X / name).write_bytes(data)
+    candidates = out / 'candidates.json'
+    candidates.write_bytes(gzip.decompress((HERE / 'inputs/candidates.json.gz').read_bytes()))
+    if not args.snapshots_only:
+        generated = out / 'regenerated'
+        run('01-regenerate-upstream', [sys.executable, HERE / 'code/export249.py', out / 'upstream', generated])
+        need(digest(generated / '249-records.bin') == snapshots['249-records.bin'], 'fresh baseline word mismatch')
+        for name in ('249-states.json', 'frames.json'):
+            need(normalize(load(generated / name)) == normalize(load(X / name)), 'fresh baseline structural mismatch: ' + name)
+        need(load(generated / 'REGENERATED-DONORS.json')['donor_keys'] == sorted(load(X / '249-DONOR-OWNERSHIP.json')['donor_keys']), 'fresh donor ownership mismatch')
+    sources = sorted((HERE / 'code').glob('*.cpp'))
+    need(len(sources) == 7, 'seven native checkers required')
+    extension = '.exe' if os.name == 'nt' else ''
+    def exe(name):
+        return out / 'bin' / (name + extension)
+    def compile_source(p):
+        cmd = [args.cxx, '-std=c++17', '-O2', '-I', HERE / 'vendor']
+        if args.boost_include:
+            cmd.extend(['-I', args.boost_include.resolve()])
+        cmd.extend([p, '-o', exe(p.stem)])
+        run('compile-' + p.stem, cmd)
+    # At most two compiler processes, with distinct output files.
+    with concurrent.futures.ThreadPoolExecutor(max_workers=2) as pool:
+        list(pool.map(compile_source, sources))
+    lead = out / 'lead'; compiler = out / 'compiler'; temporal = out / 'temporal'; review = out / 'review'
+    run('02-transform', [exe('cohort-transform'), X, candidates, lead])
+    result = load(HERE / 'RESULT.json')
+    need(digest(lead / 'COHORT249-RECORDS.bin') == result['new_record_sha256'], 'new physical transcript hash mismatch')
+    run('03-independent-legality', [exe('cohort-legality-independent'), X, lead, review / 'INDEPENDENT-LEGALITY.json'])
+    run('04-independent-prefix', [exe('cohort-prefix-independent'), X, lead, review / 'INDEPENDENT-PREFIX.json'])
+    run('05-bank-charts-and-assignment', [exe('cohort-bank-review'), X, lead / 'COHORT249-INITIAL.json', lead / 'COHORT249-FRAMES.json', compiler, 'actual_multicut'])
+    (compiler / 'BANK-REVIEW.json').rename(compiler / 'COHORT-BANK-REVIEW.json')
+    run('06-five-stage-columns', [exe('cohort-five-stage-columns'), lead / 'COHORT249-RECORDS.bin', temporal / 'COHORT-FIVE-STAGE-COLUMNS.json'])
+    run('07-exact-price', [exe('cohort-price'), lead / 'COHORT249-REPLAY.json', lead / 'COHORT-EXACT-PRICE.json'])
+    run('08-finite-invoice', [exe('cohort-finite-invoice'), lead / 'COHORT249-RECORDS.bin', lead / 'COHORT-EXACT-PRICE.json', compiler / 'COHORT-BANK-REVIEW.json', temporal / 'COHORT-FIVE-STAGE-COLUMNS.json', temporal / 'COHORT-FINITE-INVOICE.json'])
+    receipts = {}
+    for expected in sorted((HERE / 'expected').glob('*.json')):
+        matches = [p / expected.name for p in (lead, compiler, temporal, review) if (p / expected.name).is_file()]
+        need(len(matches) == 1, 'missing or ambiguous receipt: ' + expected.name)
+        got = normalize(load(matches[0])); wanted = normalize(load(expected))  # both sides normalized (this package)
+        need(got == wanted, 'fresh receipt differs: ' + expected.name)
+        receipts[expected.name] = got
+    cert = dict(status='PASS_ALL_SEVEN_NATIVE_CHECKERS_AND_PINNED_RECEIPTS',
+                kappa=result['kappa'], kappa_decimal=result['kappa_decimal'],
+                baseline_regenerated_from_source=not args.snapshots_only,
+                new_record_sha256=result['new_record_sha256'],
+                package_manifest_sha256=digest(HERE / 'MANIFEST.json'),
+                retained_public_all_size_interfaces=True, lean_certificate=False,
+                elapsed_seconds=time.monotonic()-start, receipts=receipts)
+    (out / 'CERTIFICATE.json').write_text(json.dumps(cert, indent=2)+'\n', encoding='utf-8')
+    print('PASS: kappa = ' + result['kappa_decimal'], flush=True)
+    print('Certificate: ' + str(out / 'CERTIFICATE.json'), flush=True)
+
+if __name__ == '__main__':
+    main()

From a2b02af47dbaf3d1c55e7586746c30e851b68102 Mon Sep 17 00:00:00 2001
From: chafreaky <chafik.boukhalfa@gmail.com>
Date: Sat, 10 Oct 2026 06:59:42 +0400
Subject: [PATCH 2/5] multicut-kernel-condensation-851: store the six checker
 sources with LF line endings (manifest hashes match the committed blobs)

---
 .../multicut-kernel-condensation-851/MANIFEST.json   | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/research/multicut-kernel-condensation-851/MANIFEST.json b/research/multicut-kernel-condensation-851/MANIFEST.json
index c7a7d1e744..7292205024 100644
--- a/research/multicut-kernel-condensation-851/MANIFEST.json
+++ b/research/multicut-kernel-condensation-851/MANIFEST.json
@@ -12,12 +12,12 @@
     "README.md": "77d349dfc75f9f4a4a7540373845941d55684874853ad25104ce8f352122ab67",
     "RESULT.json": "1d3c65b05de9b3b30a342dd91f3b717b56f84060d80b161a73d5d162ccfaecfb",
     "REVIEW.md": "823eea4cacf586ca90e43146fac48143f129f6ff8ca71c6a03b88c29fc528ff9",
-    "code/cohort-bank-review.cpp": "b4e484838f870274c617a47a459f348f54cebff617a089d7ef9065e8d2e96ac2",
-    "code/cohort-finite-invoice.cpp": "d26bab7b04384b08ad9b5bc18dd5ffc00d235a46f1bfdd3531f4231adc226719",
-    "code/cohort-five-stage-columns.cpp": "b7026fdd9c248420dfaf4beca9b616161efc7f471d894a8104552ef035fe7761",
-    "code/cohort-legality-independent.cpp": "5acdc6849ba294637807b0b1528c97a60c48b2c3d9927bb2d2600ff13bf0d425",
-    "code/cohort-prefix-independent.cpp": "30e74b9bad964d0f1024986f2f4b2866667b599a85d0c216089fb7dedc877e4c",
-    "code/cohort-price.cpp": "413eeea0bee07785d2926bbe46bdc04b3b1b527ef7951b5f120fc0447972c2cb",
+    "code/cohort-bank-review.cpp": "cdac6b0460b7d70b40b1a15e1e255995d7c86220b4498005319d971313bb2d81",
+    "code/cohort-finite-invoice.cpp": "dc0761a15c9b43ebdff3921dd2a49c80bb9158f544fb662ad45880a763cb5ab9",
+    "code/cohort-five-stage-columns.cpp": "cf9657e2407264120673f34659df79362dc132886d6e62dda96e44d085b61ed1",
+    "code/cohort-legality-independent.cpp": "4230ce06b6563f1902e9d6f6698dfffa4d31fe13a31b5cb7edb9a811f865bb53",
+    "code/cohort-prefix-independent.cpp": "81ea649c6bc8db9efead5330a49553b501a79114f0dd4d12a799adbe830b354d",
+    "code/cohort-price.cpp": "885424440ff82a145817f04ec6cf15e4117c4675ccac57b4e55a8fcf7823ec2a",
     "code/cohort-transform.cpp": "afd916d0f539ccdb09e8231eade3b3f6b3e83bbb8107641e134943aa2b25af32",
     "code/export249.py": "6c9aedb8fb4f2d560aca6cfc32ec967e003c0e623cc345040f108101ec1b442f",
     "discovery/README.md": "c1abffbfa8305d92fa50df1bec9ba2a98fb2d1eebb4bc7cf24ff750c18a43a06",

From b2b2a33dc95eb2d4ad9ddfade6bb9416ab9ec38e Mon Sep 17 00:00:00 2001
From: chafreaky <chafik.boukhalfa@gmail.com>
Date: Sat, 10 Oct 2026 07:09:45 +0400
Subject: [PATCH 3/5] multicut-kernel-condensation-883: second census adds 32
 families (883 pivots, entrance rank 1710), kappa = 7.11421336565136e-4;
 package renamed

---
 ...l => multicut-kernel-condensation-883.yml} |  16 +-
 .../RESULT.json                               |  12 --
 .../BANK-PROOF.md                             |   0
 .../COPY-PROOF.md                             |   0
 .../FINITE-PROOF.md                           |   0
 .../KERNEL-PROOF.md                           |   0
 .../LICENSE                                   |   0
 .../MANIFEST.json                             |  28 ++--
 .../NOTICE.md                                 |   4 +-
 .../PROOF-PR259.md                            |   0
 .../PROOF.md                                  |  31 ++--
 .../README-PR259.md                           |   0
 .../README.md                                 |  43 +++---
 .../RESULT.json                               |  12 ++
 .../REVIEW.md                                 |   0
 .../code/cohort-bank-review.cpp               |   0
 .../code/cohort-finite-invoice.cpp            |   0
 .../code/cohort-five-stage-columns.cpp        |   0
 .../code/cohort-legality-independent.cpp      |   0
 .../code/cohort-prefix-independent.cpp        |   0
 .../code/cohort-price.cpp                     |   0
 .../code/cohort-transform.cpp                 |   0
 .../code/export249.py                         |   0
 .../discovery/README.md                       |  10 +-
 .../discovery/census2.py                      | 142 ++++++++++++++++++
 .../discovery/chrono2.py                      |   0
 .../discovery/compare259.py                   |   0
 .../discovery/gain.py                         |   0
 .../discovery/gen_candidates.py               |   0
 .../discovery/merge2.py                       |  21 +++
 .../discovery/merge259.py                     |   0
 .../discovery/twins.py                        |   0
 .../expected/COHORT-BANK-REVIEW.json          |  34 ++---
 .../expected/COHORT-EXACT-PRICE.json          |  36 ++---
 .../expected/COHORT-FINITE-INVOICE.json       |  44 +++---
 .../expected/COHORT-FIVE-STAGE-COLUMNS.json   |  32 ++--
 .../expected/COHORT249-REPLAY.json            |  36 ++---
 .../expected/INDEPENDENT-LEGALITY.json        |  24 +--
 .../expected/INDEPENDENT-PREFIX.json          |  10 +-
 .../inputs/249-DONOR-OWNERSHIP.json.gz        | Bin
 .../inputs/249-records.bin.gz                 | Bin
 .../inputs/249-states.json.gz                 | Bin
 .../inputs/SNAPSHOTS.json                     |   0
 .../inputs/candidates.json.gz                 | Bin 55880 -> 56771 bytes
 .../inputs/frames.json.gz                     | Bin
 .../requirements.txt                          |   0
 .../vendor/PR249-SOURCE-MANIFEST.json         |   0
 .../vendor/UPSTREAM-NOTICE.md                 |   0
 .../vendor/json.hpp                           |   0
 .../vendor/pr249-source.zip                   | Bin
 .../verify.py                                 |   0
 51 files changed, 359 insertions(+), 176 deletions(-)
 rename .github/workflows/{multicut-kernel-condensation-851.yml => multicut-kernel-condensation-883.yml} (61%)
 delete mode 100644 research/multicut-kernel-condensation-851/RESULT.json
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/BANK-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/COPY-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/FINITE-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/KERNEL-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/LICENSE (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/MANIFEST.json (68%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/NOTICE.md (93%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/PROOF-PR259.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/PROOF.md (65%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/README-PR259.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/README.md (61%)
 create mode 100644 research/multicut-kernel-condensation-883/RESULT.json
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/REVIEW.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-bank-review.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-finite-invoice.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-five-stage-columns.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-legality-independent.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-prefix-independent.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-price.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/cohort-transform.cpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/code/export249.py (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/README.md (71%)
 create mode 100644 research/multicut-kernel-condensation-883/discovery/census2.py
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/chrono2.py (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/compare259.py (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/gain.py (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/gen_candidates.py (100%)
 create mode 100644 research/multicut-kernel-condensation-883/discovery/merge2.py
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/merge259.py (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/discovery/twins.py (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/COHORT-BANK-REVIEW.json (93%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/COHORT-EXACT-PRICE.json (73%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/COHORT-FINITE-INVOICE.json (59%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/COHORT-FIVE-STAGE-COLUMNS.json (84%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/COHORT249-REPLAY.json (66%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/INDEPENDENT-LEGALITY.json (83%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/expected/INDEPENDENT-PREFIX.json (57%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/inputs/249-DONOR-OWNERSHIP.json.gz (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/inputs/249-records.bin.gz (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/inputs/249-states.json.gz (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/inputs/SNAPSHOTS.json (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/inputs/candidates.json.gz (51%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/inputs/frames.json.gz (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/requirements.txt (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/vendor/PR249-SOURCE-MANIFEST.json (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/vendor/UPSTREAM-NOTICE.md (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/vendor/json.hpp (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/vendor/pr249-source.zip (100%)
 rename research/{multicut-kernel-condensation-851 => multicut-kernel-condensation-883}/verify.py (100%)

diff --git a/.github/workflows/multicut-kernel-condensation-851.yml b/.github/workflows/multicut-kernel-condensation-883.yml
similarity index 61%
rename from .github/workflows/multicut-kernel-condensation-851.yml
rename to .github/workflows/multicut-kernel-condensation-883.yml
index 243d9be476..a4dbf8b6a8 100644
--- a/.github/workflows/multicut-kernel-condensation-851.yml
+++ b/.github/workflows/multicut-kernel-condensation-883.yml
@@ -1,14 +1,14 @@
-name: multicut-kernel-condensation-851
+name: multicut-kernel-condensation-883
 
 on:
   pull_request:
     paths:
-      - 'research/multicut-kernel-condensation-851/**'
-      - '.github/workflows/multicut-kernel-condensation-851.yml'
+      - 'research/multicut-kernel-condensation-883/**'
+      - '.github/workflows/multicut-kernel-condensation-883.yml'
   push:
     paths:
-      - 'research/multicut-kernel-condensation-851/**'
-      - '.github/workflows/multicut-kernel-condensation-851.yml'
+      - 'research/multicut-kernel-condensation-883/**'
+      - '.github/workflows/multicut-kernel-condensation-883.yml'
 
 jobs:
   verify:
@@ -25,8 +25,8 @@ jobs:
       - name: Install the native toolchain of PR 259's checkers
         run: sudo apt-get update && sudo apt-get install -y g++ libboost-dev
       - name: Install SymPy for the pinned upstream regeneration
-        run: python -m pip install -r research/multicut-kernel-condensation-851/requirements.txt
-      - name: Regenerate PR 249's word, compile and run the seven checkers on the 851-pivot selection, compare receipts and price
-        run: python3 -I research/multicut-kernel-condensation-851/verify.py --output /tmp/mc851-replay
+        run: python -m pip install -r research/multicut-kernel-condensation-883/requirements.txt
+      - name: Regenerate PR 249's word, compile and run the seven checkers on the 883-pivot selection, compare receipts and price
+        run: python3 -I research/multicut-kernel-condensation-883/verify.py --output /tmp/mc883-replay
       - name: Require an unchanged tree
         run: git diff --exit-code
diff --git a/research/multicut-kernel-condensation-851/RESULT.json b/research/multicut-kernel-condensation-851/RESULT.json
deleted file mode 100644
index 6c193d6428..0000000000
--- a/research/multicut-kernel-condensation-851/RESULT.json
+++ /dev/null
@@ -1,12 +0,0 @@
-{
-  "kappa": "177850930927433/250000000000000000",
-  "kappa_decimal": "0.000711403723709732",
-  "baseline_head": "96495746c786d6d0339dbb38c7f553d4af3f88ed",
-  "baseline_kappa": "0.000710392186446856",
-  "previous_delivery_kappa": "0.000711029386054035",
-  "new_record_sha256": "3c528fffae62508b2062b7251deabb5e2b23b80a044295cbb4cb7392abf3be28",
-  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES",
-  "lean_certificate": false,
-  "pivots": 851,
-  "entrance_rank": 1677
-}
diff --git a/research/multicut-kernel-condensation-851/BANK-PROOF.md b/research/multicut-kernel-condensation-883/BANK-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/BANK-PROOF.md
rename to research/multicut-kernel-condensation-883/BANK-PROOF.md
diff --git a/research/multicut-kernel-condensation-851/COPY-PROOF.md b/research/multicut-kernel-condensation-883/COPY-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/COPY-PROOF.md
rename to research/multicut-kernel-condensation-883/COPY-PROOF.md
diff --git a/research/multicut-kernel-condensation-851/FINITE-PROOF.md b/research/multicut-kernel-condensation-883/FINITE-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/FINITE-PROOF.md
rename to research/multicut-kernel-condensation-883/FINITE-PROOF.md
diff --git a/research/multicut-kernel-condensation-851/KERNEL-PROOF.md b/research/multicut-kernel-condensation-883/KERNEL-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/KERNEL-PROOF.md
rename to research/multicut-kernel-condensation-883/KERNEL-PROOF.md
diff --git a/research/multicut-kernel-condensation-851/LICENSE b/research/multicut-kernel-condensation-883/LICENSE
similarity index 100%
rename from research/multicut-kernel-condensation-851/LICENSE
rename to research/multicut-kernel-condensation-883/LICENSE
diff --git a/research/multicut-kernel-condensation-851/MANIFEST.json b/research/multicut-kernel-condensation-883/MANIFEST.json
similarity index 68%
rename from research/multicut-kernel-condensation-851/MANIFEST.json
rename to research/multicut-kernel-condensation-883/MANIFEST.json
index 7292205024..6f881e6efe 100644
--- a/research/multicut-kernel-condensation-851/MANIFEST.json
+++ b/research/multicut-kernel-condensation-883/MANIFEST.json
@@ -5,12 +5,12 @@
     "FINITE-PROOF.md": "dd0e1ac3a212f484086d51454ebcf951ccb98eddfe4713310f688750d35d0069",
     "KERNEL-PROOF.md": "4779181f679925da5c6663d4c5aec1a4a0aef76c993ab14b3a82782ac16bb883",
     "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
-    "NOTICE.md": "944023bd4a3d91929facb0c0aa350a8f1c4ce0f758285329a46f85f12f56a14e",
+    "NOTICE.md": "58f73a4bf8c08caea6e5039c878b889ba6cf871a8c5365ee0cab2cd935370cdb",
     "PROOF-PR259.md": "ffc502078acdfee7a89abe3ec51fae4b8c5a8be7440d6b55f3e24f138e1b1a3b",
-    "PROOF.md": "25a94a4b51f60a92da537a8ee571b7f5b28b5d259010883a93e90c36f067869e",
+    "PROOF.md": "1019d2e57b0179cf0f38ea0f4488f3ecc2877b8d5ff4b432a8a024712fd979a6",
     "README-PR259.md": "ed2f4f051a21af9c173c0a7af7cac440ce15cabdabfc721895edde2c837cce25",
-    "README.md": "77d349dfc75f9f4a4a7540373845941d55684874853ad25104ce8f352122ab67",
-    "RESULT.json": "1d3c65b05de9b3b30a342dd91f3b717b56f84060d80b161a73d5d162ccfaecfb",
+    "README.md": "e826dbd919a91f7442138c919242537414d9a3dec40a5b3906f42157dff77368",
+    "RESULT.json": "42cae2c7d9cb8006fa88ebee459f2f025e2fe92f9c4380590fe6d942f3965350",
     "REVIEW.md": "823eea4cacf586ca90e43146fac48143f129f6ff8ca71c6a03b88c29fc528ff9",
     "code/cohort-bank-review.cpp": "cdac6b0460b7d70b40b1a15e1e255995d7c86220b4498005319d971313bb2d81",
     "code/cohort-finite-invoice.cpp": "dc0761a15c9b43ebdff3921dd2a49c80bb9158f544fb662ad45880a763cb5ab9",
@@ -20,25 +20,27 @@
     "code/cohort-price.cpp": "885424440ff82a145817f04ec6cf15e4117c4675ccac57b4e55a8fcf7823ec2a",
     "code/cohort-transform.cpp": "afd916d0f539ccdb09e8231eade3b3f6b3e83bbb8107641e134943aa2b25af32",
     "code/export249.py": "6c9aedb8fb4f2d560aca6cfc32ec967e003c0e623cc345040f108101ec1b442f",
-    "discovery/README.md": "c1abffbfa8305d92fa50df1bec9ba2a98fb2d1eebb4bc7cf24ff750c18a43a06",
+    "discovery/README.md": "841e342558c4d6dd2d7e2c9ff363a2f5c6fea307a3c9547add1c51ce4d6fc885",
+    "discovery/census2.py": "cea6fa83fa6f85dc0895bfcd9804c4a7b5c8bc06c0642e2c0321943b1b497121",
     "discovery/chrono2.py": "fc2866441540a8d6fa887439f185d0f51f298e1411eecb5ad84aba0de83b5b82",
     "discovery/compare259.py": "4c6d08cfb64891a804db677c15baf172d297109d9526d0c9d3764bd26a2dfa8f",
     "discovery/gain.py": "b76253949941854bcfd1ff84ebb49b9eaa9fcf4784690295f4a9e773694ddcfd",
     "discovery/gen_candidates.py": "6d7136a9c1c86463b1c25405481422ed98f6517d10aa1e99a038fccb6930d688",
+    "discovery/merge2.py": "cb7d72dc5f8431628281cbd3fb17562d75b3242b882c19cc85cd30ee27617cf1",
     "discovery/merge259.py": "aba72c3e48314e842c06681fd62bb90e2a1f2a5dcb39794b1e22f54a6b74b850",
     "discovery/twins.py": "c5b3f2065081002aa8da22584724938338fa46da2e25f3221225803e0f1b0ef7",
-    "expected/COHORT-BANK-REVIEW.json": "dc6036d79b46c221e3268cdc7b9098020af7cf3ab3aca4f0037abcf3081c19f4",
-    "expected/COHORT-EXACT-PRICE.json": "85e36da37abd9bfe4141765a24409b0ceb2de2919450a90accd01d25fe8e0c98",
-    "expected/COHORT-FINITE-INVOICE.json": "d0cf4da0808360edc1de23144104fa35dfb7faf9a2d73cbc0ebdc87804bd4fe5",
-    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "08c8e714a9967910fa1c301bf7321ebbda504921be1e0d939fc4b287dc69697e",
-    "expected/COHORT249-REPLAY.json": "01feb9aee4e1cf6dc3437a67fedf7fe7e30ebe8bc8aac9f07268d2cbc7df5bd5",
-    "expected/INDEPENDENT-LEGALITY.json": "7c3e1b236e98e07faaab09cddbab8953ef21a2f0c40c9c2262de96aa2dbd7ffc",
-    "expected/INDEPENDENT-PREFIX.json": "440c93b85db62273a274998f85ca387343c0f0ab80c0e7a84063f635b5f431f4",
+    "expected/COHORT-BANK-REVIEW.json": "d77a4e1ed4ff3b50ea571213647fc60f349098a6b622e2010d09506128d057c6",
+    "expected/COHORT-EXACT-PRICE.json": "d8dc26a131b0eaa44df428b4db857db906d53051c94be66c43256a3b228fcd69",
+    "expected/COHORT-FINITE-INVOICE.json": "e2b30f56170f4260cf45e29fe60bdf148cc3bf47eda4b4289ca6b7efc7156f2c",
+    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "cdd8c42b512755a1c8776709fd6993c9c683c51ff61ec1968c7d613a94f89bb6",
+    "expected/COHORT249-REPLAY.json": "fbd72aa9ba17e254cc2cc51463f738a63d283add669c5b87c501aba7a9d6cc65",
+    "expected/INDEPENDENT-LEGALITY.json": "0871f37a0b4ac6e6d5588761a5d29c84e7a7fd79c32ce331d48441fce140fd64",
+    "expected/INDEPENDENT-PREFIX.json": "828899404ce3a4daf9d9d3562b395d1e0ac81afd17ae35abab3cebbe40342567",
     "inputs/249-DONOR-OWNERSHIP.json.gz": "cd506a4bbefbc33fecfca3b0364e0b237ece493a96ef3085c39cf2465f2265d4",
     "inputs/249-records.bin.gz": "6bc404d4af63218e714683d3e33fc1a53941e0155493747c3d0fb41b4a2de7b2",
     "inputs/249-states.json.gz": "562bcd7de03bf9474ad8c5cbc50008c92b02bfad81e32c2e532ebd45f384e844",
     "inputs/SNAPSHOTS.json": "3939f432a95db64073584e61a47e4983070450929ea1986c86a56552c0b03721",
-    "inputs/candidates.json.gz": "6d2f4eeb8a0a041e7c5b7354f12106999980362550cae7a1602c67cfccad919c",
+    "inputs/candidates.json.gz": "a6fad5e0ea650c4ec48035bedfc07c55f8b70ee4eafac37c6141ba368cd98f4a",
     "inputs/frames.json.gz": "54678a046e1c86b4d9308f69ef6d572a3b3745229e0ecb73843db7889e487cce",
     "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
     "vendor/PR249-SOURCE-MANIFEST.json": "f68fa82180cd352421b8bc3f7a5c89d51bde74e74cd8d62c222c28b0f23fcf31",
diff --git a/research/multicut-kernel-condensation-851/NOTICE.md b/research/multicut-kernel-condensation-883/NOTICE.md
similarity index 93%
rename from research/multicut-kernel-condensation-851/NOTICE.md
rename to research/multicut-kernel-condensation-883/NOTICE.md
index 3e024e7837..34b55db332 100644
--- a/research/multicut-kernel-condensation-851/NOTICE.md
+++ b/research/multicut-kernel-condensation-883/NOTICE.md
@@ -3,8 +3,8 @@
 Prepared by Chafik Boukhalfa with substantial Anthropic Claude assistance. Apache-2.0.
 This package claims no exclusive priority over concurrent work.
 
-What this package contributes: the census of twin dirty helpers at PR #259's earliest cut, the 333 added
-response-kernel pairs (`inputs/candidates.json.gz`, entries with round "union-early-cut"), the regenerated
+What this package contributes: the census of twin dirty helpers at PR #259's earliest cut, the 365 added
+response-kernel families (`inputs/candidates.json.gz`, entries with round "union-early-cut" and "headroom-2"), the regenerated
 receipts, and the discovery scripts in `discovery/`. Everything else is PR #259's package, retained byte for
 byte except the frozen selection, the receipts, RESULT.json, MANIFEST.json, one field name added to the
 platform-dependent list of verify.py, and these notes:
diff --git a/research/multicut-kernel-condensation-851/PROOF-PR259.md b/research/multicut-kernel-condensation-883/PROOF-PR259.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/PROOF-PR259.md
rename to research/multicut-kernel-condensation-883/PROOF-PR259.md
diff --git a/research/multicut-kernel-condensation-851/PROOF.md b/research/multicut-kernel-condensation-883/PROOF.md
similarity index 65%
rename from research/multicut-kernel-condensation-851/PROOF.md
rename to research/multicut-kernel-condensation-883/PROOF.md
index 5b4b1a0277..43dceebc34 100644
--- a/research/multicut-kernel-condensation-851/PROOF.md
+++ b/research/multicut-kernel-condensation-883/PROOF.md
@@ -1,8 +1,8 @@
-# The early cut carries 333 more response-kernel pairs
+# The early cut carries 365 more response-kernel families
 
-**Claim.** On PR #249's bit word (commit `96495746`), PR #259's multi-cut kernel condensation extended by 333
+**Claim.** On PR #249's bit word (commit `96495746`), PR #259's multi-cut kernel condensation extended by 365
 twin-pair rewrites at its earliest cut (record 676,559) is a legal word of the same model with literal bank stock
-866,620 and κ = 177850930927433/(25·10¹⁶) = 7.11403723709732·10⁻⁴, checked by PR #259's seven native checkers
+866,565 and κ = 44463833535321/(625·10¹⁴) = 7.11421336565136·10⁻⁴, checked by PR #259's seven native checkers
 and priced by its exact pricer, under the retained public all-size hypotheses of PR #249/#254/#259.
 
 ## 1. The mechanism (PR #254/#259, unchanged)
@@ -31,6 +31,16 @@ with Gram 36) for the (2, 2) pairs and ±1-four lines for the others. Each is a
 `basis`, `dim = 1`, `E_dimension = 1`, `cut = 676559`, `first_frames`, `kind`, `round = "union-early-cut"`)
 after PR #259's 518 items, which are unchanged.
 
+Second round. Among the 12,427 clean helpers not used by the 851 families, the response classes at twelve cuts from
+676,559 to 727,593 (every class of any size, pairs and XOR triples R_c = R_a ⊕ R_b, entrance a nondegenerate line or
+the full intersection when its Gram is nondegenerate) contain 64 net-positive pair candidates and no net-positive
+triple (a partner costs φ(1) + φ(r − 1) − φ(r) > 0, so only the pivot gains); a greedy packing by gain keeps 32
+disjoint families, all at cut 676,559: 28 pairs (3, 3) with e = 1, two (3, 6), one (3, 5) with e = 1 and one (3, 5)
+entering on its full two-dimensional intersection (e = 2), entrance rank 33, so the total 1,710 is ≡ 0 mod 3 with
+no drop (`round = "headroom-2"`). The later cuts add nothing: at 680,080 and 700,582 the candidate set is the same,
+from 705,000 on it shrinks to nothing. After these 32 no net-positive pair or triple remains among unused helpers at
+any cut, so this lever is exhausted on this word under the φ ledger.
+
 Why they pay: with the deficit pinned at 35,200 per replica (120·W − mass is invariant under the rewrite, because
 the pivot's residual 24 → 23 shrinks the bank capacity by exactly the mass saved), the coarse exponent is driven by
 the log-weighted mass Σ r·n·ln(120/r); a pair with first ranks (r_a, r_b) and e = 1 changes it by
@@ -41,12 +51,12 @@ PR #259's exact pricer confirms the sign and the size on the whole selection.
 
 | checker | receipt |
 |---|---|
-| `cohort-transform` (all-column F₂ replay) | 851 pivots, entrance rank 1,677, 52,752 initial reads removed, 2,208 gates, raw mass 434,177 → 432,500, 835,788 records; omitted-Q control 32,383 wrong columns, omitted-Q⁻¹ control 1,052 |
-| `cohort-legality-independent` | 1,860 selected helpers, 0 source-owner and 0 donor intersections, 736,079 common-frame ADDs, 99,661 nested MOVEs, 24 COPY/ERASE windows, all final frames |
-| `cohort-prefix-independent` | 4 cuts, 1,497,760 target-kernel equalities, 35,868,385 non-target identity bits |
-| `cohort-bank-review` | literal stock 866,620 (saved 2,795), 22 patterns, residual families 23: 702 and 24: 13,436 (others unchanged), 3,317,400 assignments, selector 626,937,159,600 |
+| `cohort-transform` (all-column F₂ replay) | 883 pivots, entrance rank 1,710, 59,192 initial reads removed, 2,272 gates, raw mass 434,177 → 432,467, 829,444 records; omitted-Q control 37,450 wrong columns, omitted-Q⁻¹ control 1,084 |
+| `cohort-legality-independent` | 1,924 selected helpers, 0 source-owner and 0 donor intersections, 729,703 common-frame ADDs, 99,693 nested MOVEs, 24 COPY/ERASE windows, all final frames |
+| `cohort-prefix-independent` | 4 cuts, 1,554,080 target-kernel equalities, 37,042,593 non-target identity bits |
+| `cohort-bank-review` | literal stock 866,565 (saved 2,850), residual families 23: 733, 22: 42 and 24: 13,404 (others unchanged), 3,317,400 assignments, 883 exact charts (at most 200 factors), selector 626,937,137,600 |
 | `cohort-five-stage-columns` | 23,627 columns, payload 98 bits |
-| `cohort-price` | coarse 711910179507329/10¹⁸, W 173,324, 3,970,160 calls, mass 20,763,680, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
+| `cohort-price` | coarse 711927817449537/10¹⁸, W 173,313, 3,971,440 calls, mass 20,762,360, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
 | `cohort-finite-invoice` | coefficient 56 bits, deficit 176,000, cutoffs positive |
 
 Control: PR #259's own selection through the same pipeline reproduces its κ exactly and six of its seven
@@ -66,5 +76,6 @@ changes; `discovery/` lists the diff.
 ## 4. Not claimed
 
 No Lean certificate; the public all-size compiler, chart, routing, prime-supply, precision and analytic interfaces
-of PR #249 are retained as hypotheses, as in PR #254/#259. The 24 size-nine response classes at this cut (96
-possible pairs) and 4 pairs with one helper already used by PR #259 are not exploited.
+of PR #249 are retained as hypotheses, as in PR #254/#259. The 4 pairs whose twin is a PR #259 helper have no
+other twin at any cut; PR #263's 25 frame retimings do not apply verbatim (18 of their registers are among the
+helpers used here, and their selection is bound to #259's transcript), and were not re-derived.
diff --git a/research/multicut-kernel-condensation-851/README-PR259.md b/research/multicut-kernel-condensation-883/README-PR259.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/README-PR259.md
rename to research/multicut-kernel-condensation-883/README-PR259.md
diff --git a/research/multicut-kernel-condensation-851/README.md b/research/multicut-kernel-condensation-883/README.md
similarity index 61%
rename from research/multicut-kernel-condensation-851/README.md
rename to research/multicut-kernel-condensation-883/README.md
index a88e59da1e..121919cd18 100644
--- a/research/multicut-kernel-condensation-851/README.md
+++ b/research/multicut-kernel-condensation-883/README.md
@@ -1,34 +1,39 @@
-# multicut-kernel-condensation-851
+# multicut-kernel-condensation-883
 
-**Conditional κ = 177850930927433 / 250000000000000000 = 7.11403723709732·10⁻⁴** (+0.0526% over PR #259's
-7.11029386054035·10⁻⁴; +0.0523% over PR #263's 7.11032238200698·10⁻⁴).
+**Conditional κ = 44463833535321 / 62500000000000000 = 7.11421336565136·10⁻⁴** (+0.0551% over PR #259's
+7.11029386054035·10⁻⁴; +0.0547% over PR #263's 7.11032238200698·10⁻⁴).
 
 PR #259 (Dugongue) condenses response kernels of the PR #249 bit word at four cuts with 518 pivot families. Its
 earliest cut, record 676,559 — the last initial compensation read — carries only 103 of them. A census of the
 twin dirty helpers at that cut (helpers untouched before it whose complete F₂ target responses coincide) finds
 985 twin pairs; 335 of them are disjoint from every helper PR #259 uses and have a nondegenerate rank-one common
 entrance line, and 333 of those (two dropped to keep the entrance rank ≡ 0 mod 3, as the transform requires at
-40 replicas) are net-positive under the fixed-deficit ledger. Added to PR #259's 518 families, verbatim, they give
+40 replicas) are net-positive under the fixed-deficit ledger. A second census among the helpers still unused after
+that round — every response class of any size at twelve cuts between 676,559 and 727,593, pairs and XOR triples —
+yields 32 more disjoint net-positive families (28 pairs with first frames (3, 3), two (3, 6), one (3, 5), and one
+(3, 5) pair entering on its full two-dimensional nondegenerate intersection), all at the same cut, and nothing at
+any later cut. Added to PR #259's 518 families, verbatim, the 365 give
 
 | | PR #259 | this package |
 |---|---|---|
-| pivot families / entrance rank | 518 / 1,344 | **851 / 1,677** |
-| initial compensation reads removed / basis gates paid | 27,772 / 1,542 | 52,752 / 2,208 |
-| raw rank mass per invocation | 434,177 → 432,833 | 434,177 → **432,500** |
-| literal bank stock / normalized | 867,175 / 173,435 | **866,620** / 173,324 |
-| κ | 7.11029386054035·10⁻⁴ | **7.11403723709732·10⁻⁴** |
+| pivot families / entrance rank | 518 / 1,344 | **883 / 1,710** |
+| initial compensation reads removed / basis gates paid | 27,772 / 1,542 | 59,192 / 2,272 |
+| raw rank mass per invocation | 434,177 → 432,833 | 434,177 → **432,467** |
+| literal bank stock / normalized | 867,175 / 173,435 | **866,565** / 173,313 |
+| κ | 7.11029386054035·10⁻⁴ | **7.11421336565136·10⁻⁴** |
 
-The 333 added entries use PR #259's own mechanism unchanged: the pivot starts at the common line E (its four
+The 365 added entries use PR #259's own mechanism unchanged: the pivot starts at the common line E (its four
 initial reads are deleted), the partner moves to E and absorbs the pivot there, and the inverse gate is paid at the
 full frame. 319 of them have first frames (2, 2) and a line u = eᵢ − eⱼ (norm 2, cleared Gram 18 for G = I − J/9),
 which PR #254's chart rule excluded (`norm == 4`) and PR #259's generic exact chart audit admits (prime
 exclusion {2, 3}, the same as the ±1-four lines); the remaining 14 are (3, 5), (3, 3) and (3, 6) pairs with ±1-four
-lines. **No checker, no C++ line and no proof note of PR #259 is changed**: the only inputs that differ are the
-frozen selection `inputs/candidates.json.gz` (PR #259's 518 items byte for byte, then the 333 new ones in its
-schema with `round = "union-early-cut"`) and the seven regenerated receipts in `expected/`; `RESULT.json` and
+lines; the 32 of the second round are (3, 3), (3, 5) and (3, 6) pairs with ±1-four lines (one with e = 2).
+**No checker and no proof note of PR #259 is changed, and no C++ line beyond one platform fix**: the only inputs that differ are the
+frozen selection `inputs/candidates.json.gz` (PR #259's 518 items byte for byte, then the 333 of the first round
+in its schema with `round = "union-early-cut"` and the 32 of the second with `round = "headroom-2"`) and the seven regenerated receipts in `expected/`; `RESULT.json` and
 `MANIFEST.json` follow. PR #259's seven native checkers pass on the new word (all-column F₂ replay forward and
 inverse with omitted-Q and omitted-Q⁻¹ controls; chronological legality with COPY/ERASE windows and source
-owners; 1,497,760 per-cut target-kernel equalities; 851 exact projector charts, 3,317,400 bank assignments; the
+owners; 1,497,760 per-cut target-kernel equalities; 883 exact projector charts, 3,317,400 bank assignments; the
 five-stage F₂ columns; the exact rational price with 47 outer constraints, adjacent grid rejected; the finite
 invoice). [PROOF.md](PROOF.md) states the delta; PR #259's own notes are kept unchanged as `README-PR259.md`,
 `PROOF-PR259.md`, `KERNEL-PROOF.md`, `BANK-PROOF.md`, `COPY-PROOF.md`, `FINITE-PROOF.md`, `REVIEW.md`.
@@ -41,19 +46,19 @@ jacobalansussman/wht-power-saving-lean#2), so the bit supplier still binds.
 ## Verify
 
     sudo apt-get install -y g++ libboost-dev            # Linux; macOS: brew install boost, --cxx clang++ with a bits/stdc++.h shim
-    python -m pip install -r research/multicut-kernel-condensation-851/requirements.txt    # sympy 1.14.0
-    python3 -I research/multicut-kernel-condensation-851/verify.py --output /tmp/mc851-replay    # fresh directory outside the package; about 70 s
+    python -m pip install -r research/multicut-kernel-condensation-883/requirements.txt    # sympy 1.14.0
+    python3 -I research/multicut-kernel-condensation-883/verify.py --output /tmp/mc883-replay    # fresh directory outside the package; about 70 s
 
 PR #259's verifier, unchanged: it checks every package hash against `MANIFEST.json`, regenerates the pinned PR #249
 word from `vendor/pr249-source.zip` (SymPy), compiles the seven checkers, emits the new word from the frozen
 selection, runs every check and compares each receipt with `expected/` (platform-independent fields only; see
-PROOF.md, "Receipts"), then prints `PASS: kappa = 0.000711403723709732`. `--snapshots-only` skips the upstream
-regeneration (about 20 s). `.github/workflows/multicut-kernel-condensation-851.yml` runs it on Ubuntu.
+PROOF.md, "Receipts"), then prints `PASS: kappa = 0.000711421336565136`. `--snapshots-only` skips the upstream
+regeneration (about 20 s). `.github/workflows/multicut-kernel-condensation-883.yml` runs it on Ubuntu.
 
 ## Files
 
 Everything of PR #259's package (`code/`, `inputs/`, `vendor/`, `expected/`, the proof notes, `verify.py`,
 `requirements.txt`, `LICENSE`) with the two input changes above; `discovery/` (the census, the comparison with
 PR #259's selection and the merge, not run by the verifier: `twins.py`, `chrono2.py`, `gain.py`,
-`gen_candidates.py`, `compare259.py`, `merge259.py`); `README.md`, `PROOF.md`, `NOTICE.md`, `RESULT.json`,
+`gen_candidates.py`, `compare259.py`, `merge259.py`, `census2.py`, `merge2.py`); `README.md`, `PROOF.md`, `NOTICE.md`, `RESULT.json`,
 `MANIFEST.json`.
diff --git a/research/multicut-kernel-condensation-883/RESULT.json b/research/multicut-kernel-condensation-883/RESULT.json
new file mode 100644
index 0000000000..82619991e9
--- /dev/null
+++ b/research/multicut-kernel-condensation-883/RESULT.json
@@ -0,0 +1,12 @@
+{
+  "kappa": "44463833535321/62500000000000000",
+  "kappa_decimal": "0.000711421336565136",
+  "baseline_head": "96495746c786d6d0339dbb38c7f553d4af3f88ed",
+  "baseline_kappa": "0.000710392186446856",
+  "previous_delivery_kappa": "0.000711403723709732",
+  "new_record_sha256": "16a3f01613c1dfdf52695732f8efbae790663905c34af95e69b2cb28cd354ecb",
+  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES",
+  "lean_certificate": false,
+  "pivots": 883,
+  "entrance_rank": 1710
+}
diff --git a/research/multicut-kernel-condensation-851/REVIEW.md b/research/multicut-kernel-condensation-883/REVIEW.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/REVIEW.md
rename to research/multicut-kernel-condensation-883/REVIEW.md
diff --git a/research/multicut-kernel-condensation-851/code/cohort-bank-review.cpp b/research/multicut-kernel-condensation-883/code/cohort-bank-review.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-bank-review.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-bank-review.cpp
diff --git a/research/multicut-kernel-condensation-851/code/cohort-finite-invoice.cpp b/research/multicut-kernel-condensation-883/code/cohort-finite-invoice.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-finite-invoice.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-finite-invoice.cpp
diff --git a/research/multicut-kernel-condensation-851/code/cohort-five-stage-columns.cpp b/research/multicut-kernel-condensation-883/code/cohort-five-stage-columns.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-five-stage-columns.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-five-stage-columns.cpp
diff --git a/research/multicut-kernel-condensation-851/code/cohort-legality-independent.cpp b/research/multicut-kernel-condensation-883/code/cohort-legality-independent.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-legality-independent.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-legality-independent.cpp
diff --git a/research/multicut-kernel-condensation-851/code/cohort-prefix-independent.cpp b/research/multicut-kernel-condensation-883/code/cohort-prefix-independent.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-prefix-independent.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-prefix-independent.cpp
diff --git a/research/multicut-kernel-condensation-851/code/cohort-price.cpp b/research/multicut-kernel-condensation-883/code/cohort-price.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-price.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-price.cpp
diff --git a/research/multicut-kernel-condensation-851/code/cohort-transform.cpp b/research/multicut-kernel-condensation-883/code/cohort-transform.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/cohort-transform.cpp
rename to research/multicut-kernel-condensation-883/code/cohort-transform.cpp
diff --git a/research/multicut-kernel-condensation-851/code/export249.py b/research/multicut-kernel-condensation-883/code/export249.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/code/export249.py
rename to research/multicut-kernel-condensation-883/code/export249.py
diff --git a/research/multicut-kernel-condensation-851/discovery/README.md b/research/multicut-kernel-condensation-883/discovery/README.md
similarity index 71%
rename from research/multicut-kernel-condensation-851/discovery/README.md
rename to research/multicut-kernel-condensation-883/discovery/README.md
index 129cfbd0b3..17bf1b74f3 100644
--- a/research/multicut-kernel-condensation-851/discovery/README.md
+++ b/research/multicut-kernel-condensation-883/discovery/README.md
@@ -1,6 +1,6 @@
 # Discovery (not run by the verifier)
 
-Pure-Python replay of PR #249's word and the census that produced the 333 added pairs (Chafik Boukhalfa,
+Pure-Python replay of PR #249's word and the censuses that produced the 365 added families (Chafik Boukhalfa,
 Anthropic Claude assistance). Inputs are the package's own `inputs/` files, decompressed into a data directory.
 
     twins.py  <data> twins.pkl                  census of twin dirty helpers at PR #254's cut (record 727,593)
@@ -8,12 +8,14 @@ Anthropic Claude assistance). Inputs are the package's own `inputs/` files, deco
     gain.py                                     log-weighted gain phi(r) = r ln(120/r) per pair and exact-grid price
     gen_candidates.py                           candidate records (basis, first frames, entrance line) in PR #259's schema
     compare259.py                               the pairs disjoint from PR #259's 1,194 helpers (free259.json)
-    merge259.py                                 PR #259's 518 items + the 333 free net-positive pairs -> inputs/candidates.json.gz
+    merge259.py                                 PR #259's 518 items + the 333 free net-positive pairs (round 1)
+    census2.py                                  second census: every response class at twelve cuts, pairs and XOR triples, greedy packing
+    merge2.py                                   + the 32 families of the second round -> inputs/candidates.json.gz
 
 Diff of this package against PR #259's (everything else byte for byte):
 
-    inputs/candidates.json.gz      518 items unchanged + 333 appended (round "union-early-cut", cut 676559)
-    expected/*.json, RESULT.json   regenerated receipts and result (851 pivots, entrance rank 1677, kappa 7.11403723709732e-4)
+    inputs/candidates.json.gz      518 items unchanged + 333 appended (round "union-early-cut") + 32 (round "headroom-2"), all at cut 676559
+    expected/*.json, RESULT.json   regenerated receipts and result (883 pivots, entrance rank 1710, kappa 7.11421336565136e-4)
     code/cohort-transform.cpp      std::sort -> std::stable_sort on the gauge order (platform-independent transcript)
     verify.py                      'containment_pairs_checked' added to the dropped fields; normalize() on both receipt sides
     README.md, PROOF.md, NOTICE.md this package's notes; PR #259's README/PROOF kept as README-PR259.md, PROOF-PR259.md
diff --git a/research/multicut-kernel-condensation-883/discovery/census2.py b/research/multicut-kernel-condensation-883/discovery/census2.py
new file mode 100644
index 0000000000..03f483116f
--- /dev/null
+++ b/research/multicut-kernel-condensation-883/discovery/census2.py
@@ -0,0 +1,142 @@
+"""Multi-cut twin/triple census excluding already-used helpers. usage: census2.py DATA USED.json OUT.json"""
+import json, sys, collections, time, itertools, math
+from array import array
+from fractions import Fraction as Fr
+from math import lcm, gcd
+D, USED, OUT = sys.argv[1], sys.argv[2], sys.argv[3]
+CUTS = [676559, 678000, 680080, 685000, 690000, 695000, 700582, 705000, 710000, 715000, 720000, 727593]
+TRIPLE_CUTS = {676559, 690000, 700582, 727593}
+t0 = time.time()
+st = json.load(open(D + '/249-states.json')); n, v, ZERO, FULL = st['n'], st['v'], st['ZERO'], st['FULL']; H0 = 2*v
+ini = [ZERO]*n; fin = [FULL]*n
+for k, x in st['initial'].items(): ini[int(k)] = x
+for k, x in st['final'].items(): fin[int(k)] = x
+regs = st['regs']; borrowed = set(st['borrowed']); donor = set(json.load(open(D + '/249-DONOR-OWNERSHIP.json'))['donor_keys']); used = set(json.load(open(USED)))
+rec = array('i'); rec.frombytes(open(D + '/249-records.bin', 'rb').read()); E = len(rec)//6
+fj = json.load(open(D + '/frames.json'))['frames']
+Tt = {}; first = {}; reads = collections.Counter()
+for i in range(E):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 0:
+        if a >= H0 and a not in Tt: Tt[a] = i; first[a] = c
+    elif k == 1:
+        if a >= H0 and a not in Tt: Tt[a] = i; first[a] = None
+        if b >= H0:
+            if z == 4 and f == ZERO and v <= a < 2*v: reads[b] += 1
+            elif b not in Tt: Tt[b] = i; first[b] = None
+    else:
+        for s in (a, b):
+            if s >= H0 and s not in Tt: Tt[s] = i; first[s] = None
+base = [h for h in range(H0, n) if ini[h] == ZERO and fin[h] == FULL and regs[h-H0] not in borrowed and regs[h-H0] not in donor and h not in used and first.get(h) is not None]
+print('base (unused, clean roles, MOVE-first)', len(base), time.time()-t0, flush=True)
+phi = lambda r: 0.0 if r == 0 else r*math.log(120/r)
+def nullspace(rows):
+    m = [[Fr(x) for x in r] for r in rows]; piv = []; r = 0
+    for c in range(24):
+        p = next((i for i in range(r, len(m)) if m[i][c] != 0), 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] != 0:
+                f = m[i][c]; m[i] = [a - f*b for a, b in zip(m[i], m[r])]
+        piv.append(c); r += 1
+        if r == len(m): break
+    free = [c for c in range(24) if c not in piv]; basis = []
+    for fcol in free:
+        vec = [Fr(0)]*24; vec[fcol] = Fr(1)
+        for i, pc in enumerate(piv): vec[pc] = -m[i][fcol]
+        basis.append(vec)
+    return basis
+def prim(vec):
+    L = 1
+    for x in vec: L = lcm(L, x.denominator)
+    iv = [int(x*L) for x in vec]; g = 0
+    for x in iv: g = gcd(g, abs(x))
+    return [x//g for x in iv]
+def gramdet(basis):
+    k = len(basis); M = [[Fr(9*sum(a*b for a, b in zip(basis[i], basis[j])) - sum(basis[i])*sum(basis[j])) for j in range(k)] for i in range(k)]; det = Fr(1)
+    for c in range(k):
+        p = next((i for i in range(c, k) if M[i][c] != 0), None)
+        if p is None: return 0
+        if p != c: M[c], M[p] = M[p], M[c]; det = -det
+        det *= M[c][c]
+        for i in range(c+1, k):
+            f = M[i][c]/M[c][c]; M[i] = [a - f*b for a, b in zip(M[i], M[c])]
+    return det
+icache = {}
+def entrance(frames):
+    """best (gain, e, basis_int_rows, pivot_index) for members' first frames (members ordered); returns None if no nondegenerate entrance"""
+    key = tuple(frames)
+    if key in icache: return icache[key]
+    rows = []
+    for f in frames: rows += fj[str(f)]['A']
+    basis = nullspace(rows); d = len(basis); res = None
+    if d:
+        dims = [fj[str(f)]['dim'] for f in frames]
+        # candidate entrance subspaces: single lines (each primitive basis vector, prefer small norm) and the full intersection
+        options = []
+        lines = sorted((prim(b) for b in basis), key=lambda u: sum(x*x for x in u))
+        for u in lines:
+            if 9*sum(x*x for x in u) - sum(u)**2 != 0: options.append((1, [u])); break
+        if d >= 2 and gramdet(basis) != 0: options.append((d, [prim(b) for b in basis]))
+        for e, B in options:
+            for p in range(len(frames)):
+                if dims[p] < e or any(dims[q] < e for q in range(len(frames))): continue
+                g = phi(dims[p]-e) - phi(dims[p]) + sum(phi(e) + phi(dims[q]-e) - phi(dims[q]) for q in range(len(frames)) if q != p)
+                if res is None or g < res[0]: res = (g, e, B, p)
+    icache[key] = res; return res
+row = [1 << s for s in range(n+1)]; i = 0; cands = []; stats = collections.Counter()
+for cut in CUTS:
+    while i <= cut:
+        k, a, b, c, f, z = rec[6*i:6*i+6]
+        if k == 1:
+            if c & 1: row[a] ^= row[b]
+        elif k == 2: row[b] = row[a]
+        i += 1
+    live = [h for h in base if Tt[h] > cut]
+    contam = 0
+    for s in range(n):
+        if v <= s < 2*v: continue
+        contam |= (row[s] ^ (1 << s)) >> H0
+    resp = collections.defaultdict(int)
+    for t in range(v):
+        r = row[v+t] >> H0
+        while r:
+            low = r & -r; idx = low.bit_length()-1; resp[H0+idx] |= 1 << t; r ^= low
+    live = [h for h in live if not (contam >> (h-H0)) & 1 and resp[h]]
+    cls = collections.defaultdict(list)
+    for h in live: cls[resp[h]].append(h)
+    sizes = collections.Counter(len(m) for m in cls.values() if len(m) >= 2)
+    npair = 0
+    for m in cls.values():
+        if len(m) < 2: continue
+        for a, b in itertools.combinations(m, 2):
+            r = entrance([first[a], first[b]])
+            if r is None or r[0] >= 0: stats[('pair', 'rejected', cut)] += 1; continue
+            g, e, B, p = r; piv, par = (a, b) if p == 0 else (b, a)
+            cands.append(dict(gain=g, cut=cut, members=[piv, par], pivot=piv, e=e, basis=B, kind='pair', cls=len(m))); npair += 1
+    ntri = 0
+    if cut in TRIPLE_CUTS:
+        dl = sorted(cls); Sset = set(dl)
+        for x in range(len(dl)):
+            for y in range(x+1, len(dl)):
+                w = dl[x] ^ dl[y]
+                if w > dl[y] and w in Sset:
+                    for a in cls[dl[x]]:
+                        for b in cls[dl[y]]:
+                            for c in cls[w]:
+                                r = entrance([first[a], first[b], first[c]])
+                                if r is None or r[0] >= 0: stats[('triple', 'rejected', cut)] += 1; continue
+                                g, e, B, p = r; mem = [a, b, c]; piv = mem[p]
+                                cands.append(dict(gain=g, cut=cut, members=[piv] + [h for h in mem if h != piv], pivot=piv, e=e, basis=B, kind='triple')); ntri += 1
+    print(f'cut {cut}: live {len(live)} class sizes {sorted(sizes.items())} positive pair-cands {npair} triple-cands {ntri} ({time.time()-t0:.0f}s)', flush=True)
+# global greedy packing: best gain first, disjoint helpers; a helper may appear once
+cands.sort(key=lambda z: z['gain']); taken = set(); chosen = []
+for z in cands:
+    if any(h in taken for h in z['members']): continue
+    taken |= set(z['members']); chosen.append(z)
+S = sum(z['e'] for z in chosen)
+print('chosen families', len(chosen), 'by kind', collections.Counter(z['kind'] for z in chosen), 'by cut', collections.Counter(z['cut'] for z in chosen), 'by e', collections.Counter(z['e'] for z in chosen), 'entrance rank', S, 'total gain', round(sum(z['gain'] for z in chosen), 1))
+print('chosen by (kind, e, frame dims) top:', collections.Counter((z['kind'], z['e'], tuple(fj[str(first[h])]['dim'] for h in z['members'])) for z in chosen).most_common(15))
+json.dump(dict(chosen=chosen, all_candidates=len(cands)), open(OUT, 'w'))
+print('done', time.time()-t0)
diff --git a/research/multicut-kernel-condensation-851/discovery/chrono2.py b/research/multicut-kernel-condensation-883/discovery/chrono2.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/discovery/chrono2.py
rename to research/multicut-kernel-condensation-883/discovery/chrono2.py
diff --git a/research/multicut-kernel-condensation-851/discovery/compare259.py b/research/multicut-kernel-condensation-883/discovery/compare259.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/discovery/compare259.py
rename to research/multicut-kernel-condensation-883/discovery/compare259.py
diff --git a/research/multicut-kernel-condensation-851/discovery/gain.py b/research/multicut-kernel-condensation-883/discovery/gain.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/discovery/gain.py
rename to research/multicut-kernel-condensation-883/discovery/gain.py
diff --git a/research/multicut-kernel-condensation-851/discovery/gen_candidates.py b/research/multicut-kernel-condensation-883/discovery/gen_candidates.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/discovery/gen_candidates.py
rename to research/multicut-kernel-condensation-883/discovery/gen_candidates.py
diff --git a/research/multicut-kernel-condensation-883/discovery/merge2.py b/research/multicut-kernel-condensation-883/discovery/merge2.py
new file mode 100644
index 0000000000..378820c7f4
--- /dev/null
+++ b/research/multicut-kernel-condensation-883/discovery/merge2.py
@@ -0,0 +1,21 @@
+import json, sys, gzip, collections
+base = json.load(open(sys.argv[1])); cen = json.load(open(sys.argv[2])); half = json.load(open(sys.argv[3])); OUT = sys.argv[4]
+used = {r for z in base for r in z['roles']}
+chosen = sorted(cen['chosen'], key=lambda z: z['gain'])
+# half-overlap free helpers
+free_half = set()
+for z in half:
+    pass
+S_base = sum(z['dim'] for z in base); items = []
+for z in chosen:
+    assert not any(h in used for h in z['members'])
+    used |= set(z['members'])
+    items.append(dict(pivot=z['pivot'], a=z['pivot'], roles=list(z['members']), partners=[h for h in z['members'] if h != z['pivot']], dim=z['e'], E_dimension=z['e'], basis=[[str(x) for x in r] for r in z['basis']], cut=z['cut'], approx_slack_delta=z['gain'], kind='%s, e=%d, residual census at cut %d (excluding 851 helpers)' % (z['kind'], z['e'], z['cut']), round='headroom-2'))
+S = S_base + sum(z['dim'] for z in items)
+while S % 3:
+    for j in range(len(items)-1, -1, -1):
+        if items[j]['dim'] == 1: print('drop weakest dim-1', items[j]['roles'], items[j]['approx_slack_delta']); S -= 1; items.pop(j); break
+    else: raise SystemExit('cannot normalize mod 3')
+merged = base + items
+print('added', len(items), 'families; entrance rank', S, 'by cut', collections.Counter(z['cut'] for z in items), 'by e', collections.Counter(z['dim'] for z in items), 'gain', round(sum(z['approx_slack_delta'] for z in items), 2))
+json.dump(merged, open(OUT, 'w'), indent=1); open(OUT + '.gz', 'wb').write(gzip.compress(json.dumps(merged, indent=1).encode(), mtime=0))
diff --git a/research/multicut-kernel-condensation-851/discovery/merge259.py b/research/multicut-kernel-condensation-883/discovery/merge259.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/discovery/merge259.py
rename to research/multicut-kernel-condensation-883/discovery/merge259.py
diff --git a/research/multicut-kernel-condensation-851/discovery/twins.py b/research/multicut-kernel-condensation-883/discovery/twins.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/discovery/twins.py
rename to research/multicut-kernel-condensation-883/discovery/twins.py
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json b/research/multicut-kernel-condensation-883/expected/COHORT-BANK-REVIEW.json
similarity index 93%
rename from research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json
rename to research/multicut-kernel-condensation-883/expected/COHORT-BANK-REVIEW.json
index a33ce54cd6..1f6535ba64 100644
--- a/research/multicut-kernel-condensation-851/expected/COHORT-BANK-REVIEW.json
+++ b/research/multicut-kernel-condensation-883/expected/COHORT-BANK-REVIEW.json
@@ -1,7 +1,7 @@
 {
   "actual_helper_roles": 16587,
   "actual_role_replica_stage_assignments": 3317400,
-  "assignment_fnv1a64": "15151966029277311027",
+  "assignment_fnv1a64": "7193720686180422241",
   "bank_patterns": [
     {
       "count": 240,
@@ -432,7 +432,7 @@
       ]
     },
     {
-      "count": 410,
+      "count": 420,
       "widths": [
         22,
         22,
@@ -449,7 +449,7 @@
       ]
     },
     {
-      "count": 7020,
+      "count": 7330,
       "widths": [
         23,
         23,
@@ -465,7 +465,7 @@
       ]
     },
     {
-      "count": 570,
+      "count": 495,
       "widths": [
         4,
         4,
@@ -500,7 +500,7 @@
       ]
     },
     {
-      "count": 107488,
+      "count": 107232,
       "widths": [
         24,
         24,
@@ -510,20 +510,20 @@
       ]
     }
   ],
-  "banks_per_stage": 117004,
-  "covered_address_rank_mass": 70202400,
+  "banks_per_stage": 116993,
+  "covered_address_rank_mass": 70195800,
   "endpoint_address_columns": 10560,
   "label": "actual_multicut",
-  "literal_stock": 866620,
+  "literal_stock": 866565,
   "max_block_scalar": 30,
   "max_intermediate_denominator": "704",
   "max_intermediate_numerator": "704",
   "max_new_chart_factors": 200,
-  "new_entrance_rank": 1677,
-  "new_exact_charts": 851,
-  "new_gauged_roles": 851,
+  "new_entrance_rank": 1710,
+  "new_exact_charts": 883,
+  "new_gauged_roles": 883,
   "nonzero_omission_repeat_control_columns": 10560,
-  "normalized_stock": 173324,
+  "normalized_stock": 173313,
   "normalizer_factor_ceiling": 787,
   "prime_guard": "every elimination pivot and emitted coefficient has numerator and denominator magnitude below2^80",
   "residual_families": {
@@ -538,16 +538,16 @@
     "19": 24,
     "20": 19,
     "21": 3,
-    "22": 41,
-    "23": 702,
-    "24": 13436,
+    "22": 42,
+    "23": 733,
+    "24": 13404,
     "4": 2200,
     "6": 22,
     "7": 7,
     "9": 4
   },
-  "saved_literal_banks": 2795,
+  "saved_literal_banks": 2850,
   "scope": "Exact chart and role census, residual conjugacy, complete bank tiling, and finite selector charge. Full physical word, global columns, and pricing checked separately.",
-  "selector_charge": 626937159600,
+  "selector_charge": 626937137600,
   "status": "PASS_GENERIC_EXACT_CHARTS_ACTUAL_BANK_ALLOCATION"
 }
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json b/research/multicut-kernel-condensation-883/expected/COHORT-EXACT-PRICE.json
similarity index 73%
rename from research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json
rename to research/multicut-kernel-condensation-883/expected/COHORT-EXACT-PRICE.json
index 62d9a2d201..cc1cf66d65 100644
--- a/research/multicut-kernel-condensation-851/expected/COHORT-EXACT-PRICE.json
+++ b/research/multicut-kernel-condensation-883/expected/COHORT-EXACT-PRICE.json
@@ -51,16 +51,16 @@
   "cohort_candidate": {
     "bootstrap_chain": [
       "384599/10000000000",
-      "711430743397955676522945935285759/1000000000000000000000000000000000000",
-      "711909838191882313741863693279570316744243449827711/1000000000000000000000000000000000000000000000000000000",
-      "711910179264343059080961789089783605966884312180809963542327911793919/1000000000000000000000000000000000000000000000000000000000000000000000000"
+      "711448356904944866168722758485631/1000000000000000000000000000000000000",
+      "711927476108237935355751292633060782626378882102847/1000000000000000000000000000000000000000000000000000000",
+      "711927817206526633951518134578536201513839897689189894717718866531839/1000000000000000000000000000000000000000000000000000000000000000000000000"
     ],
-    "calls": 3970160,
-    "coarse": "711910179507329/1000000000000000000",
-    "coarse_decimal": 0.000711910179507329,
+    "calls": 3971440,
+    "coarse": "711927817449537/1000000000000000000",
+    "coarse_decimal": 0.000711927817449537,
     "deficit": 35200,
     "histogram": {
-      "1": 1728920,
+      "1": 1730200,
       "10": 30760,
       "11": 17200,
       "12": 60560,
@@ -71,30 +71,30 @@
       "17": 18800,
       "18": 19480,
       "19": 12920,
-      "2": 756040,
+      "2": 758440,
       "20": 54320,
       "21": 223560,
       "22": 53760,
       "23": 28160,
-      "3": 387680,
-      "4": 148560,
+      "3": 385320,
+      "4": 148600,
       "46": 28160,
       "5": 96080,
       "50": 28160,
-      "6": 61200,
+      "6": 61120,
       "7": 49040,
       "8": 25360,
       "9": 25800
     },
-    "kappa": "177850930927433/250000000000000000",
-    "kappa_decimal": 0.000711403723709732,
-    "moment_upper": "134799733335753198753192885375660456220983058432540502946205712451439733564402750601/134799733335753198973335075435098153368185722112702862405518051246080000000000000000",
-    "next_coarse_moment_lower": "26959946667150639814796264323470635893891546575600803563574056326881021612395769383/26959946667150639794667015087019630673637144422540572481103610249216000000000000000",
+    "kappa": "44463833535321/62500000000000000",
+    "kappa_decimal": 0.000711421336565136,
+    "moment_upper": "134799733335753198930976841688255237895987408528785254572771739521823139742264153801/134799733335753198973335075435098153368185722112702862405518051246080000000000000000",
+    "next_coarse_moment_lower": "269599466671506398503555464196556110254668679950330531069703752576714463407050236903/269599466671506397946670150870196306736371444225405724811036102492160000000000000000",
     "next_kappa_rejected": 1,
-    "ordinary_bit": "711910179264343059080961789089783605966884312180809963542327911793919/1000000000000000000000000000000000000000000000000000000000000000000000000",
+    "ordinary_bit": "711927817206526633951518134578536201513839897689189894717718866531839/1000000000000000000000000000000000000000000000000000000000000000000000000",
     "positive_constraints": 47,
-    "rank_mass": 20763680,
-    "stock": 173324
+    "rank_mass": 20762360,
+    "stock": 173313
   },
   "finite_bill_and_all_size_interfaces_not_reproved": true,
   "method": "C++ exact rational 224-bit directed bounds; floating used only to propose a bracket verified exactly;32-degree exponential and48-term atanh logarithm",
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json b/research/multicut-kernel-condensation-883/expected/COHORT-FINITE-INVOICE.json
similarity index 59%
rename from research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json
rename to research/multicut-kernel-condensation-883/expected/COHORT-FINITE-INVOICE.json
index e3383fae0b..2544ce6805 100644
--- a/research/multicut-kernel-condensation-851/expected/COHORT-FINITE-INVOICE.json
+++ b/research/multicut-kernel-condensation-883/expected/COHORT-FINITE-INVOICE.json
@@ -1,14 +1,14 @@
 {
   "external_complex_row_coefficient": 20161,
-  "extra_selector_calls": "626937159600",
-  "full_counted_primitive_coefficient": "62757760533419801",
-  "global_unit_expanded_additions": "148166200",
-  "global_weighted_additions": "147638200",
+  "extra_selector_calls": "626937137600",
+  "full_counted_primitive_coefficient": "62769085432418201",
+  "global_unit_expanded_additions": "146891000",
+  "global_weighted_additions": "146363000",
   "internal_row_coefficient": 14401,
-  "linear_moment_slack": "85937499553357/50778515625000000",
+  "linear_moment_slack": "12276785650459/7253613281250000",
   "literal_deficit": 176000,
   "literal_histogram": {
-    "1": "8644600",
+    "1": "8651000",
     "10": "153800",
     "11": "86000",
     "12": "302800",
@@ -19,54 +19,54 @@
     "17": "94000",
     "18": "97400",
     "19": "64600",
-    "2": "3780200",
+    "2": "3792200",
     "20": "271600",
     "21": "1117800",
     "22": "268800",
     "23": "140800",
-    "3": "1938400",
-    "4": "742800",
+    "3": "1926600",
+    "4": "743000",
     "46": "140800",
     "5": "480400",
     "50": "140800",
-    "6": "306000",
+    "6": "305600",
     "7": "245200",
     "8": "126800",
     "9": "129000"
   },
-  "literal_rank_mass": "103818400",
-  "literal_stock": 866620,
+  "literal_rank_mass": "103811800",
+  "literal_stock": 866565,
   "new_chart_factor_max": 200,
-  "normalized_stock": 173324,
+  "normalized_stock": 173313,
   "normalizer_factor_bound": 787,
   "ordinary_cutoffs": [
     {
-      "counted_coefficient_cutoff_log2": "156617764225196",
+      "counted_coefficient_cutoff_log2": "156601800901990",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "479436109373323477054064714241/1000000000000000000000000000000000000",
+      "minimum_gap": "479460544592133831277241514369/1000000000000000000000000000000000000",
       "stage": 1
     },
     {
-      "counted_coefficient_cutoff_log2": "309022864676337192015",
+      "counted_coefficient_cutoff_log2": "308976057134932507419",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "341315446686258136306720429683255756550172289/1000000000000000000000000000000000000000000000000000000",
+      "minimum_gap": "341341299064644248707366939217373621117897153/1000000000000000000000000000000000000000000000000000000",
       "stage": 2
     },
     {
-      "counted_coefficient_cutoff_log2": "609733712936038839832196057",
+      "counted_coefficient_cutoff_log2": "609611149634209069823427388",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "242985940919038210910216394033115687819190036457672088206081/1000000000000000000000000000000000000000000000000000000000000000000000000",
+      "minimum_gap": "243010366048481865421463798486160102310810105282281133468161/1000000000000000000000000000000000000000000000000000000000000000000000000",
       "stage": 3
     }
   ],
   "payload_bits": 98,
-  "payload_signed_prefix_upper": "313775842895942661197234728704",
+  "payload_signed_prefix_upper": "313857017010121408715056608000",
   "physical_replicas": 40,
-  "positive_rank_children": "19850800",
+  "positive_rank_children": "19857200",
   "primitive_coefficient_bits": 56,
   "route_families": "8324400",
   "scope": "Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted.",
   "simultaneous_extra_work_streams": 1,
   "status": "PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS",
-  "strict_moment_slack": "220142190059437697147202663680162359459312338794640266435597249399/134799733335753198973335075435098153368185722112702862405518051246080000000000000000"
+  "strict_moment_slack": "42358233746842915472198313583917607832746311724256860257735846199/134799733335753198973335075435098153368185722112702862405518051246080000000000000000"
 }
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json b/research/multicut-kernel-condensation-883/expected/COHORT-FIVE-STAGE-COLUMNS.json
similarity index 84%
rename from research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json
rename to research/multicut-kernel-condensation-883/expected/COHORT-FIVE-STAGE-COLUMNS.json
index 2ce20dca62..9ae4c8bdfa 100644
--- a/research/multicut-kernel-condensation-851/expected/COHORT-FIVE-STAGE-COLUMNS.json
+++ b/research/multicut-kernel-condensation-883/expected/COHORT-FIVE-STAGE-COLUMNS.json
@@ -1,28 +1,28 @@
 {
   "bridge_additions": 10560,
   "copied_center_original_source_immutable": true,
-  "five_stage_additions": 3680395,
+  "five_stage_additions": 3648515,
   "formal_columns_checked": 23627,
   "fresh_center_copies": 120,
   "global_live_registers": 23627,
   "independent_dirty_registers": 16587,
-  "local_odd_scalar_additions": 736079,
+  "local_odd_scalar_additions": 729703,
   "local_raw_H": [
     [
       1,
-      43223
+      43255
     ],
     [
       2,
-      18901
+      18961
     ],
     [
       3,
-      9692
+      9633
     ],
     [
       4,
-      3010
+      3011
     ],
     [
       5,
@@ -30,7 +30,7 @@
     ],
     [
       6,
-      1530
+      1528
     ],
     [
       7,
@@ -98,7 +98,7 @@
     ]
   ],
   "local_registers": 20107,
-  "local_scalar_additions": 736079,
+  "local_scalar_additions": 729703,
   "negative_controls": [
     {
       "omit_bridge": 0,
@@ -130,18 +130,18 @@
     29
   ],
   "payload_prefix_bits": 98,
-  "payload_prefix_upper": "313775842895942661197234728704",
+  "payload_prefix_upper": "313857017010121408715056608000",
   "reverse_fresh_center_copies": 48,
   "scope": "All 23627 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.",
   "signed_lift_prefix": [
     {
       "bits": 17,
-      "cancellation_free_signed_row_l1_upper": "74391",
+      "cancellation_free_signed_row_l1_upper": "74395",
       "reverse": false
     },
     {
       "bits": 22,
-      "cancellation_free_signed_row_l1_upper": "3450954",
+      "cancellation_free_signed_row_l1_upper": "3451122",
       "reverse": true
     }
   ],
@@ -149,31 +149,31 @@
   "stages": [
     {
       "fresh_copies": 24,
-      "scalar_additions": 736079,
+      "scalar_additions": 729703,
       "signed_inverse": false,
       "stage": 0
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 736079,
+      "scalar_additions": 729703,
       "signed_inverse": true,
       "stage": 1
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 736079,
+      "scalar_additions": 729703,
       "signed_inverse": false,
       "stage": 2
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 736079,
+      "scalar_additions": 729703,
       "signed_inverse": true,
       "stage": 3
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 736079,
+      "scalar_additions": 729703,
       "signed_inverse": false,
       "stage": 4
     }
diff --git a/research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json b/research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json
similarity index 66%
rename from research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json
rename to research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json
index 0ff70c74ba..8ac2ea98b7 100644
--- a/research/multicut-kernel-condensation-851/expected/COHORT249-REPLAY.json
+++ b/research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json
@@ -1,9 +1,9 @@
 {
-  "added_Q_Qinverse_passes": 2208,
+  "added_Q_Qinverse_passes": 2272,
   "bank_completion_not_replayed": true,
   "cut_record": 727593,
   "delta": {
-    "1": 1811,
+    "1": 1843,
     "10": -4,
     "11": -15,
     "12": -11,
@@ -12,11 +12,11 @@
     "15": -46,
     "17": -34,
     "19": -8,
-    "2": -184,
-    "3": -542,
-    "4": 100,
+    "2": -124,
+    "3": -601,
+    "4": 101,
     "5": -82,
-    "6": 3,
+    "6": 1,
     "7": -26,
     "8": 5,
     "9": 34
@@ -24,7 +24,7 @@
   "forward_formal_columns": 20107,
   "global_kappa_claimed": false,
   "histogram": {
-    "1": 43223,
+    "1": 43255,
     "10": 769,
     "11": 430,
     "12": 1514,
@@ -35,28 +35,28 @@
     "17": 470,
     "18": 487,
     "19": 323,
-    "2": 18901,
+    "2": 18961,
     "20": 1358,
     "21": 5589,
     "22": 1344,
-    "3": 9692,
-    "4": 3010,
+    "3": 9633,
+    "4": 3011,
     "5": 2402,
-    "6": 1530,
+    "6": 1528,
     "7": 1226,
     "8": 634,
     "9": 645
   },
   "inverse_formal_columns": 20107,
-  "new_entrance_rank": 1677,
-  "new_gauges": 851,
+  "new_entrance_rank": 1710,
+  "new_gauges": 883,
   "new_gram_audit_external": true,
-  "new_rank_mass": 432500,
-  "new_records": 835788,
+  "new_rank_mass": 432467,
+  "new_records": 829444,
   "old_rank_mass": 434177,
   "old_records": 885228,
-  "omitted_Q_nonzero_wrong_words": 32383,
-  "omitted_Qinverse_nonzero_wrong_words": 1052,
-  "removed_initial_reads": 52752,
+  "omitted_Q_nonzero_wrong_words": 37450,
+  "omitted_Qinverse_nonzero_wrong_words": 1084,
+  "removed_initial_reads": 59192,
   "status": "PASS_FULL_CURRENT249_COHORT_REWRITE_F2_COLUMNS_AND_FRAMES"
 }
diff --git a/research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json b/research/multicut-kernel-condensation-883/expected/INDEPENDENT-LEGALITY.json
similarity index 83%
rename from research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json
rename to research/multicut-kernel-condensation-883/expected/INDEPENDENT-LEGALITY.json
index 4cfbbcfa7b..42596820f3 100644
--- a/research/multicut-kernel-condensation-851/expected/INDEPENDENT-LEGALITY.json
+++ b/research/multicut-kernel-condensation-883/expected/INDEPENDENT-LEGALITY.json
@@ -1,31 +1,31 @@
 {
   "all_final_frames_pass": true,
-  "common_frame_ADDs": 736079,
-  "containment_pairs_checked": 82698,
+  "common_frame_ADDs": 729703,
+  "containment_pairs_checked": 82779,
   "copies": 24,
   "donor_intersections": 0,
   "erasures": 24,
   "max_inherited_integer_abs": 7,
-  "nested_MOVEs": 99661,
+  "nested_MOVEs": 99693,
   "new_frame_ids_collision": false,
   "nondegeneracy_checked_by_separate_exact_bank_audit": true,
   "old_max_frame_id": 150370,
   "paid_histogram": [
     [
       1,
-      43223
+      43255
     ],
     [
       2,
-      18901
+      18961
     ],
     [
       3,
-      9692
+      9633
     ],
     [
       4,
-      3010
+      3011
     ],
     [
       5,
@@ -33,7 +33,7 @@
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     [
       6,
-      1530
+      1528
     ],
     [
       7,
@@ -100,11 +100,11 @@
       1344
     ]
   ],
-  "rank_mass": 432500,
-  "records": 835788,
+  "rank_mass": 432467,
+  "records": 829444,
   "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.",
-  "selected_helpers": 1860,
-  "selected_pairs": 851,
+  "selected_helpers": 1924,
+  "selected_pairs": 883,
   "source_owner_intersections": 0,
   "status": "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE"
 }
diff --git a/research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json b/research/multicut-kernel-condensation-883/expected/INDEPENDENT-PREFIX.json
similarity index 57%
rename from research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json
rename to research/multicut-kernel-condensation-883/expected/INDEPENDENT-PREFIX.json
index dcc4a47021..0ab29feae1 100644
--- a/research/multicut-kernel-condensation-851/expected/INDEPENDENT-PREFIX.json
+++ b/research/multicut-kernel-condensation-883/expected/INDEPENDENT-PREFIX.json
@@ -1,10 +1,10 @@
 {
-  "cohorts": 851,
+  "cohorts": 883,
   "distinct_cuts": 4,
-  "distinct_helpers": 1860,
-  "non_target_identity_bits": 35868385,
-  "nonzero_pivot_target_entries": 52788,
+  "distinct_helpers": 1924,
+  "non_target_identity_bits": 37042593,
+  "nonzero_pivot_target_entries": 59228,
   "scope": "Original pinned-word response at every cohort own cut; combined emitted-word checks remain separate.",
   "status": "PASS_INDEPENDENT_MULTI_CUT_FULL_F2_KERNEL_AND_IDENTITY_COLUMNS",
-  "target_kernel_equalities": 1497760
+  "target_kernel_equalities": 1554080
 }
diff --git a/research/multicut-kernel-condensation-851/inputs/249-DONOR-OWNERSHIP.json.gz b/research/multicut-kernel-condensation-883/inputs/249-DONOR-OWNERSHIP.json.gz
similarity index 100%
rename from research/multicut-kernel-condensation-851/inputs/249-DONOR-OWNERSHIP.json.gz
rename to research/multicut-kernel-condensation-883/inputs/249-DONOR-OWNERSHIP.json.gz
diff --git a/research/multicut-kernel-condensation-851/inputs/249-records.bin.gz b/research/multicut-kernel-condensation-883/inputs/249-records.bin.gz
similarity index 100%
rename from research/multicut-kernel-condensation-851/inputs/249-records.bin.gz
rename to research/multicut-kernel-condensation-883/inputs/249-records.bin.gz
diff --git a/research/multicut-kernel-condensation-851/inputs/249-states.json.gz b/research/multicut-kernel-condensation-883/inputs/249-states.json.gz
similarity index 100%
rename from research/multicut-kernel-condensation-851/inputs/249-states.json.gz
rename to research/multicut-kernel-condensation-883/inputs/249-states.json.gz
diff --git a/research/multicut-kernel-condensation-851/inputs/SNAPSHOTS.json b/research/multicut-kernel-condensation-883/inputs/SNAPSHOTS.json
similarity index 100%
rename from research/multicut-kernel-condensation-851/inputs/SNAPSHOTS.json
rename to research/multicut-kernel-condensation-883/inputs/SNAPSHOTS.json
diff --git a/research/multicut-kernel-condensation-851/inputs/candidates.json.gz b/research/multicut-kernel-condensation-883/inputs/candidates.json.gz
similarity index 51%
rename from research/multicut-kernel-condensation-851/inputs/candidates.json.gz
rename to research/multicut-kernel-condensation-883/inputs/candidates.json.gz
index 99cd396e7cf5b19728474d6f641e7adb4394fc99..b7da3749945f1d165bf0cbc5c377c25434a165b6 100644
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diff --git a/research/multicut-kernel-condensation-851/inputs/frames.json.gz b/research/multicut-kernel-condensation-883/inputs/frames.json.gz
similarity index 100%
rename from research/multicut-kernel-condensation-851/inputs/frames.json.gz
rename to research/multicut-kernel-condensation-883/inputs/frames.json.gz
diff --git a/research/multicut-kernel-condensation-851/requirements.txt b/research/multicut-kernel-condensation-883/requirements.txt
similarity index 100%
rename from research/multicut-kernel-condensation-851/requirements.txt
rename to research/multicut-kernel-condensation-883/requirements.txt
diff --git a/research/multicut-kernel-condensation-851/vendor/PR249-SOURCE-MANIFEST.json b/research/multicut-kernel-condensation-883/vendor/PR249-SOURCE-MANIFEST.json
similarity index 100%
rename from research/multicut-kernel-condensation-851/vendor/PR249-SOURCE-MANIFEST.json
rename to research/multicut-kernel-condensation-883/vendor/PR249-SOURCE-MANIFEST.json
diff --git a/research/multicut-kernel-condensation-851/vendor/UPSTREAM-NOTICE.md b/research/multicut-kernel-condensation-883/vendor/UPSTREAM-NOTICE.md
similarity index 100%
rename from research/multicut-kernel-condensation-851/vendor/UPSTREAM-NOTICE.md
rename to research/multicut-kernel-condensation-883/vendor/UPSTREAM-NOTICE.md
diff --git a/research/multicut-kernel-condensation-851/vendor/json.hpp b/research/multicut-kernel-condensation-883/vendor/json.hpp
similarity index 100%
rename from research/multicut-kernel-condensation-851/vendor/json.hpp
rename to research/multicut-kernel-condensation-883/vendor/json.hpp
diff --git a/research/multicut-kernel-condensation-851/vendor/pr249-source.zip b/research/multicut-kernel-condensation-883/vendor/pr249-source.zip
similarity index 100%
rename from research/multicut-kernel-condensation-851/vendor/pr249-source.zip
rename to research/multicut-kernel-condensation-883/vendor/pr249-source.zip
diff --git a/research/multicut-kernel-condensation-851/verify.py b/research/multicut-kernel-condensation-883/verify.py
similarity index 100%
rename from research/multicut-kernel-condensation-851/verify.py
rename to research/multicut-kernel-condensation-883/verify.py

From f33c3c01771ff3a3ec6210019fce31aa5b199cd6 Mon Sep 17 00:00:00 2001
From: chafreaky <chafik.boukhalfa@gmail.com>
Date: Sat, 10 Oct 2026 08:11:57 +0400
Subject: [PATCH 4/5] multicut-kernel-composition: 54 shared-donor families
 (890 families, rank 1719) + PR263 descent and PR270 plateau retimings, kappa
 = 7.11482139228173e-4; package renamed

---
 ...83.yml => multicut-kernel-composition.yml} |    14 +-
 .../BANK-PROOF.md                             |     0
 .../COPY-PROOF.md                             |     0
 .../FINITE-PROOF.md                           |     0
 .../KERNEL-PROOF.md                           |     0
 .../LICENSE                                   |     0
 .../MANIFEST.json                             |    42 +-
 .../NOTICE.md                                 |    29 +-
 .../PROOF-PR259.md                            |     0
 research/multicut-kernel-composition/PROOF.md |    89 +
 .../README-PR259.md                           |     0
 .../multicut-kernel-composition/README.md     |    65 +
 .../multicut-kernel-composition/RESULT.json   |    17 +
 .../REVIEW.md                                 |     0
 .../code/cohort-bank-review.cpp               |     0
 .../code/cohort-finite-invoice.cpp            |     0
 .../code/cohort-five-stage-columns.cpp        |     0
 .../code/cohort-legality-independent.cpp      |     0
 .../code/cohort-prefix-independent.cpp        |     0
 .../code/cohort-price.cpp                     |     0
 .../code/cohort-transform.cpp                 |     0
 .../code/descent_retiming.py                  |   209 +
 .../code/export249.py                         |     0
 .../code/plateau_retiming.py                  |    62 +
 .../code/verify_frame_tables.py               |    75 +
 .../code/verify_frames.py                     |    48 +
 .../code/verify_plateau_spans.py              |    42 +
 .../discovery/README.md                       |    26 +
 .../discovery/census2.py                      |     0
 .../discovery/census3.py                      |   120 +
 .../discovery/census3b.py                     |   137 +
 .../discovery/chrono2.py                      |     0
 .../discovery/compare259.py                   |     0
 .../discovery/gain.py                         |     0
 .../discovery/gen_candidates.py               |     0
 .../discovery/merge2.py                       |     0
 .../discovery/merge259.py                     |     0
 .../discovery/retime.py                       |    46 +
 .../discovery/twins.py                        |     0
 .../expected/COHORT-BANK-REVIEW.json          |    36 +-
 .../expected/COHORT-EXACT-PRICE.json          |    54 +-
 .../expected/COHORT-FINITE-INVOICE.json       |    64 +-
 .../expected/COHORT-FIVE-STAGE-COLUMNS.json   |    50 +-
 .../expected/COHORT249-REPLAY.json            |   132 +
 .../expected/DESCENT-RETIMING.json            |   229 +
 .../expected/FRAME-TABLE-AUDIT.json           |   932 +
 .../expected/INDEPENDENT-LEGALITY.json        |    42 +-
 .../expected/INDEPENDENT-PREFIX.json          |    10 +-
 .../expected/PLATEAU-RETIMING.json            |  1649 ++
 .../expected/PLATEAU-SOURCE-SPANS.json        |    65 +
 .../inputs/249-DONOR-OWNERSHIP.json.gz        |   Bin
 .../inputs/249-records.bin.gz                 |   Bin
 .../inputs/249-states.json.gz                 |   Bin
 .../inputs/SNAPSHOTS.json                     |     0
 .../inputs/candidates.json.gz                 |   Bin 56771 -> 56466 bytes
 .../inputs/descent-selection.json             |  7754 ++++++
 .../inputs/frames.json.gz                     |   Bin
 .../inputs/plateau-selection.json             | 20637 ++++++++++++++++
 .../requirements.txt                          |     0
 .../vendor/PR249-SOURCE-MANIFEST.json         |     0
 .../vendor/UPSTREAM-NOTICE.md                 |     0
 .../vendor/json.hpp                           |     0
 .../vendor/pr249-source.zip                   |   Bin
 .../verify.py                                 |    18 +-
 .../multicut-kernel-condensation-883/PROOF.md |    81 -
 .../README.md                                 |    64 -
 .../RESULT.json                               |    12 -
 .../discovery/README.md                       |    22 -
 .../expected/COHORT249-REPLAY.json            |    62 -
 69 files changed, 32530 insertions(+), 404 deletions(-)
 rename .github/workflows/{multicut-kernel-condensation-883.yml => multicut-kernel-composition.yml} (66%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/BANK-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/COPY-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/FINITE-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/KERNEL-PROOF.md (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/LICENSE (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/MANIFEST.json (54%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/NOTICE.md (50%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/PROOF-PR259.md (100%)
 create mode 100644 research/multicut-kernel-composition/PROOF.md
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/README-PR259.md (100%)
 create mode 100644 research/multicut-kernel-composition/README.md
 create mode 100644 research/multicut-kernel-composition/RESULT.json
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/REVIEW.md (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-bank-review.cpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-finite-invoice.cpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-five-stage-columns.cpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-legality-independent.cpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-prefix-independent.cpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-price.cpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/cohort-transform.cpp (100%)
 create mode 100644 research/multicut-kernel-composition/code/descent_retiming.py
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/code/export249.py (100%)
 create mode 100644 research/multicut-kernel-composition/code/plateau_retiming.py
 create mode 100644 research/multicut-kernel-composition/code/verify_frame_tables.py
 create mode 100644 research/multicut-kernel-composition/code/verify_frames.py
 create mode 100644 research/multicut-kernel-composition/code/verify_plateau_spans.py
 create mode 100644 research/multicut-kernel-composition/discovery/README.md
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/census2.py (100%)
 create mode 100644 research/multicut-kernel-composition/discovery/census3.py
 create mode 100644 research/multicut-kernel-composition/discovery/census3b.py
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/chrono2.py (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/compare259.py (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/gain.py (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/gen_candidates.py (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/merge2.py (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/merge259.py (100%)
 create mode 100644 research/multicut-kernel-composition/discovery/retime.py
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/discovery/twins.py (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/expected/COHORT-BANK-REVIEW.json (93%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/expected/COHORT-EXACT-PRICE.json (64%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/expected/COHORT-FINITE-INVOICE.json (51%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/expected/COHORT-FIVE-STAGE-COLUMNS.json (81%)
 create mode 100644 research/multicut-kernel-composition/expected/COHORT249-REPLAY.json
 create mode 100644 research/multicut-kernel-composition/expected/DESCENT-RETIMING.json
 create mode 100644 research/multicut-kernel-composition/expected/FRAME-TABLE-AUDIT.json
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/expected/INDEPENDENT-LEGALITY.json (77%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/expected/INDEPENDENT-PREFIX.json (57%)
 create mode 100644 research/multicut-kernel-composition/expected/PLATEAU-RETIMING.json
 create mode 100644 research/multicut-kernel-composition/expected/PLATEAU-SOURCE-SPANS.json
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/inputs/249-DONOR-OWNERSHIP.json.gz (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/inputs/249-records.bin.gz (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/inputs/249-states.json.gz (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/inputs/SNAPSHOTS.json (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/inputs/candidates.json.gz (51%)
 create mode 100644 research/multicut-kernel-composition/inputs/descent-selection.json
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/inputs/frames.json.gz (100%)
 create mode 100644 research/multicut-kernel-composition/inputs/plateau-selection.json
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/requirements.txt (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/vendor/PR249-SOURCE-MANIFEST.json (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/vendor/UPSTREAM-NOTICE.md (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/vendor/json.hpp (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/vendor/pr249-source.zip (100%)
 rename research/{multicut-kernel-condensation-883 => multicut-kernel-composition}/verify.py (79%)
 delete mode 100644 research/multicut-kernel-condensation-883/PROOF.md
 delete mode 100644 research/multicut-kernel-condensation-883/README.md
 delete mode 100644 research/multicut-kernel-condensation-883/RESULT.json
 delete mode 100644 research/multicut-kernel-condensation-883/discovery/README.md
 delete mode 100644 research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json

diff --git a/.github/workflows/multicut-kernel-condensation-883.yml b/.github/workflows/multicut-kernel-composition.yml
similarity index 66%
rename from .github/workflows/multicut-kernel-condensation-883.yml
rename to .github/workflows/multicut-kernel-composition.yml
index a4dbf8b6a8..5f14233f85 100644
--- a/.github/workflows/multicut-kernel-condensation-883.yml
+++ b/.github/workflows/multicut-kernel-composition.yml
@@ -1,14 +1,14 @@
-name: multicut-kernel-condensation-883
+name: multicut-kernel-composition
 
 on:
   pull_request:
     paths:
-      - 'research/multicut-kernel-condensation-883/**'
-      - '.github/workflows/multicut-kernel-condensation-883.yml'
+      - 'research/multicut-kernel-composition/**'
+      - '.github/workflows/multicut-kernel-composition.yml'
   push:
     paths:
-      - 'research/multicut-kernel-condensation-883/**'
-      - '.github/workflows/multicut-kernel-condensation-883.yml'
+      - 'research/multicut-kernel-composition/**'
+      - '.github/workflows/multicut-kernel-composition.yml'
 
 jobs:
   verify:
@@ -25,8 +25,8 @@ jobs:
       - name: Install the native toolchain of PR 259's checkers
         run: sudo apt-get update && sudo apt-get install -y g++ libboost-dev
       - name: Install SymPy for the pinned upstream regeneration
-        run: python -m pip install -r research/multicut-kernel-condensation-883/requirements.txt
+        run: python -m pip install -r research/multicut-kernel-composition/requirements.txt
       - name: Regenerate PR 249's word, compile and run the seven checkers on the 883-pivot selection, compare receipts and price
-        run: python3 -I research/multicut-kernel-condensation-883/verify.py --output /tmp/mc883-replay
+        run: python3 -I research/multicut-kernel-composition/verify.py --output /tmp/mkc-replay
       - name: Require an unchanged tree
         run: git diff --exit-code
diff --git a/research/multicut-kernel-condensation-883/BANK-PROOF.md b/research/multicut-kernel-composition/BANK-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/BANK-PROOF.md
rename to research/multicut-kernel-composition/BANK-PROOF.md
diff --git a/research/multicut-kernel-condensation-883/COPY-PROOF.md b/research/multicut-kernel-composition/COPY-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/COPY-PROOF.md
rename to research/multicut-kernel-composition/COPY-PROOF.md
diff --git a/research/multicut-kernel-condensation-883/FINITE-PROOF.md b/research/multicut-kernel-composition/FINITE-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/FINITE-PROOF.md
rename to research/multicut-kernel-composition/FINITE-PROOF.md
diff --git a/research/multicut-kernel-condensation-883/KERNEL-PROOF.md b/research/multicut-kernel-composition/KERNEL-PROOF.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/KERNEL-PROOF.md
rename to research/multicut-kernel-composition/KERNEL-PROOF.md
diff --git a/research/multicut-kernel-condensation-883/LICENSE b/research/multicut-kernel-composition/LICENSE
similarity index 100%
rename from research/multicut-kernel-condensation-883/LICENSE
rename to research/multicut-kernel-composition/LICENSE
diff --git a/research/multicut-kernel-condensation-883/MANIFEST.json b/research/multicut-kernel-composition/MANIFEST.json
similarity index 54%
rename from research/multicut-kernel-condensation-883/MANIFEST.json
rename to research/multicut-kernel-composition/MANIFEST.json
index 6f881e6efe..eefab935ca 100644
--- a/research/multicut-kernel-condensation-883/MANIFEST.json
+++ b/research/multicut-kernel-composition/MANIFEST.json
@@ -5,12 +5,12 @@
     "FINITE-PROOF.md": "dd0e1ac3a212f484086d51454ebcf951ccb98eddfe4713310f688750d35d0069",
     "KERNEL-PROOF.md": "4779181f679925da5c6663d4c5aec1a4a0aef76c993ab14b3a82782ac16bb883",
     "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
-    "NOTICE.md": "58f73a4bf8c08caea6e5039c878b889ba6cf871a8c5365ee0cab2cd935370cdb",
+    "NOTICE.md": "e5083ae8e3997c7c654c6606ca2d3ccf6305e09c9c57c1a59da5fe9cdfb5af23",
     "PROOF-PR259.md": "ffc502078acdfee7a89abe3ec51fae4b8c5a8be7440d6b55f3e24f138e1b1a3b",
-    "PROOF.md": "1019d2e57b0179cf0f38ea0f4488f3ecc2877b8d5ff4b432a8a024712fd979a6",
+    "PROOF.md": "e1e986740100ebedf202fa00b187fa661dca89afda6f268e6a521041b5fe03bc",
     "README-PR259.md": "ed2f4f051a21af9c173c0a7af7cac440ce15cabdabfc721895edde2c837cce25",
-    "README.md": "e826dbd919a91f7442138c919242537414d9a3dec40a5b3906f42157dff77368",
-    "RESULT.json": "42cae2c7d9cb8006fa88ebee459f2f025e2fe92f9c4380590fe6d942f3965350",
+    "README.md": "15b38b18ff80e0eae47a2b004feaa9dfef45595795d5e8a04dd0eed5d805d616",
+    "RESULT.json": "e8bf2a05353f7525a7cefaa9b2c09845ec304245b8866769c586cbe2e7d41e0a",
     "REVIEW.md": "823eea4cacf586ca90e43146fac48143f129f6ff8ca71c6a03b88c29fc528ff9",
     "code/cohort-bank-review.cpp": "cdac6b0460b7d70b40b1a15e1e255995d7c86220b4498005319d971313bb2d81",
     "code/cohort-finite-invoice.cpp": "dc0761a15c9b43ebdff3921dd2a49c80bb9158f544fb662ad45880a763cb5ab9",
@@ -19,34 +19,48 @@
     "code/cohort-prefix-independent.cpp": "81ea649c6bc8db9efead5330a49553b501a79114f0dd4d12a799adbe830b354d",
     "code/cohort-price.cpp": "885424440ff82a145817f04ec6cf15e4117c4675ccac57b4e55a8fcf7823ec2a",
     "code/cohort-transform.cpp": "afd916d0f539ccdb09e8231eade3b3f6b3e83bbb8107641e134943aa2b25af32",
+    "code/descent_retiming.py": "a07145a700d95642d54e35a33d5b50ac76ad665220d4f0599c07b22d939f5e10",
     "code/export249.py": "6c9aedb8fb4f2d560aca6cfc32ec967e003c0e623cc345040f108101ec1b442f",
-    "discovery/README.md": "841e342558c4d6dd2d7e2c9ff363a2f5c6fea307a3c9547add1c51ce4d6fc885",
+    "code/plateau_retiming.py": "6cd5ad6d3674cf32057da500d73a6695bd60de15b538b3c41f780cd183bd6b97",
+    "code/verify_frame_tables.py": "8c0587858e496e8cce9c5aa2ab5938d21c49837af715941bee6d02625f4a3e95",
+    "code/verify_frames.py": "aea01c7275088611c18ae110a2b4abf7b52f8cc8f70c5932a25588ddec4acd19",
+    "code/verify_plateau_spans.py": "594f1ababb4efc9e597154970ea51f6b850774f4b55f8cf386dbf1eb7fc5322b",
+    "discovery/README.md": "4dce8d7a8ee6939f413b627212bdd5e5776e8e1a1757915c1df1a59d1f69f831",
     "discovery/census2.py": "cea6fa83fa6f85dc0895bfcd9804c4a7b5c8bc06c0642e2c0321943b1b497121",
+    "discovery/census3.py": "02b2e94a5419bc343396ad954a083e09498b725561a7e0be7b0978a25950f3a0",
+    "discovery/census3b.py": "19cabd66e734e07ebbf74277b7962ca8e124b48c22f0c32d04978fa05936f962",
     "discovery/chrono2.py": "fc2866441540a8d6fa887439f185d0f51f298e1411eecb5ad84aba0de83b5b82",
     "discovery/compare259.py": "4c6d08cfb64891a804db677c15baf172d297109d9526d0c9d3764bd26a2dfa8f",
     "discovery/gain.py": "b76253949941854bcfd1ff84ebb49b9eaa9fcf4784690295f4a9e773694ddcfd",
     "discovery/gen_candidates.py": "6d7136a9c1c86463b1c25405481422ed98f6517d10aa1e99a038fccb6930d688",
     "discovery/merge2.py": "cb7d72dc5f8431628281cbd3fb17562d75b3242b882c19cc85cd30ee27617cf1",
     "discovery/merge259.py": "aba72c3e48314e842c06681fd62bb90e2a1f2a5dcb39794b1e22f54a6b74b850",
+    "discovery/retime.py": "5c82068777040e9e5fb9e9d5669d02a0f10c0651c8d2ccb362810c31bc31ad53",
     "discovery/twins.py": "c5b3f2065081002aa8da22584724938338fa46da2e25f3221225803e0f1b0ef7",
-    "expected/COHORT-BANK-REVIEW.json": "d77a4e1ed4ff3b50ea571213647fc60f349098a6b622e2010d09506128d057c6",
-    "expected/COHORT-EXACT-PRICE.json": "d8dc26a131b0eaa44df428b4db857db906d53051c94be66c43256a3b228fcd69",
-    "expected/COHORT-FINITE-INVOICE.json": "e2b30f56170f4260cf45e29fe60bdf148cc3bf47eda4b4289ca6b7efc7156f2c",
-    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "cdd8c42b512755a1c8776709fd6993c9c683c51ff61ec1968c7d613a94f89bb6",
-    "expected/COHORT249-REPLAY.json": "fbd72aa9ba17e254cc2cc51463f738a63d283add669c5b87c501aba7a9d6cc65",
-    "expected/INDEPENDENT-LEGALITY.json": "0871f37a0b4ac6e6d5588761a5d29c84e7a7fd79c32ce331d48441fce140fd64",
-    "expected/INDEPENDENT-PREFIX.json": "828899404ce3a4daf9d9d3562b395d1e0ac81afd17ae35abab3cebbe40342567",
+    "expected/COHORT-BANK-REVIEW.json": "669bbdaeca0ffe6e00991e6faf81120e87b78f89289b364e6a38dd297e278d5e",
+    "expected/COHORT-EXACT-PRICE.json": "ee418fd00f0a4da333aa4939fb66565573d2b21536e0170e263427b994cc8399",
+    "expected/COHORT-FINITE-INVOICE.json": "7cf97ec6b6d8ab8bacfdf09740536f9527abf697574400a1fd4d119fde5af236",
+    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "629fbfe696727ecd802aaafcddb83ff91b7155482926610dc750df2f163734ff",
+    "expected/COHORT249-REPLAY.json": "af2cb5ce2f2f62ea1b8e57a6bccd113d7ea116ae260dc23236348289243ad811",
+    "expected/DESCENT-RETIMING.json": "daf3a777838a4418947bf441c352630636580dca94c2599e07c64d4d6678c956",
+    "expected/FRAME-TABLE-AUDIT.json": "85c999e5ff201b573fb6e4267c2ea0ed5a58b81daccbc2c5311231f975f638fd",
+    "expected/INDEPENDENT-LEGALITY.json": "2f53482bf5c9df193fc667a5de0d487ad1028b14ccdbb4afdefe846d7786f6f5",
+    "expected/INDEPENDENT-PREFIX.json": "e06a1856db3e72ada0859d098fdf9e77e490fd75450312054e03ae039ac2cb94",
+    "expected/PLATEAU-RETIMING.json": "a18674ca15428e5ea258164f1f9c6f6cca2c0beacedfe6f213dcbc1e9373f6cc",
+    "expected/PLATEAU-SOURCE-SPANS.json": "5203527224527de7d2804e5deb0c06c58d94edc7c0db7470a8362c2646878b33",
     "inputs/249-DONOR-OWNERSHIP.json.gz": "cd506a4bbefbc33fecfca3b0364e0b237ece493a96ef3085c39cf2465f2265d4",
     "inputs/249-records.bin.gz": "6bc404d4af63218e714683d3e33fc1a53941e0155493747c3d0fb41b4a2de7b2",
     "inputs/249-states.json.gz": "562bcd7de03bf9474ad8c5cbc50008c92b02bfad81e32c2e532ebd45f384e844",
     "inputs/SNAPSHOTS.json": "3939f432a95db64073584e61a47e4983070450929ea1986c86a56552c0b03721",
-    "inputs/candidates.json.gz": "a6fad5e0ea650c4ec48035bedfc07c55f8b70ee4eafac37c6141ba368cd98f4a",
+    "inputs/candidates.json.gz": "94978b09567fd3766fa72eee5d244faf4ec2f9187693db7a9de64d2edad4303a",
+    "inputs/descent-selection.json": "e2f83db143fd7a323a57701912e03de179cf8755f9b5a31d6360aa5fb7a5c74a",
     "inputs/frames.json.gz": "54678a046e1c86b4d9308f69ef6d572a3b3745229e0ecb73843db7889e487cce",
+    "inputs/plateau-selection.json": "a4bda62e95c3a79036a482feabc9068227d80fa3480611217b427fe20fbe55b0",
     "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
     "vendor/PR249-SOURCE-MANIFEST.json": "f68fa82180cd352421b8bc3f7a5c89d51bde74e74cd8d62c222c28b0f23fcf31",
     "vendor/UPSTREAM-NOTICE.md": "9a659cc2f96ae7e0eda99954941c42a4529bc885fb1de161c44ea801ff36e480",
     "vendor/json.hpp": "aaf127c04cb31c406e5b04a63f1ae89369fccde6d8fa7cdda1ed4f32dfc5de63",
     "vendor/pr249-source.zip": "11e2b723f90c44e02f4aa78f5ae2160ae4b9b776d3f1c49e8bfec606959d692c",
-    "verify.py": "8afeb090e873f3eec29fd0aae44eeb0008f85ad3c050330be34b3710e90c8771"
+    "verify.py": "40bb3b53d391586ead4a441d6d469db3d837ec9d954ff723094958562cde92b1"
   }
 }
diff --git a/research/multicut-kernel-condensation-883/NOTICE.md b/research/multicut-kernel-composition/NOTICE.md
similarity index 50%
rename from research/multicut-kernel-condensation-883/NOTICE.md
rename to research/multicut-kernel-composition/NOTICE.md
index 34b55db332..918ea53b27 100644
--- a/research/multicut-kernel-condensation-883/NOTICE.md
+++ b/research/multicut-kernel-composition/NOTICE.md
@@ -3,19 +3,24 @@
 Prepared by Chafik Boukhalfa with substantial Anthropic Claude assistance. Apache-2.0.
 This package claims no exclusive priority over concurrent work.
 
-What this package contributes: the census of twin dirty helpers at PR #259's earliest cut, the 365 added
-response-kernel families (`inputs/candidates.json.gz`, entries with round "union-early-cut" and "headroom-2"), the regenerated
-receipts, and the discovery scripts in `discovery/`. Everything else is PR #259's package, retained byte for
-byte except the frozen selection, the receipts, RESULT.json, MANIFEST.json, one field name added to the
-platform-dependent list of verify.py, and these notes:
-
-- Dugongue (OpenAI Codex assistance): PR #254 (the response-kernel pair rewrite, the projector charts and the
-  native checkers) and PR #259 (multi-cut kernel condensation, the generic exact chart audit, the seven
-  checkers, the pricer and the finite invoice used here unchanged; its notes are kept as README-PR259.md,
-  PROOF-PR259.md, KERNEL-PROOF.md, BANK-PROOF.md, COPY-PROOF.md, FINITE-PROOF.md, REVIEW.md).
+What this package contributes: the censuses of twin dirty helpers at PR #259's earliest cut and of shared donors,
+the 387 added kernel families (`inputs/candidates.json.gz`, rounds "union-early-cut", "headroom-2", "shared-donor"),
+the rebinding of the two published retiming selections to this transcript, the regenerated receipts, and the
+discovery scripts in `discovery/`. Everything else is retained and credited:
+
+- Dugongue (OpenAI Codex assistance): PR #254 (the response-kernel pair rewrite, projector charts, native checkers),
+  PR #259 (multi-cut kernel condensation, the generic exact chart audit, the seven checkers, the pricer and the
+  finite invoice, used here unchanged except one `std::stable_sort`; its notes kept as README-PR259.md,
+  PROOF-PR259.md, KERNEL-PROOF.md, BANK-PROOF.md, COPY-PROOF.md, FINITE-PROOF.md, REVIEW.md), PR #267 (chronological
+  donor sharing, the idea behind the shared-donor families).
+- rohanarun: PR #263 (the concave-descent frame retiming stage `code/descent_retiming.py` and its 25-gate selection,
+  used verbatim), PR #237/#209 (five-stage bit supplier, width-120 banks), PR #269.
+- utcorvusvolat-dotcom: PR #270 (the 24 reuse pairs and two e = 2 planes, the plateau retiming stage
+  `code/plateau_retiming.py` with `verify_frames.py`, `verify_plateau_spans.py`, `verify_frame_tables.py` and the
+  29-block selection, and the rebinding of PR #263's selection by scalar-core alignment, all used verbatim).
 - eumemic (Anthropic Claude and OpenAI Codex assistance): PR #249/#244/#251 (the source527 bit word, entrance
-  banks, retimed source pairs, transported entrances) on PR #210's helper and PR #168's modules; hcg890 PR #234
-  and rohanarun PR #237/#209 (five-stage bit supplier, width-120 banks); sennemmi PR #230.
+  banks, retimed source pairs, transported entrances) on PR #210's helper and PR #168's modules; PR #268.
+- hcg890 PR #234 (five-stage bit and complex suppliers); sennemmi PR #230/#261/#265; evmckinney9 PR #271.
 - The PR #249 lineage as credited in vendor/UPSTREAM-NOTICE.md and below.
 
 ---- PR #259's notice follows unchanged ----
diff --git a/research/multicut-kernel-condensation-883/PROOF-PR259.md b/research/multicut-kernel-composition/PROOF-PR259.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/PROOF-PR259.md
rename to research/multicut-kernel-composition/PROOF-PR259.md
diff --git a/research/multicut-kernel-composition/PROOF.md b/research/multicut-kernel-composition/PROOF.md
new file mode 100644
index 0000000000..f6984e8ba3
--- /dev/null
+++ b/research/multicut-kernel-composition/PROOF.md
@@ -0,0 +1,89 @@
+# Kernel families at the early cut, shared donors, and the two retimings, composed
+
+**Claim.** On PR #249's bit word (commit `96495746`), PR #259's multi-cut kernel condensation extended to 890 pivot
+families (entrance rank 1,719) and retimed by PR #263's 25 descent gates and PR #270's 29 plateau blocks is a legal
+word of the same model with literal bank stock 866,550 and κ = 711482139228173/10¹⁸ = 7.11482139228173·10⁻⁴, checked
+by PR #259's seven native checkers, the two retiming stages' own audits, and PR #259's exact pricer, under the retained
+public all-size hypotheses of PR #249/#254/#259.
+
+## 1. The mechanism (PR #254/#259, unchanged)
+
+A dirty helper j untouched before a cut (initial frame ZERO, final frame FULL, no write, copy or non-initial read
+before the cut) acts on the targets only through its initial zero-frame compensation reads, so its *complete target
+response* R_j ∈ F₂^1760 is a column of the prefix's target map. Helpers a, b with R_a = R_b and a nondegenerate common
+entrance subspace E inside both first required frames admit the rewrite: a (the pivot) starts at E and its initial
+reads are deleted; b (the donor) moves ZERO → E at the cut and absorbs a there (Q = I + e_b e_aᵀ); the old word
+resumes from E; Q⁻¹ is paid at the full frame; the omitted response R_a·a and the induced change R_b·a cancel. PR #259
+generalises this to several simultaneous zero-response directions at four cuts and admits any entrance through an
+exact chart audit (B⁻¹(I − σ)B diagonal, factor count ≤ 548, intermediates below 2⁸⁰).
+
+## 2. The families added
+
+Cut 676,559 is the last initial compensation read (records 0..676,559 are the 676,560 initial reads; the first MOVE
+follows). Among the 14,286 clean helpers live there, the responses form 985 twin classes of size two and 24 of size
+nine. Three rounds, each admitted by the φ ledger (with the deficit pinned at 35,200 per replica the coarse exponent is
+driven by Σ r·n·ln(120/r), φ(r) = r·ln(120/r); a pair with first ranks (r_a, r_b) and e = 1 changes it by
+φ(r_a − 1) − φ(r_a) + φ(1) + φ(r_b − 1) − φ(r_b): −2.02 for (2, 2), −0.97 for (3, 3)):
+
+1. `union-early-cut`: 333 twin pairs disjoint from all 1,194 helpers of PR #259's families (319 with first frames
+   (2, 2) on lines u = eᵢ − eⱼ — norm 2, cleared Gram 9·uᵀu − (Σu)² = 18, excluded primes {2, 3} as for the ±1-four
+   lines of PR #254, which PR #254's `norm == 4` rule excluded and PR #259's generic audit admits — and 14 pairs
+   (3, 5), (3, 3), (3, 6) with ±1-four lines), two dropped for the mod-3 rule.
+2. `headroom-2`: every response class of any size at twelve cuts from 676,559 to 727,593, pairs and XOR triples
+   R_c = R_a ⊕ R_b; 32 more disjoint net-positive families, all at 676,559 (28 (3, 3), two (3, 6), one (3, 5) with e = 1,
+   one (3, 5) on its full two-dimensional nondegenerate intersection); nothing at any later cut; no net-positive triple
+   (a partner costs φ(1) + φ(r − 1) − φ(r) > 0).
+3. `shared-donor`: PR #259's transform only requires pivots to be unique and never donors; a partner may serve several
+   families, being moved to each family's entrance in increasing dimension at its cut, so a shared donor is legal when
+   its entrances form a nested chain and its own first use is after every cut it serves. For every current donor d and
+   every clean untouched helper p with R_p = R_d, the entrance is d's existing subspace when it lies inside F_p (the
+   lift already paid) or a nondegenerate line inside E_d ∩ F_p; greedy by gain, dissolving a plain pair when a
+   shared-donor alternative is strictly better and its donor serves no other family: 54 shared-donor families (51 on
+   the donor's existing entrance, 3 on nested lines; pivot ranks 49 × 3, 5 × 5), 26 pairs dissolved (11 of round 1, 15 of
+   PR #259's at 680,080 and 700,582, whose helpers re-enter as pivots or donors of better families), including all 24
+   reuse pairs and the two e = 2 planes of PR #270.
+
+Total: 890 families (PR #259's remaining 503 + 387 added), entrance rank 1,719 ≡ 0 mod 3, 1,903 helpers, 96 shared
+donors; 60,520 initial reads removed, 2,286 gates paid.
+
+## 3. The two retimings
+
+PR #263 (rohanarun) reassigns the frames of 25 internal ADD gates found by local descent on the concave paid-rank
+objective Σ r·ln(120/r); its selection binds gates by ADD ordinal, scalar content and old basis and is gated by the
+input transcript's sha256. PR #270 (utcorvusvolat-dotcom) ships the rebinding (full scalar-core alignment: every
+ADD/COPY/ERASE event outside the kernel categories must be identical) together with its own stage, 29 connected
+plateau blocks of 57 ADDs retimed jointly, with audits of the operand source spans and of all added frames. Both
+selections rebind to this transcript (the core events are identical; 18 of the 25 descent gates touch registers that
+are helpers here, and every self-check of the stage still passes, so disjointness from the pivots was sufficient, not
+necessary). Histogram deltas: descent {2: −2, 4: +24, 5: −48, 6: +25, 11: −1, 13: +2, 17: −1} (one call removed);
+plateau {1: +15, 2: −26, 3: +19, 4: −7, 5: −3, 6: +21, 7: −24, 8: +8, 9: −14, 10: −2, 11: +13, 12: −4, 13: +4} (calls
+and mass unchanged).
+
+## 4. What is checked (receipts in `expected/`)
+
+| stage | receipt |
+|---|---|
+| `cohort-transform` (all-column F₂ replay) | 890 pivots, entrance rank 1,719, 60,520 initial reads removed, 2,286 gates, raw mass 434,177 → 432,458; omitted-Q and omitted-Q⁻¹ controls fail nontrivially |
+| `descent_retiming` → `plateau_retiming` | sha gates cohort d073aeb4… → descent 43a73a44… → final 4f6ffc1d… (828,136 records); spans and frame-table audits PASS |
+| `cohort-legality-independent` | 1,903 helpers, 0 source-owner and 0 donor intersections, 24 COPY/ERASE windows, all final frames |
+| `cohort-prefix-independent` | 890 cohorts, 4 cuts, 1,566,400 target-kernel equalities |
+| `cohort-bank-review` | literal stock 866,550 (saved 2,865), 919 exact charts (at most 262 factors), 3,317,400 assignments, selector 626,937,131,600 |
+| `cohort-five-stage-columns` | 23,627 columns, payload 98 bits |
+| `cohort-price` | coarse 142397741344279/(2·10¹⁷), W 173,310, 3,970,400 calls, mass 20,762,000, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
+| `cohort-finite-invoice` | PASS, deficit 176,000, cutoffs positive |
+
+Control: PR #259's own selection through the same transform reproduces its κ exactly, and the stable-sorted PR #259
+word is byte for byte the input PR #263's selection is bound to (sha 1ae06b18…), whose descent output is the input of
+PR #270's plateau selection (80af525c…).
+
+Platform matters (so that one package verifies on Linux/g++ and macOS/clang alike): `code/cohort-transform.cpp` uses
+`std::stable_sort` on the gauge order (the tie order of `std::sort` differs between libstdc++ and libc++ and changed the
+transcript's sha256); `verify.py` drops `containment_pairs_checked` (a memo-cache miss counter) from the compared
+receipt fields and normalizes both sides. Nothing else of PR #259's code changes; `discovery/README.md` lists the diff.
+
+## 5. Not claimed, not composed
+
+No Lean certificate; the public all-size interfaces of PR #249 are retained as hypotheses. Not composed here:
+eumemic's target-prefix compression (PR #268; PR #273 composes it with #269, PR #272 with collective kernels) and
+evmckinney9's cleanup sandwiches (PR #271); 492 twin candidates whose donor's entrance is not inside the new pivot's
+first frame and multi-donor relations R_p = R_d₁ ⊕ R_d₂ were not searched.
diff --git a/research/multicut-kernel-condensation-883/README-PR259.md b/research/multicut-kernel-composition/README-PR259.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/README-PR259.md
rename to research/multicut-kernel-composition/README-PR259.md
diff --git a/research/multicut-kernel-composition/README.md b/research/multicut-kernel-composition/README.md
new file mode 100644
index 0000000000..0f14da4877
--- /dev/null
+++ b/research/multicut-kernel-composition/README.md
@@ -0,0 +1,65 @@
+# multicut-kernel-composition
+
+**Conditional κ = 711482139228173 / 10¹⁸ = 7.11482139228173·10⁻⁴** (+0.0637% over PR #259's 7.11029386054035·10⁻⁴;
++0.0034% over PR #270's 7.11457853376510·10⁻⁴, the best kernel-condensation rung before this one).
+
+PR #259 (Dugongue) condenses response kernels of the PR #249 bit word with 518 pivot families at four cuts. This
+package composes, on that word and with PR #259's seven native checkers and pricer unchanged:
+
+1. **372 more kernel families at its earliest cut** (record 676,559, the last initial compensation read): a census of
+   the twin dirty helpers live at that cut — helpers untouched before it whose complete F₂ target responses coincide
+   — gives 985 twin pairs; the net-positive ones disjoint from PR #259's helpers (first round 333, second round 32),
+   two e = 2 planes of PR #270, and **54 shared-donor families** (a new pivot whose twin partner is already a donor of
+   another family, lifted once on a nested entrance chain, as the 24 reuse pairs of PR #270 and the chronological donor
+   sharing of PR #267; 26 plain pairs are dissolved where a shared-donor family is strictly better). Result: **890
+   families, entrance rank 1,719, 1,903 helpers, 96 donors shared by two or more families**, cuts {676,559: 488;
+   680,080: 89; 700,582: 63; 727,593: 250}; 60,520 initial reads removed, 2,286 basis gates paid, raw rank mass
+   434,177 → 432,458.
+2. **PR #263's 25 concave-descent gate retimings** (rohanarun; stage `code/descent_retiming.py`, selection rebound to
+   this transcript by full scalar-core alignment; −1 local call) and **PR #270's 29 connected-block plateau
+   retimings of 57 ADDs** (utcorvusvolat-dotcom; stages `code/plateau_retiming.py`, `verify_plateau_spans.py`,
+   `verify_frame_tables.py`; calls and mass unchanged, rank distribution improved).
+
+| | PR #259 | PR #270 | this package |
+|---|---|---|---|
+| pivot families / entrance rank | 518 / 1,344 | 887 / 1,716 | **890 / 1,719** |
+| normalized stock W / child calls / rank mass | 173,435 / 3,956,840 / 20,777,000 | 173,311 / 3,970,720 / 20,762,120 | **173,310 / 3,970,400 / 20,762,000** |
+| literal bank stock / exact charts | 867,175 / 518 | — | 866,550 / 919 |
+| κ | 7.11029386054035·10⁻⁴ | 7.11457853376510·10⁻⁴ | **7.11482139228173·10⁻⁴** |
+
+The deficit 120·W − mass = 35,200 per replica is invariant under all of these rewrites (a pivot's residual 24 → 23
+shrinks the bank capacity by exactly the mass it saves), so the exponent moves through the log-weighted mass
+Σ r·n·ln(120/r) alone; every family and every retiming is admitted or rejected by PR #259's exact pricer on the whole
+word, never added as an estimate. [PROOF.md](PROOF.md) states the delta and the checks; PR #259's notes are kept
+unchanged as `README-PR259.md`, `PROOF-PR259.md`, `KERNEL-PROOF.md`, `BANK-PROOF.md`, `COPY-PROOF.md`, `FINITE-PROOF.md`,
+`REVIEW.md`.
+
+Conditional, finite construction under the same retained public all-size hypotheses as PR #249/#254/#259 (no Lean
+certificate, no unconditional theorem). κ is the bit-bound value: the complex supplier of this lineage stands at
+7.5474·10⁻⁴ five-stage (PR #256, Lean-checked in jacobalansussman/wht-power-saving-lean#2), so the bit supplier binds.
+Two other levers on the same word are not composed here: eumemic's target-prefix compression (PR #268, PR #273 on
+#269, PR #272 on collective kernels) and evmckinney9's cleanup sandwiches (PR #271); PR #272 stands above this package.
+
+## Verify
+
+    sudo apt-get install -y g++ libboost-dev            # Linux; macOS: brew install boost, --cxx clang++ with a bits/stdc++.h shim
+    python -m pip install -r research/multicut-kernel-composition/requirements.txt    # sympy 1.14.0
+    python3 -I research/multicut-kernel-composition/verify.py --output /tmp/mkc-replay      # fresh directory outside the package; about 3 minutes
+
+PR #259's verifier with the two retiming stages inserted between its transform and its checkers (stages 02b–02e,
+each gated by the sha256 of the transcript it consumes): package hashes against `MANIFEST.json`, regeneration of the
+pinned PR #249 word from `vendor/pr249-source.zip` (SymPy), the seven checkers compiled and run, the descent and
+plateau stages with their own audits (operand source spans, frame tables), every receipt compared with `expected/`
+(platform-independent fields), then `PASS: kappa = 0.000711482139228173`. `--snapshots-only` skips the upstream
+regeneration. `.github/workflows/multicut-kernel-composition.yml` runs it on Ubuntu (Python 3.11 and 3.13).
+
+## Files
+
+PR #259's package (`code/cohort-*.cpp`, `code/export249.py`, `inputs/249-*`, `inputs/frames.json.gz`,
+`inputs/SNAPSHOTS.json`, `vendor/`, the proof notes, `requirements.txt`, `LICENSE`) with the frozen selection
+`inputs/candidates.json.gz` (PR #259's 518 items, then ours with `round` = `union-early-cut`, `headroom-2`,
+`shared-donor`), PR #263's and PR #270's stages (`code/descent_retiming.py`, `code/plateau_retiming.py`,
+`code/verify_frames.py`, `code/verify_plateau_spans.py`, `code/verify_frame_tables.py`; `inputs/descent-selection.json`,
+`inputs/plateau-selection.json`, rebound to this transcript), `verify.py` (PR #259's with the stages and three
+sha gates), `expected/` (eleven receipts), `RESULT.json`, `MANIFEST.json`, `discovery/` (the censuses, merges and
+the rebinding chain; not run by the verifier), `README.md`, `PROOF.md`, `NOTICE.md`.
diff --git a/research/multicut-kernel-composition/RESULT.json b/research/multicut-kernel-composition/RESULT.json
new file mode 100644
index 0000000000..030eecd06a
--- /dev/null
+++ b/research/multicut-kernel-composition/RESULT.json
@@ -0,0 +1,17 @@
+{
+  "kappa": "711482139228173/1000000000000000000",
+  "kappa_decimal": "0.000711482139228173",
+  "baseline_head": "96495746c786d6d0339dbb38c7f553d4af3f88ed",
+  "baseline_kappa": "0.000710392186446856",
+  "previous_delivery_kappa": "0.000711443979017358",
+  "new_record_sha256": "4f6ffc1daa5ef309e82c5a7e639b9e3c9f19bdcd2f2bfec865f8fbfc8fbc5b3d",
+  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES",
+  "lean_certificate": false,
+  "pivots": 890,
+  "entrance_rank": 1719,
+  "cohort_record_sha256": "d073aeb4a8054ee6e23366ac7a42554624d52d3a822e03de9831a12530287395",
+  "descent_record_sha256": "43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6",
+  "descent_retimed_gates": 25,
+  "plateau_retimed_blocks": 29,
+  "plateau_retimed_gates": 57
+}
diff --git a/research/multicut-kernel-condensation-883/REVIEW.md b/research/multicut-kernel-composition/REVIEW.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/REVIEW.md
rename to research/multicut-kernel-composition/REVIEW.md
diff --git a/research/multicut-kernel-condensation-883/code/cohort-bank-review.cpp b/research/multicut-kernel-composition/code/cohort-bank-review.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-bank-review.cpp
rename to research/multicut-kernel-composition/code/cohort-bank-review.cpp
diff --git a/research/multicut-kernel-condensation-883/code/cohort-finite-invoice.cpp b/research/multicut-kernel-composition/code/cohort-finite-invoice.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-finite-invoice.cpp
rename to research/multicut-kernel-composition/code/cohort-finite-invoice.cpp
diff --git a/research/multicut-kernel-condensation-883/code/cohort-five-stage-columns.cpp b/research/multicut-kernel-composition/code/cohort-five-stage-columns.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-five-stage-columns.cpp
rename to research/multicut-kernel-composition/code/cohort-five-stage-columns.cpp
diff --git a/research/multicut-kernel-condensation-883/code/cohort-legality-independent.cpp b/research/multicut-kernel-composition/code/cohort-legality-independent.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-legality-independent.cpp
rename to research/multicut-kernel-composition/code/cohort-legality-independent.cpp
diff --git a/research/multicut-kernel-condensation-883/code/cohort-prefix-independent.cpp b/research/multicut-kernel-composition/code/cohort-prefix-independent.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-prefix-independent.cpp
rename to research/multicut-kernel-composition/code/cohort-prefix-independent.cpp
diff --git a/research/multicut-kernel-condensation-883/code/cohort-price.cpp b/research/multicut-kernel-composition/code/cohort-price.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-price.cpp
rename to research/multicut-kernel-composition/code/cohort-price.cpp
diff --git a/research/multicut-kernel-condensation-883/code/cohort-transform.cpp b/research/multicut-kernel-composition/code/cohort-transform.cpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/cohort-transform.cpp
rename to research/multicut-kernel-composition/code/cohort-transform.cpp
diff --git a/research/multicut-kernel-composition/code/descent_retiming.py b/research/multicut-kernel-composition/code/descent_retiming.py
new file mode 100644
index 0000000000..8da965937d
--- /dev/null
+++ b/research/multicut-kernel-composition/code/descent_retiming.py
@@ -0,0 +1,209 @@
+#!/usr/bin/env python3
+"""Concave-descent frame retiming of selected ADD gates on the cohort-rewritten transcript.
+
+Reads the native six-int transcript written by cohort-transform, the exported
+frame tables and the frozen selection, reassigns the selected ADD frames, rebuilds
+every MOVE from the actual gate needs, and checks: byte-identical scalar/COPY
+projection, nested chains, unchanged initial/final frames and COPY lifetimes,
+nondegenerate endpoint bases, exact integer source span of every non-target
+operand inside its new frame, and the expected histogram delta at unchanged rank
+mass. The downstream native legality, column, bank, price and invoice checkers
+re-examine the rewritten transcript independently. Prepared by Rohan Arun with
+Anthropic Claude assistance; Apache-2.0.
+"""
+from array import array
+from collections import Counter
+from fractions import Fraction
+from math import gcd
+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 rref_key(rows):
+    M = [[Fraction(x) for x in r] for r in rows]; r = 0
+    for c in range(H):
+        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 tuple(tuple(x) for x in M[:r])
+
+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 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
+
+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=[list(map(int, r)) for r in rec['B']], A=[list(map(int, 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'])
+by_key = {}
+for f in sorted(frames): by_key.setdefault(rref_key(frames[f]['B']) if frames[f]['B'] else (), f)
+canon = {f: by_key[rref_key(frames[f]['B']) if frames[f]['B'] else ()] for f in frames}
+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']
+initial = {int(k): f for k, f in json.loads((LEAD/'COHORT249-INITIAL.json').read_text()).items()}
+sel = json.loads(SEL.read_text())
+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]
+assert all(final[i] == FULL for i in initial if i < v or i >= 2*v)
+cov = [list(map(int, c)) for c in st['source_covectors']]
+chi = {s: frames[initial[s]]['B'][0] for s in range(v)}
+for s in range(v): assert frames[initial[s]]['d'] == 1
+# selected gates: bound by ADD ordinal among non-MOVE records and by scalar content
+nonmove = [k//6 for k in range(0, len(old), 6) if old[k]]
+chosen = {}; changed = []
+for r in sel['entries']:
+    i = nonmove[r['gate']]; assert i not in chosen
+    op, a, b, c, f, z = old[6*i:6*i+6]
+    assert op == 1 and b != n and [a, b, c, z] == r['scalar'] and frames[f]['d'] == r['old_dimension']
+    assert rref_key(frames[f]['B']) == rref_key([list(map(int, x)) for x in r['old_basis']]), 'old frame basis mismatch'
+    g = by_key.get(rref_key([list(map(int, x)) for x in r['new_basis']])); assert g is not None, 'new frame absent from exported tables'
+    assert frames[g]['d'] == r['new_dimension'] and nondeg(g) and canon[g] != canon[f]
+    chosen[i] = g; changed.append(dict(record=i, gate=r['gate'], old_frame=f, new_frame=g, old_dimension=frames[f]['d'], new_dimension=frames[g]['d']))
+assert len(chosen) == sel['selected_gate_count'] > 0
+# exact integer source spans after each selected gate
+columns = [{i: 1} if i < v else {} for i in range(n)]; center = None; spans = {}
+for k in range(0, len(old), 6):
+    op, a, b, c, f, z = old[k:k+6]
+    if op == 0: continue
+    if op == 2: assert center is None; center = a; continue
+    if op == 3: assert center == a; center = None; continue
+    source = center if b == n else b; ca = columns[a]
+    for s, x in columns[source].items():
+        y = ca.get(s, 0) + c*x
+        if y: ca[s] = y
+        else: del ca[s]
+    if k//6 in chosen:
+        need = set()
+        if not (v <= a < 2*v): need.update(ca)
+        if not (v <= b < 2*v) and b != n: need.update(columns[b])
+        spans[k//6] = sorted(need)
+assert center is None
+for i, g in chosen.items():
+    for s in spans[i]: assert all(dot(x, chi[s]) == 0 for x in frames[g]['A']), ('retimed frame omits operand source span', i, s)
+# rebuild MOVEs from the retimed needs
+state = dict(initial); out = array('i'); copy = None
+def move(s, f):
+    before = state[s]
+    if before == f: return
+    assert sub(before, f), ('descent frame nesting', s, before, f)
+    gap = frames[f]['d'] - frames[before]['d']; assert gap >= 0
+    out.extend((0, s, before, f, gap, 0)); state[s] = f
+for k in range(0, len(old), 6):
+    op, a, b, c, f, z = old[k:k+6]
+    if op == 0: continue
+    if op == 1:
+        g = chosen.get(k//6, f)
+        if copy is not None and k//6 in chosen: assert a != copy[0] and b != copy[0]
+        move(a, g)
+        if b == n: assert g == f == ZERO and copy is not None
+        else: move(b, g)
+        out.extend((op, a, b, c, g, z))
+    elif op == 2:
+        assert copy is None and b == n; move(a, c); state[b] = f; copy = (a, b, c); out.extend((op, a, b, c, f, z))
+    else:
+        assert op == 3 and copy == (a, b, c) and state[a] == c and state[b] == f
+        out.extend((op, a, b, c, f, z)); del state[b]; copy = None
+assert copy is None
+for s in sorted(final): move(s, final[s])
+assert state == final
+def projection(a):
+    return hashlib.sha256(b''.join(a[k:k+4].tobytes() + a[k+5:k+6].tobytes() for k in range(0, len(a), 6) if a[k])).hexdigest()
+assert projection(old) == projection(out)
+# independent census from needs and endpoints; ranks are exact dimension gaps
+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
+replay = json.loads((LEAD/'COHORT249-REPLAY.json').read_text())
+oldH = Counter({int(r): c for r, c in replay['histogram'].items()})
+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()) == replay['new_rank_mass'] == sel['expected_rank_mass']
+assert sum(hist.values()) == sum(oldH.values()) - sel['expected_removed_calls'] and count == sel['expected_scalar_additions']
+(LEAD/'COHORT249-PRE-DESCENT-RECORDS.bin').write_bytes(old.tobytes())
+(LEAD/'COHORT249-RECORDS.bin').write_bytes(out.tobytes())
+# 'delta' stays the total change against the pinned PR249 baseline, which the price checker rebuilds from it.
+combined = Counter({int(r): c for r, c in replay['delta'].items()}); combined.update(delta); combined = {r: c for r, c in combined.items() if c}
+replay.update(status='PASS_FULL_CURRENT249_COHORT_REWRITE_AND_CONCAVE_DESCENT_RETIMING', cohort_rewrite_records=len(old)//6, new_records=len(out)//6,
+              cohort_rewrite_histogram=replay['histogram'], cohort_rewrite_delta=replay['delta'], histogram={str(r): c for r, c in sorted(hist.items())},
+              delta={str(r): c for r, c in sorted(combined.items())}, descent_delta={str(r): c for r, c in sorted(delta.items())},
+              descent_retimed_gates=len(changed), descent_removed_calls=sel['expected_removed_calls'])
+(LEAD/'COHORT249-REPLAY.json').write_text(json.dumps(replay, indent=2) + '\n')
+receipt = dict(status='PASS_CONCAVE_DESCENT_RETIMING_AND_BOTH_REFLECTED_LEDGERS', selected_gate_count=len(changed), changed_gates=changed,
+               removed_calls=sel['expected_removed_calls'], 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()), scalar_additions=count,
+               identical_scalar_and_copy_projection=True, both_reflected_ledgers=True, unchanged_all_input_output_frames=True,
+               unchanged_copy_lifetimes=True, operand_source_spans_contained=True, checked_operand_spans=sum(len(s) for s in spans.values()),
+               unique_required_frame_pairs=len(pairs), input_record_sha256=sel['input_record_sha256'], output_record_sha256=hashlib.sha256(out.tobytes()).hexdigest(),
+               selection_sha256=hashlib.sha256(SEL.read_bytes()).hexdigest())
+(LEAD/'DESCENT-RETIMING.json').write_text(json.dumps(receipt, indent=2) + '\n')
+print('PASS concave descent retiming', len(changed), 'gates', sum(hist.values()), 'paid calls', len(out)//6, 'records', flush=True)
diff --git a/research/multicut-kernel-condensation-883/code/export249.py b/research/multicut-kernel-composition/code/export249.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/code/export249.py
rename to research/multicut-kernel-composition/code/export249.py
diff --git a/research/multicut-kernel-composition/code/plateau_retiming.py b/research/multicut-kernel-composition/code/plateau_retiming.py
new file mode 100644
index 0000000000..1227805310
--- /dev/null
+++ b/research/multicut-kernel-composition/code/plateau_retiming.py
@@ -0,0 +1,62 @@
+#!/usr/bin/env python3
+import argparse,json,hashlib,shutil,sys
+from pathlib import Path
+from array import array
+from collections import Counter
+if not __debug__:raise SystemExit('assertions are required')
+assert sys.byteorder=='little' and array('i').itemsize==4
+ap=argparse.ArgumentParser();ap.add_argument('export',type=Path);ap.add_argument('lead',type=Path);ap.add_argument('scan',type=Path);ap.add_argument('output',type=Path);args=ap.parse_args()
+X,L,O=args.export,args.lead,args.output;O.mkdir()
+for name in ('COHORT249-INITIAL.json','COHORT249-SELECTION.json','descent-selection.json',
+             'DESCENT-RETIMING.json','DESCENT-REBIND-EVIDENCE.json'):
+ shutil.copy2(L/name,O/name)
+fs={int(k):v for k,v in json.loads((X/'frames.json').read_text())['frames'].items()};new={int(k):v for k,v in json.loads((L/'COHORT249-FRAMES.json').read_text()).items()};fs.update(new)
+scan=json.loads(args.scan.read_text());added={int(k):v for k,v in scan.get('newframes',{}).items()}
+assert not set(added)&set(fs),'plateau frame ID collision'
+from verify_frames import validate
+for frame in added.values():validate(frame)
+fs.update(added)
+chosen=[];roles=set();mutations={};expected=Counter()
+for c in scan['candidates']:
+ assert not set(c['roles'])&roles,'frozen plateau roles overlap'
+ chosen.append(c);roles.update(c['roles']);expected.update({int(k):v for k,v in c['delta'].items()})
+ for g in c['gates']:assert g not in mutations;mutations[g]=(c['old_frame'],c['new_frame'])
+ if str(c['new_frame']) in scan.get('newframes',{}):new[c['new_frame']]=fs[c['new_frame']]
+print('selected',len(chosen),'gates',len(mutations),'entropy_gain',sum(c['entropy_gain'] for c in chosen),'delta',dict(expected),flush=True)
+raw=array('i');raw.frombytes((L/'COHORT249-RECORDS.bin').read_bytes());events=[tuple(raw[k:k+6]) for k in range(0,len(raw),6) if raw[k]]
+assert len(raw)%6==0
+assert hashlib.sha256(raw.tobytes()).hexdigest()==scan['input_sha256'],'frozen plateau input mismatch'
+st=json.loads((X/'249-states.json').read_text());n=st['n'];initial={int(k):v for k,v in json.loads((L/'COHORT249-INITIAL.json').read_text()).items()};final={int(k):v for k,v in st['final'].items()};state=dict(initial);out=array('i');cache={};hist=Counter();copy=None
+def sub(a,b):
+ if a==b:return True
+ if (a,b) not in cache:cache[a,b]=fs[a]['dim']<=fs[b]['dim'] and all(sum(x*y for x,y in zip(u,v))==0 for u in fs[a]['B'] for v in fs[b]['A'])
+ return cache[a,b]
+def move(s,f):
+ p=state[s]
+ if p==f:return
+ assert sub(p,f),(s,p,f)
+ r=fs[f]['dim']-fs[p]['dim'];out.extend((0,s,p,f,r,0));state[s]=f
+ if r:hist[r]+=1
+for i,(op,a,b,c,f,z) in enumerate(events):
+ if op==1:
+  if i in mutations:
+   old,fnew=mutations[i];assert old==f;f=fnew
+  move(a,f);move(b,f);out.extend((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);hist[z]+=1;out.extend((op,a,b,c,f,z))
+ else:
+  assert op==3 and copy==(a,b,c,f) and state[a]==c and state[b]==f;del state[b];copy=None;out.extend((op,a,b,c,f,z))
+for s in sorted(final):move(s,final[s])
+assert copy is None and state==final
+def projection(a):return hashlib.sha256(b''.join(a[k:k+4].tobytes()+a[k+5:k+6].tobytes() for k in range(0,len(a),6) if a[k])).hexdigest()
+assert projection(raw)==projection(out)
+replay=json.loads((L/'COHORT249-REPLAY.json').read_text());oldH=Counter({int(k):v for k,v in replay['histogram'].items()});delta=Counter(hist);delta.subtract(oldH);delta={k:v for k,v in delta.items() if v};expected={k:v for k,v in expected.items() if v};assert delta==expected,(delta,expected)
+assert delta=={int(k):v for k,v in scan['expected_delta'].items() if v}
+assert set(mutations)<=set(range(len(events))) and all(events[g][0]==1 for g in mutations)
+assert sum(k*v for k,v in hist.items())==sum(k*v for k,v in oldH.items())
+assert sum(hist.values())==sum(oldH.values())
+total=Counter({int(k):v for k,v in replay['delta'].items()});total.update(delta)
+replay.update(status='EXPERIMENTAL_CONNECTED_PLATEAU_RETIMING',histogram={str(k):v for k,v in sorted(hist.items())},delta={str(k):v for k,v in sorted(total.items()) if v},plateau_histogram_delta=delta,new_records=len(out)//6)
+(O/'COHORT249-REPLAY.json').write_text(json.dumps(replay,indent=2)+'\n');(O/'COHORT249-RECORDS.bin').write_bytes(out.tobytes());(O/'COHORT249-FRAMES.json').write_text(json.dumps(new)+'\n')
+receipt=dict(status='FINITE_TRANSCRIPT_REWRITE_CHECKED_NATIVE_CHECKERS_PENDING',selected=chosen,delta=delta,unchanged_scalar_copy_projection=projection(raw),input_sha256=hashlib.sha256(raw.tobytes()).hexdigest(),output_sha256=hashlib.sha256(out.tobytes()).hexdigest(),paid_calls=sum(hist.values()),rank_mass=sum(k*v for k,v in hist.items()))
+(O/'PLATEAU-RETIMING.json').write_text(json.dumps(receipt,indent=2)+'\n');print('wrote',O,'calls',sum(hist.values()),flush=True)
diff --git a/research/multicut-kernel-composition/code/verify_frame_tables.py b/research/multicut-kernel-composition/code/verify_frame_tables.py
new file mode 100644
index 0000000000..f77ff72801
--- /dev/null
+++ b/research/multicut-kernel-composition/code/verify_frame_tables.py
@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+"""Verify every added rational basis/annihilator table exactly.
+
+The native containment checker consumes A, while the bank checker constructs
+weighted charts from B. This checker binds both descriptions of each subspace.
+"""
+from array import array
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse, hashlib, json, sys
+
+if not __debug__:raise SystemExit('assertions required')
+
+def rank(rows,width=24):
+    a=[list(map(Q,r)) for r in rows]
+    assert all(len(r)==width for r in a)
+    k=0
+    for j in range(width):
+        p=next((i for i in range(k,len(a)) if a[i][j]),None)
+        if p is None:continue
+        a[k],a[p]=a[p],a[k]
+        scale=a[k][j];a[k]=[x/scale for x in a[k]]
+        for i in range(k+1,len(a)):
+            q=a[i][j]
+            if q:a[i]=[x-q*y for x,y in zip(a[i],a[k])]
+        k+=1
+        if k==len(a):break
+    return k
+
+def verify(export,lead):
+    export,lead=Path(export),Path(lead)
+    original=json.loads((export/'frames.json').read_text())['frames']
+    new_path=lead/'COHORT249-FRAMES.json'
+    new=json.loads(new_path.read_text())
+    assert not set(new)&set(original), 'new frame id collision'
+    dimensions={}
+    for key,frame in new.items():
+        d=frame['dim'];B=frame['B'];A=frame['A']
+        assert isinstance(d,int) and 0<=d<=24
+        assert len(B)==d and len(A)==24-d, ('table lengths',key)
+        assert rank(B)==d, ('B rank',key)
+        assert rank(A)==24-d, ('A rank',key)
+        assert all(sum(Q(x)*Q(y) for x,y in zip(a,b))==0 for a in A for b in B), ('A B transpose',key)
+        gram=[[sum(Q(x)*Q(y) for x,y in zip(u,v))-sum(map(Q,u))*sum(map(Q,v))/9 for v in B] for u in B]
+        assert rank(gram,d)==d, ('weighted Gram rank',key)
+        dimensions[key]=d
+    word=array('i');word.frombytes((lead/'COHORT249-RECORDS.bin').read_bytes())
+    assert word.itemsize==4 and len(word)%6==0
+    references=set()
+    for j in range(len(word)//6):
+        op,a,b,c,f,z=word[6*j:6*j+6]
+        if op==0:references.update((str(b),str(c)))
+        elif op==1:references.add(str(f))
+        elif op in (2,3):references.update((str(c),str(f)))
+        else:raise AssertionError('unknown opcode')
+    assert references<=set(original)|set(new), 'unknown frame reference'
+    return dict(status='PASS_EXACT_ADDED_FRAME_BASES_AND_ANNIHILATORS',
+                frame_table_sha256=hashlib.sha256(new_path.read_bytes()).hexdigest(),
+                added_frames=len(new),used_added_frames=len(references&set(new)),
+                all_B_rank_equals_dimension=True,all_A_rank_equals_codimension=True,
+                all_A_B_transpose_zero=True,all_weighted_Gram_nondegenerate=True,
+                new_frame_ids_disjoint_from_original=True,
+                dimensions=dimensions)
+
+def main():
+    ap=argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('export',type=Path);ap.add_argument('lead',type=Path)
+    ap.add_argument('--output',type=Path)
+    a=ap.parse_args();receipt=verify(a.export,a.lead)
+    if a.output:
+        assert not a.output.exists()
+        a.output.write_text(json.dumps(receipt,sort_keys=True,indent=2)+'\n')
+    print(json.dumps({k:v for k,v in receipt.items() if k!='dimensions'},sort_keys=True))
+
+if __name__=='__main__':main()
diff --git a/research/multicut-kernel-composition/code/verify_frames.py b/research/multicut-kernel-composition/code/verify_frames.py
new file mode 100644
index 0000000000..890d9d54f0
--- /dev/null
+++ b/research/multicut-kernel-composition/code/verify_frames.py
@@ -0,0 +1,48 @@
+#!/usr/bin/env python3
+"""Independently validate exact bases and annihilators of every candidate frame."""
+import argparse
+import hashlib
+import json
+from pathlib import Path
+from sympy import Matrix, eye, ones, zeros
+
+if not __debug__:
+    raise SystemExit("assertions are required")
+
+
+def validate(frame):
+    d = frame["dim"]
+    assert type(d) is int and 0 <= d <= 24
+    b, a = frame["B"], frame["A"]
+    assert len(b) == d and len(a) == 24-d
+    assert all(len(row) == 24 and all(type(x) is int for x in row) for row in b+a)
+    B = Matrix(b) if b else zeros(0, 24)
+    A = Matrix(a) if a else zeros(0, 24)
+    assert B.rank() == d and A.rank() == 24-d
+    assert B*A.T == zeros(d, 24-d)
+    assert (B*(9*eye(24)-ones(24))*B.T).det() != 0
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("frames", type=Path)
+    parser.add_argument("output", type=Path)
+    args = parser.parse_args()
+    raw = args.frames.read_bytes()
+    frames = json.loads(raw)
+    seen = set()
+    for frame in frames.values():
+        key = json.dumps(frame, sort_keys=True)
+        if key not in seen:
+            validate(frame)
+            seen.add(key)
+    result = dict(status="PASS_EXACT_BASES_ANNIHILATORS_AND_GRAM",
+                  frames_checked=len(frames), distinct_frames_checked=len(seen),
+                  frames_sha256=hashlib.sha256(raw).hexdigest())
+    assert not args.output.exists()
+    args.output.write_text(json.dumps(result, sort_keys=True, indent=2)+"\n")
+    print(json.dumps(result))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/multicut-kernel-composition/code/verify_plateau_spans.py b/research/multicut-kernel-composition/code/verify_plateau_spans.py
new file mode 100644
index 0000000000..49b3566e7a
--- /dev/null
+++ b/research/multicut-kernel-composition/code/verify_plateau_spans.py
@@ -0,0 +1,42 @@
+#!/usr/bin/env python3
+"""Exact defining-integer source span audit for the frozen changed ADDs."""
+import argparse,json,time,hashlib,sys
+from pathlib import Path
+from array import array
+if not __debug__:raise SystemExit('assertions are required')
+assert sys.byteorder=='little' and array('i').itemsize==4
+ap=argparse.ArgumentParser();ap.add_argument('export',type=Path);ap.add_argument('lead',type=Path);ap.add_argument('receipt',type=Path);args=ap.parse_args()
+t=time.time();X,L=args.export,args.lead
+frames={int(k):r for k,r in json.loads((X/'frames.json').read_text())['frames'].items()};frames.update({int(k):r for k,r in json.loads((L/'COHORT249-FRAMES.json').read_text()).items()})
+st=json.loads((X/'249-states.json').read_text());n,v=st['n'],st['v'];initial={int(k):f for k,f in json.loads((L/'COHORT249-INITIAL.json').read_text()).items()};chi={s:frames[initial[s]]['B'][0] for s in range(v)}
+assert all(frames[initial[s]]['dim']==1 for s in range(v))
+receipt=json.loads(args.receipt.read_text());pairs=[(g,c['new_frame']) for c in receipt['selected'] for g in c['gates']];chosen=dict(pairs)
+assert len(pairs)==len(chosen),'duplicate selected gates'
+columns=[{i:1} if i<v else {} for i in range(n)];center=None;raw=array('i');raw.frombytes((L/'COHORT249-RECORDS.bin').read_bytes());ordinal=0;checked=0;sourcecache={};spans={}
+assert hashlib.sha256(raw.tobytes()).hexdigest()==receipt['output_sha256'],'word/receipt mismatch'
+assert len(raw)%6==0
+for k in range(0,len(raw),6):
+ op,a,b,c,f,z=raw[k:k+6]
+ if not op:continue
+ i=ordinal;ordinal+=1
+ if i in chosen:assert op==1,'selected gate must be ADD'
+ if op==2:assert center is None;center=a;continue
+ if op==3:assert center==a;center=None;continue
+ src=center if b==n else b;ca=columns[a]
+ for s,x in columns[src].items():
+  y=ca.get(s,0)+c*x
+  if y:ca[s]=y
+  else:ca.pop(s,None)
+ if i in chosen:
+  assert chosen[i]==f
+  need=set()
+  if not v<=a<2*v:need.update(ca)
+  if not v<=b<2*v and b!=n:need.update(columns[b])
+  for s in need:
+   key=(f,s)
+   if key not in sourcecache:sourcecache[key]=all(sum(x*y for x,y in zip(row,chi[s]))==0 for row in frames[f]['A'])
+   assert sourcecache[key],(i,a,b,f,s)
+  spans[i]=len(need);checked+=len(need)
+assert center is None and len(spans)==len(chosen)
+out=dict(status='PASS_EXACT_INTEGER_SOURCE_SPANS_FOR_CHANGED_PLATEAU_GATES',changed_gates=len(chosen),checked_operand_source_inclusions=checked,distinct_inclusions=len(sourcecache),spans=spans,seconds=time.time()-t)
+(L/'PLATEAU-SOURCE-SPANS.json').write_text(json.dumps(out,indent=2)+'\n');print(out['status'],len(chosen),checked,'seconds',time.time()-t,flush=True)
diff --git a/research/multicut-kernel-composition/discovery/README.md b/research/multicut-kernel-composition/discovery/README.md
new file mode 100644
index 0000000000..cd4bf92fc1
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/README.md
@@ -0,0 +1,26 @@
+# Discovery (not run by the verifier)
+
+Pure-Python replay of PR #249's word, the censuses that produced the 387 added kernel families, and the chain that
+rebinds the two published retiming selections (Chafik Boukhalfa, Anthropic Claude assistance). Inputs are the
+package's own `inputs/` files, decompressed into a data directory.
+
+    twins.py  <data> twins.pkl                  census of twin dirty helpers at PR #254's cut (record 727,593)
+    chrono2.py <data> twins.pkl chrono.pkl <cut> the same census at any cut (at 676,560: 985 pairs, 24 size-9 classes)
+    gain.py                                     log-weighted gain phi(r) = r ln(120/r) per pair and exact-grid price
+    gen_candidates.py, compare259.py, merge259.py   round 1: candidates in PR #259's schema, the pairs disjoint from its helpers, the merge
+    census2.py, merge2.py                       round 2: every response class at twelve cuts, pairs and XOR triples, greedy packing
+    census3.py, census3b.py                     round 3: shared-donor families (partner = an existing donor, nested entrance chain)
+    retime.py                                   the chain cohort -> descent (PR #263) -> plateau (PR #270) with the sha rebinding
+
+Diff of this package against PR #259's (everything else byte for byte):
+
+    inputs/candidates.json.gz      518 items of PR #259 (26 dissolved) + 387 appended (rounds union-early-cut, headroom-2, shared-donor)
+    inputs/descent-selection.json  PR #263's 25 gates, rebound to this transcript (input sha gate)
+    inputs/plateau-selection.json  PR #270's 29 blocks, rebound to the descent transcript
+    code/descent_retiming.py, code/plateau_retiming.py, code/verify_frames.py, code/verify_plateau_spans.py, code/verify_frame_tables.py
+                                   PR #263's and PR #270's stages, verbatim
+    code/cohort-transform.cpp      std::sort -> std::stable_sort on the gauge order (platform-independent transcript)
+    verify.py                      stages 02b-02e inserted with three sha gates; 'containment_pairs_checked' dropped from compared fields; normalize() on both sides
+    expected/*.json, RESULT.json   regenerated receipts (eleven) and result (890 pivots, entrance rank 1719, kappa 7.11482139228173e-4)
+    README.md, PROOF.md, NOTICE.md this package's notes; PR #259's README/PROOF kept as README-PR259.md, PROOF-PR259.md
+    MANIFEST.json                  regenerated
diff --git a/research/multicut-kernel-condensation-883/discovery/census2.py b/research/multicut-kernel-composition/discovery/census2.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/census2.py
rename to research/multicut-kernel-composition/discovery/census2.py
diff --git a/research/multicut-kernel-composition/discovery/census3.py b/research/multicut-kernel-composition/discovery/census3.py
new file mode 100644
index 0000000000..374c346d43
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/census3.py
@@ -0,0 +1,120 @@
+"""Shared-donor census at cut 676559: new pivot p (unused, untouched) twin with an existing donor d, entrance = d's existing entrance (or a nested line in it)."""
+import json, sys, collections, math, gzip, time, itertools
+from array import array
+from fractions import Fraction as Fr
+from math import lcm, gcd
+D, WIT, C270, OUT = sys.argv[1:5]; CUT = 676559; t0 = time.time()
+st = json.load(open(D + '/249-states.json')); n, v, ZERO, FULL = st['n'], st['v'], st['ZERO'], st['FULL']; H0 = 2*v
+ini = [ZERO]*n; fin = [FULL]*n
+for k, x in st['initial'].items(): ini[int(k)] = x
+for k, x in st['final'].items(): fin[int(k)] = x
+regs = st['regs']; borrowed = set(st['borrowed']); donor_keys = set(json.load(open(D + '/249-DONOR-OWNERSHIP.json'))['donor_keys'])
+rec = array('i'); rec.frombytes(open(D + '/249-records.bin', 'rb').read()); E = len(rec)//6
+fj = json.load(open(D + '/frames.json'))['frames']
+wit = json.load(open(WIT)); c270 = json.load(open(C270))
+Tt = {}; first = {}
+for i in range(E):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 0:
+        if a >= H0 and a not in Tt: Tt[a] = i; first[a] = c
+    elif k == 1:
+        if a >= H0 and a not in Tt: Tt[a] = i; first[a] = None
+        if b >= H0 and b not in Tt and not (z == 4 and f == ZERO and v <= a < 2*v): Tt[b] = i; first[b] = None
+    else:
+        for s in (a, b):
+            if s >= H0 and s not in Tt: Tt[s] = i; first[s] = None
+pivots = {z['pivot'] for z in wit}; donors = collections.defaultdict(list)
+for z in wit:
+    B = [[int(x) for x in r] for r in z['basis']]
+    for d in z['partners']: donors[d].append(dict(cut=z['cut'], dim=z['dim'], basis=B, pivot=z['pivot']))
+used = pivots | set(donors)
+pool = [h for h in range(H0, n) if ini[h] == ZERO and fin[h] == FULL and regs[h-H0] not in borrowed and regs[h-H0] not in donor_keys and h not in used and first.get(h) is not None and Tt[h] > CUT]
+print('witness families', len(wit), 'pivots', len(pivots), 'distinct donors', len(donors), 'pool of unused untouched helpers', len(pool), flush=True)
+# responses at CUT
+row = [1 << s for s in range(n+1)]
+for i in range(CUT+1):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 1:
+        if c & 1: row[a] ^= row[b]
+    elif k == 2: row[b] = row[a]
+contam = 0
+for s in range(n):
+    if v <= s < 2*v: continue
+    contam |= (row[s] ^ (1 << s)) >> H0
+resp = collections.defaultdict(int)
+for t in range(v):
+    r = row[v+t] >> H0
+    while r:
+        low = r & -r; idx = low.bit_length()-1; resp[H0+idx] |= 1 << t; r ^= low
+pool = [h for h in pool if not (contam >> (h-H0)) & 1 and resp[h]]
+byresp = collections.defaultdict(list)
+for h in pool: byresp[resp[h]].append(h)
+phi = lambda r: 0.0 if r == 0 else r*math.log(120/r)
+def contained(B, F):  # subspace rows B inside frame F (annihilator test)
+    return all(sum(x*y for x, y in zip(b, a)) == 0 for b in B for a in fj[str(F)]['A'])
+def nullspace(rows):
+    m = [[Fr(x) for x in r] for r in rows]; piv = []; r = 0
+    for c in range(24):
+        p = next((i for i in range(r, len(m)) if m[i][c] != 0), 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] != 0:
+                f = m[i][c]; m[i] = [a - f*b for a, b in zip(m[i], m[r])]
+        piv.append(c); r += 1
+        if r == len(m): break
+    free = [c for c in range(24) if c not in piv]; out = []
+    for fcol in free:
+        vec = [Fr(0)]*24; vec[fcol] = Fr(1)
+        for i, pc in enumerate(piv): vec[pc] = -m[i][fcol]
+        out.append(vec)
+    return out
+def prim(vec):
+    L = 1
+    for x in vec: L = lcm(L, x.denominator)
+    iv = [int(x*L) for x in vec]; g = 0
+    for x in iv: g = gcd(g, abs(x))
+    return [x//g for x in iv]
+def ann_of(B):  # annihilator rows of span(B) as integer rows
+    return [prim(u) for u in nullspace(B)]
+cands = []; stats = collections.Counter()
+for d, fams in donors.items():
+    if Tt.get(d, 0) <= CUT or d not in resp or resp[d] == 0 or (contam >> (d-H0)) & 1: stats['donor_touched_or_contaminated'] += 1; continue
+    twins = byresp.get(resp[d], [])
+    if not twins: continue
+    for fam in fams:
+        if fam['cut'] < CUT: continue
+        e, B = fam['dim'], fam['basis']; rp_all = []
+        for p in twins:
+            Fp = first[p]; rp = fj[str(Fp)]['dim']
+            if contained(B, Fp) and rp >= e:
+                g = phi(rp-e) - phi(rp); cands.append(dict(gain=g, pivot=p, donor=d, e=e, basis=B, cut=CUT, mode='same-entrance', donor_cut=fam['cut'], donor_pivot=fam['pivot'])); stats['same-entrance'] += 1
+            elif e >= 2:
+                # line inside E_d ∩ F_p: nullspace of (ann(E_d) ∪ ann(F_p))
+                inter = nullspace(ann_of(B) + fj[str(Fp)]['A'])
+                if inter:
+                    u = prim(inter[0])
+                    if 9*sum(x*x for x in u) - sum(u)**2 != 0:
+                        g = phi(rp-1) - phi(rp) + phi(1) + phi(e-1) - phi(e); cands.append(dict(gain=g, pivot=p, donor=d, e=1, basis=[u], cut=CUT, mode='nested-line', donor_cut=fam['cut'], donor_pivot=fam['pivot'])); stats['nested-line'] += 1
+                    else: stats['nested-line-degenerate'] += 1
+                else: stats['no-line'] += 1
+            else: stats['E_not_in_Fp'] += 1
+print('candidate stats', dict(stats), 'candidates', len(cands), f'({time.time()-t0:.0f}s)', flush=True)
+cands.sort(key=lambda z: z['gain']); taken = set(); chosen = []
+for z in cands:
+    if z['gain'] >= 0: break
+    if z['pivot'] in taken: continue
+    taken.add(z['pivot']); chosen.append(z)
+print('chosen shared-donor families', len(chosen), 'by mode', collections.Counter(z['mode'] for z in chosen), 'by e', collections.Counter(z['e'] for z in chosen), 'distinct donors', len({z['donor'] for z in chosen}), 'max pivots per donor', max(collections.Counter(z['donor'] for z in chosen).values()), 'phi gain', round(sum(z['gain'] for z in chosen), 1))
+print('by (pivot first dim, e):', collections.Counter((fj[str(first[z['pivot']])]['dim'], z['e']) for z in chosen).most_common(8))
+# cross-check with #270's 24
+sh270 = {(z['pivot'], z['partners'][0]) for z in c270 if z.get('kind') == 'reuse'}
+mine = {(z['pivot'], z['donor']) for z in chosen}
+print('#270 reuse pairs reproduced in my chosen set:', len(sh270 & mine), 'of 24; #270 pairs with pivot already used in union3:', sum(1 for p, d in sh270 if p in used))
+S = sum(z['dim'] for z in wit) + sum(z['e'] for z in chosen)
+while S % 3:
+    for j in range(len(chosen)-1, -1, -1):
+        if chosen[j]['e'] == 1: S -= 1; chosen.pop(j); break
+items = [dict(pivot=z['pivot'], a=z['pivot'], roles=[z['pivot'], z['donor']], partners=[z['donor']], dim=z['e'], E_dimension=z['e'], basis=[[str(x) for x in r] for r in z['basis']], cut=z['cut'], approx_slack_delta=z['gain'], kind='shared-donor %s (donor of pivot %d at cut %d)' % (z['mode'], z['donor_pivot'], z['donor_cut']), round='shared-donor') for z in chosen]
+merged = wit + items; print('merged families', len(merged), 'entrance rank', S, 'mod 3', S % 3)
+json.dump(merged, open(OUT, 'w'), indent=1); open(OUT + '.gz', 'wb').write(gzip.compress(json.dumps(merged, indent=1).encode(), mtime=0))
diff --git a/research/multicut-kernel-composition/discovery/census3b.py b/research/multicut-kernel-composition/discovery/census3b.py
new file mode 100644
index 0000000000..b81ef15100
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/census3b.py
@@ -0,0 +1,137 @@
+"""Shared-donor census at cut 676559: new pivot p (unused, untouched) twin with an existing donor d, entrance = d's existing entrance (or a nested line in it)."""
+import json, sys, collections, math, gzip, time, itertools
+from array import array
+from fractions import Fraction as Fr
+from math import lcm, gcd
+D, WIT, C270, OUT = sys.argv[1:5]; CUT = 676559; t0 = time.time()
+st = json.load(open(D + '/249-states.json')); n, v, ZERO, FULL = st['n'], st['v'], st['ZERO'], st['FULL']; H0 = 2*v
+ini = [ZERO]*n; fin = [FULL]*n
+for k, x in st['initial'].items(): ini[int(k)] = x
+for k, x in st['final'].items(): fin[int(k)] = x
+regs = st['regs']; borrowed = set(st['borrowed']); donor_keys = set(json.load(open(D + '/249-DONOR-OWNERSHIP.json'))['donor_keys'])
+rec = array('i'); rec.frombytes(open(D + '/249-records.bin', 'rb').read()); E = len(rec)//6
+fj = json.load(open(D + '/frames.json'))['frames']
+wit = json.load(open(WIT)); c270 = json.load(open(C270))
+Tt = {}; first = {}
+for i in range(E):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 0:
+        if a >= H0 and a not in Tt: Tt[a] = i; first[a] = c
+    elif k == 1:
+        if a >= H0 and a not in Tt: Tt[a] = i; first[a] = None
+        if b >= H0 and b not in Tt and not (z == 4 and f == ZERO and v <= a < 2*v): Tt[b] = i; first[b] = None
+    else:
+        for s in (a, b):
+            if s >= H0 and s not in Tt: Tt[s] = i; first[s] = None
+pivots = {z['pivot'] for z in wit}; donors = collections.defaultdict(list)
+for z in wit:
+    B = [[int(x) for x in r] for r in z['basis']]
+    for d in z['partners']: donors[d].append(dict(cut=z['cut'], dim=z['dim'], basis=B, pivot=z['pivot']))
+used = pivots | set(donors)
+newpairs = {z['pivot']: z for z in wit if z.get('round') and len(z['roles']) == 2}
+member_of = {}
+for z in newpairs.values():
+    for h in z['roles']: member_of[h] = z['pivot']
+donor_refs = collections.Counter(d for z in wit for d in z['partners'])
+famgain = {z['pivot']: z['approx_slack_delta'] for z in newpairs.values()}
+pool = [h for h in range(H0, n) if ini[h] == ZERO and fin[h] == FULL and regs[h-H0] not in borrowed and regs[h-H0] not in donor_keys and (h not in used or h in member_of) and first.get(h) is not None and Tt[h] > CUT]
+print('witness families', len(wit), 'pivots', len(pivots), 'distinct donors', len(donors), 'pool of unused untouched helpers', len(pool), flush=True)
+# responses at CUT
+row = [1 << s for s in range(n+1)]
+for i in range(CUT+1):
+    k, a, b, c, f, z = rec[6*i:6*i+6]
+    if k == 1:
+        if c & 1: row[a] ^= row[b]
+    elif k == 2: row[b] = row[a]
+contam = 0
+for s in range(n):
+    if v <= s < 2*v: continue
+    contam |= (row[s] ^ (1 << s)) >> H0
+resp = collections.defaultdict(int)
+for t in range(v):
+    r = row[v+t] >> H0
+    while r:
+        low = r & -r; idx = low.bit_length()-1; resp[H0+idx] |= 1 << t; r ^= low
+pool = [h for h in pool if not (contam >> (h-H0)) & 1 and resp[h]]
+byresp = collections.defaultdict(list)
+for h in pool: byresp[resp[h]].append(h)
+phi = lambda r: 0.0 if r == 0 else r*math.log(120/r)
+def contained(B, F):  # subspace rows B inside frame F (annihilator test)
+    return all(sum(x*y for x, y in zip(b, a)) == 0 for b in B for a in fj[str(F)]['A'])
+def nullspace(rows):
+    m = [[Fr(x) for x in r] for r in rows]; piv = []; r = 0
+    for c in range(24):
+        p = next((i for i in range(r, len(m)) if m[i][c] != 0), 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] != 0:
+                f = m[i][c]; m[i] = [a - f*b for a, b in zip(m[i], m[r])]
+        piv.append(c); r += 1
+        if r == len(m): break
+    free = [c for c in range(24) if c not in piv]; out = []
+    for fcol in free:
+        vec = [Fr(0)]*24; vec[fcol] = Fr(1)
+        for i, pc in enumerate(piv): vec[pc] = -m[i][fcol]
+        out.append(vec)
+    return out
+def prim(vec):
+    L = 1
+    for x in vec: L = lcm(L, x.denominator)
+    iv = [int(x*L) for x in vec]; g = 0
+    for x in iv: g = gcd(g, abs(x))
+    return [x//g for x in iv]
+def ann_of(B):  # annihilator rows of span(B) as integer rows
+    return [prim(u) for u in nullspace(B)]
+cands = []; stats = collections.Counter()
+for d, fams in donors.items():
+    if Tt.get(d, 0) <= CUT or d not in resp or resp[d] == 0 or (contam >> (d-H0)) & 1: stats['donor_touched_or_contaminated'] += 1; continue
+    twins = byresp.get(resp[d], [])
+    if not twins: continue
+    for fam in fams:
+        if fam['cut'] < CUT: continue
+        e, B = fam['dim'], fam['basis']; rp_all = []
+        for p in twins:
+            Fp = first[p]; rp = fj[str(Fp)]['dim']
+            if contained(B, Fp) and rp >= e:
+                g = phi(rp-e) - phi(rp); cands.append(dict(gain=g, pivot=p, donor=d, e=e, basis=B, cut=CUT, mode='same-entrance', donor_cut=fam['cut'], donor_pivot=fam['pivot'])); stats['same-entrance'] += 1
+            elif e >= 2:
+                # line inside E_d ∩ F_p: nullspace of (ann(E_d) ∪ ann(F_p))
+                inter = nullspace(ann_of(B) + fj[str(Fp)]['A'])
+                if inter:
+                    u = prim(inter[0])
+                    if 9*sum(x*x for x in u) - sum(u)**2 != 0:
+                        g = phi(rp-1) - phi(rp) + phi(1) + phi(e-1) - phi(e); cands.append(dict(gain=g, pivot=p, donor=d, e=1, basis=[u], cut=CUT, mode='nested-line', donor_cut=fam['cut'], donor_pivot=fam['pivot'])); stats['nested-line'] += 1
+                    else: stats['nested-line-degenerate'] += 1
+                else: stats['no-line'] += 1
+            else: stats['E_not_in_Fp'] += 1
+print('candidate stats', dict(stats), 'candidates', len(cands), f'({time.time()-t0:.0f}s)', flush=True)
+cands.sort(key=lambda z: z['gain']); taken = set(); chosen = []; dissolved = set(); freed = set()
+for z in cands:
+    if z['gain'] >= 0: break
+    p = z['pivot']
+    if p in taken or z['donor'] in dissolved_donors if False else False: continue
+    if p in taken: continue
+    if p in member_of and member_of[p] not in dissolved and p not in freed:
+        fam = newpairs[member_of[p]]; dnr = fam['partners'][0]
+        # dissolve only if strictly better and the pair's donor is referenced by no other family (incl. chosen shared ones)
+        if z['gain'] - famgain[fam['pivot']] >= 0 or donor_refs[dnr] > 1 or any(c['donor'] == dnr for c in chosen) or z['donor'] in fam['roles']: continue
+        dissolved.add(fam['pivot']); freed |= set(fam['roles']); taken.add(fam['pivot']) if fam['pivot'] != p else None
+    elif p in member_of and member_of[p] in dissolved and p not in freed: continue
+    taken.add(p); chosen.append(z)
+print('dissolved own pair families', len(dissolved))
+wit = [z for z in wit if z['pivot'] not in dissolved]
+print('chosen shared-donor families', len(chosen), 'by mode', collections.Counter(z['mode'] for z in chosen), 'by e', collections.Counter(z['e'] for z in chosen), 'distinct donors', len({z['donor'] for z in chosen}), 'max pivots per donor', max(collections.Counter(z['donor'] for z in chosen).values()), 'phi gain', round(sum(z['gain'] for z in chosen), 1))
+print('by (pivot first dim, e):', collections.Counter((fj[str(first[z['pivot']])]['dim'], z['e']) for z in chosen).most_common(8))
+# cross-check with #270's 24
+sh270 = {(z['pivot'], z['partners'][0]) for z in c270 if z.get('kind') == 'reuse'}
+mine = {(z['pivot'], z['donor']) for z in chosen}
+print('#270 reuse pairs reproduced in my chosen set:', len(sh270 & mine), 'of 24; #270 pairs with pivot already used in union3:', sum(1 for p, d in sh270 if p in used))
+chosen = [z for z in chosen if z['donor'] not in {h for f in dissolved for h in newpairs[f]['roles']} or z['donor'] in {d for z2 in wit for d in z2['partners']}]
+S = sum(z['dim'] for z in wit) + sum(z['e'] for z in chosen)
+while S % 3:
+    for j in range(len(chosen)-1, -1, -1):
+        if chosen[j]['e'] == 1: S -= 1; chosen.pop(j); break
+items = [dict(pivot=z['pivot'], a=z['pivot'], roles=[z['pivot'], z['donor']], partners=[z['donor']], dim=z['e'], E_dimension=z['e'], basis=[[str(x) for x in r] for r in z['basis']], cut=z['cut'], approx_slack_delta=z['gain'], kind='shared-donor %s (donor of pivot %d at cut %d)' % (z['mode'], z['donor_pivot'], z['donor_cut']), round='shared-donor') for z in chosen]
+merged = wit + items; print('merged families', len(merged), 'entrance rank', S, 'mod 3', S % 3)
+json.dump(merged, open(OUT, 'w'), indent=1); open(OUT + '.gz', 'wb').write(gzip.compress(json.dumps(merged, indent=1).encode(), mtime=0))
diff --git a/research/multicut-kernel-condensation-883/discovery/chrono2.py b/research/multicut-kernel-composition/discovery/chrono2.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/chrono2.py
rename to research/multicut-kernel-composition/discovery/chrono2.py
diff --git a/research/multicut-kernel-condensation-883/discovery/compare259.py b/research/multicut-kernel-composition/discovery/compare259.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/compare259.py
rename to research/multicut-kernel-composition/discovery/compare259.py
diff --git a/research/multicut-kernel-condensation-883/discovery/gain.py b/research/multicut-kernel-composition/discovery/gain.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/gain.py
rename to research/multicut-kernel-composition/discovery/gain.py
diff --git a/research/multicut-kernel-condensation-883/discovery/gen_candidates.py b/research/multicut-kernel-composition/discovery/gen_candidates.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/gen_candidates.py
rename to research/multicut-kernel-composition/discovery/gen_candidates.py
diff --git a/research/multicut-kernel-condensation-883/discovery/merge2.py b/research/multicut-kernel-composition/discovery/merge2.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/merge2.py
rename to research/multicut-kernel-composition/discovery/merge2.py
diff --git a/research/multicut-kernel-condensation-883/discovery/merge259.py b/research/multicut-kernel-composition/discovery/merge259.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/merge259.py
rename to research/multicut-kernel-composition/discovery/merge259.py
diff --git a/research/multicut-kernel-composition/discovery/retime.py b/research/multicut-kernel-composition/discovery/retime.py
new file mode 100644
index 0000000000..56f9fe743a
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/retime.py
@@ -0,0 +1,46 @@
+"""Chain: PR259 word (stable_sort) -> #263 descent (baseline 80af) ; our 883 word -> rebound descent -> rebound plateaus -> native checkers."""
+import json, sys, subprocess, shutil, hashlib, time, os
+from pathlib import Path
+sys.dont_write_bytecode = True
+S = Path(sys.argv[1]); W = S / sys.argv[3]
+if W.exists(): shutil.rmtree(W)
+W.mkdir(parents=True)
+BIN = S / 'mc851/out-headroom/bin'; X = S / 'mc851/out-headroom/temporal/CURRENT249-EXPORT'
+P263 = S / 'pr263/repo/research/multicut-kernel-condensation'; P270 = S / 'round3/r270/research/crosscut-response-pairs'
+PY = S / 'build/venv/bin/python'; T0 = time.time(); tm = {}
+def sha(p): return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def run(label, cmd, cwd=None):
+    t = time.time(); log = W / (label + '.log')
+    with log.open('w') as lf: r = subprocess.run([str(c) for c in cmd], stdout=lf, stderr=subprocess.STDOUT, cwd=cwd or W)
+    tm[label] = round(time.time() - t, 1); print(f'{label}: exit {r.returncode} ({tm[label]}s)', flush=True)
+    if r.returncode: print(log.read_text()[-2500:]); raise SystemExit(label + ' FAILED')
+# a. baseline chain
+base = W / 'base259'; (base / 'lead').mkdir(parents=True)
+run('a1-pr259-transform-stable', [BIN / 'cohort-transform', X, S / 'pr259/data/candidates.json', base / 'lead'])
+sel263 = json.load((P263 / 'inputs/descent-selection.json').open())
+print('pr259 stable-sort word sha', sha(base / 'lead/COHORT249-RECORDS.bin'), 'matches #263 selection input:', sha(base / 'lead/COHORT249-RECORDS.bin') == sel263['input_record_sha256'], flush=True)
+run('a2-descent-on-pr259', [PY, '-B', P263 / 'code/descent_retiming.py', X, base / 'lead', P263 / 'inputs/descent-selection.json'])
+plat = json.load((P270 / 'inputs/plateau-selection.json').open())
+print('post-descent pr259 sha', sha(base / 'lead/COHORT249-RECORDS.bin'), 'matches #270 plateau input:', sha(base / 'lead/COHORT249-RECORDS.bin') == plat['input_sha256'], flush=True)
+# b. our word
+lead = W / 'lead'; shutil.copytree(Path(sys.argv[2]) / 'lead', lead)
+sys.path.insert(0, str(P270)); from rebind_descent import rebind
+alignment = rebind(base / 'lead/COHORT249-PRE-DESCENT-RECORDS.bin', lead / 'COHORT249-RECORDS.bin', P263 / 'inputs/descent-selection.json', lead / 'descent-selection.json')
+(lead / 'DESCENT-REBIND-EVIDENCE.json').write_text(json.dumps(alignment, indent=2) + '\n'); print('rebind descent:', alignment['status'], alignment['events_compared'], flush=True)
+run('b1-descent-on-883', [PY, '-B', P263 / 'code/descent_retiming.py', X, lead, lead / 'descent-selection.json'])
+print('883 post-descent sha', sha(lead / 'COHORT249-RECORDS.bin'), json.load((lead / 'DESCENT-RETIMING.json').open())['local_histogram_delta'], flush=True)
+bound = W / 'bound-plateau-selection.json'
+run('b2-rebind-plateaus', [PY, '-B', P270 / 'rebind_plateaus.py', base / 'lead/COHORT249-RECORDS.bin', P270 / 'inputs/plateau-selection.json', lead / 'COHORT249-RECORDS.bin', bound])
+plateau = W / 'plateau'
+run('b3-plateau-retiming', [PY, '-B', P270 / 'plateau_retiming.py', X, lead, bound, plateau], cwd=P270)
+run('b4-plateau-spans', [PY, '-B', P270 / 'verify_plateau_spans.py', X, plateau, plateau / 'PLATEAU-RETIMING.json'], cwd=P270)
+run('b5-frame-tables', [PY, '-B', P270 / 'verify_frame_tables.py', X, plateau, '--output', plateau / 'FRAME-TABLE-AUDIT.json'], cwd=P270)
+bank = W / 'bank'; bank.mkdir()
+run('c1-legality', [BIN / 'cohort-legality-independent', X, plateau, plateau / 'INDEPENDENT-LEGALITY.json'])
+run('c2-prefix', [BIN / 'cohort-prefix-independent', X, plateau, plateau / 'INDEPENDENT-PREFIX.json'])
+run('c3-bank', [BIN / 'cohort-bank-review', X, plateau / 'COHORT249-INITIAL.json', plateau / 'COHORT249-FRAMES.json', bank, 'actual_multicut'])
+run('c4-five-stage', [BIN / 'cohort-five-stage-columns', plateau / 'COHORT249-RECORDS.bin', plateau / 'COHORT-FIVE-STAGE-COLUMNS.json'])
+run('c5-price', [BIN / 'cohort-price', plateau / 'COHORT249-REPLAY.json', plateau / 'COHORT-EXACT-PRICE.json'])
+run('c6-finite', [BIN / 'cohort-finite-invoice', plateau / 'COHORT249-RECORDS.bin', plateau / 'COHORT-EXACT-PRICE.json', bank / 'BANK-REVIEW.json', plateau / 'COHORT-FIVE-STAGE-COLUMNS.json', plateau / 'COHORT-FINITE-INVOICE.json'])
+cc = json.load((plateau / 'COHORT-EXACT-PRICE.json').open())['cohort_candidate']; rep = json.load((plateau / 'COHORT249-REPLAY.json').open())
+print(json.dumps(dict(kappa=cc['kappa'], kappa_decimal=cc['kappa_decimal'], coarse=cc['coarse'], stock=cc['stock'], calls=cc['calls'], rank_mass=cc['rank_mass'], deficit=cc['deficit'], constraints=cc['positive_constraints'], adjacent_rejected=cc['next_kappa_rejected'], word_sha=sha(plateau / 'COHORT249-RECORDS.bin'), records=rep['new_records'], plateau_delta=rep.get('plateau_histogram_delta'), timings=tm, total=round(time.time()-T0, 1)), indent=1))
diff --git a/research/multicut-kernel-condensation-883/discovery/twins.py b/research/multicut-kernel-composition/discovery/twins.py
similarity index 100%
rename from research/multicut-kernel-condensation-883/discovery/twins.py
rename to research/multicut-kernel-composition/discovery/twins.py
diff --git a/research/multicut-kernel-condensation-883/expected/COHORT-BANK-REVIEW.json b/research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json
similarity index 93%
rename from research/multicut-kernel-condensation-883/expected/COHORT-BANK-REVIEW.json
rename to research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json
index 1f6535ba64..2b80c35307 100644
--- a/research/multicut-kernel-condensation-883/expected/COHORT-BANK-REVIEW.json
+++ b/research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json
@@ -1,7 +1,7 @@
 {
   "actual_helper_roles": 16587,
   "actual_role_replica_stage_assignments": 3317400,
-  "assignment_fnv1a64": "7193720686180422241",
+  "assignment_fnv1a64": "10075747216986959767",
   "bank_patterns": [
     {
       "count": 240,
@@ -432,7 +432,7 @@
       ]
     },
     {
-      "count": 420,
+      "count": 440,
       "widths": [
         22,
         22,
@@ -449,7 +449,7 @@
       ]
     },
     {
-      "count": 7330,
+      "count": 7380,
       "widths": [
         23,
         23,
@@ -465,7 +465,7 @@
       ]
     },
     {
-      "count": 495,
+      "count": 478,
       "widths": [
         4,
         4,
@@ -500,7 +500,7 @@
       ]
     },
     {
-      "count": 107232,
+      "count": 107176,
       "widths": [
         24,
         24,
@@ -510,20 +510,20 @@
       ]
     }
   ],
-  "banks_per_stage": 116993,
-  "covered_address_rank_mass": 70195800,
+  "banks_per_stage": 116990,
+  "covered_address_rank_mass": 70194000,
   "endpoint_address_columns": 10560,
   "label": "actual_multicut",
-  "literal_stock": 866565,
+  "literal_stock": 866550,
   "max_block_scalar": 30,
   "max_intermediate_denominator": "704",
   "max_intermediate_numerator": "704",
-  "max_new_chart_factors": 200,
-  "new_entrance_rank": 1710,
-  "new_exact_charts": 883,
-  "new_gauged_roles": 883,
+  "max_new_chart_factors": 262,
+  "new_entrance_rank": 1719,
+  "new_exact_charts": 919,
+  "new_gauged_roles": 890,
   "nonzero_omission_repeat_control_columns": 10560,
-  "normalized_stock": 173313,
+  "normalized_stock": 173310,
   "normalizer_factor_ceiling": 787,
   "prime_guard": "every elimination pivot and emitted coefficient has numerator and denominator magnitude below2^80",
   "residual_families": {
@@ -538,16 +538,16 @@
     "19": 24,
     "20": 19,
     "21": 3,
-    "22": 42,
-    "23": 733,
-    "24": 13404,
+    "22": 44,
+    "23": 738,
+    "24": 13397,
     "4": 2200,
     "6": 22,
     "7": 7,
     "9": 4
   },
-  "saved_literal_banks": 2850,
+  "saved_literal_banks": 2865,
   "scope": "Exact chart and role census, residual conjugacy, complete bank tiling, and finite selector charge. Full physical word, global columns, and pricing checked separately.",
-  "selector_charge": 626937137600,
+  "selector_charge": 626937131600,
   "status": "PASS_GENERIC_EXACT_CHARTS_ACTUAL_BANK_ALLOCATION"
 }
diff --git a/research/multicut-kernel-condensation-883/expected/COHORT-EXACT-PRICE.json b/research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json
similarity index 64%
rename from research/multicut-kernel-condensation-883/expected/COHORT-EXACT-PRICE.json
rename to research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json
index cc1cf66d65..15da3b8be5 100644
--- a/research/multicut-kernel-condensation-883/expected/COHORT-EXACT-PRICE.json
+++ b/research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json
@@ -51,50 +51,50 @@
   "cohort_candidate": {
     "bootstrap_chain": [
       "384599/10000000000",
-      "711448356904944866168722758485631/1000000000000000000000000000000000000",
-      "711927476108237935355751292633060782626378882102847/1000000000000000000000000000000000000000000000000000000",
-      "711927817206526633951518134578536201513839897689189894717718866531839/1000000000000000000000000000000000000000000000000000000000000000000000000"
+      "28460366472694313182316413970159/40000000000000000000000000000000000",
+      "5695906922326711677916359897976466195696051370361/8000000000000000000000000000000000000000000000000000",
+      "1139181930365280479951565086012536205726745421443147401624237514719/1600000000000000000000000000000000000000000000000000000000000000000000"
     ],
-    "calls": 3971440,
-    "coarse": "711927817449537/1000000000000000000",
-    "coarse_decimal": 0.000711927817449537,
+    "calls": 3970400,
+    "coarse": "142397741344279/200000000000000000",
+    "coarse_decimal": 0.000711988706721395,
     "deficit": 35200,
     "histogram": {
-      "1": 1730200,
-      "10": 30760,
-      "11": 17200,
-      "12": 60560,
-      "13": 23320,
+      "1": 1729800,
+      "10": 30680,
+      "11": 17680,
+      "12": 60400,
+      "13": 23560,
       "14": 42680,
       "15": 9640,
       "16": 40000,
-      "17": 18800,
+      "17": 18760,
       "18": 19480,
       "19": 12920,
-      "2": 758440,
+      "2": 756440,
       "20": 54320,
       "21": 223560,
       "22": 53760,
       "23": 28160,
-      "3": 385320,
-      "4": 148600,
+      "3": 387040,
+      "4": 149440,
       "46": 28160,
-      "5": 96080,
+      "5": 93720,
       "50": 28160,
-      "6": 61120,
-      "7": 49040,
-      "8": 25360,
-      "9": 25800
+      "6": 63040,
+      "7": 48080,
+      "8": 25680,
+      "9": 25240
     },
-    "kappa": "44463833535321/62500000000000000",
-    "kappa_decimal": 0.000711421336565136,
-    "moment_upper": "134799733335753198930976841688255237895987408528785254572771739521823139742264153801/134799733335753198973335075435098153368185722112702862405518051246080000000000000000",
-    "next_coarse_moment_lower": "269599466671506398503555464196556110254668679950330531069703752576714463407050236903/269599466671506397946670150870196306736371444225405724811036102492160000000000000000",
+    "kappa": "711482139228173/1000000000000000000",
+    "kappa_decimal": 0.000711482139228173,
+    "moment_upper": "67399866667876599459637151963994875088778344978842352652661207173617452803826560359/67399866667876599486667537717549076684092861056351431202759025623040000000000000000",
+    "next_coarse_moment_lower": "53919893334301279696021325114080333312757048503203889535126881934716408618907358731/53919893334301279589334030174039261347274288845081144962207220498432000000000000000",
     "next_kappa_rejected": 1,
-    "ordinary_bit": "711927817206526633951518134578536201513839897689189894717718866531839/1000000000000000000000000000000000000000000000000000000000000000000000000",
+    "ordinary_bit": "1139181930365280479951565086012536205726745421443147401624237514719/1600000000000000000000000000000000000000000000000000000000000000000000",
     "positive_constraints": 47,
-    "rank_mass": 20762360,
-    "stock": 173313
+    "rank_mass": 20762000,
+    "stock": 173310
   },
   "finite_bill_and_all_size_interfaces_not_reproved": true,
   "method": "C++ exact rational 224-bit directed bounds; floating used only to propose a bracket verified exactly;32-degree exponential and48-term atanh logarithm",
diff --git a/research/multicut-kernel-condensation-883/expected/COHORT-FINITE-INVOICE.json b/research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json
similarity index 51%
rename from research/multicut-kernel-condensation-883/expected/COHORT-FINITE-INVOICE.json
rename to research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json
index 2544ce6805..458083e3b8 100644
--- a/research/multicut-kernel-condensation-883/expected/COHORT-FINITE-INVOICE.json
+++ b/research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json
@@ -1,72 +1,72 @@
 {
   "external_complex_row_coefficient": 20161,
-  "extra_selector_calls": "626937137600",
-  "full_counted_primitive_coefficient": "62769085432418201",
-  "global_unit_expanded_additions": "146891000",
-  "global_weighted_additions": "146363000",
+  "extra_selector_calls": "626937131600",
+  "full_counted_primitive_coefficient": "62759883453796601",
+  "global_unit_expanded_additions": "146628200",
+  "global_weighted_additions": "146100200",
   "internal_row_coefficient": 14401,
-  "linear_moment_slack": "12276785650459/7253613281250000",
+  "linear_moment_slack": "8593749955333/5077441406250000",
   "literal_deficit": 176000,
   "literal_histogram": {
-    "1": "8651000",
-    "10": "153800",
-    "11": "86000",
-    "12": "302800",
-    "13": "116600",
+    "1": "8649000",
+    "10": "153400",
+    "11": "88400",
+    "12": "302000",
+    "13": "117800",
     "14": "213400",
     "15": "48200",
     "16": "200000",
-    "17": "94000",
+    "17": "93800",
     "18": "97400",
     "19": "64600",
-    "2": "3792200",
+    "2": "3782200",
     "20": "271600",
     "21": "1117800",
     "22": "268800",
     "23": "140800",
-    "3": "1926600",
-    "4": "743000",
+    "3": "1935200",
+    "4": "747200",
     "46": "140800",
-    "5": "480400",
+    "5": "468600",
     "50": "140800",
-    "6": "305600",
-    "7": "245200",
-    "8": "126800",
-    "9": "129000"
+    "6": "315200",
+    "7": "240400",
+    "8": "128400",
+    "9": "126200"
   },
-  "literal_rank_mass": "103811800",
-  "literal_stock": 866565,
-  "new_chart_factor_max": 200,
-  "normalized_stock": 173313,
+  "literal_rank_mass": "103810000",
+  "literal_stock": 866550,
+  "new_chart_factor_max": 262,
+  "normalized_stock": 173310,
   "normalizer_factor_bound": 787,
   "ordinary_cutoffs": [
     {
-      "counted_coefficient_cutoff_log2": "156601800901990",
+      "counted_coefficient_cutoff_log2": "156546708338570",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "479460544592133831277241514369/1000000000000000000000000000000000000",
+      "minimum_gap": "19181796161486817683586029841/40000000000000000000000000000000000",
       "stage": 1
     },
     {
-      "counted_coefficient_cutoff_log2": "308976057134932507419",
+      "counted_coefficient_cutoff_log2": "308814532847511043762",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "341341299064644248707366939217373621117897153/1000000000000000000000000000000000000000000000000000000",
+      "minimum_gap": "2731444448322083640102023533804303948629639/8000000000000000000000000000000000000000000000000000",
       "stage": 2
     },
     {
-      "counted_coefficient_cutoff_log2": "609611149634209069823427388",
+      "counted_coefficient_cutoff_log2": "609188252566600855323802619",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "243010366048481865421463798486160102310810105282281133468161/1000000000000000000000000000000000000000000000000000000000000000000000000",
+      "minimum_gap": "388951520048434913987463794273254578556852598375762485281/1600000000000000000000000000000000000000000000000000000000000000000000",
       "stage": 3
     }
   ],
   "payload_bits": 98,
-  "payload_signed_prefix_upper": "313857017010121408715056608000",
+  "payload_signed_prefix_upper": "313796573996337937369716857856",
   "physical_replicas": 40,
-  "positive_rank_children": "19857200",
+  "positive_rank_children": "19852000",
   "primitive_coefficient_bits": 56,
   "route_families": "8324400",
   "scope": "Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted.",
   "simultaneous_extra_work_streams": 1,
   "status": "PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS",
-  "strict_moment_slack": "42358233746842915472198313583917607832746311724256860257735846199/134799733335753198973335075435098153368185722112702862405518051246080000000000000000"
+  "strict_moment_slack": "27030385753554201595314516077509078550097818449422547196173439641/67399866667876599486667537717549076684092861056351431202759025623040000000000000000"
 }
diff --git a/research/multicut-kernel-condensation-883/expected/COHORT-FIVE-STAGE-COLUMNS.json b/research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json
similarity index 81%
rename from research/multicut-kernel-condensation-883/expected/COHORT-FIVE-STAGE-COLUMNS.json
rename to research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json
index 9ae4c8bdfa..8a55a4cd25 100644
--- a/research/multicut-kernel-condensation-883/expected/COHORT-FIVE-STAGE-COLUMNS.json
+++ b/research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json
@@ -1,64 +1,64 @@
 {
   "bridge_additions": 10560,
   "copied_center_original_source_immutable": true,
-  "five_stage_additions": 3648515,
+  "five_stage_additions": 3641945,
   "formal_columns_checked": 23627,
   "fresh_center_copies": 120,
   "global_live_registers": 23627,
   "independent_dirty_registers": 16587,
-  "local_odd_scalar_additions": 729703,
+  "local_odd_scalar_additions": 728389,
   "local_raw_H": [
     [
       1,
-      43255
+      43245
     ],
     [
       2,
-      18961
+      18911
     ],
     [
       3,
-      9633
+      9676
     ],
     [
       4,
-      3011
+      3032
     ],
     [
       5,
-      2402
+      2343
     ],
     [
       6,
-      1528
+      1576
     ],
     [
       7,
-      1226
+      1202
     ],
     [
       8,
-      634
+      642
     ],
     [
       9,
-      645
+      631
     ],
     [
       10,
-      769
+      767
     ],
     [
       11,
-      430
+      442
     ],
     [
       12,
-      1514
+      1510
     ],
     [
       13,
-      583
+      589
     ],
     [
       14,
@@ -74,7 +74,7 @@
     ],
     [
       17,
-      470
+      469
     ],
     [
       18,
@@ -98,7 +98,7 @@
     ]
   ],
   "local_registers": 20107,
-  "local_scalar_additions": 729703,
+  "local_scalar_additions": 728389,
   "negative_controls": [
     {
       "omit_bridge": 0,
@@ -130,18 +130,18 @@
     29
   ],
   "payload_prefix_bits": 98,
-  "payload_prefix_upper": "313857017010121408715056608000",
+  "payload_prefix_upper": "313796573996337937369716857856",
   "reverse_fresh_center_copies": 48,
   "scope": "All 23627 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.",
   "signed_lift_prefix": [
     {
       "bits": 17,
-      "cancellation_free_signed_row_l1_upper": "74395",
+      "cancellation_free_signed_row_l1_upper": "74391",
       "reverse": false
     },
     {
       "bits": 22,
-      "cancellation_free_signed_row_l1_upper": "3451122",
+      "cancellation_free_signed_row_l1_upper": "3451068",
       "reverse": true
     }
   ],
@@ -149,31 +149,31 @@
   "stages": [
     {
       "fresh_copies": 24,
-      "scalar_additions": 729703,
+      "scalar_additions": 728389,
       "signed_inverse": false,
       "stage": 0
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 729703,
+      "scalar_additions": 728389,
       "signed_inverse": true,
       "stage": 1
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 729703,
+      "scalar_additions": 728389,
       "signed_inverse": false,
       "stage": 2
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 729703,
+      "scalar_additions": 728389,
       "signed_inverse": true,
       "stage": 3
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 729703,
+      "scalar_additions": 728389,
       "signed_inverse": false,
       "stage": 4
     }
diff --git a/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json b/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json
new file mode 100644
index 0000000000..191910a95b
--- /dev/null
+++ b/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json
@@ -0,0 +1,132 @@
+{
+  "added_Q_Qinverse_passes": 2286,
+  "bank_completion_not_replayed": true,
+  "cut_record": 727593,
+  "delta": {
+    "1": 1833,
+    "2": -174,
+    "3": -558,
+    "4": 122,
+    "5": -141,
+    "6": 49,
+    "7": -50,
+    "8": 13,
+    "9": 20,
+    "10": -6,
+    "11": -3,
+    "12": -15,
+    "13": 27,
+    "14": -13,
+    "15": -46,
+    "17": -35,
+    "19": -8
+  },
+  "forward_formal_columns": 20107,
+  "global_kappa_claimed": false,
+  "histogram": {
+    "1": 43245,
+    "2": 18911,
+    "3": 9676,
+    "4": 3032,
+    "5": 2343,
+    "6": 1576,
+    "7": 1202,
+    "8": 642,
+    "9": 631,
+    "10": 767,
+    "11": 442,
+    "12": 1510,
+    "13": 589,
+    "14": 1067,
+    "15": 241,
+    "16": 1000,
+    "17": 469,
+    "18": 487,
+    "19": 323,
+    "20": 1358,
+    "21": 5589,
+    "22": 1344
+  },
+  "inverse_formal_columns": 20107,
+  "new_entrance_rank": 1719,
+  "new_gauges": 890,
+  "new_gram_audit_external": true,
+  "new_rank_mass": 432458,
+  "new_records": 828136,
+  "old_rank_mass": 434177,
+  "old_records": 885228,
+  "omitted_Q_nonzero_wrong_words": 38256,
+  "omitted_Qinverse_nonzero_wrong_words": 1090,
+  "removed_initial_reads": 60520,
+  "status": "EXPERIMENTAL_CONNECTED_PLATEAU_RETIMING",
+  "cohort_rewrite_records": 828137,
+  "cohort_rewrite_histogram": {
+    "1": 43230,
+    "10": 769,
+    "11": 430,
+    "12": 1514,
+    "13": 583,
+    "14": 1067,
+    "15": 241,
+    "16": 1000,
+    "17": 470,
+    "18": 487,
+    "19": 323,
+    "2": 18939,
+    "20": 1358,
+    "21": 5589,
+    "22": 1344,
+    "3": 9657,
+    "4": 3015,
+    "5": 2394,
+    "6": 1530,
+    "7": 1226,
+    "8": 634,
+    "9": 645
+  },
+  "cohort_rewrite_delta": {
+    "1": 1818,
+    "10": -4,
+    "11": -15,
+    "12": -11,
+    "13": 21,
+    "14": -13,
+    "15": -46,
+    "17": -34,
+    "19": -8,
+    "2": -146,
+    "3": -577,
+    "4": 105,
+    "5": -90,
+    "6": 3,
+    "7": -26,
+    "8": 5,
+    "9": 34
+  },
+  "descent_delta": {
+    "2": -2,
+    "4": 24,
+    "5": -48,
+    "6": 25,
+    "11": -1,
+    "13": 2,
+    "17": -1
+  },
+  "descent_retimed_gates": 25,
+  "descent_removed_calls": 1,
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new file mode 100644
index 0000000000..09208245a9
--- /dev/null
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new file mode 100644
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diff --git a/research/multicut-kernel-condensation-883/expected/INDEPENDENT-LEGALITY.json b/research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json
similarity index 77%
rename from research/multicut-kernel-condensation-883/expected/INDEPENDENT-LEGALITY.json
rename to research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json
index 42596820f3..2a1a804942 100644
--- a/research/multicut-kernel-condensation-883/expected/INDEPENDENT-LEGALITY.json
+++ b/research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json
@@ -1,67 +1,67 @@
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similarity index 57%
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index 0ab29feae1..03272faa33 100644
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+++ b/research/multicut-kernel-composition/expected/INDEPENDENT-PREFIX.json
@@ -1,10 +1,10 @@
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new file mode 100644
index 0000000000..557cc8b704
--- /dev/null
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similarity index 100%
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similarity index 100%
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similarity index 100%
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similarity index 100%
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diff --git a/research/multicut-kernel-composition/inputs/descent-selection.json b/research/multicut-kernel-composition/inputs/descent-selection.json
new file mode 100644
index 0000000000..88cb160db4
--- /dev/null
+++ b/research/multicut-kernel-composition/inputs/descent-selection.json
@@ -0,0 +1,7754 @@
+{
+  "status": "FROZEN_CONCAVE_DESCENT_FRAME_SELECTION",
+  "input_record_sha256": "d073aeb4a8054ee6e23366ac7a42554624d52d3a822e03de9831a12530287395",
+  "input_record_count": 828137,
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+    "11": -1,
+    "13": 2,
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+  "expected_removed_calls": 1,
+  "expected_scalar_additions": 728389,
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+}
diff --git a/research/multicut-kernel-condensation-883/inputs/frames.json.gz b/research/multicut-kernel-composition/inputs/frames.json.gz
similarity index 100%
rename from research/multicut-kernel-condensation-883/inputs/frames.json.gz
rename to research/multicut-kernel-composition/inputs/frames.json.gz
diff --git a/research/multicut-kernel-composition/inputs/plateau-selection.json b/research/multicut-kernel-composition/inputs/plateau-selection.json
new file mode 100644
index 0000000000..023a6592f3
--- /dev/null
+++ b/research/multicut-kernel-composition/inputs/plateau-selection.json
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+        "candidate_gate": 654237,
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+        "event": [
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+      {
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+        "candidate_gate": 658097,
+        "event": [
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+          12
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+      },
+      {
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+        "candidate_gate": 658098,
+        "event": [
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+      },
+      {
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+        "candidate_gate": 658149,
+        "event": [
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+        ]
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+        "candidate_gate": 658150,
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+      {
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+        "candidate_gate": 658153,
+        "event": [
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+        ]
+      },
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+      {
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+      },
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+        "candidate_gate": 658297,
+        "event": [
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+          12
+        ]
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+        "event": [
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+        ]
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+      {
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+        "candidate_gate": 655505,
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+        "event": [
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+      },
+      {
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+        "candidate_gate": 655523,
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+      {
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+        "candidate_gate": 655557,
+        "event": [
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+      },
+      {
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+        "candidate_gate": 655574,
+        "event": [
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+        ]
+      },
+      {
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+        "candidate_gate": 655575,
+        "event": [
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+      },
+      {
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+        "candidate_gate": 655609,
+        "event": [
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+      {
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+        "candidate_gate": 655626,
+        "event": [
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+          1,
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+          12
+        ]
+      },
+      {
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+        "candidate_gate": 655627,
+        "event": [
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+          1,
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+          12
+        ]
+      }
+    ]
+  }
+}
diff --git a/research/multicut-kernel-condensation-883/requirements.txt b/research/multicut-kernel-composition/requirements.txt
similarity index 100%
rename from research/multicut-kernel-condensation-883/requirements.txt
rename to research/multicut-kernel-composition/requirements.txt
diff --git a/research/multicut-kernel-condensation-883/vendor/PR249-SOURCE-MANIFEST.json b/research/multicut-kernel-composition/vendor/PR249-SOURCE-MANIFEST.json
similarity index 100%
rename from research/multicut-kernel-condensation-883/vendor/PR249-SOURCE-MANIFEST.json
rename to research/multicut-kernel-composition/vendor/PR249-SOURCE-MANIFEST.json
diff --git a/research/multicut-kernel-condensation-883/vendor/UPSTREAM-NOTICE.md b/research/multicut-kernel-composition/vendor/UPSTREAM-NOTICE.md
similarity index 100%
rename from research/multicut-kernel-condensation-883/vendor/UPSTREAM-NOTICE.md
rename to research/multicut-kernel-composition/vendor/UPSTREAM-NOTICE.md
diff --git a/research/multicut-kernel-condensation-883/vendor/json.hpp b/research/multicut-kernel-composition/vendor/json.hpp
similarity index 100%
rename from research/multicut-kernel-condensation-883/vendor/json.hpp
rename to research/multicut-kernel-composition/vendor/json.hpp
diff --git a/research/multicut-kernel-condensation-883/vendor/pr249-source.zip b/research/multicut-kernel-composition/vendor/pr249-source.zip
similarity index 100%
rename from research/multicut-kernel-condensation-883/vendor/pr249-source.zip
rename to research/multicut-kernel-composition/vendor/pr249-source.zip
diff --git a/research/multicut-kernel-condensation-883/verify.py b/research/multicut-kernel-composition/verify.py
similarity index 79%
rename from research/multicut-kernel-condensation-883/verify.py
rename to research/multicut-kernel-composition/verify.py
index e533d71b61..51ed59596a 100644
--- a/research/multicut-kernel-condensation-883/verify.py
+++ b/research/multicut-kernel-composition/verify.py
@@ -1,7 +1,7 @@
 #!/usr/bin/env python3
 """Offline source-bound reproduction. No stored PASS result is accepted without execution."""
 from pathlib import Path, PurePosixPath
-import argparse, concurrent.futures, gzip, hashlib, json, os, subprocess, sys, time, zipfile
+import argparse, concurrent.futures, gzip, hashlib, json, os, shutil, subprocess, sys, time, zipfile
 sys.dont_write_bytecode = True
 HERE = Path(__file__).resolve().parent
 
@@ -41,7 +41,7 @@ def main():
     for name, expected in manifest.items():
         need(digest(HERE / name) == expected, 'package hash mismatch: ' + name)
     out.mkdir(parents=True)
-    for part in ('logs', 'bin', 'lead', 'compiler', 'review', 'temporal/CURRENT249-EXPORT', 'upstream'):
+    for part in ('logs', 'bin', 'lead', 'compiler', 'review', 'temporal/CURRENT249-EXPORT', 'upstream'):  # plateau/ is created by the 02c stage
         (out / part).mkdir(parents=True)
     start = time.monotonic()
     def run(label, cmd):
@@ -95,6 +95,20 @@ def compile_source(p):
     lead = out / 'lead'; compiler = out / 'compiler'; temporal = out / 'temporal'; review = out / 'review'
     run('02-transform', [exe('cohort-transform'), X, candidates, lead])
     result = load(HERE / 'RESULT.json')
+    need(digest(lead / 'COHORT249-RECORDS.bin') == result['cohort_record_sha256'], 'cohort physical transcript hash mismatch')
+    # 02b: concave-descent frame retiming of 25 ADD gates (rohanarun, PR263 stage), selection pre-bound by full
+    # scalar-core alignment to this package's cohort transcript; the stage self-checks and every native checker reruns.
+    (lead / 'DESCENT-REBIND-EVIDENCE.json').write_text(json.dumps(dict(status='SELECTION_PREBOUND_TO_COMMITTED_COHORT_TRANSCRIPT', cohort_record_sha256=result['cohort_record_sha256'], binding='full unchanged scalar-core event alignment (rebind_descent.py of PR270) from PR259 transcript 1ae06b18c7c23e0f96f9309fcfc4a64a59b670c21d99207192d93440021e4897'), indent=2) + '\n', encoding='utf-8')
+    shutil.copy(HERE / 'inputs/descent-selection.json', lead / 'descent-selection.json')
+    run('02b-descent-retiming', [sys.executable, '-B', HERE / 'code/descent_retiming.py', X, lead, lead / 'descent-selection.json'])
+    need(digest(lead / 'COHORT249-PRE-DESCENT-RECORDS.bin') == result['cohort_record_sha256'], 'retained cohort transcript changed')
+    need(digest(lead / 'COHORT249-RECORDS.bin') == result['descent_record_sha256'], 'descent transcript hash mismatch')
+    # 02c-02e: connected-block plateau retiming of 29 blocks / 57 ADDs (PR270 stage), witness pre-bound to the descent transcript.
+    plateau = out / 'plateau'
+    run('02c-plateau-retiming', [sys.executable, '-B', HERE / 'code/plateau_retiming.py', X, lead, HERE / 'inputs/plateau-selection.json', plateau])
+    lead = plateau
+    run('02d-plateau-source-spans', [sys.executable, '-B', HERE / 'code/verify_plateau_spans.py', X, lead, lead / 'PLATEAU-RETIMING.json'])
+    run('02e-frame-tables', [sys.executable, '-B', HERE / 'code/verify_frame_tables.py', X, lead, '--output', lead / 'FRAME-TABLE-AUDIT.json'])
     need(digest(lead / 'COHORT249-RECORDS.bin') == result['new_record_sha256'], 'new physical transcript hash mismatch')
     run('03-independent-legality', [exe('cohort-legality-independent'), X, lead, review / 'INDEPENDENT-LEGALITY.json'])
     run('04-independent-prefix', [exe('cohort-prefix-independent'), X, lead, review / 'INDEPENDENT-PREFIX.json'])
diff --git a/research/multicut-kernel-condensation-883/PROOF.md b/research/multicut-kernel-condensation-883/PROOF.md
deleted file mode 100644
index 43dceebc34..0000000000
--- a/research/multicut-kernel-condensation-883/PROOF.md
+++ /dev/null
@@ -1,81 +0,0 @@
-# The early cut carries 365 more response-kernel families
-
-**Claim.** On PR #249's bit word (commit `96495746`), PR #259's multi-cut kernel condensation extended by 365
-twin-pair rewrites at its earliest cut (record 676,559) is a legal word of the same model with literal bank stock
-866,565 and κ = 44463833535321/(625·10¹⁴) = 7.11421336565136·10⁻⁴, checked by PR #259's seven native checkers
-and priced by its exact pricer, under the retained public all-size hypotheses of PR #249/#254/#259.
-
-## 1. The mechanism (PR #254/#259, unchanged)
-
-A dirty helper j that is untouched before a cut (initial frame ZERO, final frame FULL, no write, copy or
-non-initial read before the cut) acts on the targets only through its initial zero-frame compensation reads, so
-its *complete target response* R_j ∈ F₂^1760 is the column of the prefix's target map. Two such helpers a, b with
-R_a = R_b and a common nondegenerate rank-one line E inside both first required frames admit the rewrite of PR
-#254: a starts at E (its initial reads are deleted), b moves ZERO → E at the cut and absorbs a there (Q = I +
-e_b e_aᵀ), the old word resumes from E (the first moves of a and b become E → F_a, E → F_b), and Q⁻¹ is paid at
-the full frame; the omitted response R_a·a and the induced change R_b·a cancel. PR #259 generalises this to
-several simultaneous zero-response directions at four cuts and admits any entrance line through an exact chart
-audit (B⁻¹(I − σ)B diagonal, factor count ≤ 548, intermediates below 2⁸⁰).
-
-## 2. What is added
-
-At the earliest of PR #259's four cuts, record 676,559 (the last initial compensation read; records 0..676,559
-are the 676,560 initial reads, and the first MOVE follows), 14,286 clean helpers are live. Their responses form
-985 twin classes of size two and 24 of size nine. Of the 985 pairs, 747 have a nonzero nondegenerate common
-line; 335 are disjoint from all 1,194 helpers of PR #259's 518 families (319 with first frames (2, 2), 8 with
-(3, 5), 7 with (3, 3), 1 with (3, 6)); 333 are kept (the two of smallest gain dropped so that the total entrance
-rank 1,344 + 333 = 1,677 is ≡ 0 mod 3, which PR #259's transform requires at 40 replicas). Their lines are
-u = eᵢ − eⱼ (norm 2; cleared Gram 9·uᵀu − (Σu)² = 18, so the excluded primes are {2, 3}, as for the ±1-four lines
-with Gram 36) for the (2, 2) pairs and ±1-four lines for the others. Each is a pair with e = 1, exactly PR
-#254's shape; they enter `inputs/candidates.json.gz` in PR #259's schema (`pivot`, `partners`, `roles`,
-`basis`, `dim = 1`, `E_dimension = 1`, `cut = 676559`, `first_frames`, `kind`, `round = "union-early-cut"`)
-after PR #259's 518 items, which are unchanged.
-
-Second round. Among the 12,427 clean helpers not used by the 851 families, the response classes at twelve cuts from
-676,559 to 727,593 (every class of any size, pairs and XOR triples R_c = R_a ⊕ R_b, entrance a nondegenerate line or
-the full intersection when its Gram is nondegenerate) contain 64 net-positive pair candidates and no net-positive
-triple (a partner costs φ(1) + φ(r − 1) − φ(r) > 0, so only the pivot gains); a greedy packing by gain keeps 32
-disjoint families, all at cut 676,559: 28 pairs (3, 3) with e = 1, two (3, 6), one (3, 5) with e = 1 and one (3, 5)
-entering on its full two-dimensional intersection (e = 2), entrance rank 33, so the total 1,710 is ≡ 0 mod 3 with
-no drop (`round = "headroom-2"`). The later cuts add nothing: at 680,080 and 700,582 the candidate set is the same,
-from 705,000 on it shrinks to nothing. After these 32 no net-positive pair or triple remains among unused helpers at
-any cut, so this lever is exhausted on this word under the φ ledger.
-
-Why they pay: with the deficit pinned at 35,200 per replica (120·W − mass is invariant under the rewrite, because
-the pivot's residual 24 → 23 shrinks the bank capacity by exactly the mass saved), the coarse exponent is driven by
-the log-weighted mass Σ r·n·ln(120/r); a pair with first ranks (r_a, r_b) and e = 1 changes it by
-φ(r_a − 1) − φ(r_a) + φ(1) + φ(r_b − 1) − φ(r_b), φ(r) = r·ln(120/r): −2.02 for (2, 2), −0.97 for (3, 3), and
-PR #259's exact pricer confirms the sign and the size on the whole selection.
-
-## 3. What is checked (PR #259's checkers, unchanged; receipts in `expected/`)
-
-| checker | receipt |
-|---|---|
-| `cohort-transform` (all-column F₂ replay) | 883 pivots, entrance rank 1,710, 59,192 initial reads removed, 2,272 gates, raw mass 434,177 → 432,467, 829,444 records; omitted-Q control 37,450 wrong columns, omitted-Q⁻¹ control 1,084 |
-| `cohort-legality-independent` | 1,924 selected helpers, 0 source-owner and 0 donor intersections, 729,703 common-frame ADDs, 99,693 nested MOVEs, 24 COPY/ERASE windows, all final frames |
-| `cohort-prefix-independent` | 4 cuts, 1,554,080 target-kernel equalities, 37,042,593 non-target identity bits |
-| `cohort-bank-review` | literal stock 866,565 (saved 2,850), residual families 23: 733, 22: 42 and 24: 13,404 (others unchanged), 3,317,400 assignments, 883 exact charts (at most 200 factors), selector 626,937,137,600 |
-| `cohort-five-stage-columns` | 23,627 columns, payload 98 bits |
-| `cohort-price` | coarse 711927817449537/10¹⁸, W 173,313, 3,971,440 calls, mass 20,762,360, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
-| `cohort-finite-invoice` | coefficient 56 bits, deficit 176,000, cutoffs positive |
-
-Control: PR #259's own selection through the same pipeline reproduces its κ exactly and six of its seven
-receipts byte for byte; the seventh differs only in `containment_pairs_checked`, a memo-cache miss counter of
-the legality checker that depends on the compiler's evaluation order and not on what is checked (PR #259's
-expected value 82,347 against 82,344 with Apple clang).
-
-Two platform matters, so that the same package verifies on Linux/g++ (the workflow) and on macOS/clang:
-`code/cohort-transform.cpp` orders the gauges by frame dimension with `std::sort`, whose order among equal
-dimensions differs between libstdc++ and libc++, so the emitted transcript (and its sha256 in `RESULT.json`)
-differed between the two; this package's copy uses `std::stable_sort` there (one token; the gates of equal-dimension
-gauges keep their selection order, every checker is unchanged). And `verify.py` adds `containment_pairs_checked`
-to the platform-dependent fields its `normalize` already drops (`seconds`, `local_scalar_stream`) and applies
-`normalize` to the committed receipt as well as to the fresh one (two lines). Nothing else of PR #259's code
-changes; `discovery/` lists the diff.
-
-## 4. Not claimed
-
-No Lean certificate; the public all-size compiler, chart, routing, prime-supply, precision and analytic interfaces
-of PR #249 are retained as hypotheses, as in PR #254/#259. The 4 pairs whose twin is a PR #259 helper have no
-other twin at any cut; PR #263's 25 frame retimings do not apply verbatim (18 of their registers are among the
-helpers used here, and their selection is bound to #259's transcript), and were not re-derived.
diff --git a/research/multicut-kernel-condensation-883/README.md b/research/multicut-kernel-condensation-883/README.md
deleted file mode 100644
index 121919cd18..0000000000
--- a/research/multicut-kernel-condensation-883/README.md
+++ /dev/null
@@ -1,64 +0,0 @@
-# multicut-kernel-condensation-883
-
-**Conditional κ = 44463833535321 / 62500000000000000 = 7.11421336565136·10⁻⁴** (+0.0551% over PR #259's
-7.11029386054035·10⁻⁴; +0.0547% over PR #263's 7.11032238200698·10⁻⁴).
-
-PR #259 (Dugongue) condenses response kernels of the PR #249 bit word at four cuts with 518 pivot families. Its
-earliest cut, record 676,559 — the last initial compensation read — carries only 103 of them. A census of the
-twin dirty helpers at that cut (helpers untouched before it whose complete F₂ target responses coincide) finds
-985 twin pairs; 335 of them are disjoint from every helper PR #259 uses and have a nondegenerate rank-one common
-entrance line, and 333 of those (two dropped to keep the entrance rank ≡ 0 mod 3, as the transform requires at
-40 replicas) are net-positive under the fixed-deficit ledger. A second census among the helpers still unused after
-that round — every response class of any size at twelve cuts between 676,559 and 727,593, pairs and XOR triples —
-yields 32 more disjoint net-positive families (28 pairs with first frames (3, 3), two (3, 6), one (3, 5), and one
-(3, 5) pair entering on its full two-dimensional nondegenerate intersection), all at the same cut, and nothing at
-any later cut. Added to PR #259's 518 families, verbatim, the 365 give
-
-| | PR #259 | this package |
-|---|---|---|
-| pivot families / entrance rank | 518 / 1,344 | **883 / 1,710** |
-| initial compensation reads removed / basis gates paid | 27,772 / 1,542 | 59,192 / 2,272 |
-| raw rank mass per invocation | 434,177 → 432,833 | 434,177 → **432,467** |
-| literal bank stock / normalized | 867,175 / 173,435 | **866,565** / 173,313 |
-| κ | 7.11029386054035·10⁻⁴ | **7.11421336565136·10⁻⁴** |
-
-The 365 added entries use PR #259's own mechanism unchanged: the pivot starts at the common line E (its four
-initial reads are deleted), the partner moves to E and absorbs the pivot there, and the inverse gate is paid at the
-full frame. 319 of them have first frames (2, 2) and a line u = eᵢ − eⱼ (norm 2, cleared Gram 18 for G = I − J/9),
-which PR #254's chart rule excluded (`norm == 4`) and PR #259's generic exact chart audit admits (prime
-exclusion {2, 3}, the same as the ±1-four lines); the remaining 14 are (3, 5), (3, 3) and (3, 6) pairs with ±1-four
-lines; the 32 of the second round are (3, 3), (3, 5) and (3, 6) pairs with ±1-four lines (one with e = 2).
-**No checker and no proof note of PR #259 is changed, and no C++ line beyond one platform fix**: the only inputs that differ are the
-frozen selection `inputs/candidates.json.gz` (PR #259's 518 items byte for byte, then the 333 of the first round
-in its schema with `round = "union-early-cut"` and the 32 of the second with `round = "headroom-2"`) and the seven regenerated receipts in `expected/`; `RESULT.json` and
-`MANIFEST.json` follow. PR #259's seven native checkers pass on the new word (all-column F₂ replay forward and
-inverse with omitted-Q and omitted-Q⁻¹ controls; chronological legality with COPY/ERASE windows and source
-owners; 1,497,760 per-cut target-kernel equalities; 883 exact projector charts, 3,317,400 bank assignments; the
-five-stage F₂ columns; the exact rational price with 47 outer constraints, adjacent grid rejected; the finite
-invoice). [PROOF.md](PROOF.md) states the delta; PR #259's own notes are kept unchanged as `README-PR259.md`,
-`PROOF-PR259.md`, `KERNEL-PROOF.md`, `BANK-PROOF.md`, `COPY-PROOF.md`, `FINITE-PROOF.md`, `REVIEW.md`.
-
-This is a conditional, finite construction under the same retained public all-size hypotheses as PR #249/#254/#259
-(not a Lean certificate, not an unconditional theorem). κ is the bit-bound value: the complex supplier of this
-lineage stands at 7.0991·10⁻⁴ three-stage (PR #233) and 7.5474·10⁻⁴ five-stage (PR #256, Lean-checked in
-jacobalansussman/wht-power-saving-lean#2), so the bit supplier still binds.
-
-## Verify
-
-    sudo apt-get install -y g++ libboost-dev            # Linux; macOS: brew install boost, --cxx clang++ with a bits/stdc++.h shim
-    python -m pip install -r research/multicut-kernel-condensation-883/requirements.txt    # sympy 1.14.0
-    python3 -I research/multicut-kernel-condensation-883/verify.py --output /tmp/mc883-replay    # fresh directory outside the package; about 70 s
-
-PR #259's verifier, unchanged: it checks every package hash against `MANIFEST.json`, regenerates the pinned PR #249
-word from `vendor/pr249-source.zip` (SymPy), compiles the seven checkers, emits the new word from the frozen
-selection, runs every check and compares each receipt with `expected/` (platform-independent fields only; see
-PROOF.md, "Receipts"), then prints `PASS: kappa = 0.000711421336565136`. `--snapshots-only` skips the upstream
-regeneration (about 20 s). `.github/workflows/multicut-kernel-condensation-883.yml` runs it on Ubuntu.
-
-## Files
-
-Everything of PR #259's package (`code/`, `inputs/`, `vendor/`, `expected/`, the proof notes, `verify.py`,
-`requirements.txt`, `LICENSE`) with the two input changes above; `discovery/` (the census, the comparison with
-PR #259's selection and the merge, not run by the verifier: `twins.py`, `chrono2.py`, `gain.py`,
-`gen_candidates.py`, `compare259.py`, `merge259.py`, `census2.py`, `merge2.py`); `README.md`, `PROOF.md`, `NOTICE.md`, `RESULT.json`,
-`MANIFEST.json`.
diff --git a/research/multicut-kernel-condensation-883/RESULT.json b/research/multicut-kernel-condensation-883/RESULT.json
deleted file mode 100644
index 82619991e9..0000000000
--- a/research/multicut-kernel-condensation-883/RESULT.json
+++ /dev/null
@@ -1,12 +0,0 @@
-{
-  "kappa": "44463833535321/62500000000000000",
-  "kappa_decimal": "0.000711421336565136",
-  "baseline_head": "96495746c786d6d0339dbb38c7f553d4af3f88ed",
-  "baseline_kappa": "0.000710392186446856",
-  "previous_delivery_kappa": "0.000711403723709732",
-  "new_record_sha256": "16a3f01613c1dfdf52695732f8efbae790663905c34af95e69b2cb28cd354ecb",
-  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES",
-  "lean_certificate": false,
-  "pivots": 883,
-  "entrance_rank": 1710
-}
diff --git a/research/multicut-kernel-condensation-883/discovery/README.md b/research/multicut-kernel-condensation-883/discovery/README.md
deleted file mode 100644
index 17bf1b74f3..0000000000
--- a/research/multicut-kernel-condensation-883/discovery/README.md
+++ /dev/null
@@ -1,22 +0,0 @@
-# Discovery (not run by the verifier)
-
-Pure-Python replay of PR #249's word and the censuses that produced the 365 added families (Chafik Boukhalfa,
-Anthropic Claude assistance). Inputs are the package's own `inputs/` files, decompressed into a data directory.
-
-    twins.py  <data> twins.pkl                  census of twin dirty helpers at PR #254's cut (record 727,593)
-    chrono2.py <data> twins.pkl chrono.pkl <cut> the same census at any cut (used at 676,560: 985 pairs, 24 size-9 classes)
-    gain.py                                     log-weighted gain phi(r) = r ln(120/r) per pair and exact-grid price
-    gen_candidates.py                           candidate records (basis, first frames, entrance line) in PR #259's schema
-    compare259.py                               the pairs disjoint from PR #259's 1,194 helpers (free259.json)
-    merge259.py                                 PR #259's 518 items + the 333 free net-positive pairs (round 1)
-    census2.py                                  second census: every response class at twelve cuts, pairs and XOR triples, greedy packing
-    merge2.py                                   + the 32 families of the second round -> inputs/candidates.json.gz
-
-Diff of this package against PR #259's (everything else byte for byte):
-
-    inputs/candidates.json.gz      518 items unchanged + 333 appended (round "union-early-cut") + 32 (round "headroom-2"), all at cut 676559
-    expected/*.json, RESULT.json   regenerated receipts and result (883 pivots, entrance rank 1710, kappa 7.11421336565136e-4)
-    code/cohort-transform.cpp      std::sort -> std::stable_sort on the gauge order (platform-independent transcript)
-    verify.py                      'containment_pairs_checked' added to the dropped fields; normalize() on both receipt sides
-    README.md, PROOF.md, NOTICE.md this package's notes; PR #259's README/PROOF kept as README-PR259.md, PROOF-PR259.md
-    MANIFEST.json                  regenerated
diff --git a/research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json b/research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json
deleted file mode 100644
index 8ac2ea98b7..0000000000
--- a/research/multicut-kernel-condensation-883/expected/COHORT249-REPLAY.json
+++ /dev/null
@@ -1,62 +0,0 @@
-{
-  "added_Q_Qinverse_passes": 2272,
-  "bank_completion_not_replayed": true,
-  "cut_record": 727593,
-  "delta": {
-    "1": 1843,
-    "10": -4,
-    "11": -15,
-    "12": -11,
-    "13": 21,
-    "14": -13,
-    "15": -46,
-    "17": -34,
-    "19": -8,
-    "2": -124,
-    "3": -601,
-    "4": 101,
-    "5": -82,
-    "6": 1,
-    "7": -26,
-    "8": 5,
-    "9": 34
-  },
-  "forward_formal_columns": 20107,
-  "global_kappa_claimed": false,
-  "histogram": {
-    "1": 43255,
-    "10": 769,
-    "11": 430,
-    "12": 1514,
-    "13": 583,
-    "14": 1067,
-    "15": 241,
-    "16": 1000,
-    "17": 470,
-    "18": 487,
-    "19": 323,
-    "2": 18961,
-    "20": 1358,
-    "21": 5589,
-    "22": 1344,
-    "3": 9633,
-    "4": 3011,
-    "5": 2402,
-    "6": 1528,
-    "7": 1226,
-    "8": 634,
-    "9": 645
-  },
-  "inverse_formal_columns": 20107,
-  "new_entrance_rank": 1710,
-  "new_gauges": 883,
-  "new_gram_audit_external": true,
-  "new_rank_mass": 432467,
-  "new_records": 829444,
-  "old_rank_mass": 434177,
-  "old_records": 885228,
-  "omitted_Q_nonzero_wrong_words": 37450,
-  "omitted_Qinverse_nonzero_wrong_words": 1084,
-  "removed_initial_reads": 59192,
-  "status": "PASS_FULL_CURRENT249_COHORT_REWRITE_F2_COLUMNS_AND_FRAMES"
-}

From 8cff894317648ae8d4f170b3d33456a76a7822c7 Mon Sep 17 00:00:00 2001
From: chafreaky <chafik.boukhalfa@gmail.com>
Date: Sat, 10 Oct 2026 08:37:52 +0400
Subject: [PATCH 5/5] multicut-kernel-composition: + PR273 target-prefix
 squares and PR271 cleanup sandwiches (126, after a pivot-role swap in 83
 families); kappa = 7.14026746429965e-4 (native seven checkers
 7.12005174354669e-4)

---
 .../multicut-kernel-composition/MANIFEST.json |   55 +-
 .../multicut-kernel-composition/NOTICE.md     |   13 +-
 research/multicut-kernel-composition/PROOF.md |   67 +-
 .../multicut-kernel-composition/README.md     |   67 +-
 .../multicut-kernel-composition/RESULT.json   |   28 +-
 .../code/cleanup_sandwich.py                  |  161 +
 .../code/sandwich/price-histogram.cpp         |   22 +
 .../code/sandwich_endpoints.py                |   99 +
 .../code/target_prefix.py                     |  187 +
 .../discovery/README.md                       |   13 +-
 .../discovery/chain_swap.py                   |   50 +
 .../discovery/finalize_swap.py                |   32 +
 .../discovery/rebind_target.py                |   37 +
 .../discovery/scan_sandwich.py                |   68 +
 .../expected-sandwich/CLEANUP-SANDWICH.json   | 2044 +++++++
 .../expected-sandwich/COHORT-EXACT-PRICE.json |   99 +
 .../COHORT-FINITE-INVOICE.json                |   72 +
 .../COHORT-FIVE-STAGE-COLUMNS.json            |  184 +
 .../expected-sandwich/COHORT249-REPLAY.json   |  224 +
 .../INDEPENDENT-LEGALITY.json                 |  110 +
 .../expected-sandwich/INDEPENDENT-PREFIX.json |   10 +
 .../SANDWICH-BANK-INVOICE.json                |  600 ++
 .../expected/COHORT-BANK-REVIEW.json          |    2 +-
 .../expected/COHORT-EXACT-PRICE.json          |   40 +-
 .../expected/COHORT-FINITE-INVOICE.json       |   44 +-
 .../expected/COHORT-FIVE-STAGE-COLUMNS.json   |   42 +-
 .../expected/COHORT249-REPLAY.json            |   99 +-
 .../expected/DESCENT-RETIMING.json            |    6 +-
 .../expected/INDEPENDENT-LEGALITY.json        |   26 +-
 .../expected/PLATEAU-RETIMING.json            |    6 +-
 .../expected/PLATEAU-SOURCE-SPANS.json        |    3 +-
 .../expected/TARGET-PREFIX.json               |   34 +
 .../inputs/candidates.json.gz                 |  Bin 56466 -> 45132 bytes
 .../inputs/descent-selection.json             |    2 +-
 .../inputs/plateau-selection.json             |  118 +-
 .../inputs/sandwich-selection.json            |  139 +
 .../inputs/target-selection.json              | 4840 +++++++++++++++++
 .../multicut-kernel-composition/verify.py     |   61 +-
 38 files changed, 9470 insertions(+), 234 deletions(-)
 create mode 100644 research/multicut-kernel-composition/code/cleanup_sandwich.py
 create mode 100644 research/multicut-kernel-composition/code/sandwich/price-histogram.cpp
 create mode 100644 research/multicut-kernel-composition/code/sandwich_endpoints.py
 create mode 100644 research/multicut-kernel-composition/code/target_prefix.py
 create mode 100644 research/multicut-kernel-composition/discovery/chain_swap.py
 create mode 100644 research/multicut-kernel-composition/discovery/finalize_swap.py
 create mode 100644 research/multicut-kernel-composition/discovery/rebind_target.py
 create mode 100644 research/multicut-kernel-composition/discovery/scan_sandwich.py
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/CLEANUP-SANDWICH.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/COHORT-EXACT-PRICE.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/COHORT-FINITE-INVOICE.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/COHORT-FIVE-STAGE-COLUMNS.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/COHORT249-REPLAY.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-LEGALITY.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-PREFIX.json
 create mode 100644 research/multicut-kernel-composition/expected-sandwich/SANDWICH-BANK-INVOICE.json
 create mode 100644 research/multicut-kernel-composition/expected/TARGET-PREFIX.json
 create mode 100644 research/multicut-kernel-composition/inputs/sandwich-selection.json
 create mode 100644 research/multicut-kernel-composition/inputs/target-selection.json

diff --git a/research/multicut-kernel-composition/MANIFEST.json b/research/multicut-kernel-composition/MANIFEST.json
index eefab935ca..33fc5a53bd 100644
--- a/research/multicut-kernel-composition/MANIFEST.json
+++ b/research/multicut-kernel-composition/MANIFEST.json
@@ -5,13 +5,14 @@
     "FINITE-PROOF.md": "dd0e1ac3a212f484086d51454ebcf951ccb98eddfe4713310f688750d35d0069",
     "KERNEL-PROOF.md": "4779181f679925da5c6663d4c5aec1a4a0aef76c993ab14b3a82782ac16bb883",
     "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
-    "NOTICE.md": "e5083ae8e3997c7c654c6606ca2d3ccf6305e09c9c57c1a59da5fe9cdfb5af23",
+    "NOTICE.md": "4816e2b94bff1963abe80f33e379daafd3900a3c8803afe28b589d3e9ce71ae1",
     "PROOF-PR259.md": "ffc502078acdfee7a89abe3ec51fae4b8c5a8be7440d6b55f3e24f138e1b1a3b",
-    "PROOF.md": "e1e986740100ebedf202fa00b187fa661dca89afda6f268e6a521041b5fe03bc",
+    "PROOF.md": "fe814b155c2c181a832ba81f541fcdc0195728f33f936f7d4e00b6c95a5b7ebf",
     "README-PR259.md": "ed2f4f051a21af9c173c0a7af7cac440ce15cabdabfc721895edde2c837cce25",
-    "README.md": "15b38b18ff80e0eae47a2b004feaa9dfef45595795d5e8a04dd0eed5d805d616",
-    "RESULT.json": "e8bf2a05353f7525a7cefaa9b2c09845ec304245b8866769c586cbe2e7d41e0a",
+    "README.md": "9e88fe7b9c859303433c6332854ca4b82e64c6ef1578f3f7e4ffbe02afba5043",
+    "RESULT.json": "726077b5c93ded03c0a29ad6338b68284c29c6b04a62c560192ca6d426d5a22f",
     "REVIEW.md": "823eea4cacf586ca90e43146fac48143f129f6ff8ca71c6a03b88c29fc528ff9",
+    "code/cleanup_sandwich.py": "8fb843c2b6974afc467e3c877b97d7c861be8a1ce4e6ab417f60b35ec6d19858",
     "code/cohort-bank-review.cpp": "cdac6b0460b7d70b40b1a15e1e255995d7c86220b4498005319d971313bb2d81",
     "code/cohort-finite-invoice.cpp": "dc0761a15c9b43ebdff3921dd2a49c80bb9158f544fb662ad45880a763cb5ab9",
     "code/cohort-five-stage-columns.cpp": "cf9657e2407264120673f34659df79362dc132886d6e62dda96e44d085b61ed1",
@@ -22,45 +23,63 @@
     "code/descent_retiming.py": "a07145a700d95642d54e35a33d5b50ac76ad665220d4f0599c07b22d939f5e10",
     "code/export249.py": "6c9aedb8fb4f2d560aca6cfc32ec967e003c0e623cc345040f108101ec1b442f",
     "code/plateau_retiming.py": "6cd5ad6d3674cf32057da500d73a6695bd60de15b538b3c41f780cd183bd6b97",
+    "code/sandwich/price-histogram.cpp": "3f7300f6434aa28639644260ea7e76d45dbdfc650cfbeba1d753af55cb1ed1c1",
+    "code/sandwich_endpoints.py": "44c1f25c65643c0c9e78147baaac297be77fa4c216737b7dfd7b0f88c6850ff7",
+    "code/target_prefix.py": "53cbd14a71215978dc9b8660d633b81d91bc3ee3c90ee4300c76dd4de5e8c1f8",
     "code/verify_frame_tables.py": "8c0587858e496e8cce9c5aa2ab5938d21c49837af715941bee6d02625f4a3e95",
     "code/verify_frames.py": "aea01c7275088611c18ae110a2b4abf7b52f8cc8f70c5932a25588ddec4acd19",
     "code/verify_plateau_spans.py": "594f1ababb4efc9e597154970ea51f6b850774f4b55f8cf386dbf1eb7fc5322b",
-    "discovery/README.md": "4dce8d7a8ee6939f413b627212bdd5e5776e8e1a1757915c1df1a59d1f69f831",
+    "discovery/README.md": "4e28223a25e3758ff9ec223d81053d354212c35f10e0dbc4ffd324c6046af567",
     "discovery/census2.py": "cea6fa83fa6f85dc0895bfcd9804c4a7b5c8bc06c0642e2c0321943b1b497121",
     "discovery/census3.py": "02b2e94a5419bc343396ad954a083e09498b725561a7e0be7b0978a25950f3a0",
     "discovery/census3b.py": "19cabd66e734e07ebbf74277b7962ca8e124b48c22f0c32d04978fa05936f962",
+    "discovery/chain_swap.py": "502eeee20b6cb4d504231e3bad9a81e70ca94195cc8bff9b57ce5b12af12e66f",
     "discovery/chrono2.py": "fc2866441540a8d6fa887439f185d0f51f298e1411eecb5ad84aba0de83b5b82",
     "discovery/compare259.py": "4c6d08cfb64891a804db677c15baf172d297109d9526d0c9d3764bd26a2dfa8f",
+    "discovery/finalize_swap.py": "54588aab9cc5c5a986df7aba2fc182fbb790420db0fd3d9953e5a8a2c3933391",
     "discovery/gain.py": "b76253949941854bcfd1ff84ebb49b9eaa9fcf4784690295f4a9e773694ddcfd",
     "discovery/gen_candidates.py": "6d7136a9c1c86463b1c25405481422ed98f6517d10aa1e99a038fccb6930d688",
     "discovery/merge2.py": "cb7d72dc5f8431628281cbd3fb17562d75b3242b882c19cc85cd30ee27617cf1",
     "discovery/merge259.py": "aba72c3e48314e842c06681fd62bb90e2a1f2a5dcb39794b1e22f54a6b74b850",
+    "discovery/rebind_target.py": "1498cbf88b6adbf6aa4b7ee327623c22b3dc0b385243b928a1b5e0131abbbe6b",
     "discovery/retime.py": "5c82068777040e9e5fb9e9d5669d02a0f10c0651c8d2ccb362810c31bc31ad53",
+    "discovery/scan_sandwich.py": "52873b3795ff835b1b5d02df581abaa2ea68dbfc4b9d454ad3e6483320bdb540",
     "discovery/twins.py": "c5b3f2065081002aa8da22584724938338fa46da2e25f3221225803e0f1b0ef7",
-    "expected/COHORT-BANK-REVIEW.json": "669bbdaeca0ffe6e00991e6faf81120e87b78f89289b364e6a38dd297e278d5e",
-    "expected/COHORT-EXACT-PRICE.json": "ee418fd00f0a4da333aa4939fb66565573d2b21536e0170e263427b994cc8399",
-    "expected/COHORT-FINITE-INVOICE.json": "7cf97ec6b6d8ab8bacfdf09740536f9527abf697574400a1fd4d119fde5af236",
-    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "629fbfe696727ecd802aaafcddb83ff91b7155482926610dc750df2f163734ff",
-    "expected/COHORT249-REPLAY.json": "af2cb5ce2f2f62ea1b8e57a6bccd113d7ea116ae260dc23236348289243ad811",
-    "expected/DESCENT-RETIMING.json": "daf3a777838a4418947bf441c352630636580dca94c2599e07c64d4d6678c956",
+    "expected/COHORT-BANK-REVIEW.json": "0893b75595be282eb5500845419cc69336fe1ba6d68f84266f69b43a4586c72e",
+    "expected/COHORT-EXACT-PRICE.json": "93d2656072c280af87901f8dede303581e21dce2448cd8b6eb76f7a966530f9d",
+    "expected/COHORT-FINITE-INVOICE.json": "6b6d20f03b2167438fbac3546eb82d2cb0ede6acaa1667ab88c56b97dd9cb7f6",
+    "expected/COHORT-FIVE-STAGE-COLUMNS.json": "972a4f35789bff0b34d491ff9999a6ce54f6018cef673ffbc08c4ce52e39927d",
+    "expected/COHORT249-REPLAY.json": "99b32893d55304e9cf24169453b44312b796547b4080bc8f5d8d1a52b2dbd4b1",
+    "expected/DESCENT-RETIMING.json": "25e64786cf3648ba6bf9ff9fef2ed338cc1a03e9946619bf9e1ad1a8c259f553",
     "expected/FRAME-TABLE-AUDIT.json": "85c999e5ff201b573fb6e4267c2ea0ed5a58b81daccbc2c5311231f975f638fd",
-    "expected/INDEPENDENT-LEGALITY.json": "2f53482bf5c9df193fc667a5de0d487ad1028b14ccdbb4afdefe846d7786f6f5",
+    "expected/INDEPENDENT-LEGALITY.json": "ebff85cdc7a93014db41951f9c8f3e692f3b1101f9659ba3454ae38cfff95800",
     "expected/INDEPENDENT-PREFIX.json": "e06a1856db3e72ada0859d098fdf9e77e490fd75450312054e03ae039ac2cb94",
-    "expected/PLATEAU-RETIMING.json": "a18674ca15428e5ea258164f1f9c6f6cca2c0beacedfe6f213dcbc1e9373f6cc",
-    "expected/PLATEAU-SOURCE-SPANS.json": "5203527224527de7d2804e5deb0c06c58d94edc7c0db7470a8362c2646878b33",
+    "expected/PLATEAU-RETIMING.json": "06e3833080c8b97ee8eb6b896ce9d3a072f038ad2779981101bc1147825efd85",
+    "expected/PLATEAU-SOURCE-SPANS.json": "080b1c5c8a0b5a8129eb692a07d771a12064e2acb48d0281cb0ae0b84862a25c",
+    "expected/TARGET-PREFIX.json": "86fdf1451d386c0c3b64bab0252e04ab3355c1913f50ef80256d5d9ae98f388a",
+    "expected-sandwich/CLEANUP-SANDWICH.json": "7b4fb6e6ff801fb04cc380852590164bbdfaf6f2919fa1aac1316d148662d8b8",
+    "expected-sandwich/COHORT-EXACT-PRICE.json": "c4e87e1c4feaa3abfa4770f8a210a1e5639b6bb9a2493d8ff332695d01a6e983",
+    "expected-sandwich/COHORT-FINITE-INVOICE.json": "8e746573999f57671bc3460cf1f5ee3668139ade25e8832247d14ab7690555e0",
+    "expected-sandwich/COHORT-FIVE-STAGE-COLUMNS.json": "0746b9779f51ab7940d8f41ec273bab6eac6afd1c3027ced9c01082942c7feb4",
+    "expected-sandwich/COHORT249-REPLAY.json": "b2089ebd9e21636cfccf74dc35c75d451d61e5e738d997536760ab980de51356",
+    "expected-sandwich/INDEPENDENT-LEGALITY.json": "a58a94ef35cea8e6b8704c9cdd5ee4a596b36f8a7fd5e33d8b0b6f57106dd926",
+    "expected-sandwich/INDEPENDENT-PREFIX.json": "e06a1856db3e72ada0859d098fdf9e77e490fd75450312054e03ae039ac2cb94",
+    "expected-sandwich/SANDWICH-BANK-INVOICE.json": "f2285919664c1d6f3211da10a794fcde72a20f021ae2908dbd461d5f9ad162a3",
     "inputs/249-DONOR-OWNERSHIP.json.gz": "cd506a4bbefbc33fecfca3b0364e0b237ece493a96ef3085c39cf2465f2265d4",
     "inputs/249-records.bin.gz": "6bc404d4af63218e714683d3e33fc1a53941e0155493747c3d0fb41b4a2de7b2",
     "inputs/249-states.json.gz": "562bcd7de03bf9474ad8c5cbc50008c92b02bfad81e32c2e532ebd45f384e844",
     "inputs/SNAPSHOTS.json": "3939f432a95db64073584e61a47e4983070450929ea1986c86a56552c0b03721",
-    "inputs/candidates.json.gz": "94978b09567fd3766fa72eee5d244faf4ec2f9187693db7a9de64d2edad4303a",
-    "inputs/descent-selection.json": "e2f83db143fd7a323a57701912e03de179cf8755f9b5a31d6360aa5fb7a5c74a",
+    "inputs/candidates.json.gz": "e459d51e442487a9fdef93cd1592280cfff603023f27f19f51bede00ef67f8b0",
+    "inputs/descent-selection.json": "e9009fdeaef6e5d59b935803f909453c3c1407200e60713ce3f214f378209991",
     "inputs/frames.json.gz": "54678a046e1c86b4d9308f69ef6d572a3b3745229e0ecb73843db7889e487cce",
-    "inputs/plateau-selection.json": "a4bda62e95c3a79036a482feabc9068227d80fa3480611217b427fe20fbe55b0",
+    "inputs/plateau-selection.json": "89db6c272349921f88f7a93642ce51e4d17846431fb3aae8b7a61b6367237cf0",
+    "inputs/sandwich-selection.json": "ef16f27254d2bf5dfb5d9ad104b9772e62a6a4af903e49f26aa8c61c0aee689d",
+    "inputs/target-selection.json": "7ed2069ef80d0fc3405a30bc1ed7338ff98d506a7cd7c2d82815e0b27645acb1",
     "requirements.txt": "25f9f1fb1988b230147a1d3092d34e09c069eb7a6c6d6df46b3973b9f2d36efc",
     "vendor/PR249-SOURCE-MANIFEST.json": "f68fa82180cd352421b8bc3f7a5c89d51bde74e74cd8d62c222c28b0f23fcf31",
     "vendor/UPSTREAM-NOTICE.md": "9a659cc2f96ae7e0eda99954941c42a4529bc885fb1de161c44ea801ff36e480",
     "vendor/json.hpp": "aaf127c04cb31c406e5b04a63f1ae89369fccde6d8fa7cdda1ed4f32dfc5de63",
     "vendor/pr249-source.zip": "11e2b723f90c44e02f4aa78f5ae2160ae4b9b776d3f1c49e8bfec606959d692c",
-    "verify.py": "40bb3b53d391586ead4a441d6d469db3d837ec9d954ff723094958562cde92b1"
+    "verify.py": "9851dae2e7e7d4a4ed1851555555f24f83e1c09e24483c7b861a4fd090ecd153"
   }
 }
diff --git a/research/multicut-kernel-composition/NOTICE.md b/research/multicut-kernel-composition/NOTICE.md
index 918ea53b27..2d1b3e6c12 100644
--- a/research/multicut-kernel-composition/NOTICE.md
+++ b/research/multicut-kernel-composition/NOTICE.md
@@ -5,7 +5,8 @@ This package claims no exclusive priority over concurrent work.
 
 What this package contributes: the censuses of twin dirty helpers at PR #259's earliest cut and of shared donors,
 the 387 added kernel families (`inputs/candidates.json.gz`, rounds "union-early-cut", "headroom-2", "shared-donor"),
-the rebinding of the two published retiming selections to this transcript, the regenerated receipts, and the
+the pivot-role swap that exposes 128 cleanup sandwiches, the rebinding of the published retiming and target-prefix
+selections to this transcript, the composition of the four levers in one verifier, the regenerated receipts, and the
 discovery scripts in `discovery/`. Everything else is retained and credited:
 
 - Dugongue (OpenAI Codex assistance): PR #254 (the response-kernel pair rewrite, projector charts, native checkers),
@@ -14,13 +15,17 @@ discovery scripts in `discovery/`. Everything else is retained and credited:
   PROOF-PR259.md, KERNEL-PROOF.md, BANK-PROOF.md, COPY-PROOF.md, FINITE-PROOF.md, REVIEW.md), PR #267 (chronological
   donor sharing, the idea behind the shared-donor families).
 - rohanarun: PR #263 (the concave-descent frame retiming stage `code/descent_retiming.py` and its 25-gate selection,
-  used verbatim), PR #237/#209 (five-stage bit supplier, width-120 banks), PR #269.
+  used verbatim), PR #273 (the native target-prefix stage `code/target_prefix.py` and its 209-square selection, used
+  verbatim), PR #237/#209 (five-stage bit supplier, width-120 banks), PR #269.
+- evmckinney9: PR #271 (the cleanup-sandwich rewrite, its endpoint charts and bank re-tiling and the price wrapper,
+  ported as `code/cleanup_sandwich.py`, `code/sandwich_endpoints.py`, `code/sandwich/price-histogram.cpp`).
 - utcorvusvolat-dotcom: PR #270 (the 24 reuse pairs and two e = 2 planes, the plateau retiming stage
   `code/plateau_retiming.py` with `verify_frames.py`, `verify_plateau_spans.py`, `verify_frame_tables.py` and the
   29-block selection, and the rebinding of PR #263's selection by scalar-core alignment, all used verbatim).
 - eumemic (Anthropic Claude and OpenAI Codex assistance): PR #249/#244/#251 (the source527 bit word, entrance
-  banks, retimed source pairs, transported entrances) on PR #210's helper and PR #168's modules; PR #268.
-- hcg890 PR #234 (five-stage bit and complex suppliers); sennemmi PR #230/#261/#265; evmckinney9 PR #271.
+  banks, retimed source pairs, transported entrances) on PR #210's helper and PR #168's modules; PR #268 (the
+  target-prefix compression mechanism).
+- hcg890 PR #234 (five-stage bit and complex suppliers); sennemmi PR #230/#261/#265; lydakis PR #275; DreamingOfClouds PR #276.
 - The PR #249 lineage as credited in vendor/UPSTREAM-NOTICE.md and below.
 
 ---- PR #259's notice follows unchanged ----
diff --git a/research/multicut-kernel-composition/PROOF.md b/research/multicut-kernel-composition/PROOF.md
index f6984e8ba3..4caebfb9a0 100644
--- a/research/multicut-kernel-composition/PROOF.md
+++ b/research/multicut-kernel-composition/PROOF.md
@@ -1,10 +1,12 @@
-# Kernel families at the early cut, shared donors, and the two retimings, composed
+# Kernel families, two retimings, target-prefix compression and cleanup sandwiches, composed
 
 **Claim.** On PR #249's bit word (commit `96495746`), PR #259's multi-cut kernel condensation extended to 890 pivot
-families (entrance rank 1,719) and retimed by PR #263's 25 descent gates and PR #270's 29 plateau blocks is a legal
-word of the same model with literal bank stock 866,550 and κ = 711482139228173/10¹⁸ = 7.11482139228173·10⁻⁴, checked
-by PR #259's seven native checkers, the two retiming stages' own audits, and PR #259's exact pricer, under the retained
-public all-size hypotheses of PR #249/#254/#259.
+families (entrance rank 1,719), retimed by PR #263's 25 descent gates and PR #270's 29 plateau blocks, compressed by
+PR #273's 209 target-prefix squares, is a legal word of the same model with κ = 712005174354669/10¹⁸ =
+7.12005174354669·10⁻⁴, checked by PR #259's seven native checkers, the stages' own audits and PR #259's exact pricer;
+and with 126 of its kernel pivots retired at dimension 4 by PR #271's cleanup-sandwich rewrite it is a legal word with
+normalized stock 172,470 and κ = 142805349285993/(2·10¹⁷) = 7.14026746429965·10⁻⁴, checked as in section 5 — both
+under the retained public all-size hypotheses of PR #249/#254/#259.
 
 ## 1. The mechanism (PR #254/#259, unchanged)
 
@@ -59,18 +61,54 @@ necessary). Histogram deltas: descent {2: −2, 4: +24, 5: −48, 6: +25, 11: 
 plateau {1: +15, 2: −26, 3: +19, 4: −7, 5: −3, 6: +21, 7: −24, 8: +8, 9: −14, 10: −2, 11: +13, 12: −4, 13: +4} (calls
 and mass unchanged).
 
-## 4. What is checked (receipts in `expected/`)
+## 4. Target-prefix compression (PR #268, eumemic; native stage PR #273, rohanarun)
+
+On this word every target reads five rank-20 entrance helpers at a 20-dimensional frame right after the forward
+phase. In each of 209 squares of four targets, each such helper is read by exactly two of the four, so the dependent
+target's prefix response is the F₂ sum of its three square-mates' responses: its 1,057 frame-20 reads are omitted, it
+receives t −= p_j at the zero frame at the cut and t += p_j at the square's common nondegenerate 21-dimensional frame.
+PR #273's stage `code/target_prefix.py` (verbatim) recomputes every member's literal prefix response from the actual
+word, so the selection is self-checking; its 209 squares bind to this transcript after remapping the cut (the first
+record after the last Q pass, 669,371 here) and the 209 close records (`inputs/target-selection.json`, with a
+`core_binding` block: the post-cut scalar events of the two words are identical, 84,975 compared). Histogram delta
+{1: −209, 2: −7, 3: −1, 8: −1, 12: −1, 17: −1, 18: −7, 20: −200, 21: +209}; the seven native checkers run on the
+compressed word.
+
+## 5. Cleanup sandwiches (PR #271, evmckinney9)
+
+A kernel pivot whose only gates after its cut are the full-frame cleanup t += a; a += b; t += a (F₂; t never a
+control in between) equals a += b; t += b: the first gate moves to the cut, where a and b sit at frames whose sum is a
+nondegenerate four-dimensional frame, and t += b keeps the middle gate's place; the helper then stops at dimension 4
+instead of climbing to the full frame (two rank-21 steps become two rank-1 steps and one rank-20 step; its banked
+endpoint becomes a rank-3 partial swap instead of rank 23). The helpers are found on this word by
+`discovery/scan_sandwich.py` (kernel pivots with entrance dimension 1 whose two post-cut gates are the family's pass
+and the cleanup, with joint dimension 4 at the cut). A pair family has two members and the transform is symmetric in
+cost, so in 83 two-member families of rounds 1 and 3 the pivot role is moved to the member with the sandwich shape
+(`round` suffix `+pivot-swap`; the cohort histogram, entrance rank, removed reads and native receipts are unchanged);
+the scan then finds 128 sandwiches, of which 126 are retired: each retired helper frees 20 width units in every one of
+the 40 replicas, 800k must be a multiple of 120, so k ≡ 0 mod 3. Histogram delta {1: +252, 20: +126, 21: −252};
+the re-tiled banks lose 840 per stage (stock 173,310 → 172,470), the deficit stays 35,200. Because PR
+#259's bank review and price driver assume every helper ends at the full frame, the stage is certified as PR #271 does:
+native legality with the stage's final frames, native prefix and five-stage columns on the new word, exact endpoint
+charts and bank re-tiling (`code/sandwich_endpoints.py`), the unchanged price engine through PR #271's wrapper
+(`code/sandwich/price-histogram.cpp`, which first reproduces the native price bit for bit), and the native finite
+invoice; receipts in `expected-sandwich/`. `RESULT.json` carries both κ values (the seven native checkers' word, and
+the sandwich word).
+
+## 6. What is checked (receipts in `expected/` and `expected-sandwich/`)
 
 | stage | receipt |
 |---|---|
 | `cohort-transform` (all-column F₂ replay) | 890 pivots, entrance rank 1,719, 60,520 initial reads removed, 2,286 gates, raw mass 434,177 → 432,458; omitted-Q and omitted-Q⁻¹ controls fail nontrivially |
-| `descent_retiming` → `plateau_retiming` | sha gates cohort d073aeb4… → descent 43a73a44… → final 4f6ffc1d… (828,136 records); spans and frame-table audits PASS |
+| `descent_retiming` → `plateau_retiming` → `target_prefix` | sha gates cohort 4458dce8… → descent a6d793d7… → plateau a1cf58b3… → native word eaff3c98…; spans and frame-table audits PASS; target-prefix delta {1: −209, 2: −7, 3: −1, 8: −1, 12: −1, 17: −1, 18: −7, 20: −200, 21: +209}, 1,057 reads deleted, 1,254 setup/restore additions |
 | `cohort-legality-independent` | 1,903 helpers, 0 source-owner and 0 donor intersections, 24 COPY/ERASE windows, all final frames |
 | `cohort-prefix-independent` | 890 cohorts, 4 cuts, 1,566,400 target-kernel equalities |
 | `cohort-bank-review` | literal stock 866,550 (saved 2,865), 919 exact charts (at most 262 factors), 3,317,400 assignments, selector 626,937,131,600 |
 | `cohort-five-stage-columns` | 23,627 columns, payload 98 bits |
-| `cohort-price` | coarse 142397741344279/(2·10¹⁷), W 173,310, 3,970,400 calls, mass 20,762,000, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
+| `cohort-price` (native word) | coarse exponent giving κ = 7.12005174354669·10⁻⁴, W 173,310, deficit 35,200, 47/47 constraints, adjacent grid rejected, pinned-baseline regression exact |
 | `cohort-finite-invoice` | PASS, deficit 176,000, cutoffs positive |
+| sandwich word (sha 9556bfe3…): native legality with the stage's final frames, native prefix, native five-stage columns | PASS (`expected-sandwich/`) |
+| `sandwich_endpoints` (exact SymPy endpoint charts, bank re-tiling) + price wrapper + native finite invoice | 126 rank-3 partial swaps; W 172,470, rank mass 20,661,200, deficit 35,200, κ = 7.14026746429965·10⁻⁴, 47 constraints, adjacent grid rejected |
 
 Control: PR #259's own selection through the same transform reproduces its κ exactly, and the stable-sorted PR #259
 word is byte for byte the input PR #263's selection is bound to (sha 1ae06b18…), whose descent output is the input of
@@ -81,9 +119,12 @@ Platform matters (so that one package verifies on Linux/g++ and macOS/clang alik
 transcript's sha256); `verify.py` drops `containment_pairs_checked` (a memo-cache miss counter) from the compared
 receipt fields and normalizes both sides. Nothing else of PR #259's code changes; `discovery/README.md` lists the diff.
 
-## 5. Not claimed, not composed
+## 7. Not claimed, not composed
 
-No Lean certificate; the public all-size interfaces of PR #249 are retained as hypotheses. Not composed here:
-eumemic's target-prefix compression (PR #268; PR #273 composes it with #269, PR #272 with collective kernels) and
-evmckinney9's cleanup sandwiches (PR #271); 492 twin candidates whose donor's entrance is not inside the new pivot's
-first frame and multi-donor relations R_p = R_d₁ ⊕ R_d₂ were not searched.
+No Lean certificate; the public all-size interfaces of PR #249 are retained as hypotheses. The sandwich part is not
+seen by PR #259's native bank review (hard-coded census, residual 24 − dim(initial frame)) nor by its native price
+driver (stock from the entrance rank), which is why it is certified by the checks of section 6 instead, as PR #271
+does. Not composed: PR #272's frame-filtered collective kernels (925 families), PR #275's zero-frame target restores,
+the fixed-prime refinement of PR #261/#265; the two sandwiches beyond 126 (mod-3 rule); 492 twin candidates whose
+donor's entrance is not inside the new pivot's first frame and multi-donor relations R_p = R_d₁ ⊕ R_d₂ were not
+searched. PR #276's new bit word (gen4) stands above every rung on this word.
diff --git a/research/multicut-kernel-composition/README.md b/research/multicut-kernel-composition/README.md
index 0f14da4877..bcda810d0d 100644
--- a/research/multicut-kernel-composition/README.md
+++ b/research/multicut-kernel-composition/README.md
@@ -1,10 +1,13 @@
 # multicut-kernel-composition
 
-**Conditional κ = 711482139228173 / 10¹⁸ = 7.11482139228173·10⁻⁴** (+0.0637% over PR #259's 7.11029386054035·10⁻⁴;
-+0.0034% over PR #270's 7.11457853376510·10⁻⁴, the best kernel-condensation rung before this one).
+**Conditional κ = 142805349285993 / (2·10¹⁷) = 7.14026746429965·10⁻⁴** (+0.4216% over PR #259's 7.11029386054035·10⁻⁴;
++0.0510% over PR #271's 7.1366215638961·10⁻⁴ and +0.0472% over PR #275's 7.13690108083058·10⁻⁴, the best rungs on
+PR #249's word before this one). With the seven native checkers alone (before the sandwich stage):
+κ = 7.12005174354669·10⁻⁴. PR #276's new bit word (gen4, 7.2287·10⁻⁴) stands above every rung on this word.
 
 PR #259 (Dugongue) condenses response kernels of the PR #249 bit word with 518 pivot families at four cuts. This
-package composes, on that word and with PR #259's seven native checkers and pricer unchanged:
+package composes, on that word, with PR #259's seven native checkers and pricer unchanged, four levers published
+by five authors:
 
 1. **372 more kernel families at its earliest cut** (record 676,559, the last initial compensation read): a census of
    the twin dirty helpers live at that cut — helpers untouched before it whose complete F₂ target responses coincide
@@ -19,13 +22,27 @@ package composes, on that word and with PR #259's seven native checkers and pric
    this transcript by full scalar-core alignment; −1 local call) and **PR #270's 29 connected-block plateau
    retimings of 57 ADDs** (utcorvusvolat-dotcom; stages `code/plateau_retiming.py`, `verify_plateau_spans.py`,
    `verify_frame_tables.py`; calls and mass unchanged, rank distribution improved).
+3. **eumemic's target-prefix compression** (PR #268) as rohanarun's native stage of PR #273 (`code/target_prefix.py`,
+   verbatim): 209 squares of four targets whose prefix responses are F₂-dependent; the dependent target's 1,057
+   frame-20 reads are omitted and replaced by a zero-frame setup at the cut and a restoration at the square's
+   common 21-dimensional frame (+5.23·10⁻⁷).
+4. **evmckinney9's cleanup sandwiches** (PR #271): kernel pivots whose only gates after their cut are the full-frame
+   cleanup t += a; a += b; t += a are rewritten to stop at dimension 4 instead of climbing to the full frame
+   (rank-23 banked endpoints become rank-3 partial swaps). On this word the pivot role of 83 two-member families is
+   assigned to the member with the sandwich shape (cost-neutral for the kernel transform), which raises the count of
+   admissible sandwiches from 45 to 128, of which 126 are retired (the bank re-tiling needs a multiple of 3): +2.02·10⁻⁶,
+   the largest single lever here.
 
-| | PR #259 | PR #270 | this package |
+| stage (each on the previous word) | pivot families / entrance rank | normalized stock W | κ |
 |---|---|---|---|
-| pivot families / entrance rank | 518 / 1,344 | 887 / 1,716 | **890 / 1,719** |
-| normalized stock W / child calls / rank mass | 173,435 / 3,956,840 / 20,777,000 | 173,311 / 3,970,720 / 20,762,120 | **173,310 / 3,970,400 / 20,762,000** |
-| literal bank stock / exact charts | 867,175 / 518 | — | 866,550 / 919 |
-| κ | 7.11029386054035·10⁻⁴ | 7.11457853376510·10⁻⁴ | **7.11482139228173·10⁻⁴** |
+| PR #259 | 518 / 1,344 | 173,435 | 7.11029386054035·10⁻⁴ |
+| kernel families: twins, headroom, shared donors | **890 / 1,719** | 173,310 | 7.11462218·10⁻⁴ |
+| + PR #263 descent (25 gates) + PR #270 plateau (29 blocks) retimings | 890 / 1,719 | 173,310 | 7.11482139228173·10⁻⁴ |
+| + target-prefix compression (209 squares) — seven native checkers' word | 890 / 1,719 | 173,310 | **7.12005174354669·10⁻⁴** |
+| + 126 cleanup sandwiches (pivot roles swapped in 83 families) | 890 / 1,719 | **172,470** | **7.14026746429965·10⁻⁴** |
+
+For comparison, PR #270 (887 families, rank 1,716) is 7.11457853·10⁻⁴, PR #273 (target squares on #269) 7.11948954·10⁻⁴,
+PR #271 (99 sandwiches on #272's word) 7.13662156·10⁻⁴ and PR #275 7.13690108·10⁻⁴.
 
 The deficit 120·W − mass = 35,200 per replica is invariant under all of these rewrites (a pivot's residual 24 → 23
 shrinks the bank capacity by exactly the mass it saves), so the exponent moves through the log-weighted mass
@@ -37,20 +54,25 @@ unchanged as `README-PR259.md`, `PROOF-PR259.md`, `KERNEL-PROOF.md`, `BANK-PROOF
 Conditional, finite construction under the same retained public all-size hypotheses as PR #249/#254/#259 (no Lean
 certificate, no unconditional theorem). κ is the bit-bound value: the complex supplier of this lineage stands at
 7.5474·10⁻⁴ five-stage (PR #256, Lean-checked in jacobalansussman/wht-power-saving-lean#2), so the bit supplier binds.
-Two other levers on the same word are not composed here: eumemic's target-prefix compression (PR #268, PR #273 on
-#269, PR #272 on collective kernels) and evmckinney9's cleanup sandwiches (PR #271); PR #272 stands above this package.
+The sandwich stage is certified as PR #271 certifies it (PROOF.md, section 5): PR #259's native bank review and
+price driver assume every helper ends at the full frame, so that part rests on the native legality, prefix and
+five-stage checkers on the new word, exact endpoint charts with the bank re-tiling, the unchanged price engine
+through PR #271's histogram wrapper, and the native finite invoice; `RESULT.json` carries both κ values. Not composed:
+PR #272's frame-filtered collective kernels, PR #275's zero-frame target restores, the fixed-prime refinement of
+PR #261/#265 (+4·10⁻¹²).
 
 ## Verify
 
     sudo apt-get install -y g++ libboost-dev            # Linux; macOS: brew install boost, --cxx clang++ with a bits/stdc++.h shim
     python -m pip install -r research/multicut-kernel-composition/requirements.txt    # sympy 1.14.0
-    python3 -I research/multicut-kernel-composition/verify.py --output /tmp/mkc-replay      # fresh directory outside the package; about 3 minutes
+    python3 -I research/multicut-kernel-composition/verify.py --output /tmp/mkc-replay      # fresh directory outside the package; about 4 minutes
 
-PR #259's verifier with the two retiming stages inserted between its transform and its checkers (stages 02b–02e,
-each gated by the sha256 of the transcript it consumes): package hashes against `MANIFEST.json`, regeneration of the
-pinned PR #249 word from `vendor/pr249-source.zip` (SymPy), the seven checkers compiled and run, the descent and
-plateau stages with their own audits (operand source spans, frame tables), every receipt compared with `expected/`
-(platform-independent fields), then `PASS: kappa = 0.000711482139228173`. `--snapshots-only` skips the upstream
+PR #259's verifier with the stages inserted (02b descent, 02c–02e plateau and its audits, 02f target prefix, then the
+seven native checkers 03–08, then 09–17 the sandwich stage with its legality, prefix, five-stage, endpoint/bank,
+price-wrapper and finite-invoice checks), every stage gated by the sha256 of the transcript it consumes: package
+hashes against `MANIFEST.json`, regeneration of the pinned PR #249 word from `vendor/pr249-source.zip` (SymPy), the
+checkers compiled and run, every receipt compared with `expected/` and `expected-sandwich/` (platform-independent
+fields), then `PASS: kappa = 0.000714026746429965`. `--snapshots-only` skips the upstream
 regeneration. `.github/workflows/multicut-kernel-composition.yml` runs it on Ubuntu (Python 3.11 and 3.13).
 
 ## Files
@@ -58,8 +80,11 @@ regeneration. `.github/workflows/multicut-kernel-composition.yml` runs it on Ubu
 PR #259's package (`code/cohort-*.cpp`, `code/export249.py`, `inputs/249-*`, `inputs/frames.json.gz`,
 `inputs/SNAPSHOTS.json`, `vendor/`, the proof notes, `requirements.txt`, `LICENSE`) with the frozen selection
 `inputs/candidates.json.gz` (PR #259's 518 items, then ours with `round` = `union-early-cut`, `headroom-2`,
-`shared-donor`), PR #263's and PR #270's stages (`code/descent_retiming.py`, `code/plateau_retiming.py`,
-`code/verify_frames.py`, `code/verify_plateau_spans.py`, `code/verify_frame_tables.py`; `inputs/descent-selection.json`,
-`inputs/plateau-selection.json`, rebound to this transcript), `verify.py` (PR #259's with the stages and three
-sha gates), `expected/` (eleven receipts), `RESULT.json`, `MANIFEST.json`, `discovery/` (the censuses, merges and
-the rebinding chain; not run by the verifier), `README.md`, `PROOF.md`, `NOTICE.md`.
+`shared-donor`, with `+pivot-swap` where the pivot role was moved), PR #263's and PR #270's stages
+(`code/descent_retiming.py`, `code/plateau_retiming.py`, `code/verify_frames.py`, `code/verify_plateau_spans.py`,
+`code/verify_frame_tables.py`; `inputs/descent-selection.json`, `inputs/plateau-selection.json`, rebound to this
+transcript), PR #273's `code/target_prefix.py` with `inputs/target-selection.json` (rebound), PR #271's mechanism as
+`code/cleanup_sandwich.py`, `code/sandwich_endpoints.py`, `code/sandwich/price-histogram.cpp` with
+`inputs/sandwich-selection.json`, `verify.py` (PR #259's with the stages and sha gates), `expected/` (twelve receipts)
+and `expected-sandwich/` (eight), `RESULT.json`, `MANIFEST.json`, `discovery/` (the censuses, merges, the rebinding
+chain and the sandwich scan; not run by the verifier), `README.md`, `PROOF.md`, `NOTICE.md`.
diff --git a/research/multicut-kernel-composition/RESULT.json b/research/multicut-kernel-composition/RESULT.json
index 030eecd06a..f95eca42eb 100644
--- a/research/multicut-kernel-composition/RESULT.json
+++ b/research/multicut-kernel-composition/RESULT.json
@@ -1,17 +1,29 @@
 {
-  "kappa": "711482139228173/1000000000000000000",
-  "kappa_decimal": "0.000711482139228173",
+  "kappa": "142805349285993/200000000000000000",
+  "kappa_decimal": "0.000714026746429965",
   "baseline_head": "96495746c786d6d0339dbb38c7f553d4af3f88ed",
   "baseline_kappa": "0.000710392186446856",
-  "previous_delivery_kappa": "0.000711443979017358",
-  "new_record_sha256": "4f6ffc1daa5ef309e82c5a7e639b9e3c9f19bdcd2f2bfec865f8fbfc8fbc5b3d",
-  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES",
+  "previous_delivery_kappa": "0.000712725850053909",
+  "new_record_sha256": "eaff3c9828ed15e1c24998331f0d3b482efc9984dd86bf5dbcefca0c76e717c6",
+  "status": "FINITE_CONSTRUCTION_UNDER_RETAINED_PUBLIC_ALL_SIZE_HYPOTHESES_SANDWICH_STAGE_BANKS_RETILED_OUTSIDE_NATIVE_BANK_REVIEW",
   "lean_certificate": false,
   "pivots": 890,
   "entrance_rank": 1719,
-  "cohort_record_sha256": "d073aeb4a8054ee6e23366ac7a42554624d52d3a822e03de9831a12530287395",
-  "descent_record_sha256": "43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6",
+  "cohort_record_sha256": "4458dce8218c9a0e0e55f494e33b2ad320649e953d108470ba0c8ac077660505",
+  "descent_record_sha256": "a6d793d7fd4f902436fd64c1d0e9467adc93844e058578994400d30fcf4171c3",
   "descent_retimed_gates": 25,
   "plateau_retimed_blocks": 29,
-  "plateau_retimed_gates": 57
+  "plateau_retimed_gates": 57,
+  "plateau_record_sha256": "a1cf58b3b0d23775a07fd0ebc276c40a9c52a41a2ea285b935d062d314699d7b",
+  "kappa_native_seven_checkers": "712005174354669/1000000000000000000",
+  "kappa_native_decimal": "0.000712005174354669",
+  "target_prefix_groups": 209,
+  "target_prefix_deleted_reads": 1057,
+  "target_prefix_setup_restore_additions": 1254,
+  "sandwich_record_sha256": "9556bfe3045eb23a2613a8f7b5cfc3824e321d4cbe2ec08f6993317a8bf816f7",
+  "sandwich_helpers_retired": 126,
+  "sandwich_normalized_stock": 172470,
+  "native_normalized_stock": 173310,
+  "pivot_role_swapped_pair_families": 83,
+  "sandwich_helpers_scanned": 128
 }
diff --git a/research/multicut-kernel-composition/code/cleanup_sandwich.py b/research/multicut-kernel-composition/code/cleanup_sandwich.py
new file mode 100644
index 0000000000..7061ac3117
--- /dev/null
+++ b/research/multicut-kernel-composition/code/cleanup_sandwich.py
@@ -0,0 +1,161 @@
+#!/usr/bin/env python3
+"""Cleanup-sandwich cancellation (PR271's mechanism, evmckinney9) as a stage on the native six-int transcript.
+
+For each frozen helper a, the suffix of the word after the first kernel cut contains exactly three gates on a,
+    t += a,   a += b,   t += a          (F2, in this order; the last is the family's Q^-1 pass)
+and t is not a control strictly between the first and the last. Over F2 these equal a += b; t += b. The rewrite
+emits a += b at the cut at the joint frame of a and b there (four-dimensional, nondegenerate for 9I - J), replaces
+the middle gate by t += b at its frame and drops the first and last gates. The helper then has no gate after the
+cut and ends at the joint frame instead of climbing to the full frame. Every MOVE is rebuilt from the actual
+needs, every new connector is checked for exact rational inclusion, and the emitted word is replayed over F2 on
+every formal source, target and dirty column with both omission controls. The stage writes the rewritten lead
+directory, an export directory whose 249-states.json carries the new final frames (for the native legality
+checker), and folds its histogram delta into the replay receipt.
+usage: cleanup_sandwich.py EXPORT LEAD SELECTION OUTPUT
+Adapted from research/cleanup-sandwich-263/sandwich263.py (Apache-2.0); Anthropic Claude assistance.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from math import lcm
+from pathlib import Path
+import json, shutil, struct, sys
+if not __debug__: raise SystemExit('assertions required')
+H = 24; PRIME = 1000003
+X, L, SEL, O = map(Path, sys.argv[1:5])
+def load(p): return json.loads(Path(p).read_text())
+def rational_basis(rows):
+    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):
+    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)):
+        vec = [Q(i == free) for i in range(H)]
+        for p, row in reversed(list(zip(pivots, B))): vec[p] = -sum(Q(row[j])*vec[j] for j in range(p+1, H)) / row[p]
+        d = lcm(*(x.denominator for x in vec)); out.append([int(x*d) for x in vec])
+    return out
+def histogram(records):
+    h = Counter()
+    for op, a, b, c, f, z in records:
+        if op == 0 and f: h[f] += 1
+        elif op == 2: h[z] += 1
+    return h
+sel = load(SEL); helpers = sel['helpers']
+frames = load(X/'frames.json')['frames']; lead_frames = load(L/'COHORT249-FRAMES.json'); frames.update(lead_frames)
+states = load(X/'249-states.json'); n, v = states['n'], states['v']
+initial = {int(a): f for a, f in load(L/'COHORT249-INITIAL.json').items()}
+blob = (L/'COHORT249-RECORDS.bin').read_bytes(); assert sha256(blob).hexdigest() == sel['input_record_sha256']
+old = list(struct.iter_unpack('<6i', blob))
+cut = next(i for i, r in enumerate(old) if r[0] == 1 and r[5] == 3)
+zmax = max(r[5] for r in old if r[0] == 1); EARLY, SANDWICH = zmax + 1, zmax + 2
+at_cut = dict(initial)
+for op, a, b, c, f, z in old[:cut]:
+    if op == 1: at_cut[a] = at_cut[b] = f
+    elif op == 2: at_cut[a], at_cut[b] = c, f
+    elif op == 3: del at_cut[b]
+edits, skip, replace, new_frames = [], set(), {}, {}
+next_id = max(int(k) for k in frames) + 1
+for a in helpers:
+    assert 2*v <= a < n and frames[str(initial[a])]['dim'] == 1
+    gates = [(i, r) for i, r in enumerate(old) if i >= cut and r[0] == 1 and a in r[1:3]]
+    assert len(gates) == 3, ('helper must have exactly three gates after the cut', a)
+    (first, x), (middle, y), (last, w) = gates
+    t, b = x[1], y[2]
+    assert x[2] == a and y[1] == a and w[1:3] == (t, a), ('not a sandwich t+=a, a+=b, t+=a', a)
+    assert all(r[0] != 1 or r[2] != t for r in old[first+1:last]), ('t is a control inside the sandwich', a)
+    assert b not in helpers and t not in helpers, ('overlapping sandwiches', a)
+    B = rational_basis(frames[str(at_cut[a])]['B'] + frames[str(at_cut[b])]['B'])
+    assert len(B) == 4, ('the joint frame of a and b at the cut is not four-dimensional', a)
+    sums = [sum(u) for u in B]
+    gram = [[9*sum(p*q for p, q in zip(u, w2)) - su*sw for w2, sw in zip(B, sums)] for u, su in zip(B, sums)]
+    assert rank_mod_prime(gram) == 4, ('new frame is degenerate for 9I - J', a)
+    frame = next_id; next_id += 1; assert str(frame) not in frames
+    frames[str(frame)] = new_frames[str(frame)] = {'dim': 4, 'B': B, 'A': annihilator(B)}
+    skip.update((first, last)); replace[middle] = (1, t, b, y[3], y[4], SANDWICH)
+    edits.append({'helper': a, 'source': b, 'target': t, 'frame': frame, 'old_indices': [first, middle, last], 'entrance_frame': initial[a], 'cut_frames': [at_cut[a], at_cut[b]]})
+state, new, checked = dict(initial), [], set()
+inherited = {(b, c) for op, a, b, c, f, z in old if op == 0}
+def move(a, f):
+    before = state[a]
+    if before == f: return
+    if (before, f) not in inherited and (before, f) not in checked:
+        B, A = frames[str(before)]['B'], frames[str(f)]['A']
+        assert all(sum(Q(p)*Q(q) for p, q in zip(u, w2)) == 0 for u in B for w2 in A), ('not nested', before, f)
+        checked.add((before, f))
+    rank = frames[str(f)]['dim'] - frames[str(before)]['dim']; assert rank >= 0, ('frame retreats', a, before, f)
+    new.append((0, a, before, f, rank, 0)); state[a] = f
+def emit(r):
+    op, a, b, c, f, z = r
+    if op == 1: move(a, f); move(b, f)
+    elif op == 2: move(a, c); state[b] = f
+    elif op == 3: assert state[a] == c and state[b] == f; del state[b]
+    new.append(r)
+for i, r in enumerate(old):
+    if i == cut:
+        for e in edits: emit((1, e['helper'], e['source'], 1, e['frame'], EARLY))
+    if r[0] != 0 and i not in skip: emit(replace.get(i, r))
+final = {int(a): f for a, f in states['final'].items()}; final.update({e['helper']: e['frame'] for e in edits})
+for a in range(n): move(a, final[a])
+assert state == final
+def wrong_rows(records, omit=None):
+    rows = [1 << a for a in range(n)] + [0]
+    for op, a, b, c, f, z in records:
+        if op == 1 and c % 2 and z != omit: rows[a] ^= rows[b]
+        elif op == 2: rows[b] = rows[a]
+        elif op == 3: assert rows[a] == rows[b]; rows[b] = 0
+    return sum(rows[a] != ((1 << a) ^ ((1 << (a - v)) if v <= a < 2*v else 0)) for a in range(n))
+assert wrong_rows(new) == 0, 'rewritten word fails the formal replay'
+controls = {'omit early a += b': wrong_rows(new, EARLY), 'omit sandwich t += b': wrong_rows(new, SANDWICH)}
+assert all(controls.values()), 'an omission control was accepted'
+# chronological frame legality of the emitted word against the new final frames
+st = dict(initial); copy = None; hist = Counter(); count = 0
+for op, a, b, c, f, z in new:
+    if op == 0:
+        assert st[a] == b and frames[str(c)]['dim'] - frames[str(b)]['dim'] == f; st[a] = c
+        if f: hist[f] += 1
+    elif op == 1: assert st[a] == st[b] == f and a != b; count += 1
+    elif op == 2: assert copy is None and st[a] == c; st[b] = f; hist[z] += 1; copy = (a, b, c)
+    else: assert copy == (a, b, c) and st[a] == c and st[b] == f; del st[b]; copy = None
+assert st == final and copy is None
+delta = Counter(hist); delta.subtract(histogram(old)); delta = {r: c for r, c in delta.items() if c}
+assert sum(r*c for r, c in delta.items()) == -20*len(edits), 'endpoint rank mass must drop by 20 per helper'
+assert delta == {int(k): c for k, c in sel['expected_local_histogram_delta'].items()}, ('histogram delta', delta)
+data = b''.join(struct.pack('<6i', *r) for r in new)
+# outputs: rewritten lead, export with the new final frames, folded replay receipt
+O.mkdir(); (O/'export').mkdir()
+for name in ('COHORT249-INITIAL.json', 'COHORT249-SELECTION.json', 'descent-selection.json', 'DESCENT-RETIMING.json', 'DESCENT-REBIND-EVIDENCE.json', 'PLATEAU-RETIMING.json', 'PLATEAU-SOURCE-SPANS.json', 'FRAME-TABLE-AUDIT.json', 'target-selection.json', 'TARGET-PREFIX.json'):
+    if (L/name).exists(): shutil.copy2(L/name, O/name)
+(O/'COHORT249-RECORDS.bin').write_bytes(data); (O/'COHORT249-PRE-SANDWICH-RECORDS.bin').write_bytes(blob)
+lead_frames.update(new_frames); (O/'COHORT249-FRAMES.json').write_text(json.dumps(lead_frames) + '\n')
+for name in ('frames.json', '249-records.bin', '249-DONOR-OWNERSHIP.json'): shutil.copyfile(X/name, O/'export'/name)
+states['final'].update({str(e['helper']): e['frame'] for e in edits}); (O/'export/249-states.json').write_text(json.dumps(states) + '\n')
+replay = load(L/'COHORT249-REPLAY.json'); oldH = Counter({int(k): c for k, c in replay['histogram'].items()}); assert oldH == histogram(old)
+total = Counter({int(k): c for k, c in replay['delta'].items()}); total.update(delta)
+replay.update(status='CLEANUP_SANDWICH_CANCELLATION_NATIVE_BANK_REVIEW_NOT_APPLICABLE', pre_sandwich_records=len(old), new_records=len(new), pre_sandwich_histogram=replay['histogram'],
+              histogram={str(r): c for r, c in sorted(hist.items())}, delta={str(r): c for r, c in sorted(total.items()) if c}, sandwich_histogram_delta={str(r): c for r, c in sorted(delta.items())},
+              sandwich_helpers_retired=len(edits), new_rank_mass=sum(r*c for r, c in hist.items()))
+(O/'COHORT249-REPLAY.json').write_text(json.dumps(replay, indent=2) + '\n')
+receipt = {'status': 'PASS_CLEANUP_SANDWICH_REWRITE_FORMAL_F2_COLUMNS_AND_FRAMES', 'helpers_retired': len(edits), 'cut_record': cut, 'input_sha256': sha256(blob).hexdigest(), 'output_sha256': sha256(data).hexdigest(),
+           'formal_columns': n, 'omission_controls_wrong_rows': controls, 'new_connectors_checked': len(checked), 'new_frames': len(new_frames), 'histogram_delta': {str(r): c for r, c in sorted(delta.items()) if c},
+           'endpoint_rank_mass_drop': 20*len(edits), 'rank_mass': sum(r*c for r, c in hist.items()), 'paid_calls': sum(hist.values()), 'scalar_additions': count, 'early_category': EARLY, 'sandwich_category': SANDWICH,
+           'selection_sha256': sha256(SEL.read_bytes()).hexdigest(), 'edits': edits}
+(O/'CLEANUP-SANDWICH.json').write_text(json.dumps(receipt, indent=2) + '\n')
+print('PASS cleanup sandwich', len(edits), 'helpers', 'controls', controls, 'delta', receipt['histogram_delta'], 'records', len(new), flush=True)
diff --git a/research/multicut-kernel-composition/code/sandwich/price-histogram.cpp b/research/multicut-kernel-composition/code/sandwich/price-histogram.cpp
new file mode 100644
index 0000000000..79db4e214d
--- /dev/null
+++ b/research/multicut-kernel-composition/code/sandwich/price-histogram.cpp
@@ -0,0 +1,22 @@
+// Price a word histogram with the base package's exact rational interval engine and 47-constraint assembly, unchanged.
+// Compile with -DPR254_PRICE_SOURCE naming the base package's code/cohort-price.cpp. A price alone is not a certificate:
+// verify.py also runs the base finite invoice.
+#define main inherited_pr254_main
+#include PR254_PRICE_SOURCE
+#undef main
+
+int main(int argc, char** argv) {
+    if (argc != 4) return 2;
+    auto word = load(argv[1]);
+    auto banks = load(argv[2]);
+    map<int, long long> H;
+    for (auto it = word["histogram"].begin(); it != word["histogram"].end(); ++it)
+        H[stoi(it.key())] = 40 * it.value().get<long long>();
+    for (int r : {4, 23, 46, 50}) H[r] += 16 * 1760;
+    int stock = banks["literal_stock"];
+    if (stock % 5) throw runtime_error("nonintegral normalized stock");
+    auto result = price(H, stock / 5);
+    ofstream(argv[3]) << J{{"status", "PASS_REUSED_PR254_EXACT_PRICE_AND_OUTER47"},
+        {"candidate", result}, {"finite_invoice_required", true}}.dump(2) << '\n';
+    cout << "kappa " << result["kappa"] << '\n';
+}
diff --git a/research/multicut-kernel-composition/code/sandwich_endpoints.py b/research/multicut-kernel-composition/code/sandwich_endpoints.py
new file mode 100644
index 0000000000..21493ddb9c
--- /dev/null
+++ b/research/multicut-kernel-composition/code/sandwich_endpoints.py
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Exact rational checks of the shortened endpoints, the bank re-tiling and the new normalizers (SymPy), for the
+cleanup-sandwich stage. Adapted from research/cleanup-sandwich-263/endpoints263.py (evmckinney9, Apache-2.0).
+
+Address geometry is over Q with G = 9I - J; a frame with row basis B has projector P = B^T (B G B^T)^-1 B G.
+banks: each retired helper keeps its rank-one entrance S and now ends at its four-dimensional frame F; since
+P_S P_F = P_F P_S = P_S its completed relative endpoint is the partial swap D_(P_F - P_S) of rank 3 (completed-core
+identity, research/community-round8-audit/BANK-SCHEDULE.md), so its bank residual changes from width 23 to width 3.
+The width-120 bank patterns of the native bank review (run on the pre-sandwich word, whose helper entrances are
+unchanged) are re-tiled and must fill every slot exactly.
+normalizers: every new frame Gram matrix, every connector touching a new frame and every new endpoint has an exact
+chart reducing it to a coordinate projector by elementary factors, all entries below 2^80.
+usage: sandwich_endpoints.py EXPORT LEAD BANK_REVIEW_JSON OUTPUT_DIR
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+import json, struct, sys, time
+import sympy as sp
+if not __debug__: raise SystemExit('assertions required')
+H = 24; BOUND = 2 ** 80; MAX_FACTORS = 548; G = 9 * sp.eye(H) - sp.ones(H)
+X, L, BANK, O = map(Path, sys.argv[1:5]); t0 = time.time()
+def load(p): return json.loads(Path(p).read_text())
+receipt = load(L / 'CLEANUP-SANDWICH.json'); records = (L / 'COHORT249-RECORDS.bin').read_bytes()
+frames = load(X / 'frames.json')['frames']; frames.update(load(L / 'COHORT249-FRAMES.json'))
+new_frames = {str(e['frame']) for e in receipt['edits']}
+def projector(f):
+    d = frames[str(f)]['dim']
+    if d == H: return sp.eye(H), None
+    if d == 0: return sp.zeros(H), None
+    B = sp.Matrix(frames[str(f)]['B']); gram = B * G * B.T
+    return B.T * gram.inv() * B * G, gram
+def make_guard():
+    state = {'max': 1}
+    def guard(values):
+        for value in values:
+            x = Q(value); state['max'] = max(state['max'], abs(x.numerator), x.denominator)
+        assert state['max'] < BOUND, 'normalizer entry exceeds 2^80'
+    return guard, state
+def chart(E, rank, guard):
+    C = sp.Matrix.hstack(*E.columnspace(), *E.nullspace()); inverse = C.inv()
+    assert inverse * E * C == sp.diag(*([1] * rank + [0] * (H - rank))), 'chart does not normalize the projector'
+    guard(list(E) + list(C) + list(inverse) + [C.det()])
+    A = [[Q(x) for x in C.row(i)] for i in range(H)]; factors = 0
+    for j in range(H):
+        k = next(k for k in range(j, H) if A[k][j])
+        if k != j: A[j], A[k] = A[k], A[j]; factors += 1
+        pivot = A[j][j]; guard([pivot, 1 / pivot])
+        if pivot != 1: A[j] = [x / pivot for x in A[j]]; factors += 1
+        for i in range(H):
+            if i != j and A[i][j]:
+                c = A[i][j]; guard([c]); A[i] = [x - c * y for x, y in zip(A[i], A[j])]; factors += 1
+    assert A == [[Q(i == j) for j in range(H)] for i in range(H)]
+    assert factors <= MAX_FACTORS, 'chart exceeds the inherited factor bound'
+    return factors
+# banks
+guard, state = make_guard()
+for e in receipt['edits']:
+    assert frames[str(e['entrance_frame'])]['dim'] == 1 and frames[str(e['frame'])]['dim'] == 4
+    S, _ = projector(e['entrance_frame']); F, _ = projector(e['frame'])
+    assert S * F == F * S == S, 'entrance is not inside the new exit frame'
+    E = F - S; assert E * E == E and E.rank() == 3; chart(E, 3, guard)
+bank = load(BANK); k = len(receipt['edits']); patterns = [dict(p) for p in bank['bank_patterns']]
+# 40 replicas: k helpers x 40 width-23 residuals become width-3 residuals. 10k banks [23]*4+[4]*7 release their
+# 40k width-23 slots; their 70k width-4 slots refill 7k/3 banks [4]*30 (k = 45: 105); the 40k width-3 residuals fill k banks [3]*40.
+assert (70 * k) % 30 == 0, 'width-4 remainder'
+next(p for p in patterns if p['widths'] == [23] * 4 + [4] * 7)['count'] -= 10 * k
+next(p for p in patterns if p['widths'] == [4] * 30)['count'] += 70 * k // 30
+patterns.append({'widths': [3] * 40, 'count': k})
+family = Counter({int(r): c for r, c in bank['residual_families'].items()}); family[23] -= k; family[3] += k
+slots, count = Counter(), 0
+for p in patterns:
+    assert p['count'] >= 0 and sum(p['widths']) == 120, 'bank pattern does not fill width 120'
+    count += p['count']
+    for r in p['widths']: slots[r] += p['count']
+assert slots == Counter({r: 40 * c for r, c in family.items() if c}), 'residuals do not tile the banks exactly'
+fewer = bank['banks_per_stage'] - count; assert fewer == 10 * k - 70 * k // 30 - k
+banks = {'literal_stock': bank['literal_stock'] - 5 * fewer, 'banks_per_stage': count, 'banks_fewer_per_stage': fewer,
+         'actual_role_replica_stage_assignments': bank['actual_role_replica_stage_assignments'], 'bank_patterns': patterns,
+         'residual_families': {str(r): c for r, c in sorted(family.items()) if c}, 'endpoint_max_entry': state['max']}
+# normalizers
+guard, state = make_guard()
+for f in new_frames:
+    _, gram = projector(f); guard(list(gram) + list(gram.inv()) + [gram.det()])
+pairs = {(b, c, r) for op, a, b, c, r, z in struct.iter_unpack('<6i', records) if op == 0 and (str(b) in new_frames or str(c) in new_frames)}
+moves = len(pairs); pairs |= {(e['entrance_frame'], e['frame'], 3) for e in receipt['edits']}; most = 0
+for before, after, rank in sorted(pairs):
+    E = projector(after)[0] - projector(before)[0]
+    assert E * E == E and E.rank() == rank, ('connector is not a projector of its rank', before, after)
+    most = max(most, chart(E, rank, guard))
+norm = {'new_frames': len(new_frames), 'move_pairs': moves, 'charts': len(pairs), 'max_factors': most, 'max_numerator_denominator': state['max']}
+M = max(norm['max_numerator_denominator'], int(bank['max_intermediate_numerator']), int(bank['max_intermediate_denominator'])); U = 40 * M * M; g = 2 * U * U; assert g < 2 ** 80
+invoice = dict(banks, normalized_stock=banks['literal_stock'] // 5, new_exact_charts=bank['new_exact_charts'] + k + norm['move_pairs'],
+               max_new_chart_factors=max(bank['max_new_chart_factors'], norm['max_factors']) + 24, max_intermediate_numerator=str(g), max_intermediate_denominator=str(g),
+               selector_charge=2 * 5 * 40 * (banks['literal_stock'] - 1 + 16587 * 120 * 787), routing_prime_guard={'normalized_scaled_chart_entry_bound': U, 'pairwise_difference_numerator_bound': g},
+               status='PASS_SANDWICH_ENDPOINTS_EXACT_CHARTS_AND_BANK_RETILING', base_bank_review_sha256=__import__('hashlib').sha256(BANK.read_bytes()).hexdigest(), normalizers=norm)
+assert banks['literal_stock'] % 5 == 0
+O.mkdir(parents=True, exist_ok=True); (O / 'SANDWICH-BANK-INVOICE.json').write_text(json.dumps(invoice, indent=2) + '\n')
+print('PASS sandwich endpoints: %d helpers, %d charts, max factors %d, banks per stage %d (-%d), literal stock %d, %.0fs' % (k, norm['charts'], most, count, fewer, banks['literal_stock'], time.time() - t0), flush=True)
diff --git a/research/multicut-kernel-composition/code/target_prefix.py b/research/multicut-kernel-composition/code/target_prefix.py
new file mode 100644
index 0000000000..f3c1c73a45
--- /dev/null
+++ b/research/multicut-kernel-composition/code/target_prefix.py
@@ -0,0 +1,187 @@
+#!/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
+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=[list(map(int, r)) for r in rec_['B']], A=[list(map(int, 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_json = json.loads((LEAD/'COHORT249-REPLAY.json').read_text())
+oldH = Counter({int(r): c for r, c in replay_json['histogram'].items()})
+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()) == 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())
+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/multicut-kernel-composition/discovery/README.md b/research/multicut-kernel-composition/discovery/README.md
index cd4bf92fc1..a253d4f2c4 100644
--- a/research/multicut-kernel-composition/discovery/README.md
+++ b/research/multicut-kernel-composition/discovery/README.md
@@ -11,16 +11,23 @@ package's own `inputs/` files, decompressed into a data directory.
     census2.py, merge2.py                       round 2: every response class at twelve cuts, pairs and XOR triples, greedy packing
     census3.py, census3b.py                     round 3: shared-donor families (partner = an existing donor, nested entrance chain)
     retime.py                                   the chain cohort -> descent (PR #263) -> plateau (PR #270) with the sha rebinding
+    rebind_target.py                            PR #273's 209 squares rebound to this transcript (post-cut scalar alignment)
+    scan_sandwich.py                            the cleanup-sandwich scan (pivots with the three-gate cleanup shape, joint dimension 4)
+    chain_swap.py, finalize_swap.py             the pivot-role swap in 83 families, the full stage chain and the packaging
 
 Diff of this package against PR #259's (everything else byte for byte):
 
-    inputs/candidates.json.gz      518 items of PR #259 (26 dissolved) + 387 appended (rounds union-early-cut, headroom-2, shared-donor)
+    inputs/candidates.json.gz      518 items of PR #259 (26 dissolved) + 387 appended (rounds union-early-cut, headroom-2, shared-donor; 83 with the pivot role swapped)
+    inputs/target-selection.json   PR #273's 209 squares, rebound (core_binding block)
+    inputs/sandwich-selection.json the 126 retired helpers (128 scanned)
+    code/target_prefix.py          PR #273's stage, verbatim
+    code/cleanup_sandwich.py, code/sandwich_endpoints.py, code/sandwich/price-histogram.cpp   PR #271's mechanism, ported
     inputs/descent-selection.json  PR #263's 25 gates, rebound to this transcript (input sha gate)
     inputs/plateau-selection.json  PR #270's 29 blocks, rebound to the descent transcript
     code/descent_retiming.py, code/plateau_retiming.py, code/verify_frames.py, code/verify_plateau_spans.py, code/verify_frame_tables.py
                                    PR #263's and PR #270's stages, verbatim
     code/cohort-transform.cpp      std::sort -> std::stable_sort on the gauge order (platform-independent transcript)
-    verify.py                      stages 02b-02e inserted with three sha gates; 'containment_pairs_checked' dropped from compared fields; normalize() on both sides
-    expected/*.json, RESULT.json   regenerated receipts (eleven) and result (890 pivots, entrance rank 1719, kappa 7.11482139228173e-4)
+    verify.py                      stages 02b-02f and 09-17 inserted with sha gates; 'containment_pairs_checked' dropped from compared fields; normalize() on both sides
+    expected/*.json, expected-sandwich/*.json, RESULT.json   regenerated receipts (twelve + eight) and result (890 pivots, rank 1719, kappa 7.12005174354669e-4 native, 7.14026746429965e-4 with sandwiches)
     README.md, PROOF.md, NOTICE.md this package's notes; PR #259's README/PROOF kept as README-PR259.md, PROOF-PR259.md
     MANIFEST.json                  regenerated
diff --git a/research/multicut-kernel-composition/discovery/chain_swap.py b/research/multicut-kernel-composition/discovery/chain_swap.py
new file mode 100644
index 0000000000..1cf6aa5511
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/chain_swap.py
@@ -0,0 +1,50 @@
+"""Chain with rebinding: new cohort lead -> rebound descent -> rebound plateau -> rebound target-prefix -> seven native checkers -> sandwich (k=126) + checks.
+usage: chain_swap.py PKG LEAD_SRC X BIN W269WORD SEL273 OLD_PRE_DESCENT OLD_POST_DESCENT P270 OUT"""
+import json, sys, subprocess, shutil, hashlib, time
+from pathlib import Path
+sys.dont_write_bytecode = True
+PKG, LEADSRC, X, BIN, W269, SEL273, OLDPRE, OLDPOST, P270, W = map(Path, sys.argv[1:11]); PY = sys.executable; T0 = time.time(); tm = {}
+HERE = Path(__file__).resolve().parent; SHIM = sys.argv[11] if len(sys.argv) > 11 else None
+if W.exists(): shutil.rmtree(W)
+W.mkdir(parents=True)
+def sha(p): return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def run(label, cmd, cwd=None):
+    t = time.time(); log = W / (label + '.log')
+    with log.open('w') as lf: r = subprocess.run([str(c) for c in cmd], stdout=lf, stderr=subprocess.STDOUT, cwd=cwd or W)
+    tm[label] = round(time.time() - t, 1); print(f'{label}: exit {r.returncode} ({tm[label]}s)', flush=True)
+    if r.returncode: print(log.read_text()[-3000:]); raise SystemExit(label + ' FAILED')
+lead = W / 'lead'; shutil.copytree(LEADSRC, lead)
+sys.path.insert(0, str(P270)); from rebind_descent import rebind
+al = rebind(OLDPRE, lead / 'COHORT249-RECORDS.bin', PKG / 'inputs/descent-selection.json', W / 'descent-selection.json')
+print('rebind descent:', al['status'], al['events_compared'], flush=True)
+shutil.copy(W / 'descent-selection.json', lead / 'descent-selection.json'); (lead / 'DESCENT-REBIND-EVIDENCE.json').write_text(json.dumps(al, indent=2) + '\n')
+run('descent', [PY, '-B', PKG / 'code/descent_retiming.py', X, lead, lead / 'descent-selection.json'])
+print('post-descent sha', sha(lead / 'COHORT249-RECORDS.bin'), json.load((lead / 'DESCENT-RETIMING.json').open())['local_histogram_delta'], flush=True)
+run('rebind-plateaus', [PY, '-B', P270 / 'rebind_plateaus.py', OLDPOST, PKG / 'inputs/plateau-selection.json', lead / 'COHORT249-RECORDS.bin', W / 'plateau-selection.json'])
+plateau = W / 'plateau'
+run('plateau', [PY, '-B', PKG / 'code/plateau_retiming.py', X, lead, W / 'plateau-selection.json', plateau], cwd=PKG / 'code')
+run('plateau-spans', [PY, '-B', PKG / 'code/verify_plateau_spans.py', X, plateau, plateau / 'PLATEAU-RETIMING.json'], cwd=PKG / 'code')
+print('post-plateau sha', sha(plateau / 'COHORT249-RECORDS.bin'), flush=True)
+bound = plateau / 'target-selection.json'
+run('rebind-target', [PY, '-B', HERE / 'rebind_target.py', W269, SEL273, plateau / 'COHORT249-RECORDS.bin', bound])
+run('target-prefix', [PY, '-B', PKG / 'code/target_prefix.py', X, plateau, bound])
+print('post-target sha', sha(plateau / 'COHORT249-RECORDS.bin'), json.load((plateau / 'TARGET-PREFIX.json').open())['local_histogram_delta'], flush=True)
+run('frame-tables', [PY, '-B', PKG / 'code/verify_frame_tables.py', X, plateau, '--output', plateau / 'FRAME-TABLE-AUDIT.json'], cwd=PKG / 'code')
+bank = W / 'bank'; bank.mkdir()
+run('c1-legality', [BIN / 'cohort-legality-independent', X, plateau, plateau / 'INDEPENDENT-LEGALITY.json'])
+run('c2-prefix', [BIN / 'cohort-prefix-independent', X, plateau, plateau / 'INDEPENDENT-PREFIX.json'])
+run('c3-bank', [BIN / 'cohort-bank-review', X, plateau / 'COHORT249-INITIAL.json', plateau / 'COHORT249-FRAMES.json', bank, 'actual_multicut'])
+run('c4-five-stage', [BIN / 'cohort-five-stage-columns', plateau / 'COHORT249-RECORDS.bin', plateau / 'COHORT-FIVE-STAGE-COLUMNS.json'])
+run('c5-price', [BIN / 'cohort-price', plateau / 'COHORT249-REPLAY.json', plateau / 'COHORT-EXACT-PRICE.json'])
+run('c6-finite', [BIN / 'cohort-finite-invoice', plateau / 'COHORT249-RECORDS.bin', plateau / 'COHORT-EXACT-PRICE.json', bank / 'BANK-REVIEW.json', plateau / 'COHORT-FIVE-STAGE-COLUMNS.json', plateau / 'COHORT-FINITE-INVOICE.json'])
+cc = json.load((plateau / 'COHORT-EXACT-PRICE.json').open())['cohort_candidate']
+print('NATIVE', json.dumps(dict(kappa=cc['kappa'], kappa_decimal=cc['kappa_decimal'], stock=cc['stock'], rank_mass=cc['rank_mass'], deficit=cc['deficit'], word_sha=sha(plateau / 'COHORT249-RECORDS.bin'))), flush=True)
+# sandwiches: rescan, maximal set with k = 0 mod 3
+run('scan-sandwich', [PY, '-B', HERE / 'scan_sandwich.py', X, plateau, W / 'scan-sandwich.json'])
+scan = json.load((W / 'scan-sandwich.json').open()); helpers = sorted(c['helper'] for c in scan['chosen']); k = len(helpers) - len(helpers) % 3; helpers = helpers[:k]
+sel = dict(status='FROZEN_CLEANUP_SANDWICH_HELPERS', input_record_sha256=sha(plateau / 'COHORT249-RECORDS.bin'), helpers=helpers, expected_local_histogram_delta={'1': 2*k, '20': k, '21': -2*k},
+           scanned_sandwich_helpers=len(scan['chosen']), provenance='Helpers with exactly the three-gate cleanup sandwich t += a; a += b; t += a after the first kernel cut, rescanned on this package word after the target-prefix stage (PR271 mechanism, evmckinney9); the largest subset with k = 0 mod 3 (each helper-replica frees 20 bank width units, 800k in total, which must tile width-120 banks), taken in helper-id order. Each joint cut frame of (a, b) is four-dimensional and nondegenerate for 9I - J.')
+(PKG / 'inputs/sandwich-selection.json').write_text(json.dumps(sel, indent=1) + '\n'); print('sandwich helpers', len(scan['chosen']), '-> k', k, flush=True)
+run('sandwich', [PY, '-B', PKG / 'code/cleanup_sandwich.py', X, plateau, PKG / 'inputs/sandwich-selection.json', plateau / 'sandwich'])
+run('sandwich-verify', [PY, '-B', HERE / 'sandwich_verify.py', PKG, X, plateau / 'sandwich', bank / 'BANK-REVIEW.json', BIN, W / 'sandwich-verify', plateau / 'COHORT-EXACT-PRICE.json', 'clang++'] + ([SHIM] if SHIM else []))
+print((W / 'sandwich-verify.log').read_text()[-900:]); print('timings', tm, 'total', round(time.time() - T0, 1))
diff --git a/research/multicut-kernel-composition/discovery/finalize_swap.py b/research/multicut-kernel-composition/discovery/finalize_swap.py
new file mode 100644
index 0000000000..6863abd747
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/finalize_swap.py
@@ -0,0 +1,32 @@
+"""Fill the swap package from chain_swap outputs. usage: finalize_swap.py PKG CHAIN_DIR"""
+import json, hashlib, shutil, sys
+from fractions import Fraction
+from pathlib import Path
+PKG, RUN = map(Path, sys.argv[1:3]); lead = RUN / 'lead'; plateau = RUN / 'plateau'; sand = plateau / 'sandwich'; SV = RUN / 'sandwich-verify'
+def sha(p): return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def load(p): return json.loads(Path(p).read_text())
+exp = PKG / 'expected'
+for name, src in {'COHORT249-REPLAY.json': plateau, 'INDEPENDENT-LEGALITY.json': plateau, 'INDEPENDENT-PREFIX.json': plateau, 'COHORT-BANK-REVIEW.json': RUN / 'bank', 'COHORT-FIVE-STAGE-COLUMNS.json': plateau,
+                  'COHORT-EXACT-PRICE.json': plateau, 'COHORT-FINITE-INVOICE.json': plateau, 'DESCENT-RETIMING.json': plateau, 'PLATEAU-RETIMING.json': plateau, 'PLATEAU-SOURCE-SPANS.json': plateau, 'FRAME-TABLE-AUDIT.json': plateau, 'TARGET-PREFIX.json': plateau}.items():
+    shutil.copy(src / ('BANK-REVIEW.json' if name == 'COHORT-BANK-REVIEW.json' else name), exp / name)
+exps = PKG / 'expected-sandwich'
+for name, src in {'CLEANUP-SANDWICH.json': sand, 'COHORT249-REPLAY.json': sand, 'INDEPENDENT-LEGALITY.json': SV, 'INDEPENDENT-PREFIX.json': SV, 'COHORT-FIVE-STAGE-COLUMNS.json': SV, 'SANDWICH-BANK-INVOICE.json': SV, 'COHORT-EXACT-PRICE.json': SV, 'COHORT-FINITE-INVOICE.json': SV}.items():
+    shutil.copy(src / name, exps / name)
+shutil.copy(plateau / 'target-selection.json', PKG / 'inputs/target-selection.json')
+shutil.copy(RUN / 'descent-selection.json', PKG / 'inputs/descent-selection.json'); shutil.copy(RUN / 'plateau-selection.json', PKG / 'inputs/plateau-selection.json')
+res = load(PKG / 'RESULT.json'); native = load(plateau / 'COHORT-EXACT-PRICE.json')['cohort_candidate']; sw = load(SV / 'COHORT-EXACT-PRICE.json')['cohort_candidate']
+tp = load(plateau / 'TARGET-PREFIX.json'); cs = load(sand / 'CLEANUP-SANDWICH.json'); rep = load(lead / 'COHORT249-REPLAY.json')
+def decimal(k):
+    x = Fraction(k); q, r = divmod(x.numerator * 10**18, x.denominator); assert r == 0; s = str(q).rjust(19, '0'); return s[:-18] + '.' + s[-18:]
+res.update(previous_delivery_kappa=res['kappa_decimal'], cohort_record_sha256=sha(lead / 'COHORT249-PRE-DESCENT-RECORDS.bin'), descent_record_sha256=sha(lead / 'COHORT249-RECORDS.bin'),
+           plateau_record_sha256=sha(plateau / 'COHORT249-PRE-TARGET-RECORDS.bin'), new_record_sha256=sha(plateau / 'COHORT249-RECORDS.bin'),
+           kappa_native_seven_checkers=native['kappa'], kappa_native_decimal=decimal(native['kappa']), kappa=sw['kappa'], kappa_decimal=decimal(sw['kappa']),
+           pivots=rep['new_gauges'], entrance_rank=rep['new_entrance_rank'], pivot_role_swapped_pair_families=83,
+           target_prefix_groups=tp['selected_groups'], target_prefix_deleted_reads=tp['deleted_prefix_adds'], target_prefix_setup_restore_additions=tp['inserted_setup_restore_adds'],
+           sandwich_record_sha256=sha(sand / 'COHORT249-RECORDS.bin'), sandwich_helpers_retired=cs['helpers_retired'], sandwich_helpers_scanned=load(PKG / 'inputs/sandwich-selection.json')['scanned_sandwich_helpers'],
+           sandwich_normalized_stock=sw['stock'], native_normalized_stock=native['stock'])
+(PKG / 'RESULT.json').write_text(json.dumps(res, indent=2) + '\n')
+for p in PKG.rglob('__pycache__'): shutil.rmtree(p)
+files = {p.relative_to(PKG).as_posix(): sha(p) for p in sorted(PKG.rglob('*')) if p.is_file() and p.name != 'MANIFEST.json'}
+(PKG / 'MANIFEST.json').write_text(json.dumps({'files': files}, indent=2) + '\n')
+print(json.dumps({k: res[k] for k in ('kappa', 'kappa_decimal', 'kappa_native_seven_checkers', 'kappa_native_decimal', 'cohort_record_sha256', 'descent_record_sha256', 'plateau_record_sha256', 'new_record_sha256', 'sandwich_record_sha256', 'sandwich_helpers_retired', 'sandwich_helpers_scanned')}, indent=1), 'files', len(files))
diff --git a/research/multicut-kernel-composition/discovery/rebind_target.py b/research/multicut-kernel-composition/discovery/rebind_target.py
new file mode 100644
index 0000000000..cbfb6c69bf
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/rebind_target.py
@@ -0,0 +1,37 @@
+#!/usr/bin/env python3
+"""Bind PR273's frozen target-prefix square groups to a different cohort transcript.
+
+The groups are identified by target ids and a close frame; only the cut record and each group's close record are
+transcript-bound. After the kernel cut the two words carry the same scalar events (the kernel families only differ
+in the pre-cut compensation reads and the Q/Q^-1 passes), so every post-cut non-MOVE event is aligned by its scalar
+content (op, a, b, c, z), ignoring frames (descent/plateau retimings change frames only). The cut is the first record
+after the last Q pass (category 28), as in PR273's word."""
+import hashlib, json, struct, sys
+from pathlib import Path
+if not __debug__: raise SystemExit('assertions required')
+base, sel_path, cand, out = map(Path, sys.argv[1:5])
+E = struct.Struct('<6i')
+sel = json.loads(sel_path.read_text())
+b = base.read_bytes(); n = cand.read_bytes()
+assert hashlib.sha256(b).hexdigest() == sel['input_record_sha256']
+be = list(E.iter_unpack(b)); ne = list(E.iter_unpack(n))
+def cut_of(ev):
+    last = max(i for i, e in enumerate(ev) if e[0] == 1 and e[5] == 28); return last + 1
+cut_b, cut_n = cut_of(be), cut_of(ne)
+assert cut_b == sel['cut_record'], (cut_b, sel['cut_record'])
+def core(ev, cut): return [(i, (e[0], e[1], e[2], e[3], e[5])) for i, e in enumerate(ev) if i > cut and e[0] and not (e[0] == 1 and e[5] in (28, 29))]
+cb, cn = core(be, cut_b), core(ne, cut_n)
+assert [e for _, e in cb] == [e for _, e in cn], 'post-cut scalar event sequence differs'
+mapping = {i: j for (i, _), (j, _) in zip(cb, cn)}
+bindings = []
+for g in sel['groups']:
+    i = g['close_after_record']; j = mapping[i]
+    assert be[i][0] == 1 and (be[i][1], be[i][2], be[i][3], be[i][5]) == (ne[j][1], ne[j][2], ne[j][3], ne[j][5])
+    bindings.append(dict(baseline_close=i, candidate_close=j, event=list(be[i])))
+    g['close_after_record'] = j
+adds = sum(e[0] == 1 for e in ne)
+sel.update(baseline_input_record_sha256=sel['input_record_sha256'], baseline_cut_record=cut_b, input_record_sha256=hashlib.sha256(n).hexdigest(),
+           input_record_count=len(ne), cut_record=cut_n, expected_scalar_additions=adds - sel['expected_deleted_reads'] + sel['expected_inserted_additions'],
+           core_binding=dict(status='PASS_POST_CUT_SCALAR_EVENT_ALIGNMENT_FRAMES_IGNORED', events_compared=len(cb), cut_record=cut_n, bindings=bindings))
+out.write_text(json.dumps(sel, indent=2) + '\n')
+print('bound', len(bindings), 'groups; cut', cut_b, '->', cut_n, 'post-cut events', len(cb), 'scalar additions expected', sel['expected_scalar_additions'], flush=True)
diff --git a/research/multicut-kernel-composition/discovery/scan_sandwich.py b/research/multicut-kernel-composition/discovery/scan_sandwich.py
new file mode 100644
index 0000000000..0709da2a7b
--- /dev/null
+++ b/research/multicut-kernel-composition/discovery/scan_sandwich.py
@@ -0,0 +1,68 @@
+"""Scan a six-int word for cleanup-sandwich helpers (PR271 pattern) and check the frame conditions. usage: scan_sandwich.py X LEAD OUT.json"""
+import json, struct, sys
+from fractions import Fraction as Q
+from math import lcm
+from collections import Counter
+from pathlib import Path
+X, LEAD, OUT = map(Path, sys.argv[1:4]); H = 24; PRIME = 1000003
+frames = json.loads((X/'frames.json').read_text())['frames']; frames.update(json.loads((LEAD/'COHORT249-FRAMES.json').read_text()))
+st = json.loads((X/'249-states.json').read_text()); n, v = st['n'], st['v']
+initial = {int(a): f for a, f in json.loads((LEAD/'COHORT249-INITIAL.json').read_text()).items()}
+old = list(struct.iter_unpack('<6i', (LEAD/'COHORT249-RECORDS.bin').read_bytes()))
+cut = next(i for i, r in enumerate(old) if r[0] == 1 and r[5] == 3)
+at_cut = dict(initial)
+for op, a, b, c, f, z in old[:cut]:
+    if op == 1: at_cut[a] = at_cut[b] = f
+    elif op == 2: at_cut[a], at_cut[b] = c, f
+    elif op == 3: del at_cut[b]
+def rational_basis(rows):
+    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)
+gates = {a: [] for a in range(2*v, n)}
+for i in range(cut, len(old)):
+    r = old[i]
+    if r[0] == 1:
+        for x in (r[1], r[2]):
+            if 2*v <= x < n: gates[x].append((i, r))
+census = Counter(len(g) for g in gates.values()); print('cut', cut, 'helpers by post-cut gate count', sorted(census.items())[:12], flush=True)
+cands = []; reasons = Counter()
+for a, g in gates.items():
+    if len(g) != 3: continue
+    (first, x), (middle, y), (last, w) = g
+    if not (x[2] == a and y[1] == a and w[1:3] == x[1:3] and x[1] == w[1]): reasons['not sandwich shape'] += 1; continue
+    t, b = x[1], y[2]
+    if any(r[0] == 1 and r[2] == t for r in old[first+1:last]): reasons['t control inside'] += 1; continue
+    B = rational_basis(frames[str(at_cut[a])]['B'] + frames[str(at_cut[b])]['B'])
+    if len(B) != 4: reasons['joint dim %d' % len(B)] += 1; continue
+    sums = [sum(u) for u in B]
+    gram = [[9*sum(p*q for p, q in zip(u, w2)) - su*sw for w2, sw in zip(B, sums)] for u, su in zip(B, sums)]
+    if rank_mod_prime(gram) != 4: reasons['degenerate'] += 1; continue
+    cands.append(dict(helper=a, source=b, target=t, indices=[first, middle, last], frames=[x[4], y[4], w[4]], cats=[x[5], y[5], w[5]], a_cut=at_cut[a], b_cut=at_cut[b], dims=[frames[str(at_cut[a])]['dim'], frames[str(at_cut[b])]['dim']], entrance_dim=frames[str(initial[a])]['dim']))
+print('rejections', dict(reasons), 'candidates', len(cands), flush=True)
+# non-overlap: b and t of one may not be a selected helper; greedy in helper order
+chosen, used = [], set()
+for c in sorted(cands, key=lambda c: c['helper']):
+    if c['helper'] in used or c['source'] in {d['helper'] for d in chosen} or c['target'] in {d['helper'] for d in chosen}: continue
+    if any(c['helper'] in (d['source'], d['target']) for d in chosen): continue
+    chosen.append(c); used.add(c['helper'])
+print('chosen', len(chosen), 'entrance dims', Counter(c['entrance_dim'] for c in chosen), 'cut dims', Counter(tuple(c['dims']) for c in chosen), 'frames', Counter(tuple(c['frames']) for c in chosen).most_common(3), 'cats', Counter(tuple(c['cats']) for c in chosen))
+print('sample', chosen[:2])
+OUT.write_text(json.dumps(dict(cut=cut, candidates=cands, chosen=chosen), indent=1) + '\n')
diff --git a/research/multicut-kernel-composition/expected-sandwich/CLEANUP-SANDWICH.json b/research/multicut-kernel-composition/expected-sandwich/CLEANUP-SANDWICH.json
new file mode 100644
index 0000000000..67ae5b9124
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/CLEANUP-SANDWICH.json
@@ -0,0 +1,2044 @@
+{
+  "status": "PASS_CLEANUP_SANDWICH_REWRITE_FORMAL_F2_COLUMNS_AND_FRAMES",
+  "helpers_retired": 126,
+  "cut_record": 764480,
+  "input_sha256": "eaff3c9828ed15e1c24998331f0d3b482efc9984dd86bf5dbcefca0c76e717c6",
+  "output_sha256": "9556bfe3045eb23a2613a8f7b5cfc3824e321d4cbe2ec08f6993317a8bf816f7",
+  "formal_columns": 20107,
+  "omission_controls_wrong_rows": {
+    "omit early a += b": 126,
+    "omit sandwich t += b": 126
+  },
+  "new_connectors_checked": 378,
+  "new_frames": 126,
+  "histogram_delta": {
+    "1": 252,
+    "20": 126,
+    "21": -252
+  },
+  "endpoint_rank_mass_drop": 2520,
+  "rank_mass": 429938,
+  "paid_calls": 96352,
+  "scalar_additions": 728460,
+  "early_category": 32,
+  "sandwich_category": 33,
+  "selection_sha256": "ef16f27254d2bf5dfb5d9ad104b9772e62a6a4af903e49f26aa8c61c0aee689d",
+  "edits": [
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+      "old_indices": [
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+        816176,
+        825213
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+      "entrance_frame": 200340,
+      "cut_frames": [
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+      ]
+    },
+    {
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+      "entrance_frame": 200510,
+      "cut_frames": [
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+    },
+    {
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+      "entrance_frame": 200511,
+      "cut_frames": [
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+    },
+    {
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+    },
+    {
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+      "entrance_frame": 200342,
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+    },
+    {
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+      "entrance_frame": 200344,
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+    },
+    {
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+    {
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+      "cut_frames": [
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+    },
+    {
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+      "entrance_frame": 200525,
+      "cut_frames": [
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+    },
+    {
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+      "cut_frames": [
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+    },
+    {
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+    },
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+    },
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+    },
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+      "cut_frames": [
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+    },
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+    {
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+      "cut_frames": [
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+    {
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+}
diff --git a/research/multicut-kernel-composition/expected-sandwich/COHORT-EXACT-PRICE.json b/research/multicut-kernel-composition/expected-sandwich/COHORT-EXACT-PRICE.json
new file mode 100644
index 0000000000..89d4cbba23
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/COHORT-EXACT-PRICE.json
@@ -0,0 +1,99 @@
+{
+  "status": "PASS_SANDWICH_PRICE_SAME_ENGINE_STOCK_FROM_RETILED_BANKS",
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+  },
+  "cohort_candidate": {
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+  }
+}
diff --git a/research/multicut-kernel-composition/expected-sandwich/COHORT-FINITE-INVOICE.json b/research/multicut-kernel-composition/expected-sandwich/COHORT-FINITE-INVOICE.json
new file mode 100644
index 0000000000..a6fa4235f4
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/COHORT-FINITE-INVOICE.json
@@ -0,0 +1,72 @@
+{
+  "external_complex_row_coefficient": 20161,
+  "extra_selector_calls": "626935451600",
+  "full_counted_primitive_coefficient": "62727288085005201",
+  "global_unit_expanded_additions": "146642400",
+  "global_weighted_additions": "146114400",
+  "internal_row_coefficient": 14401,
+  "linear_moment_slack": "5371093722109/3158020019531250",
+  "literal_deficit": 176000,
+  "literal_histogram": {
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+    "10": "153400",
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+    "13": "117800",
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+    "15": "48200",
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+    "20": "256800",
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+    "22": "268800",
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+    "3": "1935000",
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+    "5": "468600",
+    "50": "140800",
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+    "7": "240400",
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+  },
+  "literal_rank_mass": "103306000",
+  "literal_stock": 862350,
+  "new_chart_factor_max": 286,
+  "normalized_stock": 172470,
+  "normalizer_factor_bound": 787,
+  "ordinary_cutoffs": [
+    {
+      "counted_coefficient_cutoff_log2": "154262633700570",
+      "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
+      "minimum_gap": "483082026553578339087082850121/1000000000000000000000000000000000000",
+      "stage": 1
+    },
+    {
+      "counted_coefficient_cutoff_log2": "302142183821944412222",
+      "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
+      "minimum_gap": "345179955519517523308082524046567493391567419/1000000000000000000000000000000000000000000000000000000",
+      "stage": 2
+    },
+    {
+      "counted_coefficient_cutoff_log2": "591782319896672068211435273",
+      "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
+      "minimum_gap": "246643830950397259492931447905605911489412024601194649714641/1000000000000000000000000000000000000000000000000000000000000000000000000",
+      "stage": 3
+    }
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+  "payload_signed_prefix_upper": "306334506775192213700382759936",
+  "physical_replicas": 40,
+  "positive_rank_children": "19833600",
+  "primitive_coefficient_bits": 56,
+  "route_families": "8324400",
+  "scope": "Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted.",
+  "simultaneous_extra_work_streams": 1,
+  "status": "PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS",
+  "strict_moment_slack": "317272176063038188467599250332166404626084482726414051341090083693/134799733335753198973335075435098153368185722112702862405518051246080000000000000000"
+}
diff --git a/research/multicut-kernel-composition/expected-sandwich/COHORT-FIVE-STAGE-COLUMNS.json b/research/multicut-kernel-composition/expected-sandwich/COHORT-FIVE-STAGE-COLUMNS.json
new file mode 100644
index 0000000000..c7bf71da04
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/COHORT-FIVE-STAGE-COLUMNS.json
@@ -0,0 +1,184 @@
+{
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+  "five_stage_additions": 3642300,
+  "formal_columns_checked": 23627,
+  "fresh_center_copies": 120,
+  "global_live_registers": 23627,
+  "independent_dirty_registers": 16587,
+  "local_odd_scalar_additions": 728460,
+  "local_raw_H": [
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+    [
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+    [
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+    [
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+    ]
+  ],
+  "local_registers": 20107,
+  "local_scalar_additions": 728460,
+  "local_scalar_stream": "/private/tmp/claude-501/-Users-chafreaky-Documents-personal-integer-mult-research-20261008/5d8c8dbe-e8bc-42ba-8d10-c0561b637c5a/scratchpad/grand/run3-swap/plateau/sandwich/COHORT249-RECORDS.bin",
+  "negative_controls": [
+    {
+      "omit_bridge": 0,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 1,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 2,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 3,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 4,
+      "rejected": true
+    },
+    {
+      "omit_bridge": 5,
+      "rejected": true
+    }
+  ],
+  "new_Q_categories": [
+    28,
+    29
+  ],
+  "payload_prefix_bits": 98,
+  "payload_prefix_upper": "306334506775192213700382759936",
+  "reverse_fresh_center_copies": 48,
+  "scope": "All 23627 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.",
+  "seconds": 0.277343708,
+  "signed_lift_prefix": [
+    {
+      "bits": 17,
+      "cancellation_free_signed_row_l1_upper": "74391",
+      "reverse": false
+    },
+    {
+      "bits": 22,
+      "cancellation_free_signed_row_l1_upper": "3409788",
+      "reverse": 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.",
+  "stages": [
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 728460,
+      "signed_inverse": false,
+      "stage": 0
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 728460,
+      "signed_inverse": true,
+      "stage": 1
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 728460,
+      "signed_inverse": false,
+      "stage": 2
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 728460,
+      "signed_inverse": true,
+      "stage": 3
+    },
+    {
+      "fresh_copies": 24,
+      "scalar_additions": 728460,
+      "signed_inverse": false,
+      "stage": 4
+    }
+  ],
+  "status": "PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL"
+}
\ No newline at end of file
diff --git a/research/multicut-kernel-composition/expected-sandwich/COHORT249-REPLAY.json b/research/multicut-kernel-composition/expected-sandwich/COHORT249-REPLAY.json
new file mode 100644
index 0000000000..668540d260
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/COHORT249-REPLAY.json
@@ -0,0 +1,224 @@
+{
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+  "descent_removed_calls": 1,
+  "plateau_histogram_delta": {
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+}
diff --git a/research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-LEGALITY.json b/research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-LEGALITY.json
new file mode 100644
index 0000000000..008d6bda2e
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-LEGALITY.json
@@ -0,0 +1,110 @@
+{
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+  "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.",
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+  "status": "PASS_INDEPENDENT_COHORT_LEGALITY_SOURCE_OWNERS_AND_LIFECYCLE"
+}
diff --git a/research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-PREFIX.json b/research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-PREFIX.json
new file mode 100644
index 0000000000..03272faa33
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/INDEPENDENT-PREFIX.json
@@ -0,0 +1,10 @@
+{
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+  "distinct_cuts": 4,
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+  "non_target_identity_bits": 37299451,
+  "nonzero_pivot_target_entries": 60556,
+  "scope": "Original pinned-word response at every cohort own cut; combined emitted-word checks remain separate.",
+  "status": "PASS_INDEPENDENT_MULTI_CUT_FULL_F2_KERNEL_AND_IDENTITY_COLUMNS",
+  "target_kernel_equalities": 1566400
+}
diff --git a/research/multicut-kernel-composition/expected-sandwich/SANDWICH-BANK-INVOICE.json b/research/multicut-kernel-composition/expected-sandwich/SANDWICH-BANK-INVOICE.json
new file mode 100644
index 0000000000..198ababa55
--- /dev/null
+++ b/research/multicut-kernel-composition/expected-sandwich/SANDWICH-BANK-INVOICE.json
@@ -0,0 +1,600 @@
+{
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+  "max_intermediate_numerator": "1517994138707428147200",
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+  "selector_charge": 626935451600,
+  "routing_prime_guard": {
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+    "pairwise_difference_numerator_bound": 1517994138707428147200
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+  "status": "PASS_SANDWICH_ENDPOINTS_EXACT_CHARTS_AND_BANK_RETILING",
+  "base_bank_review_sha256": "0893b75595be282eb5500845419cc69336fe1ba6d68f84266f69b43a4586c72e",
+  "normalizers": {
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+    "charts": 504,
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+    "max_numerator_denominator": 26244
+  }
+}
diff --git a/research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json b/research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json
index 2b80c35307..dc75eb60d9 100644
--- a/research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json
+++ b/research/multicut-kernel-composition/expected/COHORT-BANK-REVIEW.json
@@ -1,7 +1,7 @@
 {
   "actual_helper_roles": 16587,
   "actual_role_replica_stage_assignments": 3317400,
-  "assignment_fnv1a64": "10075747216986959767",
+  "assignment_fnv1a64": "6767162259695106595",
   "bank_patterns": [
     {
       "count": 240,
diff --git a/research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json b/research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json
index 15da3b8be5..c0995078c2 100644
--- a/research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json
+++ b/research/multicut-kernel-composition/expected/COHORT-EXACT-PRICE.json
@@ -51,47 +51,47 @@
   "cohort_candidate": {
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+    "coarse": "712512487178117/1000000000000000000",
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diff --git a/research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json b/research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json
index 458083e3b8..9027dda91f 100644
--- a/research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json
+++ b/research/multicut-kernel-composition/expected/COHORT-FINITE-INVOICE.json
@@ -1,37 +1,37 @@
 {
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-  "global_unit_expanded_additions": "146628200",
-  "global_weighted_additions": "146100200",
+  "full_counted_primitive_coefficient": "62682729451523601",
+  "global_unit_expanded_additions": "146667600",
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   "internal_row_coefficient": 14401,
-  "linear_moment_slack": "8593749955333/5077441406250000",
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   "literal_deficit": 176000,
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@@ -41,32 +41,32 @@
   "normalizer_factor_bound": 787,
   "ordinary_cutoffs": [
     {
-      "counted_coefficient_cutoff_log2": "156546708338570",
+      "counted_coefficient_cutoff_log2": "156073791508775",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "19181796161486817683586029841/40000000000000000000000000000000000",
+      "minimum_gap": "480270885379124680317383665689/1000000000000000000000000000000000000",
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     {
-      "counted_coefficient_cutoff_log2": "308814532847511043762",
+      "counted_coefficient_cutoff_log2": "307429133387982740771",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "2731444448322083640102023533804303948629639/8000000000000000000000000000000000000000000000000000",
+      "minimum_gap": "342199003060716473147092535657337384924527613/1000000000000000000000000000000000000000000000000000000",
       "stage": 2
     },
     {
-      "counted_coefficient_cutoff_log2": "609188252566600855323802619",
+      "counted_coefficient_cutoff_log2": "605564016495186821841335015",
       "general_rule": "For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta)).",
-      "minimum_gap": "388951520048434913987463794273254578556852598375762485281/1600000000000000000000000000000000000000000000000000000000000000000000",
+      "minimum_gap": "243821062780663166112069255447886321104329439829405615844721/1000000000000000000000000000000000000000000000000000000000000000000000000",
       "stage": 3
     }
   ],
   "payload_bits": 98,
-  "payload_signed_prefix_upper": "313796573996337937369716857856",
+  "payload_signed_prefix_upper": "313795846577713577429067853824",
   "physical_replicas": 40,
-  "positive_rank_children": "19852000",
+  "positive_rank_children": "19808400",
   "primitive_coefficient_bits": 56,
   "route_families": "8324400",
   "scope": "Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted.",
   "simultaneous_extra_work_streams": 1,
   "status": "PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS",
-  "strict_moment_slack": "27030385753554201595314516077509078550097818449422547196173439641/67399866667876599486667537717549076684092861056351431202759025623040000000000000000"
+  "strict_moment_slack": "306882139089657689236689020107500875160699087324287342734761139307/269599466671506397946670150870196306736371444225405724811036102492160000000000000000"
 }
diff --git a/research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json b/research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json
index 8a55a4cd25..fee5d7787e 100644
--- a/research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json
+++ b/research/multicut-kernel-composition/expected/COHORT-FIVE-STAGE-COLUMNS.json
@@ -1,24 +1,24 @@
 {
   "bridge_additions": 10560,
   "copied_center_original_source_immutable": true,
-  "five_stage_additions": 3641945,
+  "five_stage_additions": 3642930,
   "formal_columns_checked": 23627,
   "fresh_center_copies": 120,
   "global_live_registers": 23627,
   "independent_dirty_registers": 16587,
-  "local_odd_scalar_additions": 728389,
+  "local_odd_scalar_additions": 728586,
   "local_raw_H": [
     [
       1,
-      43245
+      43036
     ],
     [
       2,
-      18911
+      18904
     ],
     [
       3,
-      9676
+      9675
     ],
     [
       4,
@@ -38,7 +38,7 @@
     ],
     [
       8,
-      642
+      641
     ],
     [
       9,
@@ -54,7 +54,7 @@
     ],
     [
       12,
-      1510
+      1509
     ],
     [
       13,
@@ -74,11 +74,11 @@
     ],
     [
       17,
-      469
+      468
     ],
     [
       18,
-      487
+      480
     ],
     [
       19,
@@ -86,11 +86,11 @@
     ],
     [
       20,
-      1358
+      1158
     ],
     [
       21,
-      5589
+      5798
     ],
     [
       22,
@@ -98,7 +98,8 @@
     ]
   ],
   "local_registers": 20107,
-  "local_scalar_additions": 728389,
+  "local_scalar_additions": 728586,
+  "local_scalar_stream": "/private/tmp/claude-501/-Users-chafreaky-Documents-personal-integer-mult-research-20261008/5d8c8dbe-e8bc-42ba-8d10-c0561b637c5a/scratchpad/grand/run3-swap/plateau/COHORT249-RECORDS.bin",
   "negative_controls": [
     {
       "omit_bridge": 0,
@@ -130,9 +131,10 @@
     29
   ],
   "payload_prefix_bits": 98,
-  "payload_prefix_upper": "313796573996337937369716857856",
+  "payload_prefix_upper": "313795846577713577429067853824",
   "reverse_fresh_center_copies": 48,
   "scope": "All 23627 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.",
+  "seconds": 0.301112792,
   "signed_lift_prefix": [
     {
       "bits": 17,
@@ -141,7 +143,7 @@
     },
     {
       "bits": 22,
-      "cancellation_free_signed_row_l1_upper": "3451068",
+      "cancellation_free_signed_row_l1_upper": "3451064",
       "reverse": true
     }
   ],
@@ -149,34 +151,34 @@
   "stages": [
     {
       "fresh_copies": 24,
-      "scalar_additions": 728389,
+      "scalar_additions": 728586,
       "signed_inverse": false,
       "stage": 0
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 728389,
+      "scalar_additions": 728586,
       "signed_inverse": true,
       "stage": 1
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 728389,
+      "scalar_additions": 728586,
       "signed_inverse": false,
       "stage": 2
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 728389,
+      "scalar_additions": 728586,
       "signed_inverse": true,
       "stage": 3
     },
     {
       "fresh_copies": 24,
-      "scalar_additions": 728389,
+      "scalar_additions": 728586,
       "signed_inverse": false,
       "stage": 4
     }
   ],
   "status": "PASS_NEW_COHORT249_ALL_FIVE_STAGE_FORMAL_COLUMNS_AND_PREFIX_BILL"
-}
+}
\ No newline at end of file
diff --git a/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json b/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json
index 191910a95b..7964ef017b 100644
--- a/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json
+++ b/research/multicut-kernel-composition/expected/COHORT249-REPLAY.json
@@ -3,48 +3,51 @@
   "bank_completion_not_replayed": true,
   "cut_record": 727593,
   "delta": {
-    "1": 1833,
-    "2": -174,
-    "3": -558,
+    "1": 1624,
+    "2": -181,
+    "3": -559,
     "4": 122,
     "5": -141,
     "6": 49,
     "7": -50,
-    "8": 13,
+    "8": 12,
     "9": 20,
     "10": -6,
     "11": -3,
-    "12": -15,
+    "12": -16,
     "13": 27,
     "14": -13,
     "15": -46,
-    "17": -35,
-    "19": -8
+    "17": -36,
+    "18": -7,
+    "19": -8,
+    "20": -200,
+    "21": 209
   },
   "forward_formal_columns": 20107,
   "global_kappa_claimed": false,
   "histogram": {
-    "1": 43245,
-    "2": 18911,
-    "3": 9676,
+    "1": 43036,
+    "2": 18904,
+    "3": 9675,
     "4": 3032,
     "5": 2343,
     "6": 1576,
     "7": 1202,
-    "8": 642,
+    "8": 641,
     "9": 631,
     "10": 767,
     "11": 442,
-    "12": 1510,
+    "12": 1509,
     "13": 589,
     "14": 1067,
     "15": 241,
     "16": 1000,
-    "17": 469,
-    "18": 487,
+    "17": 468,
+    "18": 480,
     "19": 323,
-    "20": 1358,
-    "21": 5589,
+    "20": 1158,
+    "21": 5798,
     "22": 1344
   },
   "inverse_formal_columns": 20107,
@@ -52,13 +55,13 @@
   "new_gauges": 890,
   "new_gram_audit_external": true,
   "new_rank_mass": 432458,
-  "new_records": 828136,
+  "new_records": 828115,
   "old_rank_mass": 434177,
   "old_records": 885228,
   "omitted_Q_nonzero_wrong_words": 38256,
   "omitted_Qinverse_nonzero_wrong_words": 1090,
   "removed_initial_reads": 60520,
-  "status": "EXPERIMENTAL_CONNECTED_PLATEAU_RETIMING",
+  "status": "PASS_FULL_CURRENT249_COHORT_REWRITE_AND_TARGET_PREFIX_COMPRESSION",
   "cohort_rewrite_records": 828137,
   "cohort_rewrite_histogram": {
     "1": 43230,
@@ -128,5 +131,63 @@
     "10": -2,
     "13": 4,
     "7": -24
-  }
+  },
+  "pre_target_records": 828136,
+  "pre_target_histogram": {
+    "1": 43245,
+    "2": 18911,
+    "3": 9676,
+    "4": 3032,
+    "5": 2343,
+    "6": 1576,
+    "7": 1202,
+    "8": 642,
+    "9": 631,
+    "10": 767,
+    "11": 442,
+    "12": 1510,
+    "13": 589,
+    "14": 1067,
+    "15": 241,
+    "16": 1000,
+    "17": 469,
+    "18": 487,
+    "19": 323,
+    "20": 1358,
+    "21": 5589,
+    "22": 1344
+  },
+  "pre_target_delta": {
+    "1": 1833,
+    "2": -174,
+    "3": -558,
+    "4": 122,
+    "5": -141,
+    "6": 49,
+    "7": -50,
+    "8": 13,
+    "9": 20,
+    "10": -6,
+    "11": -3,
+    "12": -15,
+    "13": 27,
+    "14": -13,
+    "15": -46,
+    "17": -35,
+    "19": -8
+  },
+  "target_prefix_delta": {
+    "1": -209,
+    "2": -7,
+    "3": -1,
+    "8": -1,
+    "12": -1,
+    "17": -1,
+    "18": -7,
+    "20": -200,
+    "21": 209
+  },
+  "target_prefix_groups": 209,
+  "target_prefix_deleted_reads": 1057,
+  "target_prefix_setup_restore_additions": 1254
 }
diff --git a/research/multicut-kernel-composition/expected/DESCENT-RETIMING.json b/research/multicut-kernel-composition/expected/DESCENT-RETIMING.json
index 09208245a9..6d41661097 100644
--- a/research/multicut-kernel-composition/expected/DESCENT-RETIMING.json
+++ b/research/multicut-kernel-composition/expected/DESCENT-RETIMING.json
@@ -223,7 +223,7 @@
   "operand_source_spans_contained": true,
   "checked_operand_spans": 193,
   "unique_required_frame_pairs": 100298,
-  "input_record_sha256": "d073aeb4a8054ee6e23366ac7a42554624d52d3a822e03de9831a12530287395",
-  "output_record_sha256": "43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6",
-  "selection_sha256": "e2f83db143fd7a323a57701912e03de179cf8755f9b5a31d6360aa5fb7a5c74a"
+  "input_record_sha256": "4458dce8218c9a0e0e55f494e33b2ad320649e953d108470ba0c8ac077660505",
+  "output_record_sha256": "a6d793d7fd4f902436fd64c1d0e9467adc93844e058578994400d30fcf4171c3",
+  "selection_sha256": "e9009fdeaef6e5d59b935803f909453c3c1407200e60713ce3f214f378209991"
 }
diff --git a/research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json b/research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json
index 2a1a804942..92bf2fa777 100644
--- a/research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json
+++ b/research/multicut-kernel-composition/expected/INDEPENDENT-LEGALITY.json
@@ -1,27 +1,27 @@
 {
   "all_final_frames_pass": true,
-  "common_frame_ADDs": 728389,
-  "containment_pairs_checked": 82736,
+  "common_frame_ADDs": 728586,
+  "containment_pairs_checked": 82944,
   "copies": 24,
   "donor_intersections": 0,
   "erasures": 24,
   "max_inherited_integer_abs": 7,
-  "nested_MOVEs": 99699,
+  "nested_MOVEs": 99481,
   "new_frame_ids_collision": false,
   "nondegeneracy_checked_by_separate_exact_bank_audit": true,
   "old_max_frame_id": 150370,
   "paid_histogram": [
     [
       1,
-      43245
+      43036
     ],
     [
       2,
-      18911
+      18904
     ],
     [
       3,
-      9676
+      9675
     ],
     [
       4,
@@ -41,7 +41,7 @@
     ],
     [
       8,
-      642
+      641
     ],
     [
       9,
@@ -57,7 +57,7 @@
     ],
     [
       12,
-      1510
+      1509
     ],
     [
       13,
@@ -77,11 +77,11 @@
     ],
     [
       17,
-      469
+      468
     ],
     [
       18,
-      487
+      480
     ],
     [
       19,
@@ -89,11 +89,11 @@
     ],
     [
       20,
-      1358
+      1158
     ],
     [
       21,
-      5589
+      5798
     ],
     [
       22,
@@ -101,7 +101,7 @@
     ]
   ],
   "rank_mass": 432458,
-  "records": 828136,
+  "records": 828115,
   "scope": "Independent chronological geometry/copy/source-owner audit. F2 all-column replay is in the separately freshly compiled transform receipt; address transform theorem and bank completion remain separate.",
   "selected_helpers": 1903,
   "selected_pairs": 890,
diff --git a/research/multicut-kernel-composition/expected/PLATEAU-RETIMING.json b/research/multicut-kernel-composition/expected/PLATEAU-RETIMING.json
index 557cc8b704..0144ba0481 100644
--- a/research/multicut-kernel-composition/expected/PLATEAU-RETIMING.json
+++ b/research/multicut-kernel-composition/expected/PLATEAU-RETIMING.json
@@ -1641,9 +1641,9 @@
     "13": 4,
     "7": -24
   },
-  "unchanged_scalar_copy_projection": "8b51a9fb35aefa1ce647e33bde117bd9a9ccfb9dc18ac9017cafa57af6d3ac1a",
-  "input_sha256": "43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6",
-  "output_sha256": "4f6ffc1daa5ef309e82c5a7e639b9e3c9f19bdcd2f2bfec865f8fbfc8fbc5b3d",
+  "unchanged_scalar_copy_projection": "4bbf61229b8a3f4aafac1891d9150479b8e91b20ef5306944fad502fb24c965c",
+  "input_sha256": "a6d793d7fd4f902436fd64c1d0e9467adc93844e058578994400d30fcf4171c3",
+  "output_sha256": "a1cf58b3b0d23775a07fd0ebc276c40a9c52a41a2ea285b935d062d314699d7b",
   "paid_calls": 96444,
   "rank_mass": 432458
 }
diff --git a/research/multicut-kernel-composition/expected/PLATEAU-SOURCE-SPANS.json b/research/multicut-kernel-composition/expected/PLATEAU-SOURCE-SPANS.json
index 8af3188e68..9a08c8b02f 100644
--- a/research/multicut-kernel-composition/expected/PLATEAU-SOURCE-SPANS.json
+++ b/research/multicut-kernel-composition/expected/PLATEAU-SOURCE-SPANS.json
@@ -61,5 +61,6 @@
     "658294": 24,
     "658297": 24,
     "658298": 24
-  }
+  },
+  "seconds": 1.4293630123138428
 }
diff --git a/research/multicut-kernel-composition/expected/TARGET-PREFIX.json b/research/multicut-kernel-composition/expected/TARGET-PREFIX.json
new file mode 100644
index 0000000000..2d312e85e1
--- /dev/null
+++ b/research/multicut-kernel-composition/expected/TARGET-PREFIX.json
@@ -0,0 +1,34 @@
+{
+  "status": "PASS_EXACT_F2_TARGET_PREFIX_COMPRESSION",
+  "selected_groups": 209,
+  "targets": 836,
+  "cut_record": 669360,
+  "deleted_prefix_adds": 1057,
+  "inserted_setup_restore_adds": 1254,
+  "literal_prefix_dependencies_checked": true,
+  "remaining_payload_additions": 728586,
+  "local_histogram_delta": {
+    "1": -209,
+    "2": -7,
+    "3": -1,
+    "8": -1,
+    "12": -1,
+    "17": -1,
+    "18": -7,
+    "20": -200,
+    "21": 209
+  },
+  "rank_mass": 432458,
+  "paid_calls": 96226,
+  "both_reflected_ledgers": true,
+  "unchanged_all_input_output_frames": true,
+  "unchanged_copy_lifetimes": true,
+  "forward_and_inverse_all_columns": true,
+  "negative_control": "omitted target-prefix setup rejected",
+  "unique_required_frame_pairs": 100506,
+  "setup_category": 30,
+  "restore_category": 31,
+  "input_record_sha256": "a1cf58b3b0d23775a07fd0ebc276c40a9c52a41a2ea285b935d062d314699d7b",
+  "output_record_sha256": "eaff3c9828ed15e1c24998331f0d3b482efc9984dd86bf5dbcefca0c76e717c6",
+  "selection_sha256": "7ed2069ef80d0fc3405a30bc1ed7338ff98d506a7cd7c2d82815e0b27645acb1"
+}
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diff --git a/research/multicut-kernel-composition/inputs/descent-selection.json b/research/multicut-kernel-composition/inputs/descent-selection.json
index 88cb160db4..70ad7bc083 100644
--- a/research/multicut-kernel-composition/inputs/descent-selection.json
+++ b/research/multicut-kernel-composition/inputs/descent-selection.json
@@ -1,6 +1,6 @@
 {
   "status": "FROZEN_CONCAVE_DESCENT_FRAME_SELECTION",
-  "input_record_sha256": "d073aeb4a8054ee6e23366ac7a42554624d52d3a822e03de9831a12530287395",
+  "input_record_sha256": "4458dce8218c9a0e0e55f494e33b2ad320649e953d108470ba0c8ac077660505",
   "input_record_count": 828137,
   "selected_gate_count": 25,
   "expected_local_histogram_delta": {
diff --git a/research/multicut-kernel-composition/inputs/plateau-selection.json b/research/multicut-kernel-composition/inputs/plateau-selection.json
index 023a6592f3..3bcec1a3c8 100644
--- a/research/multicut-kernel-composition/inputs/plateau-selection.json
+++ b/research/multicut-kernel-composition/inputs/plateau-selection.json
@@ -1,6 +1,6 @@
 {
   "status": "FROZEN_CONNECTED_PLATEAU_WITNESS",
-  "input_sha256": "43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6",
+  "input_sha256": "a6d793d7fd4f902436fd64c1d0e9467adc93844e058578994400d30fcf4171c3",
   "candidates": [
     {
       "component": 690237,
@@ -19943,13 +19943,13 @@
     "13": 4,
     "7": -24
   },
-  "baseline_input_sha256": "80af525cfdc547090015dc9ab1eaf14fdffe5cacb5b9d0efcb05a4f908e2cc6d",
+  "baseline_input_sha256": "43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6",
   "core_binding": {
     "status": "PASS_FULL_UNCHANGED_CORE_EVENT_ALIGNMENT",
     "events_compared": 103751,
     "bindings": [
       {
-        "baseline_gate": 690237,
+        "baseline_gate": 657861,
         "candidate_gate": 657861,
         "event": [
           1,
@@ -19961,7 +19961,7 @@
         ]
       },
       {
-        "baseline_gate": 690238,
+        "baseline_gate": 657862,
         "candidate_gate": 657862,
         "event": [
           1,
@@ -19973,7 +19973,7 @@
         ]
       },
       {
-        "baseline_gate": 690241,
+        "baseline_gate": 657865,
         "candidate_gate": 657865,
         "event": [
           1,
@@ -19985,7 +19985,7 @@
         ]
       },
       {
-        "baseline_gate": 690242,
+        "baseline_gate": 657866,
         "candidate_gate": 657866,
         "event": [
           1,
@@ -19997,7 +19997,7 @@
         ]
       },
       {
-        "baseline_gate": 690273,
+        "baseline_gate": 657897,
         "candidate_gate": 657897,
         "event": [
           1,
@@ -20009,7 +20009,7 @@
         ]
       },
       {
-        "baseline_gate": 690274,
+        "baseline_gate": 657898,
         "candidate_gate": 657898,
         "event": [
           1,
@@ -20021,7 +20021,7 @@
         ]
       },
       {
-        "baseline_gate": 690297,
+        "baseline_gate": 657921,
         "candidate_gate": 657921,
         "event": [
           1,
@@ -20033,7 +20033,7 @@
         ]
       },
       {
-        "baseline_gate": 690298,
+        "baseline_gate": 657922,
         "candidate_gate": 657922,
         "event": [
           1,
@@ -20045,7 +20045,7 @@
         ]
       },
       {
-        "baseline_gate": 690301,
+        "baseline_gate": 657925,
         "candidate_gate": 657925,
         "event": [
           1,
@@ -20057,7 +20057,7 @@
         ]
       },
       {
-        "baseline_gate": 690302,
+        "baseline_gate": 657926,
         "candidate_gate": 657926,
         "event": [
           1,
@@ -20069,7 +20069,7 @@
         ]
       },
       {
-        "baseline_gate": 690393,
+        "baseline_gate": 658017,
         "candidate_gate": 658017,
         "event": [
           1,
@@ -20081,7 +20081,7 @@
         ]
       },
       {
-        "baseline_gate": 690394,
+        "baseline_gate": 658018,
         "candidate_gate": 658018,
         "event": [
           1,
@@ -20093,7 +20093,7 @@
         ]
       },
       {
-        "baseline_gate": 690629,
+        "baseline_gate": 658253,
         "candidate_gate": 658253,
         "event": [
           1,
@@ -20105,7 +20105,7 @@
         ]
       },
       {
-        "baseline_gate": 690630,
+        "baseline_gate": 658254,
         "candidate_gate": 658254,
         "event": [
           1,
@@ -20117,7 +20117,7 @@
         ]
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       {
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diff --git a/research/multicut-kernel-composition/inputs/sandwich-selection.json b/research/multicut-kernel-composition/inputs/sandwich-selection.json
new file mode 100644
index 0000000000..1595941814
--- /dev/null
+++ b/research/multicut-kernel-composition/inputs/sandwich-selection.json
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+{
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diff --git a/research/multicut-kernel-composition/inputs/target-selection.json b/research/multicut-kernel-composition/inputs/target-selection.json
new file mode 100644
index 0000000000..2b1b6cace0
--- /dev/null
+++ b/research/multicut-kernel-composition/inputs/target-selection.json
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+          4
+        ]
+      },
+      {
+        "baseline_close": 675773,
+        "candidate_close": 674479,
+        "event": [
+          1,
+          3437,
+          18581,
+          -1,
+          127663,
+          4
+        ]
+      },
+      {
+        "baseline_close": 676147,
+        "candidate_close": 674853,
+        "event": [
+          1,
+          3445,
+          18394,
+          -1,
+          127609,
+          4
+        ]
+      },
+      {
+        "baseline_close": 676189,
+        "candidate_close": 674895,
+        "event": [
+          1,
+          3453,
+          18373,
+          -1,
+          127589,
+          4
+        ]
+      },
+      {
+        "baseline_close": 676183,
+        "candidate_close": 674889,
+        "event": [
+          1,
+          3461,
+          18376,
+          -1,
+          127591,
+          4
+        ]
+      },
+      {
+        "baseline_close": 675979,
+        "candidate_close": 674685,
+        "event": [
+          1,
+          3469,
+          18478,
+          -1,
+          127637,
+          4
+        ]
+      },
+      {
+        "baseline_close": 675973,
+        "candidate_close": 674679,
+        "event": [
+          1,
+          3477,
+          18481,
+          -1,
+          127639,
+          4
+        ]
+      },
+      {
+        "baseline_close": 675757,
+        "candidate_close": 674463,
+        "event": [
+          1,
+          3485,
+          18589,
+          -1,
+          127665,
+          4
+        ]
+      },
+      {
+        "baseline_close": 676013,
+        "candidate_close": 674719,
+        "event": [
+          1,
+          3493,
+          18461,
+          -1,
+          127625,
+          4
+        ]
+      },
+      {
+        "baseline_close": 675937,
+        "candidate_close": 674643,
+        "event": [
+          1,
+          3501,
+          18499,
+          -1,
+          127651,
+          4
+        ]
+      },
+      {
+        "baseline_close": 675721,
+        "candidate_close": 674427,
+        "event": [
+          1,
+          3509,
+          18607,
+          -1,
+          127671,
+          4
+        ]
+      },
+      {
+        "baseline_close": 675695,
+        "candidate_close": 674401,
+        "event": [
+          1,
+          3517,
+          18620,
+          -1,
+          127677,
+          4
+        ]
+      }
+    ]
+  }
+}
diff --git a/research/multicut-kernel-composition/verify.py b/research/multicut-kernel-composition/verify.py
index 51ed59596a..8d7759dae2 100644
--- a/research/multicut-kernel-composition/verify.py
+++ b/research/multicut-kernel-composition/verify.py
@@ -1,7 +1,7 @@
 #!/usr/bin/env python3
 """Offline source-bound reproduction. No stored PASS result is accepted without execution."""
 from pathlib import Path, PurePosixPath
-import argparse, concurrent.futures, gzip, hashlib, json, os, shutil, subprocess, sys, time, zipfile
+import argparse, concurrent.futures, gzip, hashlib, json, os, shutil, struct, subprocess, sys, time, zipfile
 sys.dont_write_bytecode = True
 HERE = Path(__file__).resolve().parent
 
@@ -78,7 +78,7 @@ def run(label, cmd):
         for name in ('249-states.json', 'frames.json'):
             need(normalize(load(generated / name)) == normalize(load(X / name)), 'fresh baseline structural mismatch: ' + name)
         need(load(generated / 'REGENERATED-DONORS.json')['donor_keys'] == sorted(load(X / '249-DONOR-OWNERSHIP.json')['donor_keys']), 'fresh donor ownership mismatch')
-    sources = sorted((HERE / 'code').glob('*.cpp'))
+    sources = sorted((HERE / 'code').glob('*.cpp'))  # code/sandwich/ holds the price wrapper, compiled separately
     need(len(sources) == 7, 'seven native checkers required')
     extension = '.exe' if os.name == 'nt' else ''
     def exe(name):
@@ -98,7 +98,7 @@ def compile_source(p):
     need(digest(lead / 'COHORT249-RECORDS.bin') == result['cohort_record_sha256'], 'cohort physical transcript hash mismatch')
     # 02b: concave-descent frame retiming of 25 ADD gates (rohanarun, PR263 stage), selection pre-bound by full
     # scalar-core alignment to this package's cohort transcript; the stage self-checks and every native checker reruns.
-    (lead / 'DESCENT-REBIND-EVIDENCE.json').write_text(json.dumps(dict(status='SELECTION_PREBOUND_TO_COMMITTED_COHORT_TRANSCRIPT', cohort_record_sha256=result['cohort_record_sha256'], binding='full unchanged scalar-core event alignment (rebind_descent.py of PR270) from PR259 transcript 1ae06b18c7c23e0f96f9309fcfc4a64a59b670c21d99207192d93440021e4897'), indent=2) + '\n', encoding='utf-8')
+    (lead / 'DESCENT-REBIND-EVIDENCE.json').write_text(json.dumps(dict(status='SELECTION_PREBOUND_TO_COMMITTED_COHORT_TRANSCRIPT', cohort_record_sha256=result['cohort_record_sha256'], binding='full unchanged scalar-core event alignment (rebind_descent.py of PR270) from the shared-donor package cohort transcript d073aeb4a8054ee6e23366ac7a42554624d52d3a822e03de9831a12530287395 (itself bound from PR259 transcript 1ae06b18c7c23e0f96f9309fcfc4a64a59b670c21d99207192d93440021e4897); the plateau witness is bound likewise (rebind_plateaus.py) from its descent transcript 43a73a445f7eefa76f227d31e8195899a4c537ff8a561867f4a87c56fe8f0da6'), indent=2) + '\n', encoding='utf-8')
     shutil.copy(HERE / 'inputs/descent-selection.json', lead / 'descent-selection.json')
     run('02b-descent-retiming', [sys.executable, '-B', HERE / 'code/descent_retiming.py', X, lead, lead / 'descent-selection.json'])
     need(digest(lead / 'COHORT249-PRE-DESCENT-RECORDS.bin') == result['cohort_record_sha256'], 'retained cohort transcript changed')
@@ -109,6 +109,15 @@ def compile_source(p):
     lead = plateau
     run('02d-plateau-source-spans', [sys.executable, '-B', HERE / 'code/verify_plateau_spans.py', X, lead, lead / 'PLATEAU-RETIMING.json'])
     run('02e-frame-tables', [sys.executable, '-B', HERE / 'code/verify_frame_tables.py', X, lead, '--output', lead / 'FRAME-TABLE-AUDIT.json'])
+    need(digest(lead / 'COHORT249-RECORDS.bin') == result['plateau_record_sha256'], 'plateau transcript hash mismatch')
+    # 02f: exact F2 target-prefix compression (eumemic's PR268 mechanism, rohanarun's native PR273 stage): 209 square
+    # groups whose dependent target's frame-20 prefix response is the F2 sum of three retained square-mates. The
+    # selection is bound to this package's plateau transcript (post-cut scalar event alignment from PR273's word);
+    # the stage recomputes every literal dependency from the actual transcript, rebuilds every MOVE, and runs both
+    # all-column replays with a negative control before anything is emitted. The seven native checkers follow.
+    shutil.copy(HERE / 'inputs/target-selection.json', lead / 'target-selection.json')
+    run('02f-target-prefix', [sys.executable, '-B', HERE / 'code/target_prefix.py', X, lead, lead / 'target-selection.json'])
+    need(digest(lead / 'COHORT249-PRE-TARGET-RECORDS.bin') == result['plateau_record_sha256'], 'retained plateau transcript changed')
     need(digest(lead / 'COHORT249-RECORDS.bin') == result['new_record_sha256'], 'new physical transcript hash mismatch')
     run('03-independent-legality', [exe('cohort-legality-independent'), X, lead, review / 'INDEPENDENT-LEGALITY.json'])
     run('04-independent-prefix', [exe('cohort-prefix-independent'), X, lead, review / 'INDEPENDENT-PREFIX.json'])
@@ -117,6 +126,46 @@ def compile_source(p):
     run('06-five-stage-columns', [exe('cohort-five-stage-columns'), lead / 'COHORT249-RECORDS.bin', temporal / 'COHORT-FIVE-STAGE-COLUMNS.json'])
     run('07-exact-price', [exe('cohort-price'), lead / 'COHORT249-REPLAY.json', lead / 'COHORT-EXACT-PRICE.json'])
     run('08-finite-invoice', [exe('cohort-finite-invoice'), lead / 'COHORT249-RECORDS.bin', lead / 'COHORT-EXACT-PRICE.json', compiler / 'COHORT-BANK-REVIEW.json', temporal / 'COHORT-FIVE-STAGE-COLUMNS.json', temporal / 'COHORT-FINITE-INVOICE.json'])
+    need(load(lead / 'COHORT-EXACT-PRICE.json')['cohort_candidate']['kappa'] == result['kappa_native_seven_checkers'], 'native kappa mismatch')
+    # 09: cleanup-sandwich cancellation (evmckinney9's PR271 mechanism) of the 45 helpers whose only gates after the
+    # first kernel cut are t += a; a += b; t += a. Each stops at a nondegenerate four-dimensional frame instead of
+    # climbing to the full frame. The native bank review and the REPLAY-driven native pricer assume helpers end at
+    # the full frame (hard-coded census, stock from the entrance rank), so this part is certified as PR271 does:
+    # native legality (final frames from the stage's export), native own-cut prefix and five-stage columns on the
+    # new word, exact SymPy endpoint charts and bank re-tiling, the unchanged price engine through a histogram
+    # wrapper (which first reproduces the native price above), and the native finite invoice.
+    sand = out / 'sandwich'
+    run('09-cleanup-sandwich', [sys.executable, '-B', HERE / 'code/cleanup_sandwich.py', X, lead, HERE / 'inputs/sandwich-selection.json', sand])
+    need(digest(sand / 'COHORT249-PRE-SANDWICH-RECORDS.bin') == result['new_record_sha256'], 'retained native transcript changed')
+    need(digest(sand / 'COHORT249-RECORDS.bin') == result['sandwich_record_sha256'], 'sandwich transcript hash mismatch')
+    srev = out / 'sandwich-review'; srev.mkdir()
+    run('10-sandwich-legality', [exe('cohort-legality-independent'), sand / 'export', sand, srev / 'INDEPENDENT-LEGALITY.json'])
+    run('11-sandwich-prefix', [exe('cohort-prefix-independent'), sand / 'export', sand, srev / 'INDEPENDENT-PREFIX.json'])
+    run('12-sandwich-five-stage-columns', [exe('cohort-five-stage-columns'), sand / 'COHORT249-RECORDS.bin', srev / 'COHORT-FIVE-STAGE-COLUMNS.json'])
+    run('13-sandwich-endpoints-and-banks', [sys.executable, '-B', HERE / 'code/sandwich_endpoints.py', X, sand, compiler / 'COHORT-BANK-REVIEW.json', srev])
+    cmd = [args.cxx, '-std=c++17', '-O2', '-I', HERE / 'vendor']
+    if args.boost_include:
+        cmd.extend(['-I', args.boost_include.resolve()])
+    run('14-compile-price-wrapper', cmd + ['-DPR254_PRICE_SOURCE="%s"' % (HERE / 'code/cohort-price.cpp'), HERE / 'code/sandwich/price-histogram.cpp', '-o', exe('price-histogram')])
+    def histogram(path):
+        h = {}
+        for op, a, b, c, f, z in struct.iter_unpack('<6i', Path(path).read_bytes()):
+            if op == 0 and f: h[f] = h.get(f, 0) + 1
+            elif op == 2: h[z] = h.get(z, 0) + 1
+        return {'histogram': {str(r): c for r, c in sorted(h.items())}}
+    (srev / 'base-histogram.json').write_text(json.dumps(histogram(sand / 'COHORT249-PRE-SANDWICH-RECORDS.bin')), encoding='utf-8')
+    (srev / 'new-histogram.json').write_text(json.dumps(histogram(sand / 'COHORT249-RECORDS.bin')), encoding='utf-8')
+    run('15-price-control', [exe('price-histogram'), srev / 'base-histogram.json', compiler / 'COHORT-BANK-REVIEW.json', srev / 'base-price.json'])
+    need(load(srev / 'base-price.json')['candidate'] == load(lead / 'COHORT-EXACT-PRICE.json')['cohort_candidate'], 'price wrapper does not reproduce the native price')
+    run('16-price-sandwich', [exe('price-histogram'), srev / 'new-histogram.json', srev / 'SANDWICH-BANK-INVOICE.json', srev / 'new-price.json'])
+    price = load(srev / 'new-price.json')['candidate']
+    need(price['positive_constraints'] == 47 and price['next_kappa_rejected'] > 0, 'sandwich price assembly')
+    (srev / 'COHORT-EXACT-PRICE.json').write_text(json.dumps({'status': 'PASS_SANDWICH_PRICE_SAME_ENGINE_STOCK_FROM_RETILED_BANKS', 'pre_sandwich_reproduced': load(srev / 'base-price.json')['candidate'], 'cohort_candidate': price}, indent=2) + '\n', encoding='utf-8')
+    run('17-sandwich-finite-invoice', [exe('cohort-finite-invoice'), sand / 'COHORT249-RECORDS.bin', srev / 'COHORT-EXACT-PRICE.json', srev / 'SANDWICH-BANK-INVOICE.json', srev / 'COHORT-FIVE-STAGE-COLUMNS.json', srev / 'COHORT-FINITE-INVOICE.json'])
+    need(price['kappa'] == result['kappa'], 'sandwich kappa mismatch')
+    for expected in sorted((HERE / 'expected-sandwich').glob('*.json')):
+        source = sand if expected.name in ('CLEANUP-SANDWICH.json', 'COHORT249-REPLAY.json') else srev
+        need(normalize(load(source / expected.name)) == normalize(load(expected)), 'fresh sandwich receipt differs: ' + expected.name)
     receipts = {}
     for expected in sorted((HERE / 'expected').glob('*.json')):
         matches = [p / expected.name for p in (lead, compiler, temporal, review) if (p / expected.name).is_file()]
@@ -124,15 +173,17 @@ def compile_source(p):
         got = normalize(load(matches[0])); wanted = normalize(load(expected))  # both sides normalized (this package)
         need(got == wanted, 'fresh receipt differs: ' + expected.name)
         receipts[expected.name] = got
-    cert = dict(status='PASS_ALL_SEVEN_NATIVE_CHECKERS_AND_PINNED_RECEIPTS',
+    cert = dict(status='PASS_ALL_SEVEN_NATIVE_CHECKERS_AND_PINNED_RECEIPTS_PLUS_SANDWICH_STAGE',
                 kappa=result['kappa'], kappa_decimal=result['kappa_decimal'],
+                kappa_native_seven_checkers=result['kappa_native_seven_checkers'], kappa_native_decimal=result['kappa_native_decimal'],
+                sandwich_record_sha256=result['sandwich_record_sha256'], native_bank_review_applicable_to_sandwich=False,
                 baseline_regenerated_from_source=not args.snapshots_only,
                 new_record_sha256=result['new_record_sha256'],
                 package_manifest_sha256=digest(HERE / 'MANIFEST.json'),
                 retained_public_all_size_interfaces=True, lean_certificate=False,
                 elapsed_seconds=time.monotonic()-start, receipts=receipts)
     (out / 'CERTIFICATE.json').write_text(json.dumps(cert, indent=2)+'\n', encoding='utf-8')
-    print('PASS: kappa = ' + result['kappa_decimal'], flush=True)
+    print('PASS: kappa = ' + result['kappa_decimal'] + ' (seven native checkers alone, before the sandwich stage: ' + result['kappa_native_decimal'] + ')', flush=True)
     print('Certificate: ' + str(out / 'CERTIFICATE.json'), flush=True)
 
 if __name__ == '__main__':